< % ^^./ ^s^-^ r,^"^ ^ 0. ... ^, ,^ 'O . < ^ ^^0^ 0^ . * r<^ ^^^ ^- ^^^ <^ V %,/' 'life." «^^^ '»fc^-~ ^s^ ^ . ,,.™,,.. .--. cc 1 r^ ^ '->/"". s> ,C^ A TREATISE ON PEDAGOGICS Prfparfd for Students of The Inti-rnational Correspondknce Schools SCRANTON, PA. ARITHMETIC GRAMMAR GEOGRAPHY HISTORY ORTHOGRAPHY WITH gUHSTIONS ON EACH SUBJECT First Edition SCRANTON THE COLLIERY ENGINEER CO. 1900 1. . s' ,' 18514 Library mT C*ogrre«a Two Copies Rechvcd JUL 12 1900 OpycigMMlry sEcuNoconr. 0IU)£I, page '^0, will be readily found by looking through the volume, at the inside edges of the headlines, until § 3 is found, and then through § '.] until ixige 20 is found. The Question Papers have the same section numbers as the Instruction Papers to which they refer, and are grouped at the end of the volume. Till', In ri'.RN AllONAI, CoKKKSroNDKNCF, vScnooi.S. CONTENTS. Pkdaoogics of AkrriiMKTic. Section. Page. Introducticjn 1 1 General Remarks . 1 1 Fundamental Drills 1 28 Drill Work for Addition 1 28 Drill Work for vSubtraction 1 28 Drill Work for Miiltiplieation .... 1 32 Drill Work for Division 1 ' o'-\ Notation and Numeration 1 38 Arabic Notation 1 38 Roman Notation 1 4G The Teaching of Fractions 1 48 Matter and Method 1 48 Primary Work in Detail 1 09 Preliminary Observations 1 0!) Advanced Work 2 1 Devices and Methods in Advanced Work 2 1 Addition and Subtraction 2 1 Short Methods in Multiplication ... 2 G Short Methods in Division 2 If) Proofs of Fundamental Operations . . 2 2(; Signs Used in the Fimdamental Opera- tions 2 2!) Miscellaneous Operations and vSugges- tions 2 30 Properties of Numbers 2 33 Factors, Divisors, and Muliiplcs ... 2 38 Fractions 2 45 V vi CONTENTS. Pedagogics of Arithmetic — Continued. Section. Pairc. Denominate Nunibers 2 58 Percentage 2 71 Interest 2 78 Interest Laws of Canada t ;i4 Interest Laws of the United States . . 2 Ito Proportion 2 IJO Evolution 2 1)8 Mensuration 2 110 Miscellaneous 2 113 Pedagogics of Grammar. Introduction 3 1 General Remarks ■. . 3 1 Textbooks 3 5 The Sentence 3 17 General Considerations ...... 3 17 Analysis of Sentences 3 27 Meaning of Terms 3 37 Ambiguity 3 41 Synthesis 3 4G Summary 3 5(5 Special Constructions 3 58 False Syntax 3 60 Acquiring a Vocabulary 3 G3 Etymology and Syntax 3 67 Preliminary Remarks 3 67 The Noun 3 70 . The Pronoun 4 4 The^ Adjective 4 10 Inflection of Adjectives 4 17 Anglo-Saxon Prefixes ....'... 4 25 Latin .Prefixes 4 26 Greek Prefixes 4 27 The Verb 4 29 Classification of Verbs 4 32 Modes of Verbs 4 43 The Participles 4 55 CONTENTS. Vll Pedagogics of Grammar — Continued. Section. The Tenses of Verbs 4 The Adverb 4 The Preposition 4 The Conjunction . 4 The Interjection 4 Pedagogics of Geography. Educational Values Geographical Matter Divisions and Definitions .... Concepts in Elementary Science Sensation and Perception .... General Information . Collections in Natural Science . . . Geography Without a Textbook Measures and Their Applications . Making and Recording Observations Graphic Geography Matter and Method in Geography . Books of Reference Books of Travel and Adventure Miscellaneous Books on Travel . Pedagogics of History. Introduction Preparation for Teaching History . Methodology Description of Methods Relation of History to Other vSubjects Correlations of History Pedagogics of Orthography. Introduction 7 Definitions and Classifications .... 7 Modification of Words 7 Compounding of Words ...... 7 Abbreviations and Contractions ... 7 Page. 58 73 7!) 85 88 1 26 3G 40 40 48 60 68 '68 81 95 108 132 133 134 1 14 26 26 61 64 1 1 20 20 31 viii CONTENTS. Pedagogics op' Orthography — Continued. Scctio)i. Page. Form and Punctuation of Abbreviations . T 31 General Considerations on Spelling . . 7 37 Principles and Materials 7 37 Methods in Orthography 7 82 Approved Devices and Word Lists . . 7 82 Section. Questions on Arithmetic 1 and 2 Questions on Grammar 3 and 4 Questions on Geography 5 Questions on History 6 Questions on Orthography 7 PEDAGOGICS OF ARITHMETIC (PART 1.) INTRODUCTION. GENERAIi REMARKS. 1. Tlie Term ••' Peda4>:ogics." — The word pedagogics is derived from the Greek TTai.dayoytKf], paidagogikc, which means "the art of training or teaching-." The term is com- pounded of two simpler words, iraidoq, paidos, "of a boy, " and aywyoV, agogos, "a leader." Literally, therefore, a pedagogue is a bo/s leader, and pedagogics is the art of leading or guiding boys. In ancient Greece, boys only were educated, and this work was usually entrusted to a slave, who was a constant attendant during the play and in the rambles of the boys of one or more families. This "boy-leader," or pedagogue, was usually a Greek; only he was not, by right of birth, invested with citizensliip. He was a serf, owned by tlie state and assigned to service to free-born citizens; but, being attached to the soil, he could not be sold. It was the duty of the pedagogue to supervise the play of the boys committed to his care, and to give them such mstruction as was then deemed important. His special duty, which was not to be neglected, was to attend to the development and training of the physical powers of his charge; for the possession of a healthy, strong, and § 1 2 PEDAGOGICS OF ARITHMETIC. § 1 symmetrical body was regarded as far more desirable than a well disciplined mind. 3. Distinction Between "Art" and "Science." The terms art and science are much used as the near equiv- alents, respectively, oi practice and theory — art and practice having reference to doing, science and theory to the rules that regulate actual performance. Thus, a man may be quite expert in the art or practice of argument or disputa- tion, and yet know nothing of the science of logic, by the principles of which correct argument must proceed. Again, one may be a fine performer in music, and be ignorant of the science or theory of the subject; or he may know the theory very thoroughly without having any skill in the art. At the time when the pedagogue plied his vocation in Greece, pedagogics was only an art. No code of principles had been formulated by which his work might be regulated and its defects criticized and corrected. His method might be skilful and highly successful, but his choice of means was a matter of instinct or judgment and not in accordance with an organized science of teaching. Since that far-off time, teaching, like nearly every other practical matter, has developed into a science. The nature of the child, the order in which his faculties develop, and the laws in accordance with which those faculties operate, the suitability of certain subjects as training matter for certain faculties: these, and many other facts and conditions have been investigated and discussed, until now one may learn many of the principles upon which success in teaching depends before he enters upon the actual work in the class- room. In other words, teaching is not only an art, but it is also, in a very satisfactory sense, a science. Hence, we may write the following Definition. — Pediig:og-ics is the science that treats of the principles and t lie methods of teaching. 3. Pedagogics of Avitliinetic. — It follows from what is said above that the pedagogics of arithmetic is that divi- sion of the general subject of pedagogics that has reference § 1 PEDAGOGICvS OF ARITHMETIC. 3 to the teachini^- of arithmetic. There is a general impression abroad that ahnost anybody can teach aritlimetic success- fully, provided he understands it. That this is not the case is proven by the fact that the beginner, without professional training, is almost inevitably vmskilful, however thorough may be his knowledge of mathematics. He does not know how to begin or where. He cannot get down to the level of his pupils, for he is misled by the fallacious notion that what seems so easy and clear to him must be equally so to the children he wishes to instruct. After long experiment and many failures he learns that not even high scholarship will insure him the success he courts. At first he attributes his poor results to the stupidity of his pupils. He never met children quite so dull, he thinks, and tells of it at home, perhaps, as an unaccountable fact peculiar to that one locality. But some fine day the principal, the superintendent, or some other experienced teacher comes in and gives him a shock by showing him that the pupils he thought so slow and stupid are capable of being aroused to the most eager attention and interest. He finds himself wondering how it was done, and remembers having heard somewhere that special training over and above mere scholarship is requisite to success in teaching even so simple a matter as arithmetic. He begins to believe that teaching is really a science as well as an art, and that he has missed one of its important divi- .sions — the pedagogics of arithmetic. 4. i:)ivisions of Aritlunetic-al Study. — The study of arithmetic is more or less distinctly divided into three periods : 1. Primary Aritliutclic. — This period is generally esti- mated as covering about four j-ears. The work consists in learning very thoroughly all the fundamental combinations of integers, including numeration, notation, the four fiuida- mental rules, operations with the most commonly iised denominate numbers, simple exercises in fractions, and many practical examples involving not more than two 4 PEDAGOGICS OF ARITHMETIC. § 1 operations. The leading objects to be attained during this period are rapidit}^, accuracy, and thoroughness. 2. Intermediate or Elementary Arithmetic . — This period should include a very thorough review of the primary work with larger numbers and new applications. In addition to this, properties of numbers, common and decimal fractions, denominate numbers, with areas and volumes, and many practical problems, should follow. The time should be about two years. o. Advanced ^Iritltmciic. — A review of preceding work .should be followed by percentage and its various applica- tions without and with the element of time, proportion and its applications, powers, roots, mensuration, and the metric system. The neces.sary time to do this work well is about two school years of forty weeks each. 5. Primary Teacliiii^' tlie Most DifUciilt. — The longer a course in arithinetic is pursued, the more familiar does the teacher become with the needs and capacities of the pupils. It is the beginning that is difficult. When, at the age of about six years, the little ones appear in school for the first time, their minds are very nearly a blank with respect to numbers. They all know what is meant by one and two, but few of them have a suiffcient acquaintance with three and four. Some of them, indeed, have learned to count, perhaps, as far as ten, but this really goes for little. To know auto- matically — without thought or hesitation — the arithmetic of the fundamental numbers is what is required, and of this kno:^dedge they have nothing. Not one of them, perhaps, can tell the sum of two and three, or how many twos there are in four. The fir.st discovery that the teacher will make, — and a dis- heartening one it is, — is that these children have no power of voluntary attention. Their eyes wander about in search of something novel, and a certain want of fixity in the eyes exactly denotes the nature of the mind's action. If the atten- tion of a few of them is gained for a moment, it lapses again almost immediately. It is impossible to hold their united § 1 PEDAGOGICvS OF ARITHMETIC. 5 attention steadily on one subjeet for longer than even a sing-le minute. Skilful indeed must be the teaeher that can carry them all forward along the path of knowledge without pause, miscalculation, or blunder. In all the range of a teacher's work there is nothing so difficult as this earliest task — to make a proper beginning. Obviously, it is of great importance that the teacher shall know very definitely and thoroughly what this earliest Avork should consist of, how it should be begun, and how it should be conducted during the first school years. And the fact is that this is precisely what the young teacher does not know. It is one of those matters apparently so easy as to require no kind of preparation, while in reality it should have the most elaborate and thorough attention beforehand. The popular misconception that this first work is one of extreme sim- plicity — one that any one can do — suggests an anecdote that; is related of the great painter Hogarth. A father approached the artist with a request for a place in tjie studio for his son, who had an aptitude for drawing. "What can he do ? " inquired the artist. "Well, I thought you might find him useful at first in painting the backgrounds for your portraits, and easy work of that kind," answered the father. "If he can paint backgrounds, he is just the person I want," replied Hogarth. "I have spent many years trying to learn how to paint a background for a picture, and I am not yet able to do it well." G. Selienies for Karliest Work in Aritliiiietie. — As might be expected, many educators have recognized the dif- ficulty of a proper beginning in number work, and have wrought (Hit very elaborate plans intended to be complete both in method and matter. One of the most celebrated of these is the Pestalozzian System of Primary Arithmetic. It is not in accordance with our present purpose to explain its details in this work. The system was at one time very popu- lar, and even yet there are many educators that think it excel- lent, which it undor:btedly is; others criticize it on the ground (! PEDAGOGICS OF ARITHMETIC. § 1 that it takes on difficulty with too o-reat rapidity. Whether thivS objection is warranted or not, one thing is certain — it brought to educators the conviction that a system of some kind is essential, and set them to the task of improving upon that proposed by Pestalozzi. Many modifications of the scheme of this edticator of more than a century ago have resulted from the thought and discussion that he induced. Among these is the celebrated " Grube Method," first pub- lished in Germany in 18-12. Many editions of this work, each different in some respect from the preceding ones, have appeared since. Whatever may be the plan he decides to follow, every teacher should possess copies of it, either trans- lated or in the original German; for it is onh^ by knowing and considering what others advise that he can hope to find that which is best suited to the needs peculiar to the situa- tion he is required to meet. The Grube method also, like that of Pestalozzi, has been severely criticized ; but the student should remember that no system of any kind in which there is the slightest chance, for difference of opinion has ever been accepted without protest and vigoroiis opposition. Indeed, every new departure is only a compromise, and, at any moment, is liable to be changed for something else. Doubtless, both the S3'stem of Pesta- lozzi and the method of Grube are full of faults of omission and commission; but the fact must not be forgotten that they are sharply defined plans, — well considered methods, — and therein is their chief merit; for even a poor plan of pro- cedure is incomparably better than no plan at all. The methods of the.se educators are almost certain to be better than anything the beginner could find out for himself, and to study them will set the student to thinking about ways and means. They have the effect of making him aware of th.e difficulties that await him, which goes a long way in helping him to overcome them. 7. The Plan of This Paper. — It is not intended to present the student with a novel plan of teaching arithmetic, or to direct him along a royal road to success in his work. § 1 PEDAGOGICS OF ARITHMETIC. 7 The purpose is to explain clearly and minutely a method that has been the outgrowth of long experience under many different conditions, and one that sjcms to be suited to the requirements of this country and this time better than either of the schemes mentioned above. The method is not a creation but a growth. Beginning with the Grube method, a good many years ago, the writer has watched its working in the hands of a great many teachers of every degree of skill and ability. He has heard their criticisms and objections with respect to this and that feature, and he l)clieves that many advantageous changes have from time to time been made. Much that was done for no definite future advantage, much that was merely mechanical, has been omitted or modi- fied. Additions, too, have been made. vSome of these addi- tions were owing to the conceded fact that the study of arithmetic should be for three distinct purposes; nameh': (a) Mental discipliiic. {b) Preparation for later and //i^-^'/ier niatlieniatieal work. (r) Practieal nsefnlness. Now, it is well known that in this country any scheme not distinctly utilitarian is looked upon with disfavor. Of course, we all admit the great value of mental discipline for its own sake, biU educators in this country have discovered that this end may be attained just as well — much better, indeed — when the primary object is practical usefulness. Hence, we have a generally recognized principle of peda- gogics : N^o snbjeet nnist be admitted to the sehool enrrienlnni unless it presents the donble elainj of diseipline and utility. vSo that all those arithmetical drills and exercises that were so com- mon in the schools and textbooks a score of years ago are omitted if they have no promise of ulterior usefulness. 8. Exercises in Fractions. — An impression is generally prevalent that the subject of fractions is much more difficult than that of integers. Even many teachers believe this, and the consequence is that no subject is so poorly taught as frac- tions. They are not taken up until after the pupil has been in 8 PEDAGOGICS OF ARITHMETIC. § 1 school for several years, and then they are treated by arbi- trary mechanical processes rather than by analysis, as integers are. But in these days when analogies, relations, and correlations are constantly engaging the attention of educators, it seems natural and necessary to bring out the fundamental likeness between integers and fractions, and to emphasize the fact that the same lines of analysis that are applicable to the one are equally so to the other. Every thoughtful teacher knows that a fractional imit is as really a imit as that which measures an integral number. That is to say, a fourth of a dollar is as much a i:nit as the dollar itself. Indeed, there are very few absolute units. Nearly every- thing' is a part of something else, but nearly every part may be treated as a unit. One of the most serious difficulties with beginners comes from the failure to recognize the analogy between integers and fractions. Only after years of work in arithmetic is the discovery made that tlie same reasoning by which difficulties are resolved with integers is available for the difficulties in fractions. The likeness between such examples as the f (^11 owing is not discovered until a late day in the history of arithmetical study, and very frequently not at all: ExAMi'i.K. — If 2 oranges cost 4 cents, how much must be paid for 3 oranges ? ExAMi'LE. — If 5 of a yard of ribbon cost | of a dollar, what must be paid for | of a ^-ard ? It is believed to be best, therefore, to begin the work with fractions and integers at the same time, and to carry them on side by side during the first four years, or longer, of number work. There is nothing intrinsically difficult about thirds or fo!i7'ths any more than there is about three or four. It is the notation of fractions that makes them appear differ- ent from integers and harder to imderstand. When spoken, one-fifth is just as simple as fii'e, and t7vo-tJiirds is as easy for the child to grasp as txvo threes. It is when written i, I that they seem difficult, but in reality they are not; for I does not express a compound idea any more than t%oo- tliirds or tzvo apples. In brief, the alleged complexity of the § 1 PEDAGOGICS OF ARITHMETIC. 9 subject of fractions is largely imaginary, and arises from the fact that until lately their consideration has been deferred until the fundamental rules with integers, United States money, the properties of numbers, divisors, multiples, and cancelation have been mastered. Then they are taken up and learned only so far as mechanical processes are con- cerned. Their correlation with integral numbers is systemat- ically overlooked; the student, and usually the teacher also, never suspects that three fourths and three apples are in reality concrete integers, and recpiire in problems exactly the same analytic treatment. The teacher having been badly taught himself, therefore, and having failed to master fractions properly and to learn the analogies between frac- tions and integers, proceeds to teach as he was taught and to leave obscure that which is essentially simple. 9. Drill Work. — Very little doubt can be entertained about the extreme utility of systematic and persistent drill work in the early part of the course in arithmetic. If, while reading, it is necessary for a child to stop frequently in order to spell and puzzle over words, it is impossible for him to get the meaning of what he reads. The case is similar in arithmetic. If the student must let go the main thread of an analysis or operation in order to consider how much the sum or the product of eight and seven, or some such combi- nation is, he is almost sure to be unable to resume when the uncertainty has been settled. Indeed, the one essential and indispensable object to be attained in this fundamental work with children is infallible accuracy and extreme ease and rapidity. In other words, the "divine last touch" in educa- tion is automatism — the facility by means of which a task that was before slow, laborious, and painful, seems, by some innate principle of activity and intelligence, to work out its own results; or, as we say, to "do itself." The writer, on one occasion, noticed a clerk in a large wholesale establish- ment add up very long columns of figures almost at a glance. The speed was so extreme that one could scarcely conceive a mind capable of being so trained, or believe that the result 10 PEDAGOGICS OF ARITHMETIC. § 1 was correct. When asked to explain the mental process, the clerk professed himself unable to do so. " I just run my eye along the column and I seem to know the result without any distinct sense of intermediate steps. It is very much like intuition, which is a kind of argument so rapid that the successive steps leading to the conclusion are not noted or remembered." Something like the fore- going was what he said. This is very nearly an example of automatism ; very much like~ what we do when we read — we follow the thought, giving no conscious attention to the words that express the thought. This automatic facility is what the teacher of arithmetic should aim to give the children under his care ; for, as long as their attention is diverted from the reasoning necessary to the solution of a problem to the mechanical operations involved, so long will they be lacking in confidence, and so long will they be uncertain in results. This mechanical part of the work must be like that done by a perfect machine that runs without friction or noise. Now this ease and rapidity, this automatism, is attainable only by incessant practice with suitable drill work. The clerk that, finally, is able to get his resiilts by a process almost as rapid as intuition, and to be so certain that he may neglect all possibility of error, must pay the price of years of practice. In like manner, the teacher that would secure a similar proficiency on the part of his pupils, in the inere routine of arithmetic, — in its viccJianics, — must work for it, and work very hard. And the end is a full equivalent for the Igjjor it costs. 10. No Drill Witliout a Purpose. — In the textbooks on arithmetic that were used in our schools three or four ■decades ago, there were a great many exercises that had no conceivable bearing upon any of the number work that was to follow, either in the book itself or in the actual life that was to come after the school. If they had any definite pur- pose to fill, it was not obvious. Certainly nothing beyond^ mere discipline was aimed at, and, as we have seen, this in § 1 PEDAGOGICS OF ARITHMETIC. 11 itself is no longer much sought after. vSome examples will illustrate what is meant. 1. Add by 2's from to 100; by 3's from to 99; by 3's from 1 to 100; by 7's from 2 to 100. 2. Begin at 100 and subtract by 3's until the last remain- der is less than 3. No such addition or subtraction is ever required in solving any example, nor is it in any way a preparation for any prob- able demand of the future. Much of such work that is utterly witliout definite object or purpose is done in our schools in connection with nearly every subject in the curriculum. This is a fault that is very hurtful. It mystifies the pupils and leads nowhere. It breaks the continuity of any plan the teacher may have made, inasmuch as it cannot be part of any plan. The teacher should see to it that he works in straight lines, and that everything he does shall contribrite towards giving his work symmetry and completeness. There should be much drill work. In this way he should emphasize what he has done during the day, and should connect it with what has been done before. But before any exercise of this kind is accepted and practiced, let him clearly decide about its purpose and utility. "Is it exactly what I want? Just what do I require, and why do I require it ? Is it possible for me to find soinething or devise something that will better meet my purpose ?" And, then, when he has found a useful drill or device of any kind, let him copy it into his note book for future use. These plans can be obtained from many sources. They can be found in textbooks, in educational publications, and they may be learned from other teachers, but many of the best of them for his purpose will arise from the exigencies of his own work. Whatever be their source, they should be copied in proper order in his note book, and should be accompanied by such explanations of their purpose and the manner of using them as will make them readily available for future use. ^X^l 1. Concrete Appliances. — There is a great variety of opinion about the extent to which objects should be used in 12 PEDAGOGICvS OF ARITHMETIC. § 1 early number work, and at what stage they should be laid aside and the work with abstract numbers begun. For example, one author says: "For a successful teaching of number, the teacher needs a great variety of objects. Blocks, splints, sticks, buttons, paper patterns, peas, beans, corn, spools, counters, shells, pebbles, horse chestnuts, acorns, little tin plates, cups and saucers, tin money, are inexpensive and convenient to handle. For measurements, the teacher must have inch measures, foot rules, yard measures, a set of tin measures, a set of wooden or pasteboard measures, a set of weights, and a pair of scales." This abundance of material requires a place where the many objects may be kept, and an arrangement for quickly and quietly giving them out and collecting them; and, besides, some means must be provided that they may be handled by the children without confusion. All this involves a great outlay of time, and the abiindance of illustrative material may become an obstacle instead of a help, by diverting the attention of the children from the real busi- ness in hand. The author quoted above has evidently thought of the difficulties attending this matter, but just as evidently he has never been situated where he was required to do the actual work, for in another place he observes: "It is more convenient in these exercises to have the children stand about a table on which are the objects to be handled. Let them illustrate each story ( ? ) with objects until it is evident that the relation between the numbers is as clearly seen without the objects as with them. " Without meaning to do so, this author, in another place, formulates what amounts to a serious comment in objection to the embarrassment of concrete richness advised above. " Whenever a tnental picture is formed," he says, "then the material is a hindrance to the teaching. Objects are a means to an end, but not the end. When an idea has been abstracted from the concrete, objects no longer have an office to perform and should be put aside." § 1 PEDAGOGICS OF ARITHMETIC. 13 l*-i. Other A'ieAvs on the Use of the Concrete. Another writer on the subject of teaching arithmetic advises against the use of many objects, on the ground that a multi- plicity of objects, colors, and forms attracts the attention of the children from the Jiitmbcr to the objects i:sed in teaching it. He recommends that only splints and marks made on the blackboard be used, and says that the splints should be dispensed with just as soon as the children can use lines on the blackboard for counters, and that the lines are unneces- sary after children have reached the point where they can illustrate by imaginary counters. He enunciates in the fol- lowing an important principle: "Never use apparatus for the sake of using it. Use it only when it is really needed to give a clearer conception of a truth, or when an unsatis- factory result would follow without it." This is exactly the theory of Pestalozzi; and many other writers on education agree in the opinion. The writer remembers having once yielded to the insist- ence of a teacher that believed in using a great variety and abundance of concrete material. She asked for long tables to lay across the tops of the desks, and for other tables on which to place shallow pans, very long and wide, containing sand. Her plan was to have the children surround these tables, which were covered with small objects of many kinds. These were to be used by the pupils in illustrating various operations in number, and they were to be used in concert, following the lesson as it was developed point by point by the teacher. It was quickly apparent that the objects absorbed the entire attention, and the numbens — the lesson — was only an annoying interruption of the childish delight that the toys, considered merely as playthings, would have furnished. With these alone they could have been completely happy, but not entirely so with the superadded attempt to make their toys a text for a lesson in number. Complaints from the janitor then began to reach the prin- cipal. The tables, he complained, were in the way, so that he was unable to sweep satisfactorily; the furniture could not be dusted properly, objects were piled up in disorder 14 PEDAGOGICS OF ARITHMETIC. § 1 in every available place, and were constantly falling or being knocked down. ' ' I wonder what they are all used for," he said; but upon being assured that the teacher was "conducting an experiment in pedagogics," he readily resigned himself to it for a time, a victim for the sake of scientific discovery. 13, The Experiment. — The principal was very much interested in the result of the experiment, and encouraged the teacher to make the most of it. She was really a very intelligent lady, wrote innumerable articles for educational publications, and read very extensively on the subject of teaching. And she persisted in a surprising fashion, for she had written much on the use of objects in primary teaching, and thoroughly believed in what she had written. It was quickly apparent that much time was consumed in getting ready for lessons, and, after the lesson was finished, in removing the material that she had been using; for it was impossible to get the attention of the pupils to any other lesson as long as those lovely "playthings" could be reached or even seen. Then, too, she made some discoveries about the proneness to evil — the total depravity — of " those little wretches." She found that they were carrying away her precious material — abstracting her concrete, so to speak. And some of the boys would slyly throw corn, nuts, acorns, horse chestnuts, and other missiles at one another. One boy, with an instinct for experiment, inserted a bean in one of his ears. The incident broke in upon the continuity of the work during the rest of that day's session and made the services of a surgeon necessary. The teacher paid the bill. To add to the realistic effect of the objective method, they purloined and ate her oranges and apples, and tried to eat some other things that would not have tempted the appetite of an ostrich. She reported these doings to the principal, but he was unable to help her further than to quote, " Lead us not into temptation." The story of that experiment would be, if fully told, a very long one; but the results accomplished could be told in one word — failure. In an § 1 PEDAGOGICS OF ARITHMETIC. 15 adjoining room was another class of the same size and grade. The teacher of that class also believed in the utility of the concrete in those earliest lessons, but she used only splints, and illustrations of the simplest kinds on the blackboard. At the end of the first half year she had carried her class very far beyond the point reached by the other. Fvirther experiment was given up, and the business of real teaching was resumed. Some bushels of educational illustrative material were used to gladden the heart of the janitor. Some of it he fed to his chickens, and the remainder he called, in his vulgar way, trash, and burned it in the school furnaces. 14, Ijejyitimate Use of Ajipavatiis for Illustration. Lest the writer may be misunderstood on this subject, an explanation seems to be necessary. Some kind of objective representation is absolutely indispensable in primary teach- ing, and the earlier the teaching is begun the greater should be the abundance and variety of objects required. The con- scious life of a child begins with the knowledge, acquired through the senses, of external objects. He thinks almost not at all ; he merely perceives a vast number of things and some of their most conspicuous equalities; he notes very slightly their differences and resemblances; and he begins to learn their names. To him nothing is very real except, the sensible objects around him. Sense perception is all and in all. He goes to the kindergarten. There he continues to see and to hear, and to observe the realities that make up his daily surroundings; only he does it no longer at random. Method is introduced, and plans are found to arrest and hold his attention more steadily, in order that he may observe more closely. Differences and resemblances are emphasized, and he is taught to use in easy ways the faculties of judgment and comparison. So far he has not been required to deal in any manner with abstractions. Everything that he does relates immediately to the concrete, and his chief business is to acquire a vocabulary. The noun, the adjective, and, to a slight degree, the verb, are the parts of speech he learns. 16 PEDAGOGICvS OF ARITHMETIC. § 1 This is where the concrete, and nothing but the concrete, should be found. There need be no fear that the variety of objects, their striking colors, or other qualities will divert his attention from something more important. He leaves this place of the concrete and enters the ordi- nary school region — the domain of the abstract. He carries with him, of course, his instinct and liking for the object — the reality. But however hard he may find it, he must learn to go alone — must learn to supply an imaginary object. But the transition must not be too abrupt. Some few, but very few, of the old objects may remain with him for a time. They must not, however, be very striking, for they are not the chief concern in his new work. They are only means to an end — stepping stones, by the help of which he may con- ceive of the abstract. Grube advises the use of simple marks on a blackboard, and these are perhaps all that are really required. The splints that are sold in bundles of a hundred are very useful, being easy to handle, and without any inter- est whatever except as counters; and, although they con- sume little time in handling, they should be used less and less, and should be given up as soon as possible — not earlier, however, than at the end of the first year. So that, while it is a principle in pedagogics that we must proceed from the simple to the complex, from the particular to the general, from the concrete to the abstract, it is equally a principle that the ultimate object to be sought in educa- tion is independence and divorcement from the sensible, the objective, and ease and facility with the abstract, the pure ideal. 15. The Blaclvboai'd in Teacliing. — While a multi- plicity of objects is likely to be hurtful in teaching, their representation on a blackboard is highly advantageous and helpful. Made by means of a crayon, they serve the pur- pose of counters admirably in teaching arithmetic; and, since they do not interfere with the continuity of attention on the part of the pupils, they are much better than the reality they represent. Every kind of object may be rudely § 1 PEDAGOGICS OF ARITHMETIC. 17 indicated. No teacher needs to be expert with crayon in order to use it for ilhistrative purposes; indeed, the writer has hstened to tlie most intensely interesting lessons con- ceivable, illustrated at every point with crayon sketches, and at the end of the exercise, a person that had not heard it would not, by any chance, imagine that the multitude of apparently meaningless marks covering the blackboard had been used to aid in anything that had unity and continuity. It is easy to spoil a lesson by having too many objects, but no such danger can come from using too much crayon. It would not be easy, indeed, to put too much blackboard sur- face into a classroom. Many of the matters taught from day to day can be put in some unused place and frequently reviewed. When it is desired to call special attention to anything it may be written with colored crayon. There is much that might be said on the subject of colored crayon and its great helpfulness in teaching little children, btit this is scarcely necessary, for it is now known and used by nearly every teacher. 16. Grainniai* of Aritliinetical liaiigrnage. — The teacher will hear frequent discussions concerning the gram- matical correctness of certain expressions that he is com- pelled to use almost constantly in teaching arithmetic. For example, should we say, "One and one is two," or "One and one a?'e two" ; " Twice three w six, " or " Twice three are six"; "Eight and seven is fifteen," or "Eight and seven ai'e fifteen "; "If five dollars is one-half of my money, etc."; or " If five dollars a?-i' one-half of my money, etc."; " Two- thirds of six is four," or "Two-thirds of six arc four"? If there is a right way, the teacher should know what it is and follow it steadily. The textbooks illustrate the most varied usage in the matter, and it would, perhaps, be impossible to find two writers on arithmetic that agree throughout in this respect, or one that is always consistent in his own works. One book now before me contains, amongst many other bewildering constructions, the followinu": "One time one 18 PEDAGOGICS OF ARITHMETIC. § 1 ts one," "Two times one are two," "How many t's three times two?" "Two arc contained in eight four times," "Two and one is three," "Two and two arc four." A certain grammarian says, "In multiplying ojic only, it is evidently best to use a singular verb; as, 'Twice one h two.' (He advises also, ' Twice naught ?> naught. ') And, in multiplying any number above our, I judge a plural verb to be necessary; as, ' Twice tico arc four.' " Goold Brown, in his ' ' Grammar of English Grammars, " argues this matter at great length and quotes all kinds of contradictory usages and opinions, but seems to be somewhat uncertain himself, although he disctisses with much heat and apparent intolerance the opinions of Dr. Bullion and some other writers. The teacher would do well to examine Brown's presentation of the subject (see pages 584: to 592 of his work) . Now, this whole question is resolved if it can be decided just what is to be regarded as the subject of the verb. Con- sider the following sentences, the correctness of which no grammarians dispute: "All work and no play viakcs Jack a dull boy." "Little and oiten Ji//s the purse." " Bread and butter is the staff of life. "The long and the short of the matter is, etc." "Five dollars taas too much by far." Matthew Arnold writes, "The power and value of Eng- lish literature Zi>as thereby impaired." And the following is one of many examples that may be found in Macaulay: "All the furniture, the stock of shops, the machinery which could be found in the realm zuas of less value. " In all these sentences the apparently compoiind subject is made up of elements that must be taken together to make a complete singular whole. Thus, when we say, " Bread and butter is the staff of life," we do not mean that bread alone, or butter by itself, is the'staff of life. The sense is that the combination of bread and butter — bread zvith butter on it — is the staff of life. So, when we say, " Eight and seven is § 1 PEDAGOGICvS OP^ ARITHMETIC. 19 fifteen," we do not mean that cigJit is fiftcoi or seven is fifteen; it is their combination into a single aggregate of which we are thinking. Dr. Bain, in discussing this subject of the concord of the verb and its subject, gives the following general principle: Unless IOC can resolve a plnral construction into a number of distinct singular affirmations, the employment of the plural is not justified. For example, the plural verb is required in the sentence, "John, Peter, and Mary are here," since we may separate the expression into three "distinct singular affirmations," "John is here," " Peter is here," "Mary is here." But it is impossible, without changing the fact, to separate in this manner such expressions as, " Six times five are thirty," "Three-iiftlis of my money arc nxwe. dollars," "Five shillings were the damages," "Five and four are nine, etc." Hence, the verbs in these cases should be in the singular. Dr. Webster, in his " Philosophical Grammar," writing on the same subject, remarks: When an aggregate number is expressed by the plural names of the particulars composing that amount, the verb may be in the singular. Thus, "There was a hundred and fifty thousand pounds sterling." This is, in other terms, the principle enunciated by Mr. Bain. In asking questions, the teacher is compelled to use the forms "How much" and " How many." Almost every one follows the "How much" with a singular verb, as "How much is two times six?" " How much is four and five?" With "How man}^, " however, the many seems to call atten- tion to the number — the count — instead of to the mere mass or aggregate; and many teachers will say "How many c?;'c three times two ? " According to Dr. Bain's principle, however, this is " not justified." It is at least not necessary, for we are guilty of no error when we say " How many is three-fifths of twenty ? " 17. Hemarks on the ForejEfoinia: Discussion. — It must be said that the usage is well established among the 20 PEDAGOGICvS OF ARITHMETIC. § 1 writers on arithmetic of printing' the tables belonging in the fundamental rules with plural verbs, or of evading the matter altogether by using signs. It is easy to find such cases as the following: 1 and ts 1, 1 and 1 a?'e 2; 5 less 4 is \, 5 less 3 (rre 2; 1 time 2 is 2, 2 times 2 arc 4; 2 a?'c con- tained in (j three times, 2 is contained in G three times; three 3's are or is nine, etc. One thing is pretty certain — whetlaer you use the singular or prefer the plural, in either case you can usually find as good argument and authority for your preference as any one can find against it. The matter is in hopeless confusion, and it will probably never be settled in a way to be accepta- ble to everybody; for argument on the subject never leads to any valuable conclusion. Believing that a teacher's language should be at least consistent from day to day and from sub- ject to subject, the writer would advise the student to decide upon one usage or the other, and then practice that alone and require his pupils to do the same. Whatever your choice may be, some one will say that you are in error; that, how- ever, makes but little difference. The important thing is to have reasons for what you do, and to be steadily of the same mind and practice, unless you discover that you are imdoubtedly wrong. The writer's preference is for the singular verb. The reason for this is that you do not have to abandon the singu- lar in certain cases and use the plural. But if you decide in favor of the plural verb, you are compelled very often to use the singular; as, for example, i i such sentences as the fol- lowing, in which it would be extremely difficult to justify the plural verb: " The sum of 'S and 4 is l." " Five less 3 ?s 3." " Six taken from 10 leaves 4." '■ Ten divided by 2 gives 5." " Three is contained in 12 four times." "The half of 6 is 3." " Six is 4 more than 2." Etc. 18. The Use of Sig:ns. — Some writers urge that the symbols for addition, subtraction, multiplication, division, and equality should not be introduced to the pupil until after he has been taught in number for several months. This is, § 1 PEDAGOGICS OF ARITHMETIC. 21 however, a needless precaution. The pupil able to under- stand the significance of and will just as readily understand its briefer form, +• Indeed, the latter is more vivid in effect, for the child quickly discovers that besides denoting- mere aggregation, it is a symbol of operation — it is the equivalent of a verb in the imperative mood. It says to him very distinctly, "Add the.se numbers together." The sign + indicates nothing that is not easily within the comprehension of the youngest pupil, and the sooner it is thoroughly under- stood the better. Symbols are, in general, more exactly significant, and the mental effect they produce is stronger than the significance or eft'ect of any mere verbal equiva- lent or approximation. Hence, when the idea of any opera- tion or relation is to be taught, then is the time to introduce the symbol, if there be one. And then, this work should be done thoroughly; for if there is any vagueness among the pupils with respect to the meaning of a symbol, the confi- dence so necessary to real progress will be lacking. 19. Conditions Exiiressed by Symbols. — It is not enough that the children should know what operation or relation is denoted by the signs used in arithmetic. Some of the most delightful exercises may be had with them from the very first. One of the most excellent teachers of little children that the writer has ever seen at work was the first to suggest to him the possibilities in this direction. These exercises she made to include training, not only in the mean- ing of symbols, — -the operations and the relations denoted by them, — but also in language and in rudimentary reasoning. For example, she would write on the board, say, the following : 2-f 3 = 5. "Now, Eddy," she would say, "tell me what that says?" " It says that two and three more is five." "That's right, Eddy; can you tell that in another way?" "Yes, ma'am; two added to three makes five." " Very well done. Now, can Johnny read it in any other ways ? " 22 PEDAGOGICS OF ARITHMETIC. § 1 Johnny rises and says, "Two and three is five," or "The sum of two and three is five." " Now, Harry, you tell us in the hard way — the arithmetic way," Harry follows with " Two plus three is (or equals) five." After a time they will know exactly what is meant by all the various symbols and will read them correctly. The greatest difficulty will be found with multiplication and division; especially with division, for the expressions "is contained in" and "divided by" are hard for young chil- dren, and these expressions have no constant equivalents. While, for the sake of getting the exact meaning, it is at first necessary to employ various equivalent expressions, sooner or later there should be a settling down to a uniform technical brevity. The following will illustrate : 2 + 5 — 3 = 4. " Two plus five inimts three equals four. " 4 X 2 + 1 = 9. " Four times two, plus one equals nine." 8 — 3x2 = 2. " Eight, minus three times two equals two." 6 X i = 3. •' Six times one-half equals three." 1X8 = 4. " One-half of eight equals four." 6-7-2 + 8-7-4 = 5. " Si.x; divided by two, plus eight divided by four equals five." iX6-fjOf8 = 4. "One-third of si.x, plus one-fourth of eight equals four." 20. " Telling: Stories '■• in Aritlmietic. — The work indicated above is important, and, if it be done by a very skilful teacher, it may be made pleasing to the children in a very high degree. But it is by the exercise that is known among teachers as "telling stories" in numbers, that the highest interest and delight may be aroused. A brief illus- tration will make clear w^hat is meant. The teacher puts on the board, let us suppose, 4-3 + 5 = ? She then asks, * ' Who can tell me a story about what I have written on the board ? " The hands go up all over the room. " Mary, you may tell the story." "I had four cents, and spent three cents for candy; my § 1 PEDAGOGICS OF ARITHMETIC. 23 papa then gave me five cents more. How much money did I have then ? Answer, six cents. " "That's very good," the teacher says. "Now we'll hear Annie's story." Annie says, "A girl picked four quarts of berries and spilled three quarts of them. Then she picked five more quarts. How many quarts did she have at the end ? Answer, six c|uarts. " After one or two more "stories," the teacher puts on the board another test for the exercise. The child here is deriving profit in several distinct respects: 1. He is learning the meaning of the signs. 2. He is performing indicated operations, and thus getting discipline in combining" numbers. 3. His invention is being trained. He goes to his store of experience for a situation answering a certain description. 4. He is formulating the conditions in ordinary language. Of course this work can be made of any degree of difficulty; but it is not necessary to remind the teacher that if it be too severe all interest, as well as all profit, will be destroyed. Every lesson should be in some respect different from pre- ceding lessons, and it is by such devices that the teacher of high skill diversifies her work and keeps alive the interest and attention of the pupils. 31. Types of Examples. — Closely allied to the fore- going is the indicating of operations by general symbols both of operation and quantity. This is, however, not a matter for the pupil, but for the teacher. Every teacher should have a note book in which to keep a fund of sugges- tions, plans, devices, drills, etc. Now, instead of writing down a great number of examples in the hope of getting all the useful varieties, it is possible to condense them into a few types expressed in general symbols. Thus, suppose we have the following examples: 1. If 1 orange cost 5 cents, how much will 3 oranges cost ? 2. If 3 oranges cost 15 cents, what will 1 orange cost ? 3. At 5 cents each, how many oranges can be bought for 15 cents ? 24 PEDAGOGICS OF ARITHMETIC. § 1 In these examples there are only three different elements. {a) The nui>ibcr of oranges. This may be denoted by ;/. (/;) ^\\% price of one orange, or p. ((•) The cost of all the oranges, or c. Now, the operations necessary to the solution of these examples, taken in order, may be denoted by the following- formulas : {a) c = pxii, {b) p = c-^ii, {c) 11 — c^p. Each of these formulas represents htmdreds of examples that require the same operation to solve them, but they may all contain different subject matter. Thus, formula (^r), c z=: pxn, may be translated into the following in which no allusion is made to oranges or money. If a tailor can make a coat in 5 hours, how long will he require to make 6 coats ? (Here^ = 5 hours, and n = 6.) In one week there are 7 days ; how many days are there in 4 weeks ? {p = 1 days, « = 4.) Again, introducing an additional operation, we may write the following: 4. If 3 (;/) oranges cost 15 {c) cents, how much {c') will 7 (;;') oranges cost ? 5. If 3 («) oranges cost 15 [c) cents, how many (//') oranges can be bought for 35 {c') cents ? Expressing the necessary operations by means of formulas, we have for (4) and (5), respectively, the following: («r/) c' = c^iixit', {c) n' — c' -^{c ^li). As in the case of {a), (/;), and (r), each of these formulas represents an immense variety of examples that differ in the matters to which they relate, but are alike in requiring the same analysis in their solution. Thus, formula (li) may be translated into the following among- innumerable other examples : If in 4 days I can earn $12, how many dollars can I earn in 9 days ? A boy can go 24 miles on his bicycle in 3 hours ; at that rate, how far can he go in 10 hours ? The student will, of course, notice that such formulas are available for fractions and decimals as well as for integers. § 1 PEDAGOGICS OF ARITHMETIC. 25 They are useful, therefore, in every grade of teaching. For example, the following are resolved by formula (r), n' ■=. c' -^- (r-f- ;/) : I pay §9f for | of a ton of hay ; how many tons can I buy for $39 ? If a piano is sold for $825, which is 6.'5,'f' of the catalogue price, what per cent, of the catalogue price would have been received if it had been sold for §875 ? The interest of a certain sum of money at Z}S is §21; at what rate per cent, would the interest on the same sum be §28.J- ? 3'^. Usefulness of" Type Formulas. — There are many advantages to be gained by the use of formulas that repre- sent types of examples. Some of these are the following: 1 . Tlic Teacher More Easily Works in Straight Lines. — This keeping at a thing until it is mastered is a prime necessity, and it is a matter in which most teachers fail. Arithmetic work is, in general, very desultory and without distinct pur- pose. Examples involving the widest differences in princi- ple and operation are usvt^lly given during the same lesson. The result is that pupils are discouraged and quickly come to dislike arithmetic. They are permitted to get no more than the merest hint of the logic in a problem when they are confronted with an entirely different set of conditions in another problem. Examples should be given in series, and the examples, while they contain different concrete elements, should involve the same analysis — the same logic. Mechani- cal difficulties may be slowly increased, but the invoh^ed method of solution should remain until it has been perfectly mastered. This the type formulas enable the teacher to do, 2. They Enable the 'Teacher to Secure Unity in J^ariety. It was explained in the preceding article that a great vari- ety of examples having a constant likeness in principle and operation may be made under a given formula. Thus, integers, fractions, and decimals; percentage, proportion, and interest; partnership, banking, exchange, and mensuration may be represented by the same formula. The greatest sim- plicity of primarywork and the utmost difficulty required in the high school are both wrapped up in these simple expressions. 3. They Are Extremely Useful in Review Work. — The 26 PEDAGOGICS OF ARITHMETIC. § 1 teacher that works by these formulas knows exactly what he has done, and is able at any moment to discover whether each type has been sufficiently mastered. Instead of review- ing each subject by its textbook name, and working" by rule, he may review his types, and work by reason. This method frees the pupil from the necessity of remembering, and teaches him to think. Many other advantages from using this plan might be pointed out, but it may be assumed that they will readily occur to the student as he becomes familiar with it. The writer once explained this matter to an examining superintendent of schools of one of our largest cities. The five formulas given in this paper were explained to him, together with the manner of using them. He applied them in his official work and professed to think them admirable. Some months afterwards he inquired of the writer whether these five formulas do not cover every possible example in arithmetic. When assured that there are innumerable others, he said that he had used them constantly for a long time and had never discovered any need for others. They can certainly be made very helpful in the classroom. 23. Advanced AV oi*k AVitli Formulas. — If the teacher happens to be an algebraist, he may make many excellent applications of formulas in teaching classes in arithmetic that are somewhat advanced. Very similar to the " telling of arithmetical stories," in primary grades, is the use that may be made of formulas in advanced grades. To illustrate, let us take the following very simple problem : The money ($;«) that I have now, increased by what I can earn in 10 (a) days at $2i (§<^) a day, will exactly pay for 5 (c) cords of wood at .f6|- (^d) a cord. How much money have I now ? The steps necessary in the solution of this problem are indicated in the formula, 7U = ex d— axb. Hence, the answer is found by substituting in the formula the numerical values of the letters. Thus, the money m = 5xl6i-10xl2i = 131^-125 = U\. § 1 PEDAGOGICS OF ARITHMETIC. 27 The task to be required of tlie pupils is to construet problems with different numbers and about other matters. These problems must require exactly the same operations for their solution. The pupils will at first hand in many problems that fail to meet the requirements, and the word- ing is very likely to he awkward. By persisting, however, the needed skill will come. If it seems necessary, the teacher may for a time indicate more fully some of the con- ditions. He may say, for instance : " You may each make an example about a boy that rode away from home for a certain distance on a wagon, then con- tinued his journey on a bicycle, and finally returned home by train." Obviously, an exercise like this will furnish discipline in many important matters. Not the least important will be the expression of exact thought in good English. By transposing the equation, ?/i = cd—ab^ we may obtain four other equations in each of which the left number is different. Thus, problems are provided for in which the answer required is entirely different from that in the original formula. Transposing, we have , vi-\-ab ni-\-ab cd—vi , cd—iii d = : , c = ■ — - — , a = J — , b = c d b a Having these formulas, the pupils may be required either to modify the problems they have already made so as to suit the change, or they may make new ones. Suppose that it be decided to modify the example at the beginning of this article so as to suit the fir.st of the four formulas given above, , _ ;// + trb c It may read as follows: With $6;^ and the money I can earn in 10 days at .$2J a day I can paj- for 5 cords of hickory wood. What do I pay per cord ? Or, taking the formula, , cd~ in b — ■ 28 PEDAGOGICS OF ARITHMETIC. § 1 The example may then read, Find my daily wages, if my earnings for 10 days must be increased by §6^ in order to pay for 5 cords of wood at $6|^ per cord. It may be added that a teacher may use this method with great success and yet know nothing whatever about algebra. There are, however, very few persons engaged in teaching to whom algebra is entirely unknown; and it is doubtful whether, without such knowledge, it is possible to teach arithmetic with much success. FIXDAMEXTAL DKII^LS. TUlUAu AVORK FOR ADDITIOX. 24. Tlie Entl in Tie^v. — It has already been remarked that all drill work should have a definite purpose beyond mere discipline. Every drill should bring greater mental dexterity and aptitude ; but, in addition to this, it should be a distinct preparation for some work that must be frequently done during life. Now, with respect to addition, what is this work ? Clearly, it is to add columns of figures. If one wishes to know wdaat he owes his grocer or his butcher, this is what he must do; if he becomes a clerk or an accountant of any kind, he is constantly called upon to find quickly and accurately the footings of columns of figures. Practice in addition should, therefore, begin very early, and it should bj continued throughout the school life. It is possible not to do enough of this kind of work, btit it would not be easy to do too much of it. Besides the addition of figures in columns, various devices may be resorted to in order to increase the inte.est of pupils. 25. Seliemes for the Blackboard. — Drills like the fol- lowing (Fig. 1) may be put on the blackboard in a place where they may remain without being in the way. Or, the teacher may make suitable charts on large sheets of manila paper; 1 PEDAGOGICvS OF ARITHMETIC. 29 these, when needed, may be hung np before the pupils, and removed when the exercise is finished. 8 3 12 U 5 10 1 (") 11 + 2. 3, etc. Fig. 1. The drill on the left consists in adding 2, 3, etc. to S, 3, l2, etc. The pupil should be required to announce results only, and as rapidly as possible. For the sake of variety, the circle may be used occasionally. The exercises may be varied by changing the figure at the center. The addition should be from within outwards and the reverse, and around the circle both ways, beginning at different places. The exercise on the right is intended for practice in what some one calls decimation — passing by addition from num- bers between 20 and 30 to numbers between 30 and 40, etc. The figure preceding the plus sign may be changed to 3, 4, etc. as the degree of proficiency warrants. The scheme may be used in two ways: 1. The pupil may add each figin'e on the right to 32, announcing results only. Thus, 35, 41, 37, etc. 2. He may add a designated figure on the right to 32, 92, 52, etc. Much added interest is given to such exercises by the judi- cious use of colored crayon. 20, Addition of Colimins. — Every requirement of this drill work may be met by the addition of columns upwards 30 PEDAGOGICS OF ARITHMETIC. § 1 and downwards, and in both directions from different points of beginning. By thus changing the place of beginning and the direction in which the addition is made, the intermediate numbers touched are in every case different. Ttius, in find- ing the sum of the outer circle above, if we begin with 4 and add in the same direction that the hands of a watch turn, the intermediate results will be 13, 15, 20, 29, 35, 37, 44. In the other direction, we have 11, 13, 19, 28, 33, 36, 44. These are alike only in their final sum, 44. Beginning at 8 and adding in both directions we have 11, 16, 25, 31, 33, 40, 44, and 12, 19, 21, 27, 36, 41, 44. There are, therefore, always many more orders of adding a column, one figure at a time, than there are figures to add. In adding a column, the first figure need not be pointed to or named: point to the second figure and mention the sum that it gives when added to the first. As pupils become expert they should be encouraged to omit the pointing. It is enough to pass the pointer or a pencil rapidly along the column, omitting to mention the intermediate sums. Any one that must do these things with laborious precision must not expect to add rapidly. Besides, it is a fact that the more rapidly an addition is performed, the more likely it is to be correct. DRILL ^VORK FOR SUBTRACTIOX. 37. The End to Be Aeconiplislied. — Let us consider* what it is that we must do in actual subtraction. Knowing this, we shall be able to determine the appropriate drill. There are two principal matters that must be effected with absolute accuracy, and they should both be done rapidly — automatically indeed. These two things are : 1. To subtract in turn each sub! raJicnd figure from a corresponding figure of the minuend. 2. To ^'■carryf ivJien the conditions require it. Omitting for the present the subject of " carrying," we may consider the more important matter — the subtracting. The subtrahend figure may be any one of the digits from to 9, inclusive. When the subtrahend figure is 2, we may §1 PEDAGOGICS OF ARITHMETIC. 31 be required to subtract it from any number between and including 2 and 11 ; if it is 3 we may have to subtract 3 from 3, 3 from 4, etc., up to 3 from 12, which last gives a remainder of 0. In brief, the subtraction of one number from another may involve the subtraction of each digit from every number that leaves a remainder not greater than 9. No pupil can be expected to per- form the operation of subtraction with any certainty as to the result if he does not know at once and with- out thought all these remainders. 38. The General Sclienie. The general plan of this important drill work in subtraction may be imderstood almost at a glance from the diagram shown in Fig. 2. If 1 be taken from every number from 1 to 10, both inclusive, 2 from every number from 2 to 11, and so on to 9 from every number from 9 to 1 8, the scheme is complete for subtraction. Placed on the blackboard, one at a time, with the minu- ends disarranged, to avoid singsong, these drills are as fol- lows (Fig. 3) : Fig. 3. ! '^'^ 3\ 13\ S 13^ 8 - S IS 2 12 42 12 5 5 5 tr, 9 11 ^ 11 9 ^ 11 y- — 4, etc. to 9 11 ■ ■ 1 ^ -9 \ 7 4 7 4 7 4 17 14 '1 10 10 10 10 6. G> 6> IG^ ] Fig. 3. 52 PEDAGOGICS OF ARITHMETIC. §1 29. Anotlier Drill. — Another exercise of much practi- cal value consists in giving- rapidly, at sight, the difference between 100 and numbers less than 100, 75 and numbers less than 75, etc. The teacher should place on the blackboard some- thing like Fig. 4 : It is a great convenience to be able to tell instantly how much change one shoiild receive from a dollar or a half-dollar after making a purchase. 100 — 50 — A A 1 75- 68 76 25 33 4.-, 73 68 41 16 63 87 79 etc. 17 24 etc. DRII.T. AVORK FOR MFI/riPI.IC ATIOX. 30. Plan of tlie Drill. — The drills necessary in multi- plication are of two kinds: 1. Those involving the products of elementary numbers up to 12 X 12. 2. Those involving the foregoing products, with the additional operation of carrying. The multiplication table gives the products of (1), but in an order that inevitably results in the much deprecated singsong. The teacher is therefore compelled to devise some means of avoiding this difficulty. The products indi- cated in (1) may be made familiar to the pupil by using the brace, as shown in Fig. 5. Nothing but the products should be given by the pupils ; and the drill should be continued until these products can all be given as rap- idly as the child can speak. Even after this degree of thoroughness has been attained, there shotild be frequent reviews and many examples involving the same operation as the drill requires. When the products by 2 have been thor- oughly learned, 3 should be written in its place. The examples assigned for solution should always be within the limits of the drill work. This will make it easy and gradual to learn the added operation of carrying. PEDAGOGICS OF ARITHMETIC. 33 Multiplication with carrying includes two operations : 1. Recognizing the elementary product. 2. Uniting with it the number carried. These two operations in their best development become one. Thus, 7 times 5 increased by 6 is 41, and not 35 + G. This is the first point that the teacher should fix. For the pupil to say "7 times 5 is 35," and then count G fingers or G marks on his slate is bad, and without excuse for the teacher. The pupil should, just as soon as possible, say only "41," performing both the multiplication and the addition without speech. These operations can be performed very much faster than they can be spoken. Rapid, involuntary, accu- rate mental action is the prime necessity, and for this the teacher must labor patiently and persistently. In the following exercise (Fig. G), the pupil should annoi:nce results only. When the multiplier is 2, and the greatest mul- tiplicand 12, no number carried is ever greater than 2 ; when 3" 9 8 12 7 .3^ 9 ' " ~ ~ S « 12 yx2^i^ ' 3A 9 5 S 12 ^X3+J2 I ( 1 y X4 +< etc. 1 6 4 10 2> 1 6 4 10 6 4 10 2^ 3 .4 ■ ■ 1 the multiplier is 3, the number carried is never greater than 3; etc. T>RII.L ^VORK FOK DIVISION. 31. Beveloj)nieiit of the Selienie. — The ordinary division table is quickly learned from the multiplication table. Indeed, it is an extremely easy inference or deduc- tion that if 6 times 7 is 42, then 42 divided by 7 is G, or by 34 PEDAGOGICS OF ARITHMETIC. § 1 G is 7. But to know the division table is a very small part of what must be known in order to divide rapidly and with- out error. Let us examine the following examples: 5 )38762 6 )59573 7 )183962 In order to perform the first division we must know the quotient and remainder when 5 is divided into 38, 37, 26, and 12. The respective quotients will be 7, 7, 5, 2, and the remainders 3, 2, 1, 2. In the next two examples the partial dividends, the quo- tients, and the remainders will be, 59, 55, 17, 53; 9, 9, 2, 8; and 5, 1, 5, 5. 18, 43, 19, 56, 2; 2, 6, 2, 8, 0; and 4, 1, 5, 0, 2. An examination of these results will show just the kind of drill work that is necessary in order to prepare for short division. 33. Princiiiles of the Process. — The following facts are evident from the foregoing examples: (a) The quotient must be obtained one figure at a time. (F) Any one of the ten digits may occur in the quotient. (c) During the successive steps of the operation, any digit of less value than the divisor may occur as a reinainder. If we are dividing by 2, the greatest quotient figure obtainable is 9, and the greatest possible remainder is 1. What number, divided by 2 gives a quotient of 9 and a remainder of 1? Evidently, it is 2x9+1, or 19. What number, in like inanner, when divided by 3, gives a quotient of 9 and a remainder of 2 — a remainder the greatest pos- sible ? The answer must be 3 X 9 -|-2, or 29. Again, if the divisor is, say 7, in order that the quotient and remainder may be the greatest possible, the dividend must be 7x9-1- 6, or 69. For a divisor 9, the dividend is 9x9 4-8 = 89; when 12 is the divisor, the dividend must be 12x9 + 11 = 119. From all this, it is clear that, before a child can divide by 2 easily and rapidly, he must know instantly and without PEDAGOGICS OF ARITHMETIC. 35 reflection what the quotient is, and the remainder also, when 2 is divided into any number from to I'J inclusive. When the divisor is 3, this knowledge must reach from to 29 inclusive ; when the divisor is 4, the limits of the drill are and 39 ; etc. 33. General Sclienie. -—The following is a general scheme showing this drill in a form suitable for writing in the teacher's note book: Dividend Jbimits. 2 3 012 t 1 ^9, 39, i ! _J i ..A9, t 1 1 J ♦ 1- J .-_6(>, » 4 1 J .5 ^ (} 7 S 9 . . etc. 34. The Scheme in Detail. — For daily use, the divi- dends may be written on some unused place on the black- board. They should be disarranged as shown in Fig. 8, so that no result may furnish a clue to the next. The work should begin with 2 as a divi- sor, and this drill should be practiced imtil every pupil is expert as far as 10. When this has been well mastered, the third column of dividends may be written and 3 placed above as the divisor; and so on for all divisors up to 12. The pupil should announce results only, and these as briefly and 3G PEDAGOGICS OF ARITHMETIC. g 1 rapidly as possible. Thus, in going down the first column with 2 as a divisor, all that need be said is 1, 1; 4, 0; 5, 1; 2, 1; 4, 1; 3, 0; 9, 0; 2, 0; 0, 0; 3, 1. This is the longest and by far the most important drill work that requires to be done in connection with the funda- mental rules. That it should be thoroughly done is indis- pensable; for, without it, short division will continue, during the entire life of the pupil, to be slow, laborious, and uncer- tain of correctness. Do not make the lessons so long as to cause the children to hate the exercise. Remember that the younger the pupils are the shorter should be the lessons. It is impossible to hold the attention of very young pupils for a period of more than about fifteen minutes, and their early work in arithmetic is to them the most difficult and the dullest work that they have ever luidertaken. In several of our large cities rules have been made limiting all exercises in the lowest grades to short periods. 35. Ai>plieation of Drills to Practical Examples. It will be found of the highest value to carry along with the foregoing drills a corresponding work on slate and black- board. It would be absurd, of course, to ask pupils to solve examples involving division by 9 before they have mastered the drill as far as 9. But just as soon as they have learned a new step, they should be taught what it is to be used for, and they should be made thoroughly familiar with the method of using it. We make a serious blunder when we attempt to master all the tables before we try to apply them in practice. No one any longer attempts to have children inaster the entire alphabet before he introduces them to easy words and sentences. Many children are now taught to read quite well before they are sure about the identity of certain rarely iised letters such asy, .c, and q. This failure to apply to some definite practical use each merely mechanical, abstract matter as soon as it is learned, is what robs the earliest school work of the interest it might otherwise have. All our best authorities on pedagogics are § 1 PEDAGOGICvS OF ARITHMETIC. 37 urging- the importance of coordination and correlation in the matters that are taught. 36. Frequent Reviews a Necessity. — One of the dis- coveries that every teacher of young children is sure to make is the discouraging fact that no matter how carefully a sub- ject is taught it is certain to be forgotten in a very short time. When oin^ pupils come back to us after the summer vacation we are astonished to find that they have nothing better than a vague and confused remembrance of the impor- tant things we taught them with so much painstaking. Phys- iologists tell ns that this is owing to the fact that the brain of a child is growing and changing with great rapidity. After the cranium has reached its full size, impressions that are deeply made are likely to be permanent; but before that time they are, so to speak, overgrown and hidden b}^ encroaching brain tissue. Moreover, by the time that we have nearly or quite attained maturity, the mind is stored with much information of every kind, and with this any new idea is easily and closely associated. It is then easy to remember the new fact by the aid of association and likeness. Of the occurrences that make up our life before the age of six years, nothing, or almost nothing, is remembered when we reach mattn-ity. It is only by repeating again and again those early lessons that we may expect to have them endure. Let every matter that you teach in those first years of the child's school life be carefully predetermined, and reviewed until it cannot be forgotten. Remember that this is a period of accumulation and for the establishment of tendencies rather than a period of definite development. There should be no "lost motion" in education — no wasted effort. Therefore, work systematically, and do not be dis- couraged at apparent forgetfulness on the part of your pupils. Above all, review and review again. Your work is much like making- an artificial island where shallow waters rest upon unknown depths of sediment. If the material for filling is not too widely scattered, a support for the super- structiu-e will ri.se above the surface sooner or later. 38 PEDAGOGICS OF ARITHMETIC. § i NOTATio?^ A:N^r) nijmeratio:n. ARABIC NOTATIOX. 37. The Perception of Number. — A very ciirious and interesting question of psychology is this: How many objects of the same kind, without arrangement in groups, is the mind capable of instantly perceiving ? If three separate bright points were to appear for an instant on a dark background, and vanish at once, even if there were thousands of observers, all would probably agree as to the number of illuminated points. If a bursting rocket on a dark night should show four such bright points, the difficulty would be only very slightly increased. If the number were increased to five^ or even to six^ any one catching the fleetest view of them would be very likely to be certain of their exact number. Much experiment has shown that about seven is the limit to the instantaneous perception of number, unless objects are in groups each containing a known number of units. Beyond the number seven, the mind's inability to take in at one act the several units that make up a collection, begins ; and its helplessness becomes rapidly more apparent as the number increases. This fact has an important bearing on the question of teaching notation and numeration — the wri- ting and reading of numbers. When a person of normal mind hears the expression, "three apples, "he immediately forms a mental picture or image in which the objects named appear represented in a group, very much as in an ordinary picture. If, however, the expression be "twenty-nine apples," no such picture is formed. No attempt is made to conceive them as separate imits, for the task is beyond the power of the mind, which is very quick to perceive its impotency. But what does happen in the mind ? Very nearly the same that happens when such expressions as " many apples," "much money," and the like are heard. Nothing very definite perhaps; but § 1 PEDAGOGlCvS OF ARITHMETIC. 39 it is certain that the mind sees nothing to correspond to the three or four bright points mentioned above. If, however, we insist upon forming a mental picture to represent such expressions, the mind will in every case .seek the easiest way of doing it. In the case of large numbers, this easiest way is to form a mental picture of the Arabic figures that express the numbers. Thus, the simplest form in which the mind can carry the number three hundred sixty-seven is the mental image of 3G7. If the ear hears the spoken num- ber at the same time that the eye sees its written or printed form, the greatest possible distinctness of mental effect is pro- duced. The action of the brain center that takes cognizance of sound strengthens and reenforces that of the brain center that responds to visual impressions. Every teacher is aware of the double effect produced upon the mind by addressing both the eye and the ear in teaching- any subject. It is clear, then, that the mind makes no attempt to con- ceive of large numbers by separating them into their com- ponent units; that, on the contrary, it seeks the way of least diiffculty — the " line of least resistance." 38. Ajiplicatiou to Pedag'og'ics of tlie Forego in j? Fact. — About twenty years ago one of the leading educators in this country published a very remarkable arithmetic. Believing that children should be habituated to the mental operation of exactly conceiving the real significance of the numbers they handled in their arithmetical work, he devoted many pages to an elaborate treatment of notation and nmner- ation. Very excellent and abundant were the illustrations employed. Beginning, he showed by means of pictured straws the numbers up to ten. Then, by a bundle of ten straws, placed in turn before two, three, etc. separate straws, he represented the numbers between 10 and 20. Two ten- bundles and nine straws represented 29; eight ten-bundles and five straws formed the visible representation of 85. Ten ten-bundles made the next measuring unit — the 100-bundlc, and the pupil was expected to see in the number 958, for example, nine lOO-bundles, five ten-bundles and eight 40 PEDAGOGICS OF ARITHMETIC. § 1 separate straws. Finally, ten lOU-bundles were made into a 1,000-bundle, and great ranks of these were formed to represent such numbers as 7,89o. But the author stopped at this point, and the fact that he did suggests the question why he did not stop earlier. Where is the proper place to give up the task of helping the mind to distinct conception of the real meaning of num- bers ? Opinions differ. One thing is certain; no one in actual life analyzes numbers to this extent, nor does any one ever need to do so. If seven or eight is our mental limit, why should we undertake a task that is both hopeless and needless ? Sooner or later we come to deal with numbers so great that we could not adequately conceive them even if it were necessary. Why not, then, give up the useless work as soon as possible ? In higher mathematics, quantity is represented by letters and other symbols of general value, and one of the great advantages of this is that the mind is not diverted from necessary operations with these symbols by any attempt to gain an exact conception of the aggregates denoted by the general symbols. It is pretty evident that if the work of analyzing numbers be kept up very long there will be estab- lished a tendency to analyze every number entering a problem, and, thus, the power of the mind to reason about the conditions of the problem itself will be correspondingly diminished. The application to pedagogics of the foregoing considerations seems to be the following: Teach the Arabic sy stein of notation and numeration — the decimal system — so that the pupils shall thoroughly compre- hend its essential principles, but do not carry much beyond 100 the minute analysis of number. The fact is that life and the world are full of number, and even if we try to escape knowledge of number, — more or less definite, — all indeed that we really require for the uses of life, we cannot do so. Besides, there is no more real necessity that we should conceive definitely of the real meaning of the great numbers emplo3'ed in arithmetic than there is that we should know exactly how many units are intended by the § 1 PEDAGOGICvS OF ARITHMETIC. 41 expressions, "a crowd of people," "a flock of birds," "myriads of stars," "a long- time." We are able to think and to talk about these collections very satisfactorily, with- out knowing- the number of units that make up their aggre- gates. We have been so long and so often baffled by our conditions and limitations that the mind has forgotten its instinct to demand a sharp and clear mental picture for every object that engages the attention. 39. Importance of the Lang-iiag'e of Xunibei'. — In dealing with numbers in computing, we must know how to write and to read them. This is a form of number knowl- edge that is of very great importance, for without it the teaching of arithmetic would be a task of extreme difficulty. Our children must be taught to write and read numbers expressing vague magnitudes so great that even the greatest mathematician would be unable, adequately, to conceive them. It is the language of number that is important; its real meaning beyond the first three or four figures has very little practical value or interest, and should be neglected in teaching. No one is ever conscious of an imperative mental demand to know the exact significance of a number composed of many figures, and yet we use them in computation wdth the same facility that we do numbers of small value. The newspapers often contain curious attempts at conveying, by means of ingenious comparisons, approximate notions of great numbers, such as national debts, atomic or molecular particles, stellar distances, and the like; but these are only curiosities of measure ; they have no educational value whatever. The writer believes, then, that pupils should know very intimately and familiarly all whole numbers up to 100, and somewhat less exactly the nmnbers as far as 1,000 or at the farthest 10,000; in addition to this he should understand the theory of the Arabic notation and numeration well enough to write and read numbers as far as they have any real human use or application. Perhaps, not more than one per- son in 100,000 could readily write and read numbers as far as vigintillions, and one might pretty safely assert that no 42 PEDAGOGICS OF ARITHMETIC. § 1 person has ever been confronted with a real necessity for doing so. It should be on the real utilities of the school curriculum that teachers should employ their strenglh. 40. Two Methods of Teacliing [Notation. — The names of numbei'S may be taught by two very different methods, distinguished as the couiiiwn uietJiod and the scien- tific method. As far as to ten these methods are alike, the work in each being to make pupils perfectly familiar with all elementary combinations up to that limit. The common method proceeds with numbers beyond ten just as with numbers expressed by one figure. Twelve, sixteen, and twenty are taught in exactly the same way that six or nine is. No attempt is made to have pupils see toi or tlwcc in the word thirtccji, or to learn the principles of the decimal scale. In teaching by the scientific method, when ten is reached, the idea of a ten-group is taught, and then the numbers between ten and twenty are each only this ten-group with an addition. Thus, thirteen is t/ircc-tcn, fifteen is fivc-tcn, etc., the names being exactly similar to the Latin trcdcciin^ guindcciui, etc., and to the Greek -peLOKaideKa, tj'ciskaidcka, ' ' three-and-ten, " TrevreKatdsKa, poitckaidcka^ ' ' five-and-ten, " etc. In our words eleven and twelve the cue to the decimal scale is not so obvious as in the Latin 7/;/ etc. This is suitable for slate work. Orally, such work should be done in three steps: (,,) 3-1 + 2 = 4; (^) 4 + i + l- = 4|; (c) 4|-f = ^. § 1 PEDAGOGICS OF ARITHMETIC. ST That is, (a) Find the total of the ijitcgcrs in accordaiico ivit/i the signs. {(3) To tJiis total add the fractions that are affected by the pins sign. (y) Diminish the second result by the negative fractions. 19. Multiply \ and \ by various integers, changing result to whole or mixed numbers; as, ^X 5 = f = 2|-; |-x8 = f = 2|. Many practical examples. Illustrate. 20. Multiply |, f, f, etc. by integers, reducing result. Same exercise with f, f, 4, etc. 21. Multiply mixed numbers with halves and thirds by various integers; as, 1^x4, lfX2, 2^X5, etc. Concrete examples. vSolutions should be in the fewest possible words. Example. — Let it be required to multiply 3^ by 4; also, 3| by B. Solution. — 4 times 2\ is 8 and -|, or 9i; 3 times 3f is U and |, or 11. Do not permit the pupils to say, "4 times \ is I, or 1^; 4 times 2 is 8; 8 + 1^ is 9i." 22. Exercises to make the pupils familiar with the fact that such forms as 4-X 5, \ of 5, and 5 X ?r are equivalent. 23. Find ^, 4, and \ of integers ; first, when the result is exact; second, when the result is a mixed number. Con- crete problems. 24. Show by diagram that \ of \, or i of \, is i. This may be done by figures of many kinds; as, for example, by divi- ding circles, rectangles, or simple straight lines, as below. {a) To show that ^ of i = i (Fig. 9.) I I 2 ' 2 2 6 6 6 6' 6 Fig. 9. (b) To .show that i of ^ = f (Fig. 10.) iofi Fig. 10. 58 PEDAGOGICvS OF ARITHMETIC. § 1 25. Find ^ of i |, |, f, etc. Then i- of 1|, 2^ etc. 26. Find i of 1^, 2|, 3|-, etc. This work may be illus- trated by diagrams and is admirably suited for blackboard drills. 27. Find f of ^, and extend the operation afterwards to „ „ integers. In getting f of 5, for example, I 5 3 require the following analysis: "f of 5 is the 2 r j 3 5 I 3 same as ^ of 10, or -y-, equal to 3^. " Turn this "^ ^ \ finally into blackboard drills with other frac- ■^ '^ tions. The following will illustrate: Require the pupils in solving the second form to say, " 8 times f is the same as | of 8; f of 8 is ^ of 24, or 6." Give many concrete examples. 28. Train the pupils to tell instantly all the exact divi- sors of 6, of 8, of 10, of 12, and so on, as far as they have studied numbers. 29. Ask for the least number that may be exactly divided by every number in each of the following groups : By 2 and 3; 2 and 4; 2 and 5; 2, 3, and 4; 2, 3, and 6; 2, 4, and 6; 2, 3, 4, and 6; 2, 3, 4, 6, and 12; and so on. Require a form of answer like the following: " The least number that can be exactly divided by 2, 3, 4, and 6 is 12; 12 divided by 2 gives G; by 3, gives 4; by 4, gives 3 ; and by 6 gives 2." 30. Train the pupils in changing groups of fractions to equivalent fractions having a common denominator. Thus, require them to change ^ and ^ to Oths, to 12ths, to 18ths, etc. ; 4- and \ to 4ths, 8ths, etc. ; |-, -j, f to 6ths, to 12ths, etc. ; i, |-, ^, f, f, f to 12ths, 24ths. These equivalences are very important and the children should know them as they do the multiplication table — without reflection or hesitation. 31. Change fractions to simplest forms. This should be persisted in tmtil all the various forms of the fractions in common use are changed withoiit the slightest delay. Pupils should be able to glance down a long list of simple denomi- nators, decide instantly what is the least common denomi- nator, and then add the reduced forms as they would a col- umn of integers. Thus, suppose the following fractions were to be added: i-f ^-f | + | + | + f + | + |^^ A glance S 1 PEDAGOCilCS OF ARITHMETIC. 59 should show that they must all be changed to 12ths. With- out writing anything, except, finally, the answer, they should add " 0; 4, 2, 3, 8, 9, 10, and 11." In doing this they should say, "0, 10, 12, 15, 23, 32, 42, 53 twelfths, or 4j\:' To attain to this degree of excellence will require considerable time, but the work should be continued until this end has been reached. 32. A fractional part of an imknown number being given, to find the number. The following will illustrate: If S niaii)les are I of all the marbles that John has, how many has lie ? After many easy concrete examples, the pure number may be used and a blackboard drill will soon give expert- ness. The form of such a drill is shown below: 8 4 10 6 13 etc. ^ r -, Analysis. — If | of a number is 8, i of the number = of ? ^ ■* is I of 8, or 4 ; and the number is 3 times 4, or 12. 33. Extend the work in (32) t(~) numbers that will give a mixed number for the residt. Thus, If I of a number is 5, what is the ntimber ? Analysis. — If | of a number is 5, J of the number is ^ of 5, or :} ; and the number is 3 times |, or -^J'-, equal to Ih. This is suitable for drill and for concrete examples. 34. Extend the work of (32) to such examples as the fol- lowing, the result being in each case an integer: If a boy can walk 5 miles in 1 j hours, find his rate per hour. Analysis. — If hours are ;; hours. If the boy can walk 5 miles in I hours, in i of an hour he can walk i of 5 miles, or 1 mile ; and in an hoi:r he can walk 3 times 1 mile, or 3 miles. 35. Work like that in (33), the result being a mixed number. Thus, If 1| of a number is 6, what is the number ? Analysis. — 1| = f. If f of a number is 6, J of the number is -J- of 6, or I ; and the number is 3 times |, or y , equal to 3|. GO PEDAGOGICvS OF ARITHMETIC. § 1 30. What part of 5 is 3 ? Analysis. — 1 is i of 5, and 3 is 3 times i of 5, or | of 5. 37. Wliat part of 21 is U ? Analysis.— 2| = |, and 1}, — |; J is i of |; § is 3 times i of §, or f of |. Hence, li is § of 2J. The conclusion i.s stated in this example. vSome teachers prefer to do so in all cases. There is no serious objection that can be urged against the practice. 38. What part of f is f ? Analysis.— | = J>^, and | = j**, ; ^i^ is J of ^%; j% is 8 times J of Z^, or I of j%. Hence, -| is | of |. 39. How many times is 2^ contained in 6 ? Analysis. — 2', = §, and 6 = -V- ; 2|^is contained in 6 as many times as I is contained in y, which is as often as 5 is contained in 12, or -^^, equal to 2|. Hence, 21 is contained 2| times in 6. 40. If I of I of a number is 6, what is the number ? Analysis. — i of ^ of a number is ^^ of it; J of ^ the number is 2 times y*.^ of it or i of it; f of | of the number is 3 times i of it, or J of it. Then, if }, of a number is 6, the number is 2 times 6, or 12. Hence, 6 is I of I of 12. 41. How much is 5 of | of IJ ? Analysis.— I'of | = x*, I I o^ t = 1: f of f = 3 times |, or J. 4 of U r= I, of § ; i of 1 = ^; i of I = 3 times ^, or |. Hence, | of f of iUsf. 53. Reniai'ks on the Foregoing Selienie. — The plan of fraction work outlined above may seem to be a long- one, but, even so, it is by no means complete. These are only the simple fundamental operations that every person mtist know if he is to use fractions with any ease and effect in the operations of actual life. The combinations possible among these simple processes are nearly beyond computation. Still, if children are taught all these operations and are made thoroughly expert in them, the combinations will give them little trouble. The student will notice that every one of the types indi- cated above may, by the use of the simplest fractions, be § 1 PEDAGOGICS OF ARITHMETIC. 61 brought within the limits of difficulty for oral work; and, as has been stated, the simplest fractions are just those having the highest value in practice. It is very rarely indeed that any one is called upon to com- pute with sevenths or elevenths, and one is not likely, during the business of an entire lifetime, to be confronted with a calculation involving thirteenths, seventeenths, or nineteenths. Clearl}-, then, the teacher should lay out most of his effort in giving his pupils a mastery over halves, thirds, fourths, fifths, sixths, eighths, ninths, tenths, and twelfths. Of course, in the operations of addition and sub- traction, he must frequently reduce fractions to twelfths, sixteenths, eighteenths, twentieths, twenty-fourths, etc. These higher denominators, however, are not numerous, being usually such numbers as have many exact divisors, such as 12, 20, 24, 30, 36, 48, 72, etc. In seeking for a variety of good concrete examples for these various types, the teacher cannot do better than refer to the many mental arithmetics. He may be very expert in making examples to meet the requirements of his pupils; but, even so, he may get many valuable suggestions both as to matter and method in these useful little books. Where so many of them are excellent, it would be invidious to mention any in particular. With respect to the time necessary to work out the fore- going outline, it must not be imagined that this is a task that may be begun and ended within the limits of a few weeks or months. It should cover the entire school period in arith- metic, and may be repeated several times, each time witli more difficult numbers and new applications. If it be hur- ried over or be made too abstract and mechanical, it will become very tiresome to both teacher and pupil, and the result will be, in a very large measure, a failure. Above all, do not neglect very frequent reviews. 54. Orig-inal Examples Made by Pupils. — No rule or process either in arithmetic or algebra has been thoroughly mastered by the pupil if he is not able to exemplify its 62 PEDAGOGICS OF ARITHMETIC. § 1 processes and principles by means of problems that lie himself has made. And this test should always be applied to him. The teacher may at first suggest what such an example is to be about. For instance, he may say : " You may make me an example similar to (here specify the example), only it must not contain the same numbers, and it must be about something else." Or, he may say; " If I knew the hourly rates of A and B, and how much longer A is than B in making a certain journey, I could find out the length of the journey. Make me such a problem." After some dexterity has been attained, the directions by the teacher may be made less and less specific. Care should be taken that no contradictory, absurd, or ambiguous con- ditions are found in these examples. They should be care- fully written on paper, in good English, and correctly punctuated. Very frequently the teacher will find some examples so good that he will desire to copy them into his note book for future u.se. One of the faults to be avoided is too great difficulty. This is a besetting sin with beginners. Pupils constructing original examples are likely to make some that neither they nor the teacher can solve. It is to be remembered that the chief purpose of these problems is to exemplify in each case some principle. If they are difficult, the principle will be obscured or lost in the complexity of the solution. The best arithmetics are, in general, the easiest. One other characteristic of these original problems is that they should be of wide variety, and yet illustrate the same principle and method of solution. It is wonderful how widely examples may sccj/i to differ and yet all belong in the same type. 55. The tiearniug' of Rules and Deflnltions. — Begin- ners in arithmetic, as well as in nearly every other subject, should not be required to commit rules and principles to memory. These being as far as possible from the concrete, are utterly beyond the powers of young children. The}'^ have just been removed from that early domain where reality § 1 PEDAGOGICS OF ARITHMETIC. G3 is all ill all. So far they have never been required to general- ize or reason or discriminate or, without objective aids, to do any serious mental work. They have merely observed the qualities and activities of real things; those faculties that will, by and by, furnish them a very high degree of pleasure in dealing with pure abstractions are, as yet, dormant and incapable of action. Children should, at first, be shown only the processes; — -the liow; — the ivJiy is a matter that should not come until later. Require them to do again and again the work that will finally make them very expert in useful processes. When such expertness has been attained they may easily and gradually be led to investigate the reasons for their processes and to discover the involved laws and prin- ciples. The inductive method is the only method that can be successfully used with young pupils. Eveiy principle should be preceded by many simple exercises and problems, each of which contributes something towards suggesting and illustrating it. By the aid of many particulars, the child comes at length to see the general ; and, if at first he sees it only vaguely and dimly, there is no need for the teacher to worry or be discouraged. Remember that if the pupil is set to the task of learning principles expressed in exact scientific language, the effect is certain to be disastrous to mental growth and progress. He will surely come to hate the subject, and will fail to get that confidence in his own powers that is indispensable to real progress. In the ideal teaching of arithmetic, the pupil should be able to infer principles and to deduce rules for himself. 5(>. Gi'apliic Illiisti'ations in Fractions. — In teaching fractions, the question of success turns largely on the facility in illustrating possessed by the teacher. In this subject of fractions, no point is well taught unless it is absolutely clear in every point. The work of graphic illustration should begin at the very first, and as the actual object is gradually dis- carded, the diagram should be the last step towards the pure number. Almost any simple problem in fractions may be solved graphically — by means of diagrams. For this purpose. 64 PEDAGOGICS OF ARITHMETIC. §1 the square or rectangle, the circle, and the straight line may be used. Which is best in any given case must be determined by the teacher. In order to show just how this work should be done, a number of illustrations follow (Figs. 11 to IS): 1. How many sixths in ^ ? Fig. U. 3. What is i of J? jo/j^n #«/■# I of ? = I : 4. Compare = with ^. 2 • ? Fig. 18. 5. Divide | by |. t Fig. IJ. Fig. 15. 1 — n 3 — 15 2 — in. 3 — 15- 1 — 8 "5 — T5 3 — 9 . 5 — T5' 10 _9_ -- J_ — T2 ~ T2 — " • "^ — 9- 8 1 PEDAGOGICS OF ARITHMETIC. G5 S. Iff oi a certain number is 8, w hat i^i of the same number ? 1 1 t 1 1 t 1 9 = 1 1 1 t 1 i = 8 1 1 1 3 lO 4 2 3 -"^ < 1 1 1 3 ! 4 \ 1 1 3 \ 1 i 1 1 1 i 1 \ \ 1 '1 r 1 4 t = 3 \ Analysis. — If | of a number is 8, i of the number is \ of 8, or 4, and I of the number is 3 times 4, or 13; if tlie number is 12, \ of the number is 3, and f of the number is 3 times 3, or 9. 7. Find % of 4. Fig. ir. fofl = |; 2 of 4 = •3. + 24.21.2 _ § of 4 = 4 times |, or |. 8. How many times is | contained in 4 ? Or, 4 - 1 1 1 ] r 1 ' ' ^^ — ^ 1^ Y Y Y Y Y > 1 = I; 4 Fk;. is. 1X4 \2^'l 5*7. T^sofxil Drills iii Fractions. — Some blackboard drills in fractions have already been i^iven, but the extreme value of such exercises would seem to require that the sub- ject should be illustrated more fully, and that suggestions as to the manner of using them should accompany them. A very excellent method of pa-eparing these exercises is to mark them with a lettering brush on sheets of stiff manila paper about the usual size of school charts. These charts can then be kept for an indefinite time, especially if they are reen- forced by means of a flat stick above and below. Otherwise, 66 PEDAGOGICS OF ARITHMETIC. 1 they may be copied on the blackboard when required for use. It is very important that they shall be nsed every day once or oftener. The lessons should not be long, however, for it must be remembered that they are drills in pure number, and children soon weary of abstract exercises. There is much variety possible in the arrangement, on the blackboard or chart, of the inatter for drills. In general, the brace is very convenient for this purpose, but every teacher knows that children weary of sameness, and that they will do the same work over -many times and enjoy it as if it were something entirely new, provided that it is pre- sented to them in a new form. A circle, therefore, may be used for one drill, a square for another, the brace for still another, and so on. In the work suggested below, there is no intention to indicate the very best blackboard arrange- ment; it is the kind of work that is deemed important. Change : To halves. IS. To third S. To To fourths. 4^ 5i, 71 si. 9 J etc. To sixt] 3i, 4|, 5|, 61, ;tc. 3f, 4>, 5| etc. twelfths. h h 1 21, 3f, 4 etc. 1 1 2> t h 1 6> 1. 1 3- 15 3 ?' 6' ¥ U, H. If etc. Give analyses at first, and after a good degree of facility has been attained, announce rapidly results only. Rapidity is the end in view. Of course, the numbers must be chosen to suit the grade of the pupils. Chans^e to ones- -^7 lettering and numbering in the man- ner shown, no pointing is necessary, for any one of the 16 squares may be indicated by a letter joined to a number. Thus, Al means ^; Cr^, J/; B2, J/-, etc. This same plan is always possible with the rectangular arrange- FiG. 19. ment shown in Fig. 19. A B C D 23 11 li 3 22 3 3 1* 5 la 18 '4 n 4 1 4 IS 3 9 7 IS 4 .19 3 XT 6 S3 6 §1 PEDAGOGICS OF ARITHMETIC. 67 5 2 3 B 7 8' 6' 3' T' ¥' 1 i 4 7 9 4 8 9 3' ^' 8' ¥' T2' 12 Find sums: n ! , I 9^ 41. n\.,H ^ [+\si 71 I ] 6i 5i, 6H ^ 81 5| ^ 1 9H etc. J [ etc. etc. J [ etc. etc. J |^ etc. In doing the foreg-oing work the pupils may be instructed to add to 4^ each number in the second column, then to l^ 7j, and so on down. Or, each number in turn in the first column may be added to 5^ in the second column, then to 9^, etc. Again, the pairs may be added horizontally. Change to Sixths- 1 1 S - i 11 11 21 13. Twelfths- I112S425SS412 Twenty-fourths: i i, j% ^, i i, 5 7 1 : Ti' 8' 12 Change to simplest form (Fig. 20): A JB C J) E 1 2 3 4 M Fig. 20. Multiply At first the pupils may find these products separately and then go through the formal addition. Thus, in finding the product of 5| by 2, they may for a time be permitted to say, "Two times 5 is 10; 2 times f is |-, or li; 10 plus l-|-is 111. " As soon as possible, however, they should say only, " Two times 5f is 10 and |, or Hi " ; " Seven times 5f is 35 and ■■y*-, or 40f. " Nearly all the exercises described in the general scheme of work in fractions may be supplemented by suitable oral drills, and whenever this can be done advantageously, the teacher shoidd prepare the drills in the best possible form. From what has been said about the likeness of ordinary integers to fractions, the teacher will, doubtless, see that while he is training pupils in fractions, he is training them, 9 i2 8 10 * 6 IS 24 !•■! IS 9 IS 6 9 lU 16 12 16 JO 73 e 10 .6- 8 8 1* 80 24 7 14 6 S 14 94 IX 90 14 16 JO le 15 as 4 IS 14 18 14 21 H n] • 2 81 45 s 11 8| '■■i ^ by - 3 6 H 91 4 n 54 J L7 08 PEDAGOGICvS OP^ ARITHMETIC. §1 also, in integers. Hence, there should be no arbitrary sep- aration of the two — no deferring of fraction work to the time when the pupil has gained expertness in dealing with integers. It is just by this separate treatment that children are led to assume that there is some material difference between frac- tions and integers, and that they require essentially different methods of treatment, and, having once acquired this notion, they rarely, often never, get rid of it. 58. Written Work. — The ratio of the time to be given to oral work in arithmetic to that which should be devoted to written w^ork is not constant. At first the w^ork should be entirely oral; but just as soon as the pupils have learned to write the figures and other characters used in their exer- cises, they should begin to do so, and to express relations between numbers by means of the equation. While not engaged in actual recitation, various forms of "busy work," as some one calls it, should be required of them. Otherwise, they are likely to find other means of being "busy " that will not be conducive to the best order. After this very early period, the written work should steadily increase in quantity and severity, and should consist less and less in purely routine mechanical operations. The application of the processes of arithmetic to the solution of practical business problems is, of course, the principal end in view, and to lead the pupils to make this use of the study is a work requiring much time and care. The ratio that oral and mere drill exercises should bear to written work combined with book work is perhaps pretty accurately shown in the following diagram: 6 to 8 pears. S to 10 years. 10 to H years. Cr:il and Drill work. Written work atuljiook study Fig. 21. § 1 peda(t()(tICvS of arithmetic. ou This diagram (Fig. 21) is intended to represent about the ages during which arithmetic is pursued in the graded schools of our large cities. In the country and village schools, the school terms are usually shorter, and the study is likely to be continued during the entire school life of the pupils. PRIMARY AVORK IX DETAIIi. PRELIMIXAKY OHSERVATIOXS. 59. A Year's AVork. — There is much difference of opinion among writers on education as to what amount of number work can be well done in a year, — especially in the first year. After the first year the progress of pupils that begin together is strongly suggestive of an ordinary race in which there are many "starters." It soon appears that a few forge rapidly ahead, while all are strung out in a long procession. Many fall out before the goal is* reached, and show clearly that their powers were unequal to the require- ments of the struggle. It is well known that two pupils cannot be found whose powers are so nearly alike in kind and degree that they can begin and end their school work at the same time and with equal results. For a brief time the difference between them may not be appreciable, and they may advantageously be kept together and be under the same training; and, although, for reasons arising from the advan- tages of the division of labor, it may be best to keep them in the same class and under the care of the same teacher; yet, if it were possible, it would be better if each child cotild have different treatment. It is clear, therefore, that a year's work is, with respect to what may or should be accomplished, a very vague and varying expression. Again, there is no uniformity in the length of the school year. In our largest cities the usual tnne that school is in session is about 200 days annually, covering a period of ten months ; but in towns and villages the period is variable. 70 PEDAGOGlCvS UF ARITHMETIC. § 1 and is usually less, never more, than ten months. In country districts the time is rarely more than eight months, and is often as low as four months. Obviously, then, no definite amount of work could be prescribed for a general curriculum. The unequal capacities of children, the varied notions of what constitutes sufficient thoroughness in number knowledge, the different degrees of skill of teachers, the various methods employed, and many other circumstances all go to make it impossible to fix the amount of a year's work. And yet this has been attempted and has been done with the utmost definiteness, not only for the graded schools of large cities, but for schools in general. But different writers are not agreed on this subject, even when they assume school years of equal length. Many authorities think that if the subject be thoroughly mastered as far as 9, omitting all fractions, a year of ten months will be required. Others again would carry the work to 20 during this period, and, besides, do much with fractions. It is certain that no substantial agree- ment concerning this matter will ever be reached by the authorities, rror is such an agreement either necessary or desirable. 60. Plan Important Ratlier tlian Amount. — The greatest fault to be found with the teaching of arithmetic is that it so often proceeds without orderly plan. Such systems as have been arranged and brought forward have been suc- cessful, not so much because of some peculiar pedagogical excellence as because they necessitated an orderly method of procedure — a sequence and gradation that made progress easy and rapid. At every stage of a pupil's progress there is always something that, logically, should come next; some- thing that, if it be omitted, deferred, or only partially mas- tered, will cause the pupil ever afterwards to proceed weakly and uncertainly. It is by enabling the teacher to work in straight lines and without wasted effort toward a definite object that systems of teaching arithmetic are used with so much advantage. The young teacher entirely without experi- ence needs above all things else a plan. It makes but little § 1 PEDAGOGICvS OF ARITHMETIC. 71 difference by whom it was devised, or when, provided its value has been proved by the test of actual trial. 61, Every Lesson Should. Be a Iiangviage licsson. From the child's first day in school the work of teaching Jiim to express his thoughts fully and in good English should be begun. This is a matter of more importance than that he should learn arithmetic or grammar or geography ; and it is, besides, the most difficult task that awaits him. This lan- guage training can be done with special effect in the unwrit- ten work of the first lessons in arithmetic. During this early period the teacher should refuse to accept partial or otherwise faulty answers to questions. Thus, if the question were, "How many splints have I in my hand?" the answer should be, not " Five," but " You have five splints in your hand. " It is objected to this that insistence on formal exactness diverts the mind from the arithmetical side of the lesson and delays progress in the study of number. This is, doubtless, the case ; but it must not be forgotten that the correct, full, and graceful expression of thought is of more consequence than a knowledge of arithmetic. Moreover, the fact that arithmetic is one of the exact sciences would seem to require equal exactness in its vehicle, language. If children are taught from the first that careless and erroneous speech is not to be accepted, the necessity of interrupting them on that account will soon become infrequent, and correct lan- guage will speedily become involuntary. It is now almost an axiom among educators that every lesson should be a lesson in the correct use of language. 63. Plan of Ti^eatnient. — One of the chief needs of young students of arithmetic is a good working knowledge and facility in the language of the subject. They should be carefully exercised, therefore, both in the notation and in the ordinary language of number. This training should begin with the language pertaining to oic and tzvo ; for, 72 PEDAGOGICS OF ARITHMETIC. § 1 while most children have a pretty good knowledge of these numbers, they are not able to use to any sufficient extent and correctly the necessary notation. The teacher must be careful that all answers and statements are in good English and complete. Nothing else should ever be accepted. In teaching number, the ordinal is almost as important as the cardinal. Frequent exercises should be had in naming the order of certain indicated marks or objects placed in a row. For example, the child should often be required to say such sentences as the following: "John is the first boy on the line." "The third figure in this number is 8." "Wednesday is the fourth day of the week." " Jnly is the seventh month of the year." In the scheme that follows, four matters should engage the attention witli reference to each number that is specially studied. 1. The Notatnvi of the Nujiiber. 2. The Pure {or Abstract') Number. 3. The Applied (or Concrete) Number. 4. The Subdivided Unit. The Grube method considers only the second and third of these phases, and yet the others are of extreme importance, and should not be left to incidental mention. By the sub- divided unit is meant that when the pupil is studying any integral niimber, as 3, for example, he should become acquainted with thirds; when he studies -i he should learn fourths and halves; and with G should be treated sixths, halves, and thirds. With these fractions should be performed the same fundamental operations as are common with integers. They are, as has been said, a kind of units as readily understood as any others, and their notation and language are very easily learned. 63. The Niimber 1.— The important matter with refer- ence to this number is that pupils should understand the exact meaning of the language relating to it, and should acquire expertness in using that language. They should aLso have much practice on slate, paper, and blackboard in the appro- priate notation; in pronouncing distinctly and easily the § 1 PEDAGOGICvS OF ARITHMETIC. 73 necessary names and statements; and in recognizing and reading them when written in script. And in this place it should be remarked that children should not be required to imitate print, nor should the teacher attempt to make their tasks easier by printing lessons on the blackboard. From the very first, nothing but script should be used out- side of the textbook. The reasons for this are many and obvious. Notation.— 1 -i {\ U {Is, oiu\ once, jirst 64, The ISTumber 3.— I. .otauon.- QQ , ..„ ]r;JtL,i| II. The Pure Xuniber. — n r 1 + 1 = 2. [J!2X1 = 2; 1X3 = 2. Measiirins: i^'ith 1. \ 12-1 = 1. Q hi = 2. The task of learning to distinguish from one another, clearly and sharply, these four fundamental facts, and to understand the exact meaning of all the characters used, is not so easy for 3"oung children as it may seem. Much skil- ful questioning and many repetitions in various forms must be employed. The teacher that can do it quickly and thor- oughly may fairly be regarded as something of an artist in his profession. Objects that can be distinctly seen by all the class should be used. Questions and answers should be as precise as possible. Although it is assumed that under this head the teacher is dealing only with number in the abstract, there is no practical objection to having the ques- tions and answers contain the names of the objects (splints, pencils, etc.) used in the lessons. III. The Applied Number. — Under this head, the teacher must make the application of the facts taught in pure number. Many examples, all very simple and easy, are given to the class and are rapidly answered in language that, day 74 PEDAGOGICS OF ARITHMETIC. § 1 by day, gains in variety, correctness, and precision. Every example should relate to matters that lie within the experi- ence of the children. In no case should the teacher intro- duce difficulties beyond the average powers of the pupils. In this early teaching a puzzle of any kind should be care- fully avoided. A few examples involving a knowledge of 2 are given. (a) Katie had 1 cent and her mamma gave her 1 cent more. How many had she then ? (d) If a pencil costs 1 cent, what do 2 pencils cost ? (c) Harry had 2 cherries and gave 1 of them to his sister. How many had he left ? {d) If apples are 1 cent apiece, how many apples can I buy for 2 cents ? Very soon the children themselves should be called on to make problems like the above; and later, they will be delighted with telling arithmetical "stories "; that is, making problems answering to such expressions as 3 + 2 = , 2x2-f 1 = , etc. IV. The Subdivided Unit. — As has been stated, the fraction is a kind of unit; the same operations may be per- formed upon it as upon integers. Its notation is different from that of units, but it is scarcely more difficult. Real objects, or representations of real objects, may be separated into parts as nearly equal as possible until the children know what is meant by one-half. This division should be made by the pupils rather than by the teacher. It must not be forgotten that Jialvcs of the same thing or of equal things are equal, and that in these exercises they should be made to appear as nearly equal as possible. Be very sure that the notation of fractions is well understood. Such expressions as the following should be so thoroughly taught as to be per- fectly easy to the children; - I 2 = ^ or 2. J ij 1 PEDAGOGICS OF ARITHMETIC. 75 The teacher will notice that nothing more is to be attempted in fractions than is indicated above. Obviously, this traction work affords an excellent training in whole numbers; indeed, as one writer observes, if we take care of the fraction the integer will take care of itself. Many simple problems illus- trating each of the foregoing equations should be given to the children, and the best of these problems should be pre- served in a note book for future use. The signs -{-, — , X, -^, and = must be read with facility and understood as precisely as the figures and words associated with them. There is no general agreeinent among teachers about the names that, in the earliest arithmetic work, should be given to these signs. It is thought better by many teachers to defer somewhat the terms ////.s-, viiinis^ multiplied by, divided by, and equals or is equal ic\ and to use instead, and for -|-, less or take atoay for — , time or times for X, and is or are for =. No good substitute has been found for divided by, and in this fact lies an argument in favor of teaching at the very first the names that, sooner or later, we all use. Provided the children understand exactly what is meant hy plus, it is just as satisfactory as and, and so for the rest. 65. The Xuniber 3. — I. Notation.— ,;, three, third, -^ | f -1 LI U ( t ^3 II. Tlie Pure ]N'uniber. — Measuring and Comparing. f 1 + 1 + 1 = 3. Measuring icil/i 1. j\Ieasuri7ig ivith 2. I 3X1 = 3; 1X3 = 3. ^ 3-1-1 = 1. U 13-^1 = 3. n n|-^-^=3; l.. = B. U U I 1 X 2 + 1 = 3 ; 2 X 1 + 1 =^ 3. n 13-3 = ,; 3-,=.. U L 3h-2 = 1 and 1 left (U). 70 PEDAGOGICS OF ARITHMETIC. § 1 Comparing. — 3 is 1 more than 2; 3 is 3 more than 1. 2 is 1 less than 3; 2 is 1 more than 1. 1 is 2 less than 3; 1 is 1 less than 2. 3 is 8 times 1 ; 1 is one-third of 3. 1 and 1 are equal numbers ; 2 and 2 are equal numbers. 1 and 2 are unequal (unlike) numbers ; 2 and 3 are etc. 3 is composed of 3 equal numbers; what are they ? 3 is composed of 2 unequal numbers ; what are they ? Rapid Work.— 3x1-2x1-1 = ? 3x1-1-1 = ? 3-1-1+2=? 3-1-1-1=? 3x1-2+1=? 1x1+1+1=? Note. — Much rapid oral work of this kind should be given until the answers can be obtained without hesitation. From what number can 2 times 1 be taken and 1 be left ? What number is 3 times 1 ? If one 2 is taken away from a number, 1 is left; what is the number ? III. The Applied Number. — Louis had 1 cent, his father gave him 1 cent, and he found 1 cent. How many cents had he then ? Kate had 3 apples, she atel and gave her brother 1. How many had she left ? How many cents will 3 apples cost at 1 cent each ? Harry had 3 pencils and lost 2 of them. How many had lie left ? IV. Tlie Subdivided Unit.— ('^) J + i + i = f . or 1 ; I + 1 = I, or 1 ; i + f = §, or 1. {b) 3X^ = §, orl; iX3 = 1, or |. tr\ 3_1 — 1 — 1- ?L—'i. — \- 2_1— 1.1_2 — 1--|_1_2 V' / 3 "3 3 — 3 ' 3 3 — 3 • 3 3 — 3 ' ^ 3 — "3 ' 3 — 3 " (./) 1-1 = 3; 1^1 = 3; 3 -^ t = 2; |^| = 1 and i left (H). {e) 1 of 3 = 1 ; I of 3 = 2 ; i of 3 = 3; 1 = i of 3 ; 2 = 2 of 3 ; 3 = § of 3. RapidWork.— ix3-J = ? ^ + i-|=? l-i = ? l-§ = ? etc. Applied Fractions. — A boy divided an apple into 3 equal parts and ate 1 of the parts; how much did he eat, and how much was left ? Mary had a cherry jjie; she ate \ of it at dinner and \ of it at supper; how much was left ? What part of 3 cents is 1 cent ? 2 cents ? A boy had 3 marbles and lost \ of them ; how many did he lose ? How many were left ? How much less is i of a pie than | of a pie ? § 1 PEDAGOGICS OF ARITHMETIC. GO. Tlie Xiimbei' -t. — 77 13 11 4 4 ^ I. I^otation.— Ml '^' ^^^^^^'' f^^"''^^'^ \ I t II. Tlie Pure Xuniber. — Measuring and Coinparin^ 4 etc. Mcasuriiiir with 1. 1 + 1+1 + 1=4; 1+1 = 2; 3 + 1 = ;] ; 3+1=4. 4X1 = 4; 1X4 = 4. 4-1-1-1 = 1. 4 -f- 1 =4. Measic?-i;ii (Us greater than i); i>^; i>i. R(7/^l(/ Work.— iof 4 + { = ? 1-i + l = ? l + i + 1 = ? etc. Applied Fractions. — A pie was divided equally among 4 children ; what part of a whole pie did each child get ? How many fourths of an apple in 1 apple ? In i an apple ? If a boy pays 1 cent for 4 marbles, how much does 1 marble cost him ? How much do 2 marbles cost him ? Harry had 4 cents and gave his brother \ of them ; how many cents had he left ? . Willie lost I of his marbles ; how many did he lose if he had 4 marbles at first ? 3 i_ 1 = |, or 1; i + l = f, or 1 or 1 ; fx3 = |, orl. 1 ■ 4 _2 — 2. 4 1 — 3. T — T' ¥ T — ¥' 1 _ 3 — 1 §1 PEDAGOGICS OF ARITHMETIC. 79 In 1 gallon there are 4 quarts; how many quarts in | of a gallon ? In f of a gallon ? In i a gallon ? Katie had 1 orange ; she gave Mary | of it, and ^ of it to each of her 2 brothers. How much had she left for herself ? Bessie had 4 sticks of candy and ate i of them. How many did she eat? 67. The ISTunibei* 5 I. T^otatioii. — ( 1 1 A 92. II. The Pure I<"unibei* Measuring with 1. 1 + 1+1+1+1 = 5; 1 + 1 --2; 2 + 1 = 3; 3 + 1 = 4; 4 + 1 = 5. Measuring with 2. /Measuring with 3. Measuring -cL'ith 4. 5X1=5; 1X5 = 5. 5-1-1-1-1 = 1. 5-1 = 5. 2 + 2 + 1 = 5. 2X2 + 1 = 5. 5 _ 2 - 2 = 1. 5 -- 2 = 2 and 1 left (2i). 3 + 2 = 5; 2 + 3 = 5. 1X3 + 2 = 5-; 3x1+2 = 5. 5-3 = 2; 5-2 = 3. 5-V-8 = 1 and 2 left (1|). D QD 00 Q 000 00 \'^' = ''- '^'-'- U LI U U ilx4 + l = 5; 4x1 + 1 = 5 j 5 _ 4 = 1 ; 5-1=4. [ 5^4 = 1 and 1 left (1|). 80 PEDAGOGICS OF ARITHMETIC. § 1 Comparing. — 5 is 1 more than 4, 5 is 2 moie than 3, 5 is 3 more than 3, 5 is 4 more than 1. 4 is 1 less than 5, 1 more than 3, 2 more than 3, 3 more than 1. 3 is 2 less than 5, 1 less than 4, 1 more than 3, 2 more than 1. 2 is 3 less than 5, 2 less than 4, 1 less than 3, 1 more than 1. 1 is 4 less than 5, 3 less than 4, 2 less than 3, 1 less than 2. 5 is 5 times 1, 1 is i of 5. 5 is 1 more than 2 times 2, 5 is 3 more than 3 times 1. 5 is composed of 5 equal numbers ; what are they ? 5 is composed of 2 unequal numbers ; what are they ? 5 is composed of 3 numbers of which 2 are equal ; what are they ? 5 is 1 more than twice what number ? How much more is 5 than 2 times 2 ? III. The Applied :Niinil)er. — John ate 3 chestnuts and had 2 left; how many had he at first ? Jane cut ofif 3 fingers of one of her gloves ; how many fingers were left on the glove ? How many quarts in 1 gallon and 1 quart ? Eddie went to school 3 days one week and 2 days the next week. How many days did he go to school in the two weeks ? How many yards and feet in 5 feet if there are 3 feet in 1 yard ? Susie had 5 cents ; she bought some candy for 1 cent and an orange for 2 cents. How much money had she left ? A father divided 5 peaches among his 3 children. He gave the youngest only 1 and the rest he divided equally between the other 2 children. How many did each get ? How many quarts are there in 5 pints ? There were 5 cherries on a limb; 3 birds came and each bird took 1 cherry. How many cherries were left ? IV. The Siibdi\ ided Unit.— ('0 k+l + \ + \+l = I. oi- 1; f + 5 = i or 1; i + l = l> o^ 1; i + t = hovl; f + l = f, orl. (/;) 5 X I = I, or 1 ; I X 5 = §, or 1. {,-\ r>__l__l 1 1 — 1- 4_S — 1- 3__i — 2- 2 i — 1- 1 4 — 1. V ) 5 5 5 5 5^ — 5'5 5 — 5'5 5 — 5'5 5 5'^ 5 ^> 1_3 _ 2- 1 2 _ .■?. 1_1 — 4 ^ 5 — 5 ' ^ 5^ — 6'^ 5 — 5- (,/) 5^1 = 5; i-^i = 2 andileft (3,1); f -f- f = 1 and | left (If); f-| = landileft(H); 1-^1 = 5; l^f = 2i; l-| = li; 1 -^ | == U. (c-) i of 5 = 1; fof5 = 2; | of 5 = 3; | of 5 = 4; f of 5 = 5; 1 = 1 of 5; 2 = f of 5; 3 = f of 5; 4 = I of 5; 5 = I of 5. ( f\ R — 4 — 3 — 2 — 1- 1^1^1<--1. l\i-^l\l [/ ) ^ — T— 3 — 2 — '^•5^^^3^i' 2 > -i > X > 5- PEDAGOGICS OF ARITHMETIC. 81 Rapid Work. — | x ••^ 5 + 5 — • 5 T^ 5 5 — 3 = ? f of 5 - 1 -1+1 = ? etc. — ? Applied Fractions. — How much is left of 1 pie after eating | of the pie ? How many fifths of an orange in 1 orange ? If 5 marbles cost 1 cent, liow much will 1 marble cost ? 2 marbles ? 3 marbles ? A boy picked 5 quarts of berries and spilled | of them ; how many quarts had he left ? Nellie spent \ of her money ; how much had she left if she had 5 cents at hrst ? Katy ate ^ of a pie and her brother ate ^ of it ; which ate more ? A boy bought 5 quarts of vinegar and spilled i of it; liow many quarts had he left ? Susie cut an orange into 5 equal parts ; she gave her brother 3 of the pieces and kept the rest. What part of an orange had eacli ? A girl was in school 5 hours one day. If | of the time was in the forenoon, how many hours was she there in the afternoon ? Tommy's papa gave him a nickel. After spending \ of it how much was left ? 68. The IS^mnber 6. — I. Notation. — D Q Q D D Q ^'- ^"•' -■■••'''- * ' * ^ '* '^ ") 2 4 6. 95 \\ ^6 6 6 -^6 ^6 11. Tlie Pure N^vimber, Q ' Measuring with 1. 1+1+1+1+1+1 = 6 1 + 1 = 3 ; 2 + 1 = 3 3+1 = 4; 4 + 1=5 5 + 1 = 6. J 6X1 = 6; 1X6 = 6. 6-1-1-1-1-1 = 1. 6 -- 1 = 6. PEDAGOGICS OF ARITHMETIC. Measuring with Measuring with 3. Measuring with /■. Meastiring with , DO QO DO DQO DDO ODOQ QD DDQDO 2 + 242 = 6. 3X3 = 6. 6-2-3 = 3. L 6 -J- 3 ^ S. 3 + 3 = 6. 3X2 = 6; 2X3 = 6. I 6-3 = 3. [ 6 H- 3 = 3. f 4 + 2 = 6; 2 + 4 = 6. j 1x4 + 2 = 6; 4x1+3 = 6. ^6-4 = 2; 6-3 = 4. 6-4 = 1 and 2 left (If, li). Q < 5 + 1=6; 1 + 5 = 6. 1X5+1=6; 5x1 + 1 = 6. 6-5 = 1; 6-1 = 5. [ 6--5 = 1 and 1 left (1^). Comparing. — 6 is 1 more than 5, 2 more than 4, 3 more than 3, 4 more than 2, 5 more than 1. 5 is 1 less than 6, 1 more than 4, 2 more than 3, 3 more than 2, 4 more than 1. 4 is 2 less than 6, 1 less than 5, 1 more than 3, 2 more than 3, 3 more than 1. 3 is 8 less than 6, 2 less than 5, 1 less than 4, 1 more than 2, 2 more than 1. 2 is 4 less than 6, 3 less than 5, 2 less than 4, 1 less than 3, 1 more than 1. 1 is 5 less than 6, 4 less than 5, 3 less than 4, 2 less than 3, 1 less than 2. 6 is 6 times 1, 3 times 2, 3 times 3. 1 is the sixth of 6, 3 is the third of 6, 3 is the half of 6. Of what 3 equal numbers is 6 composed ? Of what 2 equal numbers is 6 composed ? Of what 2 unequal numbers is 6 composed ? Of what 3 unequal numbers is 6 composed ? § 1 PEDAGOGICS OF ARITHMETIC. 83 III. Tlie Applied dumber. — Charles worked 3 hours at 2 cents an hour ; how much should he get ? There are 2 pints in 1 quart; how many pints are there in 6 quarts ? How many quarts are there in 1 gallon and 2 quarts ? A pie worth 6 cents was cut into 6 equal pieces; how much is 1 piece worth ? Six marbles were equally divided among 'S boys. How many did each boy get ? Ernest has a 2-cent piece and 2 cents. How many more cents must he get to have 6 cents ? How many apples at 2 cents each can be bought for 6 cents ? Mary paid 6 cents for a piece of ribbon and cut it into 2 equal pieces. How much should she get for one of the pieces ? Henry had some marbles and gave 2 of them to each of 3 boys. If he then had none left, how many had he at first ? IV. Tlio Subdivided 1 nit. — ('^) 5 + c + g + e + g + fi = ii- »!• 1; ^ + 1 = 8. or 1; i + l = i, or 1; I + g = i- or 1 ; I + (/;) 6X^ = I, or 1; 1X6 (C) 6 _ 1 _ 1 _ i _ 1 _ V"-^ « 6 6 .6 6 ((/) f--i=6; 1^1 = 3; «h-? = 2; jl--| = l and | left (1|, U); §-=-1 = 1 and 1 left (U); l-=-i=6; 1^,^=3; l-=-| = 2; 1-^4 = 1}(U); 1-i = 11; 1-1 = 1. (6-) 1 of 6 = 1 ; ^; of 6 = 2 ; | of 6 = 3 ; | of 6 = 4 ; | of 6 = 5 ; g of 6 = 6; 1 = 1 of 6; 2 = I of 6; 3 = I of 6; 4 = 4 of 6; 5 = I of 6; 6 = I of 6. \J I 6 — 5 — T— 3 — 2— ^' U^5^?^3^3'2->a->T^5>e- ( )r) 2 — 6 l_3.3_fi 1 — 2 2 — 4.2 — 1 t — 2 3 — 1 y^S ' 2 6' 2 li'3 «'3 — 6'3 — B'li — ^'i; — 3'6 — 2" (^) i + l = i + S = I; n+l = 21; 21 + I5 = 4; etc. Ra/>u/ Work. — ix2 + l = ? fx3+i = ? i+|x2,= ? t-f + H = ? |-i + U = ? 1 + 1 + 1 = ? 1 + 1+3=? etc. Applied Fractions. — A pie was cut into 6 equal pieces and then 1 of them was eaten. What part of the pie was left ? If I of a yard of ribbon is worth 4 cents, what is i of a yard worth ? A boy gets 6 chestnuts for 1 cent; what does 1 chestnut cost hini ? What do 2 cost ? 3 ? 5 ? Katy had 6 apples and ate 3 of them ; what part of them did she eat ? Harry had an orange. He gave \ of it to his sister; how many sixths of it had he left ? 1 = i, or 1; l + \ = e.orl; h or 1 ■ 3 -L 3 = i, or 1. 1X6 = ij, or 1. 1 — I « — r; • 5 4 — ' « 6 — 14 3 — 1.3 « • G G G ' G _ 3 .? ; 1 - ? = 1; 1- I =p. 84 PEDAGOGICvS OF ARITHMETIC. § 1 John lost i of his marbles. How many had he left, if lie had 6 at first ? A girl ate i of a pie for dinner and i of a pie for supper. How many sixths did she eat ? Louis had 6 cents and bought an orange for i of his money. How much had he left ? 69. Contiuiiation of This Course. — The explanation of this system of elementary work has been carried far enotigh to show the exact plan of treatment. The teacher will understand that the examples given under each number and each subdivision are intended only to exemplify the method. It must not be assumed that when a teacher has given all these he has given all that are required. Innumerable problems of similar kinds to these should be invented, given out, and reviewed until the children can do very easily and rapidly what is at first done slowly and with difficulty. In the manner shown, this work should be continued up to and including 10, which, when thoroughly taught, is treated as a unit of a higher grade or order. After this point is reached, much of the minute detail work may be passed over more rapidly. For example, it is unnecessary to measure each number with all less numbers, and much of the compar- ing and combining may be oinitted. It is important that the children should understand exactly the relation of each num- ber to 10, and any of them that have exact divisors should be measured by using those divisors as measures. Thtis, 15 should be measured by 3 and 5; 16 by 2, 4, and 8; 18 by 2, 3, 6, and 9; etc. The fractional parts of these composite numbers should be carefully taught and frequently reviewed. Thus, the pupils should know without thotight or calculation such facts as the following: i i I 1 [ 2. 4. 8 li] r 3, 6 J- of 12 = ^ 10, 3, 9 ?, i - of 15 = J 9, 13 g, 3-, J - v.. x^ _ -^ .v., «, ^ g, g , v.. .^ _ . ^, hh l\ t 4, 8, 6 i, I J [5, 10 After reaching 20, the students should go along rapidly to 100, by steps of 10, the important matter being that they § 1 PEDAGOGICvS OF ARITHMETIC. 85 shall be just as familiar with the order of occurrence of the 10-groups as they are with that of the unit g'roups up to 10. This result is attained in various ways — counting by units, and counting by steps of 10; as, 10, 20, 30, etc.; 7, IT, 27, etc. ; 3, 13, 23, etc. The same method is pursued above 10(). From the very first, the children should be exercised in reading and writing numbers beyond those with which they work in detail. Thus, by the time they have finished the minute study of numbers as far as 10, they should be able to read and write, without any hesitation whatever, all numbers as high as 100 or even beyond. But above all, do not neglect or abandon the work with fractions, and be very careful to avoid every real difficulty. This error of making the work too hard is just as likely to occur in dealing with integers as it is with fractions. 70. The Study of Certain Coniijosite Numbers. After pupils have reached a certain stage of maturity, — about the time when they have mastered with some degree of thoroughness the numbers as far as 100, — it is well to study pretty carefully certain of the composite numbers between 10 and 100. The reason for this is that these are the num- bers that must be used in adding fractions. The most use- ful .series is composed of the multiples of 12. They are 24, 30, 48, GO, 72, 84, DO. For example, 24 is the least common denominator if we wish to add a collection of frac- tions containing halves, 3ds, 4ths, Gths, 8ths, 12ths, and 24ths; with 3(i we may add halves, ikls, 4ths, Gths, Oths, 12ths, 18ths, and 3Gths; etc. Children very much enjoy the exercise of finding the com- ponent elements of such numbers and of changing fractions into equivalent fractions having a given denominator. Equally valuable and enjoyable is the reverse operation of changing fractions to simpler or to simplest forms. Some other numbers that are useful for the same reason are 20, 30, 40, 50, etc. ; 28, 32, 45, 56, etc. The number 100 should be mastered with even greater care. Its aliquot 86 PEDAGOGICS OF ARITHMETIC. § 1 parts, 4, 5, 0^ 8i 10, ll^ 12|, Uf, IGf, 20, 25, 33|, and 50, tog-ether with certain of their useful multiples, 18f, 31:^, 37^^ 4;3|, 62i UGf, 75, 83^ and 87| should be very familiar to the pupils. It would not be easy to pick out a number of which a complete mastery would be of greater practical use- fulness than the number 100. PEDAGOGICS OF ARITHMETIC. (PART 2.) ADVANCED AVOEK. DEVICES AIN^D METHODS IX ADVAXCED VYOIIK. AnrHTION AND SI BTRAf TIOX. 1. Addition of IjOii^ Coliimiis. — Most of the school exercise in addition is confined to columns of which the sum is less than 100, usually less than 20 or 30. Bookkeepers, however, are qnite frequently required to add very long col- umns, and it would seem to follow that the schools should furnish some training in such additions. For children may be trained to add with much expertness as far as 50 or GO, and yet, when required to add to higher aggregates, espe- cially above 100, they are slow and inaccurate. This comes from their lack of ability to "decimate," as some one calls it; that is, to pass without thought or hesitation from sixty sovictliing to seventy sovictJnng^ and the like. A good method of acquiring this ability is to begin to add at some number near 50, as shown in the margin. The large number may be placed either at the top or at the bottom of the column, according as the addition is to be upwards or downwards. Another plan is to add a long column two or more times §3 49 68 8 5 5 3 7 9 etc. etc. 2 PEDAGOGICS OF ARITHMETIC. § 2 without returning to the beginning. In this case the sum will be as many times the correct result as the addition of the column has been repeated. 2. Two Common Methods of Subtracting. — Teachers are divided in opmion as to whether it is better to diminish the next minuend figure after borrowing or to increase the next subtrahend figure. The former is the more logical method, but there is no doubt that the latter is the more convenient in practice. And since it is useless to try to explain to young children the reasons for either practice, it would seem to follow that the subtrahend figure should be increased. To subtract and explain by the method of dimin- ishing the minuend is a matter rather difficult, even for most young teachers. How then can children be expected to understand it? Suppose, for example, that the operation of subtracting 482,937 from 800,100, is to be explained. In doing so, it is necessary to 800 100) (799(9 + 1)9(10) , /, . . ... 4 8 2 9 3 7^/482 98 7 ^^"^^"8^® ^^® mmuend as mdi- „ . ^ , „ „ o 1 rr — Vl^ — W cated in the margin, in which olilbo ol7 lb. 3 o' the imits place and the thou- sands place are each occupied by two figures. This is a change that no child can be made to understand, however ingeniously the matter may be indicated and explained. It is sufficient to teach the operation without giving any atten- tion to the reasons. This coiu'se is frequently necessary in the earliest school work; indeed, it is not important or of any practical value that reasons for all operations should be perfectly known. In subtracting by the method of decreasing minuend figures, the pupils should be taught to say or think (in the example above) : "7 from 10 leaves 3, 3 from 9 leaves G, 9 from 10 leaves 1, etc." All the usual long story, " 7 from I cannot take; I therefore borrow 1 unit from the next order, etc.," should be omitted. Much time can be wasted in trying to have this said correctly, and at the best it is the merest parrot exercise. Teach the process only. If the method preferred is to increase the figures of the § 2 PEDAGOGICS OF ARITHMETIC. 3 subtrahend, the pupils should say or think: "7 from 10 leaves 3, 4 from 10 leaves G, 10 from 11 leaves 1, etc." Very soon, however, the pupils should be able to subtract faster than they can mention the steps in the operation, and when this point is reached, they should .say nothing- whatever, but write results as rapidly as possible. 3. To Subtract by Adding. — An interesting and curi- ous question is the following: Does an unconscious addition precede every act of subtracting ? Do we, for example, con- clude that 2 taken from 7 leaves 5 only by reference to the fact that the sum of 2 and 5 is 7 ? Many thinkers on the subject believe that the mental act of subtracting is complex, consisting of three steps: 1. A recognition of what is required to be done; as, that 8 is to be taken from 15. 2. An instantaneous judgment or recollection that the sum of 8 and 7 is 15, this part of the work being involuntary and so rapid that we are not distinctly conscious of it. 3. The inference that 8 taken from 15 leaves 7. Reasoning about the matter in this way, it is urged that there is a gain in time and directness by omitting the third step, and performing the subtraction by actual addition. Thus, suppose we wash to subtract as in the mar- oQ0f)4ic) 5 8 s Q r S '5 gin. We say only, "2 and 7 (writing 7) is 9, „.„„„., ^ 8 and 3 (writing 3) is 11, (carrying 1) 7 and 7 (writing 7) is 14, (carrying 1) 10 and (writing 0) is 10, (carrying 1) 4 and 8 (writing 8) is 12, (carrying 1) and 4 (writing 4) is 13, (carrying 1)6 and 2 (writing 2) is 8. " Whatever may be the psychological facts back of this method, there is little doubt that it is the best of all in prac- tice, and the writer would strongly advise the student to make himself thoroughly expert in its use. 4. Extension of the P^'oregoing; Method. — It is very frequently necessary to subtract from a given number the sum of several other numbers. Such an example as the fol- lowing requires an operation of this kind : 4 PEDAGOGICS OF ARITHMETIC. § 3 I had in bank 12,375.14 and drew out the following sums: $390.25, 1829. 08, $49.90, 1147.29, and 108.37. How much remained in bank ? Two operations seem to be necessary: (1) to ^ ^ ^ "^ ^- ^ "^ find the sum of the subtrahends; (2) to subtract 3 9 6.2 5 that sum from the minuend. But if the num- Q k^ Q /» Q bers be written as shown in the marg-in, the entire 4 9 9 6 . o ' 14 7^9 work may be done in the same manner as is g 8 3 7 explained in the last part of the preceding article. $ 8 8 3.5 9 ^® begin by finding the sum of the right-hand column as far as to the double line. This sum is 35 and the figure above is 4. We now ask what number added to 35 will give the least result greater than 35 that ends in 4. This least result is 44, and 9 is the number to be added. We write 9 as the first figure of the result, and carry 4 to the next column. Carrying 4, we find the sum of the next column to be 26; to this we must add 5 to get 31, the least number greater than 26 that ends in 1. Writing 5 as the second figure of the answer, we carry 3 to the next column. The sum of the next column as far as to the double line is 42, and the figure 5 stands above. We now say "42 and 3 (writing 3) is 45." Carrying 4, we obtain 29 for the sum of the next column, and say " 29 and 8 (writing 8) is 37. " Carrying 3, we get 15 for the last column, and say "15 and 8 (writing 8) is 23." This operation is important because it is properly introduc- tory to the beautiful French Method of Long Division, an explanation of which will be given later. The student should at this point solve, in the manner explained, many examples in ordinary subtraction and many others like those given below. From $19,381.01 3,109,621 23,105,920 ' 983.47 479,629 13.684,789 4,625.94 836,784 4,296,767 Take ^ 3,597.69 39,982 837.429 1,426.87 458,697 98,765 [ 869.96 947,684 9,876 It may be observed that the only difference between this § 2 PEDAGOGICS OF ARITHMETIC. 5 operation and ordinary subtraction by the addition method is that in the latter case the point of departure is g-ii'fu, and in the former it is obtained by adding. Thus, in the first example above, we must add the first column as far as to the double line before we step across from its sum, %y^ to 4L. In ordinary subtraction, this preliminary addition is missing — - our stepping- stone or point of departure being- given. 5. Addinji- Horizontally. — This is a method of addi- tion very frequently required in actual business, and yet it is totally neglected in our schools. The teacher should have frequent exercises of a kind that will render pupils just as rapid and accurate in adding horizontally as they are when the numbers to be added stand in vertical columns. There is really little difficulty in the matter; all that is required is practice. In writing the exercises, the plus sign should be used and the sum should be placed after the sign of equality in the manner shown below. 8,329+47, 51)G + 8!)4 + (;r5,41)S + (;7 + 018 = r3;5,3:52. *327. (Jy + •*4-2. 1 + -*1), 47(;. 0( ) + .t3'J. 78 -|- -t 1 SO. 00 = -I? 1 (>, ( )72. 20. 6. Addiiii*- by Groiii>s. — Any person that adds much comes, sooner or later, to adding by groups. At a glance he sees 20 in 8, 5, and 7; 18 in G, 8, and 4; and 38 in their sum. It soon becomes a matter of intuition to recognize the sum of several figures as if they were one. Beginning with groups of two figures, this exercise should be practiced until the pupil becomes proficient in it. Accountants of long experience add extended columns with marvelous rapidity, but the expertness is entirely the result of practice in adding by groups. If one of these expert accountants is questioned closely about his method, he is usually not able to give a very satisfactory account of it. There is one fact, however, that is very easily brought out. This is that he does not distinctly say or even think the totals obtained at each intermediate step; he only feels them, so to speak, but he relies upon the accuracy of the final result with absolute certainty. Having reached, say G7, he combines with it a C PEDAGOGICS OF ARITHMETIC. § 2 new group of figures, whose sum is perhaps 28, with light- ning rapidity and without conscious effort. He does not say or think that 07 and 28 is 95 — he knows it without thought or effort, just as he knows that 2 and 3 is 5. His rapid run along the columns is so nearly a perfectly automatic action that the mental strain or exhaustion is very slight, and, like all auto- matic work, the result has little chance of being incorrect. Besides teaching mere processes to pupils, the teacher will do well to labor somewhat to attain this rapid, easy, auto- matic expcrtness, for it is not only very pleasant to do the work that costs us so little effort, but it is a leaven of expertness that makes all subsequent progress rapid and its results enduring. Indeed, it is well known that time neces- sary to make pupils thorough in fundamentals is not wasted. *7. Adding- Tavo or More Columns at Once. — It is frequently stated that expert accountants sometimes add several columns at once. It may be doubted whether this is done to any considerable extent in actual business. Of course, it can be done, but the necessary outlay of effort takes away all pleasure from the operation and the chances of error are much increased. To show the method pursued, suppose that it were required 3 9 to add in this way the numbers in the margin. Begin- 4 6 ning at the bottom, the successive steps are indicated '5 thus: 87 + 5 + 70 + (i + 40 + 9 + 30 = 247. By this — plan each successive step is very easy, for it is neces- sary to think only 87, 92, 1G2, 1C8, 208, 217, 247. In adding three columns, the steps are, 974, 980, 1,000, 1,400, 733 1,489,1,492,1,512,2,212. It is scarcely necessary 8 9 to say that practice will enable the student to 4 2 6 perform such additions very rapidly; yet it is, no ' doubt, better to add each column separately. -^ -^ 1 ^ SHORT METHODS IX MULTIPLICATION. 8. Proper Use of 81iort Methods. — The teaching of short methods to any but advanced pupils is, perhaps, neither wise nor necessary. With pupils of all grades the § 2 PEDAGOGICS OF ARITHMETIC. 7 shortest wa}^, provided that it is the easiest, is, of course, the best way; but, usually, devices intended to save time imply considerable expertness — more than young pupils have. Just in proportion as the degree of attention neces- sary to follow a process is increased, the ability to seize the involved principles is diminished. And when it is remem- bered that with young students the mastery of principles — the rationale of processes — -is the indispensable matter, it becomes evident that the study of short methods should be withheld imtil a late stage of the work in arithmetic. The teacher, however, should be very familiar and very expert with these labor-saving devices. By means of them he may perform very rapidly, and often without written Avork, examples assigned to his class. In making proljlems for class work, too, he may have them such as to involve operations that he is able to perform mentally and briefly. To do stich work is not only convenient in testing answers, but it increases the confidence of the class in their teacher and heightens their esteem for him. Influenced by such considerations the writer has deemed it best to enter some- what fully into this subject. J). ITiiAvritten Multiplication by a Multiplier of One Fig-lire. — It is very frequently necessary to know without written work such products as 9 X 37, 8 X 45, etc. In attempt- ing to do this "mentally," most persons try to perform the work as they would on slate or paper. Thus, to multiply 37 by 9 we are likely to multiply 7 by 9, remember the 3 of the result, carry the 0, and unite it with 9 times 3. Th.cre is, however, an easier method, which is to think of 37 as equal to 30 + 7, multiply 30 by 9 and then add (K) to the priKluct. It is very easy to find the sum of a niunbcr ending in I) and a number of two figures, the last of which is signifi- cant ; as, 270 + 03, 450 -j- 81, etc. This is exactly the process employed in adding two or more columns at once. The steps necessary are illustrated below: 40 X 5 = 300 + 30, and it is necessary to think only "2(>0, 230." 8 PEDAGOGICS OF ARITHMETIC. § 2 Similarly, 83x7 = 5G0 + -21; "500, 581," or, more briefly, "560,581." 428X5 = 2,000 + 100 + 40; "2,000, 2,100, 2,140." 798X6; "4,200, 4,740, 4,788." 685x3; "1,800, 2,040, 2,055." 10, Extension of the Forejjroiiiji: Method. — When both factors contain two figures, it is not so easy to do the work without writing, on account of the difficulty of keeping the figures of the factors in the mind. But if they be written, the multiplication is very simple by the method explained above. ^^^ I ; 600, 740, 830, 851. Ijg j- ; 1,800, 2,070, 2,550, 2,622. If, however, one of the numbers can be separated into factors, it is better to multiply by the factors in succes- sion. 87X45 = 87X5X0; 400, 435, 3,600, 3,870, 3,915. 1 1 . Multipliers of Special Form. — Written multipli- cation may be much abbreviated in the case where the multiplier may be separated into groups such that one group is a multiple of another. Such multipliers as 936, 728, 244, 7,212, etc. belong in this class. In the number 936, the groups are 9 and 36, the latter being 4 times 9; in 7,212, the groups are 72 and 12; in 546, they are 6 and 9 times 6; etc. The partial products will be as many as the number of groups. To show the method, let the following examples be taken : Example 1.— [Multiply 3,859 by 507; also, 432,964 by 72,364. Solution.— 3 8 5 9 = (J 4 3 3 9 6 4 = a 567 7 2 3 6 4 37013=^X7 17318 5 6=^X4 216104 =7.^X8(0) 155867.0 4 =4.^x9(0) 2 J g 3 Q g 3 3 1173408 = 36^? X 2(000) 313 31006896 If the inultiple order is reversed, the f)peration begins on the left. § 3 PEDAGOGICS OF ARITHMETIC. Example 3.— Multiply 3,859 by 756; also, 433,964 by 43,673. Solution. — 3859 = times 3 = 18; write 8 and carry 1. (/') 1 + G times 4 + 5 times 3 = 40; write and carry 4. (6-) 4 + 5 times 4 = 24; write 24. Again, {a) 4 times 7 = 28 ; write 8 and carry 2. (/?) 2 + 4 times 6 + 5 times 7 = 01; write 1 and carry 0. {(•) ' + 5 times G =: 30; write 30. 10 PEDAGOGICS OF ARITHMETIC. S 2 Most of the cases of written multiplication in actual business are of two figures by two figures. Hence, the foregoing method is of the highest practical value, and should be taught in the classroom. The teacher will be surprised at the ease with which pupils will master and use it. The extension of the method to numbers of more than three figures, while of great value to the teacher, need not be taught in the classroom. There is, however, no objection to giving it to pupils that are well advanced. Example ::3.— Multiply 234 by 567; also 405 by 63. (See diagram. Fig. 2.) SoLLTION. — 2 34 567 40 5 063 132678 25515 XXXI (I <■ b a Fig. 2. Explanation. — The diagram on the right indicates the five steps necessary to the solution, and their order is shown by the letters. [a) 7x4 = 28 ; wa'ite 8 and carry 3. {b) 2 + 7 X 3 + (3 X 4 = 4? ; write 7 and carry 4. (r) 4 + 7x2 + 5x4 + 0x3 = 56 ; write G and carry 5. {d) 5 + 6x2 + 5x3 = 32; write 2 and carry 3. {c) 3 + 5x2 r= 13; write 13. In the next case fill the hundreds place in the multiplier with a cipher, or iinagine it to be so filled, and proceed as before. {a) 3x5 = 15; write 5 and carry 1. {b) 1 + 3x0 + 6x5 = 31 ; write 1 and carry 3. {c) ;') + 3 X 4 + X 5 + 6 X — 15 ; write 5 and carry 1 . {d) 1 + 0x4 + 0x0 = 25 ; write 5 and carry 2. [c) 2 + 0x4 = 2 ; write 2. Example 3. Solution.— -Multiply 57,043 by 68,102. (See diagram, Fig. 3.) 5 7 4 3 6 8 10 2 8884742386 X\l/ ^S/^ ~Ai^ ^v^ \/ \/ I /N Wv yh-^. .-i^V /K A, I I /« J/ / c d c b (I PEDAGOGICS OF ARITHMETIC. 11 Explanation. — 2x3 = G ; write G. 2X4 + 0X3 = 8; write 8. 2X0 + 1X3 + 0X4 = 3 ; write 3. 2x7 + 8x3 + 0x0 + 1x4 = 42 ; write 2 and carry 4. 4 + 2x5 + 0x3 + OX 7 + 8x4 + 1x0 = 04 ; write 4 and carry 6. (/) carry 3 This + 0x5 + 0x4 + 1x7 + 8x0 = 37; write 7 and 3 + 1x5 + 0X0 + 8x7 = <;4 ; write 4 and carry 6. + 8x5 + 0x7 = 88 ; write 8 and carry 8. 8 + 0x5 = 38 ; write 38. method is general, and, by practice, mnltiplication may be performed with extraordhiary rapidity. After the student has learned to add numbers of two figures rapidly and accurately, the chances of error are not so many as when the partial products are written and added in the usual man- ner. It is not necessary that the symbols be kept in mind. They are given above only to make the processes clearer. The student will notice that the operation begins on the right, with the first column, and advances towards the left, one column at each step, imtil the left-hand column is reached. Then the columns on the right are dropped, one with each step, until the last column on the left completes the opera- tion. The symbols picturing the operation are symmetrical and remind one of the development of a binomial in algebra. The following diagram will illustrate (Fig. 4) : 2 flyures^ 1 X 1 3—, 1 XXXI *___.„ __j XX x; X X 1 Oi „ 1 V V "V^ "Sl^ ^V^ "^ V" /\ A\ .yS^ ViV. //V A A 1 1 XX X X 1 Fig. 4. 13. Squares. — Numbers of two or three figures may readily be squared by utilizing the algebraic formula for the 12 PEDAGOGICS OF ARITHMETIC. § 2 square of a binomial — The squai'c of the sinii of t%uo quaiititics is equal to the square of the first, plus twiee the product of tJie first by the seeoud, plus the square of the second. Example. — Square 83 and 126. Solution 1.— (83)- = (80 + 3)' = 6,400 + 480 + 9 = 6,889. Ans. (126)= = (120 + 6)-= 14,400 + 1,440 + 36 = 15,876. Ans. Solution 2. — (See diagrams. Figs. 5 and 6.) 8 3 nSn 1 2 6 X X-X ! 6889 ■■■■■■ 15876 Fig. 5, Fig. 6. Perhaps the simplest application of thisniethod is to write the number but once, and then, (a) Square the units figure for the units figure of the square ; (/;) Take twice the product of the units and tens figures. The right-hand figure of this product will be the tens figure of the square. {c) Square the tens figure and write the result before the two figures already written. Of course, the necessary carrying must not be forgotten, and nothing but the result should be written. 14. IMultiplier Slightly Greater or Less tliaii Some PoAver of lO. — It very frequently happens that one of the factors in multiplication is within a very few units of 100, 1,000, or some other power of 10. Examples of such factors are 1»9, 908, 0095, 1,002, etc. In such cases the multiplication shoidd be performed by annexing the proper number of ciphers to the multiplicand and adding or subtracting to the result, as the case may require. A few examples will ■ illustrate. Example 1.— Multiply 1,234 by 999. Solution.— 12 3 4 = 100 times 1,234 12 34 = 1 time 1,234 1232766= 999 times 1,234 PEDAGOGICS OF ARITHMETIC. 13 Example 2.— Multiply 1,284 by 11,995. Soi.uiioN.— 1 2 o 4 = 10 times 1,234 6 170 = 5 times 1,284 12333830=: 9995 times 1,234 Example 3.— Multiply 3,596 by 1,003. Solution.— 35 9 6000 = 1000 times 3,596 107 88= 3 times 3,596 3 606788 = 1003 times 3,596 The reason for e:ieh step is so evident that no explanation seems to be necessary. 15. Multiplication by Aliquot Parts. — Abbreviated niultipHcation by the method of aliquot parts should be per- fectly familiar to every teacher. It is applicable as well to abstract numbers as to United States money. The following- table shows all of these parts that are really useful in calcti- lation: Parts of One Dollar. .12i .lOf .25 .331 1 s 1 1 4 1 3 ' of 11. 3 8 50 = i 1 ,621 = ,6G| r= , 75 = 8 I I \ of %\. 'o I If the dollar sign be removed from the foregoing- table, the equality of the decimals to the abstract number 1 is shown. Thus, .121 or .125, = \ of 1, .1G| = i of 1, .371 or .375, = I of 1, etc. By using the fractions instead of the decimal ecjuivalents, multiplications (and divisions also, as will be .shown later), may usually be performed without written work. Example 1. — Find the following products ; {vei' of 10. If a divisor is only a few units less than lOU, 1,000, etc.," division may be performed by a very brief and elegant method. Example 1.- soi.ution. — -Divide 492,863 by 9 492 2 1 95. 863 460 1 = 492 X 5 = 2X5 333 5 = 1X5 qjiotient 4 9 5 3 38 remainder ExPL.ANA'JioN. — Drawing the vertical line divides by 1,000. But, since tlie divisor is 5 less than 1,000, the dividend is 492 times 5, or 2,460 in excess of what it need be in order that 995 may be contained in it 492 times with a remainder of 803, Dividing this excess by 1,000, the quotient is 2. Again, in this division the dividend, 2,4()0, was 2 times 5, or 10, greater than it need be, and this excess can be transferred to the remainder. Adding these three remainders, the sum, 1,333, will contain 1,000 with a remainder of 333. As before, the remainder must be increased by 5 for each unit in the quotient; hence, the true remainder is 333 + '5, or 338, and the true quotient is equal to the sum of the several quotients, 492, 2, and 1, or 495. 18 PEDAGOGICS OF ARITHMETIC. §2 Example 2.— Divide 23,976,428 by 9,992 (8 less than 10,000). Solution. — 2397 1 1 6428 9 17 6 = 2397 X 8 8 = 1X8 56 12 8 IX quotient 2 3 99 5620 remainder Example 3.— Di\icle 5,607,496 by 96 (4 less than 100). Solution. — 5 6074 2242 89 3 3 qitoticnt 5 8 4 11 9 6 = 56074 X 4 6 8= 2242 X 4 5 6= 89 X 4 1 2 = 3X4 2 8 j^ = 3X4 reniaittder 4 The fact that examples of this kind may be very useful to the teacher, and that this method of solving them is not generally known, is the reason for introducing it here. Ilule. — By a vertical line, cut off on the rigJit as many figures of the dividend as there are figures in the divisor. Multiply the number on the left of this line by i^'hat the divisor lacks of being 100, or lf>00, etc. Write the product under the dividend, and if any part of this product stands on the left of the vertical line, continue to multiply as before until the product is all on the right. Add the numbers on the right, and if any part of the result falls on the left of the vertical line, multiply as before, and add again. The last sum that falls entirely on the right is the remain- der, and the sum of the numbers on the left is the quotient. 19. Special Cases of tlie Foreg:oingf Metliod. — It may sometimes happen that the apparent remainder is greater than the divisor. In this case the quotient must be increased by 1 and the divisor subtracted from the apparent remainder to find the true remainder. The following examples will illustrate : s-2 PEDAGOGICS OF ARITHMETIC. 10 Example 4.— Divide 641,458,207 by 9,930. Also 3,559,866 by 998. Solution. — (> 4 1 4 5 449 3 8 2 /7 1 5 1 43 2 1 9 9 9 7 9 9 3 - 9930 qitoiicnt ?-i'i/iai/!iicr 3559 7 5 ••) 7 8 6 () -=- 998 1 1 8 1 4 quotient ti 4 5 9 8 Again it may be desired to carry out the quotient to dec- imal places. Example 5.— Divide 732,968,473 by 995, carrying the result to five decimal places. Solution.— 7 3 2 9 6 8 4 7 3 h- 995 3664842 3 6 188242 1 9162 45 500 180 105 81 225 820 5 8 2 5 remainder quotient 7366 5 1.73165 Explanation. — Annex as many ciphers to the dividend as there are decimal places required in the quotient and divide as before. Example 6. — Divide 34,279.831 by 997 correct to four decimal places. Solution. — 3427983 10 1028394 3085 9 quotient 3438 2.9799 -^ 997 930 182 255 27 394 3 3 9 7 remainder Explanation. — Annex four ciphers to the dividend, and after dividing, point off four decimal places. 20. Divisor Slightly Greater than Some Poorer of 10. — In a manner very similar to the preceding method it is possible to divide by any number slightly greater than 20 PEDAGOGICS OF ARITHMETIC. §2 10, 100, 1,000, etc. The only difference is that the products obtained by multiplying- by the excess above 10, 100, 1,000, etc. must be subtracted and added alternately. A few exam- ples will make the student familiar with the process. Example 1.— Divide 35,692 by 12; also 28,769,408 by 106. Solution. — {a) 3569 -7 13 2- 8 -12 = («) X 2 = (/; + 1) X 2 = (t- + l)X2 = (^/ + 1)X2 = (r + l)x2 qii = (/)X2 remainde}- (a) (^) {d) 287694 -17261 8-=- 106 6 4 = (rt) X 6 (0 2855 + 142 4 8 270432 + 1 035 44 72 = (/; + l)x6 {d) 2998 - 28 2969 + 5 2 6 6 8 27 1468 62 1 6 1 6 = (r+l)x6 {e) 27 1406 + . 3 00 7 2 = (./) X 6 (/) 2975 - 1 4 2 27 1409 72 1 8 = (.') X 6 2974 -t- 3 2 otient 27 1409 5 4 remainder quotient 29 74 4 Explanation. — We shall first describe the steps of the process, and then indicate the reasons involved. Division by 12 is chosen as an illustration, not because the operation is shorter than the usual method, but because it is long enough to show several repetitions of alternate adding and sub- tracting. Draw a vertical line cutting off one figure on the right of the dividend. This divides by 10. But the real divisor is 12, or 2 in excess of 10. Multiply 3,569 by 2 and write the product with one figure to the right of the vertical line. Subtract this product from the number above, and note whether it is necessary to carry in subtracting the first figure after crossing the vertical line. Here, the quotient, 3,569, is diminished by 714 instead of by 713. Multiply 714 by 2, and writing the result as before, add it to the number above it. Multiply 143 by 2, and subtract the prod- uct from 29,982. Multiply 29 by 2 and add the product to 29,696. So continue to multiply and then to subtract and add alternately until the last product stands entirely to the § 2 PEDAGOGICS OF ARITHMETIC. 21 rig"ht of the vertical Hue. The last sum or the last remainder, as the case may be, is the true quotient and remainder. The process with the example on the right is exactly similar, except that the vertical line cuts off two figures on account of the fact that, when the true divisor is lotj, the approximate divisor is 100. The reason for adding- and subtracting alternately is as follows : To divide 35,002 by 10 instead of by 12 is equivalent to having in the dividend 2 more than is required for each unit of the quotient. For the entire quotient this excess is 3,569 times 2, or 7,138. It is clear, therefore, that the first quo- tient is too great, and must be diminished by 7,138-^12. If this deduction were made, as shown below, the result would be the correct quotient and remaijider. 35G9 and 2 re;//. = 3 5 G 8 and 12 + 2, or 1 4 rem. 7138-=-12 = 5 '■) 4 and 1 " Subtracting, 35(392 ^12 = 2 9 7 4 and 4 " But instead of doing this, we deduct 7,138-4-10, a num- ber too great; the difference, 2,855 -|- 4 remainder, is there- fore less than the correct result by (714 times 2) -=-12. Hence, it is necessary to increase 2,855 + 4 remainder, by 1,428-^12. Instead of doing so, however, we increase 2,855 + 4 remainder, by 1,428 -f- 10. This, again, being a deduction too great, the result is less than the true quotient, and must be increased. In this manner, we continue by turns to increase and diminish tlie result, approaching more and more nearly the correct cpiotient, until finally nothing remains to be added or subtracted. The examples chosen above do not illustrate the brevity of this method. They were intended to show several repe- titions of the alternate addition and subtraction, so that the student might become acquainted with the operation. If, however, the dividend contains only about twice as many figures as the divisor, the process is very brief. The follow- ing examples will exhibit this condition : 22 PEDAGOGICvS OF ARITHMETIC. Example 2.— Divide 8,328,967 by 10,008; also, 42,909,789 by 10,012. quotient Solution. — 83 8 9 6 7 6656 10008 4296 - 5 2 3 11 remainder 4 2 9 1 + 9 7 8 9 H- 10012 15 52 8237 60 8 2 9 7 remainder 31. Special Cases of the Foi'eg:oing;- Metliod. — There are two points of difficulty that may arise in using this method of division. They are the following- : (a) When the remainder contains as niaiiy figures as the divisor. In this case, one figure of the remainder would naturally fall to the left of the vertical line and be multiplied. By so continuing the operation, the correctness of the answer would be destroyed. This chance of error is avoided by noticing in each multiplication whether the product is less than the divisor. If it is, the operation of multiplying should not be repeated. (/;) Wlien in adding or subtraeting it is neeessary to carry 1 from the right to the left of the vertical line. When it is thus necessary to carry a unit across the vertical line, the next multiplicand must be increased by 1. If, however, thiscarrying occurs an even numberof times, noerrorwill arise ; butwithan<9rt'(r/numberof operations of carrying across the line, there will be error. In the first two examples in Art. 20, the errors would be equalized by the fact that in crossing the verti- cal line we carry 4 times in one example and 2 times in the other. The following examples will illustrate both {a) and (/;) : Example 3.— Divid- 317,303 by 108. Also 96,723 by 104. Solution. — 3173 - 2 5 3 3-108 8 4 = {a) X 8 (0 967 -38 928 + 1 2 3-104 68 = (rt)X4 (0 2919 + 20 2939 - 1 1 9 13 2 = (/; + l)X8 5 1 q 1(0 Hi 6 = (^) X 8 5 5 5 6 = (/; + l)X4 (^) nit 930 1 1 8 = (i- + l)X4 quot 2937 9 1 16 = (^?'+ 1)X8 10 7 remainder 3 remainder §^ PEDAGOGICS OF ARITHMETIC. 33 Example 4.— Divide 3,001,000 by 1,011; also, 89,469,212 by 1,007. Solution. — 3001 -33 (a) (0 ^uo^. 2 9 6 8 2967 -- 1011 01 1 = ('OX 11 989 188842 ^2i = (/; + l)Xll {c)\+ 4 363 1 1 = (f + l)xll (a) 18946 9; 2 12 -r- 1007 {d)\- 6 2 612 8 3 = (iso7' 8 5 7 qitoiieiit 987)83 9 674 2 dividend 500 72 3 3 3 remainder Explanation. — The first step is to multiply the divisor by the first quotient figure, 8, and subtract the product, without actually writing it, from the first partial dividend, 8,306. 8 times 7 is 56, and is 56 ; W' rite and carry 5. 5 + 8 times 8 is 60, and is 60; write and carry 6. 6 + S times 9 is 78, and 5 is 83; \vrite 5. The remainder after the first partial division is 500. The next figure, 7, of the dividend may or may not be annexed to this, as the student prefers. The next quotient figure being 5, the divisor is multiplied by 5 and the result subtracted from 5,007. 5 times 7 is 35, and 2 is 37; w'rite 2 and carry 3. 3 -f 5 times 8 is 43, and 7 is 50; write 7 and carry 5. 5 + 5 times 9 is 50, and is 50. The remainder is 72. The next partial dividend is 724, which will not contain 087. A cipher is, therefore, written in the quotient, another figure, 2, considered as annexed to 724, giving 7242. In this 087 is contained 7 times. Hence, 7 is written in the last place of the quotient and the § 2 PEDAGOGICS OF ARITHMETIC. 25 multiplication and subtraction made as before. 7 times 7 is 49 and 3 is 52; write 3 and carry 5. 5+7 times 8 is (Jl, and 3 is 64: write 3 and carry 6. + 7 times U is CD, and 3 is 72. Write 3. The final remainder is 333. Example 3.— Divide 123,456,7^9 by 5,4:33. divisor '2'2"r21 quotient Solution.— 5 4 3 3)133456-789 dividend 148 1 3953 1503 41 74 3 7 3 5 remainder 33. Division of I>eeinials. — Division of decimals is no more difficult than division of integers. The decimal point in the divisor should be moved to the right far enough to make the divisor a whole number, and the point in the divi- dend should be moved the same number of places to the right. The quotient should be written over the dividend, and its decimal point should be directly above that of the dividend. In moving the decimal point of the dividend it may be necessary to annex ciphers. The following examples will illustrate: Note.— To prevent confusion, the original position of the decimal point is indicated in the solution by an inverted period, while the posi- tion of the point after it has been changed is the same as it is usually printed. Example 3.— Divide 1.15635 by .25. Solution. — 4.6 2 5 •2 5. ) M .5.6 3 5 15 6 13 Example 4. — Divide 345.6 by' 1.44. Solution. — 2 4 0. 1-4 4. ) 3 4 5-6 0. 576 Of the methods of determining with certainty the place of the decimal point in the quotient, there is none qtiite .so easy for the pupil as that just explained. 26 PEDAGOGICS OF ARITHMETIC. § 2 The same method is appHcable with dollars and cents. Example 5. — A man bought 1.25 M shingles for $1,875. How much did they cost per M ? Solution. — $1.5 1-2 5. ) $1-8 7.5 625 Example 6. — How many books at $1.75 each can be bought for $49 ? Solution.— 2 8. $1-7 5. ) $4 9-0 0. 1 4 Of course the teacher will understand that moving the decimal point in this manner is equivalent to multiplying both dividend and divisor by lU, 100, 1,000, etc., which has no effect upon the quotient. PROOFS OF THE FUNDAMENTAL, OPERATIONS. 34. Proofs of Addition and Subtraction. — The pupil should be reqtiired to prove his work in addition by adding the columns in a direction opposite from the first, and in subtraction by showing that the sum of the subtrahend and remainder equals the minuend. 35. Proofs of Miiltii>Hcation. — For beginners the best proof of multiplication is to multiply the multiplier by the multiplicand ; that is, to reverse the order of the factors. Somewhat later, when the pupils have mastered division, they may be required to show that their work is correct by dividing the product either by the multiplier or by the multiplicand. Of cour.se, this requirement should be made only for the sake of the practice involved, for the proof by this method is longer and more difficult than the original multiplication. To advanced pupils should be taught the method of proof by casting out O's. Since many teachers are not acquainted with this method, it is explained below. § 2 PEDAGOGICS OF ARITHMETIC. 27 Rule. — Add t lie digits of the multiplicand a)id tliose of the multiplier separately. Divide each sum by 0. Multiply the remainders together, and having divided the product by .9, note the remainder. Add the digits of the product and divide the sum by '■). If the remainder is the same as that obtained with the multipli- cand and multiplier, the work is probably correct. In case either the multiplicand or the multiplier gives for a remainder, the remainder for the product must be also. Illustration. — iniiltiplicaud 4 8 2 7 multiplier 3 4 6 product 14 9 7 14 3 Pkook. — 4 + 3 + 2 + 7 = 10; 10^9 gives 7 remainder. 3 + 4 + 6 = 13; 13 -^9 gives 4 remainder. 7x4 = 28 ; 28 -=- 9 gives 1 remainder. 1 + 4 + 9 + 7+1+4 + 2 = 28; 28h-9 gives 1 remainder. In using this proof it should be noted: In finding the sum of the digits the resulting remainder is not affected by skip- ping a 9 or by dropping one at any stage of the addition. Thus, suppose the excess of 9's in the sum of the following number were desired: 359,740,823. 1. Finding the entire sum, 3 + 5 + 9 + 7 + 4 + 6 + 8 + 2 + 3 = 47. Dividing by 9 ; 47 -+ 9 = 5, remainder 2. 2. Skipping 9's, 3 + 5 + 7 (skipping 4 + G + 8) + 2 + 3 = 20. Dividing by 9; 20 -=- !» = 2, remainder 2. 3. Deducting 9 from the sum at any time during the addition, 3, 8, 15 (deducting 9 from 15), 6, 10 (deducting 9), 1, 7, 15, 6, 8, 11, remainder 2. 4. If the sum of the digits of either the multiplicand or the multiplier is an exact number of 9's, the same must be true of the prodiict. In such cases, the product of the excess need not be found, for it will always be 0. 28 PEDAGOGICS OF ARITHMETIC. § 2 To illustrate, suppose we wish to test the following: 8343 8 + 3 + 4 + 3 = 18; ranaiudcr 0. 5 G 2 1 4 6 8 9 3 4 + G + 8 + 9 + G + 3 =r 30 ; rnnaindcr 0. 5. The method fails, {a) when figures are transposed in the quotient; (//) when 9 occurs in the answer for 0, or the reverse; (r) when 9 or is omitted from the answer; {d) when a figure denotes as much too much as another does too little. It should be added, however, that none of these accidents is likely to happen, and that the test may usually be regarded as reliable. 2(5. Proofs of Division. — There are several methods of proving division. Of these the best is by casting out 9's, but this is suitable only for pupils that are pretty well advanced. For young pupils, the following should be employed : 1. To tJic p7-oduct of tJic divisor and quotient add the remainder, and if the dii'ision is correct the snni will be equal to the dividend. 2. Divide the dividend by the quotient, and if the quotient and remainder are the same, respectively, as the former divisor and remainder, the work is correct. Division by casting out 9's is proved as follows: 3. To t lie product of the excess of 9's in the quotient and the divisor add the excess ofO's in the remainder. If the excess ofO's of this sum is the same as that of the dividend, the zvork may be assumed to be correct. To illustrate, suppose that an operation in division has the following elements. Is the work correct ? dividend 3,920,438 T dividend, 8^ divisor 528 ' ' j divisor, 6 i X 2 + 5 _ quotient 7,430 . j quotient, 2 j 9 "" ' remainder 230 ' [remainder, 5 J § 2 PEDAGOGICvS OF ARITHMETIC. 29 We multiply together the excess of 'J's in the quotient and divisor; to the product, 12, we add 5, the excess of 9's in the remainder, of this sum, 17, the excess of D's, 8, the same as in the dividend. Hence, we may assume that the work is correct. SIGNS USED IN THE FUNDAMENTAL OPERATIONS. 27. Precedence of Signs. — There is nothing- in which our textbooks on arithmetic are more ambiguous than in the interpretation of signs. To illustrate the matter, let us examine the following expression : 2x30-5x4 + = ? This may be interpreted in several ways, and in the absence of definite principles of interpretation, one result. is as defensible as another. For example, the operations may be performed in any of the following ways: 2x30 = GO; (;0 - 5 = 55; 55x4 = 220; 220 + (> = 220. 2x(30-5) = 2X25 = 50; 50x4 = 200; 200 + = 200. 2X30 = 00; G0-(5X4) = 00-20 = 40; 4O + = 40. 2x30 = GO; 00 — (5x4+0) = 00-20 = 34. 2x(30-5) = 50; 50 X (4 + 0) = 50X10 = 500. 2X30 = 00; 00-5 = 55; 55 X (4 + 0) = 55X10 = 550. Again, take the expression, 144h-4x3-^0h-2x3 = ? Here we have only the signs of division and multipli- cation. A slight examination of this will make it clear that a very great nimiber of values may be found. Of course, all uncertainty may be removed by using symbols of aggregation, but these are often omitted. In order to lead to uniform interpretations where quantities are affected by several signs in sequence, some rules are indispensable. The following are believed to conform to the usage of the best authorities; biit it should be remembered that these principles have reference only to arithmetic. 30 PEDAGOGICS OF ARITHMETIC. §2 PKIXCIPT^KS. 1. 1)1 fiiidi)ig the value of a sequence of uuuibers separated by signs of the fundamental operations, begin at the left and proeecd in order toivards the right. •I. Quantities united by symbols of aggregation must be redueed to a single quantity before being used as a term of the sequence. o. Multiplications must be performed before divisions., and both before additions and subtractions. •i. When some other precedence of signs or order of reduc- tion is intended., symbols of aggregation must be used to prevent ambiguity. Reducing" the foregoing examples in accordance with the principles just given: {a) 2x;30-5x4 + «i = 60 — -^0 + (J = 40. Ans. {b) 144^-4x3^0^3x3 = 144 4-12-4-6^0 = 12, 2, f or i Ans. Again, {c) (14 - 3) X 2 + 8 -^ 4 = 11x2 + 8^4 = 22+2 = 24. Ans. (d) 24 - 8 X 2 + 3 X -=- = 24 - 1 -f 18 -^ = 24 - 10 + 2 = 10. Ans. {e) 3X12^ 9 -0X2-=- 3X2 = 30 ^ •) - 12 -h G = 4-2 = 2. Ans. (/) [42 + X 2 -^ 8 - 2 ^ 3] X 2 -^ 4 = [48 X 2 -^ H- 3] X2-f4 = J^x2 + 4 = U|. Ans. MISCELLANEOUS OPERATIONS AND SUGGESTIONS. 38. Approximation. — Every teacher has noticed the fact that children in solving examples will get answers of the most absurd kind, and, without a suspicion of their impossi- ble character, await the decision of the teacher as to whether they are right or wrong. They never consider the question, " About how much should this answer be ? " Their answer in any given case may be a million times too great, but they seem to have no means of detecting it for themselves. § 2 PEDAGOGICS OF ARITHMETIC. 31 It is clear, therefore, that in this matter they should have specific training. There is nothing better for this pur- pose than exercises in what may be called appi'oxiviatioi. To show just what this consists in, a few examples are necessary. 1. About how much is 9J times 12| ? Here we notice that 9J is slightly less than 10, and 12| is a little more than 12. Their product should therefore be about 10 times 12, or 120. It is, in fact, H'-'iV- 2. What is the approximate value of 8f X 9f X 16.^ , '5.9X121 ■ A brief examination will give something like the following as an approximation : 9X10X16 6 X 13 ' this reduces to 20. The true result is 19. 1 + . 8. Find the value, ^earl3^ of 4/riX8.125x -^'100 . 4.0275 X 4/2T It is evident that we shall not be far astray by taking as an equiv- alent of this expression, the following: 3X8X5 . ~A ^ = O. 4X0 The correct value is 6.777+. 4. About how much is 20.25-6.V-K2^XlU) , 4/19 X i'^yo As an approximation we may write, 14 + 24 38 „ or 4.4X4.3' 19 ~ The true result is 2.023+. 5. About how much is the interest of §498.75 for 3 yr. 11 mo. 25 d. at ^% ? We see at a glance that this is very nearly the same as if the principal were 1500 and the time 4 years, when the rate is4i-^. 32 PEDAGOGICS OF ARITHMETIC. § 2 Without writing anything, we say, "At 4:hfo a year, in 4 years, j^o of the principal equals the interest; y^g of 1500 is |90. Since the principal is not quite 1500 and the time is slightly less than 4 years, the interest must be slightly less than |90, say $80.50." Computation shows that the correct result is 189. 4G+. The foregoing examples have been made dif^ficult in order to show that the method of approximating is applicable to every variety of problem. Before pupils are permitted to work out exact results, they should be required to estimate as nearly as possible what the answer will be. This will add much interest to the work, besides being of the highest value. Especially is this important in examples requiring the place of the decimal point to be determined. A friend of the writer speaking of this matter recently, said that more mistakes are made in the counting room from mis- placed decimal points than from any other cause, and added that the blunder is one that no system of double- entry bookkeeping will detect. "Only recently," he re- marked, "a Boston firm sent me a bill of $22.10 for copper; it should have been $221." This exercise is so important that it should be prescribed in the course of study of every school. 29. Tlie roriniilatiiig of Operations. — Another very valuable exercise, which is closely related to that of approxi- mation, is one that may be called" /or jhh /a ting. This con- sists in indicating the steps necessary to the solution of problems. Whether or not the operation is afterwards actually performed is of no special consequence. Cancela- tion is possible in nearly all examples, and formulation, better than any other exercise, leads to its systematic use. The following exercises will illustrate the writer's meaning : Example 1. — A man walks 8| miles in 2| hours; how far at that rate can he walk in 4i hours ? 84 ,, 26X24X3 Formula.- ,1X41= ^^,^s § 2 PEDAGOGICS OF ARITHMETIC. 33 Example 2. — How much will it cost at Sl.',*5 per yard to carpet a room 24 X 30 feet with carpet f of a yard wide ? ^1 o~ vx -"^ X ^0 s §5X34X80X4 Formula.- !:,1.2a X — y— - I = 4 X 1^ X 3 ' E.xAMPLE 3.— What is the interest of §450 for 4 years 7 months at 41% 1 . , ^ 41 , , §450 X 14 X 55 Formula.- §450 X^X4^=.-^J^^^^^. Example 4. — If discounts of 40^/, 20;!, and 10?^ are allowed, what must be paid for a piano of which the catalogue price is §500. Formula.— §500 X (LOO - .40) X (1-00 - .20) X (LOO - .10) = §500 X .6 X .8 X .9 = §500 X .432. Interesting variety is added if one pupil be reqitired to for- mulate an example and another to perform the indicated work. An excellent kind of home work consists in giving a list of examples who.se solutions are to be indicated, but not per- formed. PROPERTIES OF XUMBERS. 30. Divisibility of Numbers. — The teacher very fre- quently wishes to know whether one or more numbers may be exactly divided by any integer. This happens more especially with fractions that are, perhaps, reducible to sim- pler forms. The common tests of divisibility should, there- fore, be thoroughly familiar to the teacher, and the simplest and most useful of them should be carefully taught to the pupil. The following are of this kind : 1. Every even iininber is exaetly divisible by 2. (Even numbers are such as end in 0, 2, 4, G, or 8.) 2. If the sum of tlie digits of a number is exactly divisible by 3, the number itself is exaetly divisible by 3. Thus, 0,531 is divisible by 3, since + 5 + 3 + 1, or 15, is divisible by 3. The reason for this will be shown in con- nection wnth divisibility by 9. 3. A number is exaetly divisible by J^ ivhen the nnndur expressed by its tioo right-hand figures is exaetly divisible byJf. Thus, 6,124 is divisible by 4, since 24 is divisible by 4. 34 PEDAGOGICS OF ARITHMETIC. §2 The reason for this principle is that 100 or any multiple of 100 is exactly divisible by 4. Now 6,124 is Gl ti'mes 100, and 24 besides. Since 24 contains 4 exactly, it is clear that 6,100 + 24, or 6,124, contains 4 exactly. 4. When the last figure of a miuiber is or 5, the nninber is exactly divisible by 5. Thus, 2,170 or 3,235 is divisible by 5. For, 2,170 is 217 times 10, and since 10 is exactly divisible by 5, it follows that 217 times 10 is also so divisible. Again, 3,235 is equal to 323 times 10, and 5 more. Now, 323 times 10, as well as 5, is exactly divisible by 5. 5. Any even iiuviber the sum of luhose digits may be exactly divided by S is exactly divisible by G. Thus, 3,558 is divisible by 6; for being- an even number, it is divisible by 2, and it is exactly divisible by 3, since the sum of its digits is divisible by 3. Hence, the number is divisible by 2 times 3, or 6. 6. A number is exactly divisible by 8 ivhcn the number expressed by its three right-hand figures is exactly divisible by 8. Thus, 52,168 is divisible by 8, since 168 is so divisible. For, 52,168 is equal to 52 times 1,000, and 168 besides. Now, since 1,000 exactly contains 8, it is clear that 52,000 does also. Hence, if 168 is a multiple of 8, the sum of 52,000 and 168, or 52,168, is also a multiple of 8. 7. A number is exactly divisible by 9 ivhcn the sum of its digits is a viultiple of 9. Thus, 8,451 is exactly divisible by 9, since 8 + 4 + 5 + 1, or 18, is exactly divisible by 9. The reasons for this may be seen from the following: ,451 = _ J 8000 400 50 1 999x8 + 8 99x4 + 4 9x5 + 5 + 1 Now, since each expression under a is exactly divisible by 9, and since the sum of the column under b is also divisible by 9, it follows that the sum of a and b, or 8,451, will also § 2 PEDAGOGICS OF ARITHMETIC. 35 contain 9 exactly. It is evident that if a number is exactly divisible by 0, it is exactly divisible by 3. 8. A )iu})ibcr that is exactly divisible by each of ttvo or more prime numbers is exactly divisible by their product. Thus, if 3 and 5 are each exact divisors of a number, 15 also is an exact divisor. The same is true of 3, 7, and 21 ; of 2, 3, 5, and 30; of 2, 3, 7, and 42, etc. 31. Test for Prime Numbers. — It is well known that there is no simple method of determining whether a given number is prime or not. This is imfortunate from the fact that it is often important to know whether a num- ber may be factored. Provided, however, that the number is not very large, the question whether or not it is prime may be determined without much labor, in the following manner: Suppose it is desired to test 419 for exact factors. The first step is to determine the approximate square root of the number. We see at a glance that this is between 20 and 21. It is clear, then, that it is necessary to ascertain whether the given number is exactly divisible by any number less than 21. If not so divisible, it is prime ; for if it has an exact divisor greater than 21, the quotient, which is also an exact divisor, must be less than 21. Now, it is not necessary to divide by any composite num- ber; for if 2 will not divide it, no multiple of 2, as 4, G, 8, etc. , will divide it. If 3 will not divide it, 6, 9, 12, etc. will not. It is clear, then, that the only divisors to be tested are the primes less than 21. These are 2, 3, 5, 7, 11, 13, 17, 19. Of these, the first five are quickly disposed of ; for at a glance, it is seen that neither 2, 3, nor 5 is an exact factor, and it is easy to try 7 and 11. They are not factors. Only 13, 17, and 19 remain, and but a moment is needed to try them. They are not divisors, and we may be certain, therefore, that 419 is a prime number. Again, let it be required to test the number 851. The square root of 851 being less than 30, our divisors are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29. Trying these as before, it is found 36 PEDAGOGICS OF ARITHMETIC. § 2 that 23 will exactly divide 851, giving a quotient 37. The number is, therefore, composite, and its factors are 23 and 37. Once more; let us examine the number 2,257 for exact divisors. Our test will be confined to the prime numbers less than 48, for 48^ = 2,304. These numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47. Trying these in turn, 37 proves to be an exact divisor, and the factors are 37 and Gl. In the case of large numbers, this method is somewhat tedious, but it is the only one available, and pupils should know how to apply it. Besides some other advantages, it involves valuable practice in division. 33. Prime Xuinbers. — Teachers should see to it that pupils are very familiar with all prime numbers within the upper limit of the multiplication table; that is, as far as 139, or higher. Omitting 1, these primes are, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139. 315. Table of Prime Numbers.- — For purposes of ref- erence the following table of all the prime numbers less than 0,000 will be found useful in the classroom. One of the most important applications of the table is to tell at a glance whether a given fraction is in its simplest form. Knowing that a fraction cannot be .simplified if either of its terms is a prime number, a mere glance at the table will often save the operation of finding their greatest common divisor. Of course, the terms may be prime to each other, and yet both be composite numbers, and the fraction be, therefore, irre- ducible to lower terms. In this case, the greatest common divisor test must be applied. To use the table, look for the thousands figure above one of the divisions of the table. Then, under the thousands figure, find the hundreds figure at the top of one of the ten columns. If the number is prime, the remainder of the number will be found below in this column. 8 2 PEDAGOGICS OF ARITHMETIC. 37 PRIME NUMBERS. 1 2 o I 2 3 4 5 6 7 8 9 I 2 3 4 5 6 7 8 9 I 2 3 4 5 6 7 8 9 I OI II 07 01 03 01 01 09 07 09 03 01 01 09 II 01 09 01 01 03 II 03 09 II 03 09 07 01 03 2 oy 23 II 09 09 07 09 II II 13 09 13 03 23 23 07 21 II 07: II 13 07 II 17 21 17 II 03 09 3 07 27 13 19 21 13 19 21 191 19 17 17 07 27 31 09 23 23 13 17 29 13 33 23 31 21 13 19 17 5 09 29 17 21 23 17 27 23 29 21 23 23 19 29 43 13 33 31 31' 27 31 21 39 37 39 33 19 33 27 7 13 33 31 31 41 19 33 27 37; 31 29 29 21 33 49 19 41 47 33, 29 37 37 41 41 43 47 29 37 39 II 27 39 37 33 47 31 39 29 41 33 51 31 27 39 53 21 47 bi 49 39 41 39 47 47 49 57 31 43 53 13 31 41 47 39 57 41 43 39 47i 39 53 37 bi 47 59 27 53 07 51: 53 43 43 51 59 51 59 41 51 57 17 37 51 49 43 b3 43 51 53 53 49 (>3 49 67 51 67 37 59 71 73 63 53 51 57 07 57 63 49 57 63 19 39 57 53 49 69 47 57 57 67 51 71 59 73 53 71 57 77 73 79 69 bi b7 71 73 79 71 53 bi 69 23 49 63 59 57 71 53 ()i 59 71 61 81 77 81 59 79 63 83 77 87 Si 79 69 77 77 91 77 67 79 71 29 51 69 ^7 61 77 59 69 63 77 63 87 79 99 71 83 67 87 79 93 83 73 81 93 83 77 87 99 31 57 71 73 63 87 61 73 77 83 69 93 83 81 97 69 89 89 97 87 81 83 87 89 97 37 63 77 79 67 93 73 87 81 91 87 89 83 93 99 89 87 89 89 91 41 67 Si 83 79 99 77 97 83 97 gr 91 87 97 99 93 93 93 97 43 73 83 89 87 83 87 93 97 89 99 97 99 99 47 79 93 97 91 91 97 93 53 81 99 99 59 91 6 1 93 ^1 97 71 99 73 79 83 ' 89 97 3 4 5 I 2 3 4 5 6 7 8 9 I 2 3 4 5 6 7 8 9 I 2 3 4 5 6 7 8 9 01 09 03 01 07 II 07 01 03 07 01 II 01 27 09 07 03 03 01 03 03 01 09 03 07 01 23 01 01 03 II 19 09 07 13 17 13 09 21 II 03 27 II 37 21 13 21 21 13 09 09 07 27 09 13 0; 39 II 07 23 19 21 17 13 33 27 17 19 23 17' 07 29 17 39 23 17 37 23 17 19 II 13 31 23 17 07 41 17 n 27 23 37 21 19 49 29 23 27 33 I9| 13 33 19 49 41 19 39 29 31 31 21 19 33 33 19 19 47 37 21 39 37 63 29 23 57 33 31 33 47 23 19 39 29 57 47 23 43 33 bi 33 23 47 37 47 31 21 51 41 27 53 41 67 51 29 61 39 37 39 51 29 21 53 31 63 51 47 49 51 71 37 39 53 bi 51 37 27 53 43 39 Si 49 69 53 31 63 41 43 bi 53 31 27 57 41 73 57 49 51 59 77 43 51 67 73 Si 41 31 57 49 43 87 61 Si 57 43 67 47 59 67 63 43 49 59 43 91 63 61 57 83 89 51 59 71 79 87 43 57 59 79 49 67 87 59 47 69 57 71 69 77 47 51 77 53 97 Si 67 63 87 57 77 79 Si 93 49 63 69 83 51 79 91 71 59 91 59 73 79 Si 67 57 59 83 83 73 89 67 81 89 97 99 71 69 83 91 57 83 99 61 99 71 77 93 89 89 73 61 93 91 79 93 69 87 97 77 73 89 bi 89 71 73 89 91 Si 83 93 91 97 97 79 91 93 99 71 73 83 89 97 97 91 99 73 87 93 99 99 79 83 Si 91 93 67 69 79 Si 97 38 PEDAGOGICvS OF ARITHMETIC. FACTOKS, DIVISORS, AISTD MUI.TIPLES. 34. Faetoriiij^. — In arithmetic, as in algebra, the expert- ness of pupils depends very much on their skill in factoring. Nearly all operations involve cancelation, and skill in this requires that the pupil shall be quick in recognizing the fac- tors of numbers. The subject of factoring and its various applications should be carefully taught. It will be found of great assistance in this work to have pupils leani the multi- plication table farther than the usual limit, 12 times 12. A few minutes' work each day for a few weeks will enable them to accomplish this task, and they will then have not only much added skill in factoring numbers, but a contribution to practical efficiency that will be of extreme value during all their future life. In resolving any number into factors pupils should be taught that the work is not completely done unless the result- ing factors are all prime numbers. Thus, the factors of 60 are not and 10, or 12 and 5, but 2, 2, 3, and 5. The operation of finding these factors by division should begin with the least prime number that is an exact divisor. The division of the number and each successive quotient by this divisor should be continued as long as possible. The next greater prime number should be used in like man- ner, until the last quotient is prime. All these successive divisors and the last quotient are together the required prime factors. To illustrate, let it be required to find the prime factors of 34,650. . „ ^ „ Hence, the prime factors of 34,650 are 2, 3, 3, \ „ 3 'I ^ 5, 5, 7, 11; or, 34,050 = 2X3^X5^X7X11. This ^ r. r. r result may be written 2. 3". 5^ 7.11. For small 5 7 7 5 •' „ g ^ numbers the factors may be written out at once, r-r-- the divisions being performed mentally. Thus, to find the prime factors of 120, we may say, "120 < i ~ divided by 2 (write 2) is 60; 60 divided by 2 (write 2) is 30; 30 divided by 2 (write 2) is 1 5 ; 15 divided by 3 (write 3) is 5 (write 5). The prime factors are, there- fore, 2, 2, 2, 3, 5; or, 120 = 213.5." § 2 PEDAGOGICS OF ARITHMETIC. 39 35. Greatest Coiiiniou Divisor by Factoring'. — With numbers within the range of the ordinary multiplication table, pupils should have no difficulty in determining the greatest common divisor by inspection. At any rate, they should be trained until they can do so. A good practical form of this exercise is in simplifying such fractions as |^|, 36^ ||.^ etc. When the pupils have become proficient in doing this, larger numbers may be used, and the method l)y factor- ing employed. Thus, such fractions as the following may he taken- ^.ai 5.12. 5.0.4 gf^ In simplifying such fractious, the work may be advan- tageously performed in such manner as to make the pupils familiar with various ways of indicating products. 433 ^ 2X3X2X2X3X3X3 768 3X2X3X3X3X3X3X3X3 _ 3^ X 3^ _ (2\^yxn- __ ^ _ ^ ~ 3^X3 ~ (3\3)X3^ "■ 3"^ ~ 16 504 ^ 3 X3X3X3X3X 7 ^ 3^ X 3^ X 7 ^ (3l3'0x3x7 ^ 14 540 2X3X3X3X3X5 3^ X 3--' X 5 (3^3--') X 3 X 5 15 The important matter at this stage is not to get the simplest form of the fraction in the briefest possible way, but to reveal the principles involved in the operation. The pupils should be questioned about the work, and should be required to find the greatest common divisor of the terms by multiplying together the common prime factors. In the first example above, this greatest common divisor is 2\o, or 48; in the second, it is 2". 3", or 30. By being required to reduce the fractions at one division of their terms, the pupils will understand the purpose of finding the greatest common divisor. This is especially important where the greatest common divisor must be found by the process of division. Thus, 433 --3\3 _ 432 --48 _ 9^ 768 -f- 2^3 ~ 768--48 " T6' 504-4-2^3- _ 504 -=-36 _ 14 540 --2^3- ~ 540-^36 ~ 15' The method of finding the greatest commcjn divisor by factoring is sufficient for nearly all practical needs ; but it is 40 PEDAGOGICS OF ARITHMETIC. § 2 occasionally necessary to resort to the method by division. The pupils should understand this method and the principles on which it depends. These principles are the following: 1. A /I exact divisor of a number is an exaet divisor of any multiple of that nnmber. Thus, 7, being an exact divisor of 14, is an exact divisor of 2 times 14, o times 14, etc. For, since 7 is contained 2 times in 14, it is contained 2 times X2, or 4 times, in 14x2; it is contained 2 times X 3, or G times, in 14x3; etc. 2. An exact common divisor of two numbers is an exact divisor of their sum. Thus, since 7 is an exact divisor of 14 and 35, it is an exact divisor of 14 + 35, or 40. For, 7 is contained in 14, 2 times, and in 35, 5 times; hence, 7 is contained in 14 + 35, 2 times +5 times, or 7 times. 3. An exaet common divisor of tivo numbers is an exact common divisor of their difference. Thus, since 7 is an exact common divisor of G3 and 35, it is an exact common divisor of G3 — 35, or 28. For, 7 is contained in G3, 9 times, and in 35, 5 times; hence, 7 is con- tained in 63 — 35, 9 times — 5 times, or 4 times. 4. An exact common divisor of two numbers is a)i exact common divisor of the sum of any multiples of those numbers. Thus, since 7 is an exact common divisor of 21 and 35, it is an exact common divisor of 21x5 + 35x4. For, .since 7 is contained 3 times in 21, it is contained 3 times X 5, or 15 times, in 21 X 5; and, since 7 is contained 5 times in 35, it is contained 5 times X 4, or 20 times, in 35x4. Hence, 7 is contained 15 times +20 times, or 35 times, in 21X5 + 35X4. 5. An exact connnon divisor of two numbers is an exaet common divisor of the difference between any multiples of those n7i7nbers. Thus, since 7 is an exact common divisor of 28 and of 35, it is an exact common divisor of 28 X G — 35 X 3. For, since 7 is contained 4 times in 28, it is contained 4 times X G, or 24 times, in 28 XG; also, since 7 is contained 5 times § 2 PEDAGOGICS OF ARITHMETIC. 41 in 35, it is contained 5 times X 3, or 15 times, in 35x3. Hence, 7 is contained 24 times — 15 times, or 9 times, in 28 X 6 - 35 X 3. The following illnstration will enable the student to see how these principles apply in finding the greatest common divisor of two numbers. Let us take 15 X 29 and 47 X 29, or 435 and 1,363. Here, we know in advance that the greatest common divisor is 29. Explanation. — By principle 1, we know that since 29 is a divisor of 15x29 it is a divisor of 3 times 15x29, or 15X29)47X39(3 45 times 29. By princi- 4 5x29 pie 5, 29 is a divisor of 3X39)15X29(7 47 X 29 - 45 X 29, or ^^X^^ 2 X 29. These two prin- 1X^«>)'-X~9(3 ciples account for every 3X29 other step in the proc- ess until the last difference of multiples, 1 X 29, turns out to be an exact divisor of the preceding difference of multiples, 2 X 29. But, since no divisor of 1 X 29 can be greater than 29, it is evident that the last divisor, 29, is the greatest com- mon divisor sought. Let us take now two numbers whose greatest common divisor is hidden in the numbers. Solution.— 136 5)339 5(3 8730 6 6 5)1365(3 13 3 35)66 5 ( 1 9 3 5 3 1 5 315 Explanation. — The greater number is divided by the less, the less by the first remainder, the first remainder by the second remainder, and so on, until, finally, the greatest common divisor, 35, appears as an exact divisor of the pre- ceding remainder. 36. Apj)lication of Abbreviated Division. — The short method of division already explained may be advan- 42 PEDAGOGICS OF ARITHMETIC. §3 tageously applied to finding the greatest common divisor of two numbers. To show this, both methods are given below side by side. Example 1. — Find the greatest common divisor of 437 and 943. Solution. — 437)943(3 874 9 437(6 4 1 4 437 94 3 23 69 S3 69(3 69 Example 2. — Find the greatest common divisor of 2,358 and 10,728. Solution. — qtioticnis quotients 2358)10728(4 9432 12 9 6)2358(1 1 2 9 6 10 6 2)1296(1 1062 1 2 3.58 10728 4 1062 1296 1 1 26 234 IS 1 08 2 3 4)1062(4 936 126)234(1 1 26 10 8)126(1 1 08 18)108(6 1 08 Example. — Find the greatest common divisor of 2,431 and 12,259; also, of 9,711 and 38,761. quotients quotients quotients 23 2431 12259 35 1 04 1 3 9 26 13 97 11 38761 83 9628 1 3 49 quotients 3 1 16 37. Ijeast Common Multiple by Factoring. — Few pupils understand, at least until late in their school course, the exact nature of the least common multiple of two or more numbers. And yet the operation is of much importance since it must frequently be resorted to in adding or subtract- inT^18 — 18 — 2 — ^2' o 2 — 10' ^^'"• Of these the pupils should say only, "0, 21, 37, 52, 63 eighteenths. Answer, 3V'; and " S, 3 tenths. Answer, j\." 40. Written Forms in Addition and Subtraction of Fractions. — The teacher cannot be too exacting with reference to the forms that should be used in adding and subtracting fractions when written aid is necessary in the operation. These forms should be very definitely agreed upon and afterwards they should be followed in every detail, even the least. If this is not done, confusion and error are almost inevitable. Of course, the prime requisites in these forms are neatness and brevity. The following is the form preferred by the writer. Example 1. — Find the sum of |, |, ji, and ig. Solution. — 2 6, 8, 1 8, 30 3 3 4 9 1 5 4 3 5 C. M. = 2 X 3 X 4 X 3 X 5 = 360 360 6 8 18 30 60X5 = 300 4 5 X 7 = 3 1 5 2 0X11 = 220 12X19 = 2 2 8 1063 360 ~ 9 .•! 4 .3 §2 PEDAGUGICvS OP^ ARITHMETIC. 4? Explanation. — First find the factors of the least common multiple of the denominators; indicate, and then find, this product. Divide this L. C. M. by each denominator in turn and multiply each result by the corresponding numerator. Find the sum of the products and divide it by the L. C. M. The quotient will be the sum of the fractions. Note that the reduction is made by the method of abbreviated division in which multiplication and subtraction are combined in one operation. This can always be done when the integral part of the quotient is not greater than l"^. ExAMi'i.K 2. — Find the sum of 5j\, ^Jf, 7||, and 8||. . Solution. — 7 11^, 2 !"> "> ■'>. 4 2 L. C. M. = 6 X 7 X 5 2 1 310 1 4 2 1 3 5 42 1 5 X 9 = 135 1 X 13 = 13 6X12= 72 5 X 29 = 1 4 5 48^^ 2 2 10 5+3+7+8=2 3 Ans. The form for subtraction is precisely similar. ExAMi'LE o. — From ?,'^ take },l. L. C. M. = 2 X 3 X 9 X 16 = 576 368 1 53 2 15 , ■ . Ans. 576 Solution.— - 2 3 6, 64 2 1 8 33 9 1 6 5 7 6 3 6 1 6 64 9 41, Special Cases in Addition and Subtraction of Fractions. — The sum of i- and ^ is equal to f. The numer- ator of this result is the sum, 2-}-'^) of the denominators and 48 PEDAGOGICvS OF ARITHMETIC. § 2 the denominator i.s the product, 2x3, of the same denomi- nators. Similarly, J :» + ! - 4X3 - '^ [ I "^ 5 - 5x3 - IT) I Inasmuch as it is frequently necessary to add or subtract two fractions having- 1 for numerators, children should be familiar with the following principles governing the operation : 1. The sum of ti^'o fractions each Jiaving 1 for its uiiiner- ator is expressed by a fraction wJiose numerator is the sum, and its denominator t lie product, of their denominators. 2. The difference between two fractions each Jiaving 1 for its denominator is expressed by a fraction zvhose numerator is the difference, and its denominator the product, of their denominators. It is clear that if the numerators of two fractions are each greater than 1, but alike, the same principles may be used in adding or snbtracting the fractions. Thus, since i + i = ^-^, or Vr, it follows that | + | _ '^(O + o) 1 fi . oonin 4 i 4 _ "*(' + ^) ^,. 4S Aico 3—1 — g X 3 ' T5 ' agam, ^ -|- y _ ^^^ > "i 35- ^^ii^o, 4 5 _ 3(5-4) _ _^_ ~ 5X4 ~ 2«- This method is applicable only when the sum or the differ- ence of two fractions is to be found. If three or more such fractions are to be added, the usual method should be employed. It frequently happens that operations like the following are to be performed : This may be written as follows: f-1 + l-l + f+l-l + ^ + i = f + t+l + l + i + i-3. It is obvious that the value of the last expression may be found more easily than that of the first. Hence, where a § 2 PEDAGOGICS OF ARITHMETIC. 49 series of fractions requires both addition and subtraction, change each negative fraction into a positive fraction equal to the remainder obtained by subtracting the negative frac- tion from 1 ; then add all the positive fractions and from the result subtract 1 for each chantie that was made. ExAMi'LE 1. — Find the value of | — i -f- ^^Ij i + h Solution. — l + 3 + A + A + f + i- -3. 2\4, 3, 14, 1 ( , 6, ^ 7 b 3 L. C. D. =2X7 X8X3 = 336 336 4 84X3 =-. 252 3 1 1 2X2 = 2 2 4 14 24X9 = 2 1 6 16 21X9 = 1 89 (J 56X5 = 280 8 42X7 = 294 14 5 5 3 36 3 1 JiJ^ Ans. Example 2.— Find the value of 5J - 2|' + 11 1', Solution.— J + | + ^^ + ^ + ^_3. 6A-1! 2 >f, ^, 1 5, 1 (), G 3 15 8 3 5 8 L. C. D. = 2 X 3 X ■') X 8 = 240 24 4 60X3 = 180 8 3 0X3= 90 1 5 16X7 = 112 1 15X7= 105 6 4 0X1= 40 52 7 2 4 "'" G-1 + 2^-^ 7 _Q _ 1S47 _10 — A4 Ans. 42. Multii)lyini»- Mixed ^xiiubers. — In the multiplica- tion of one mixed number by another, it is almost universal usage to change both factors to improper fractions. It is, 50 PEDAGOGICS OF ARITHMETIC. § 2 however, much better to perform the operation in four steps. [ (1) t lie fraction by tJie fraction. I (2) tJie upper number by the lozvcr fraction. Multtply \ (3) tlie upper fraction by the knver number. (-4) the upper w!ioIe number by the hm'cr whole [^ number. The sum of these four results will be the correct product. E.XAMPLE 1.— Multiply 123 by llf ; also, 273.V by 48*. Solution.— 1 2 f 2 7 3 i llf 481 i = (1) 1 X f § = (1) |X| 9 = (2) 13 X f 2 1 8 g = (2) 273 X 1 7 1 = (3) 11 X i 2 4 = (3) 48 X 1 132 = (4) 12X11 13 10 4 = (4) 273 X 48 1 4 8 f Ans. 1 3 3 4 6 i Ans. This method is peculiarly advantageous when the denomi- nators of the two fractions are equal. In this case, (2) and (3) above can be merged into one operation. Example 2.— Multiply 18f by 18J; also 15| by 121. Solution. — 18| 15f 18 4 12 4 t\ = (1) fxf i = a)ixi 27 = (2) + (3) 18X1 + 18X1 13 = (2) + (3) 15 X | + 12 X | 324 == (4) 18 X 18 1 80 = (4) 12 X 15 3 5 1 i\ Ans. 1 "3 3 I Ans. The student shottld notice that this method is only a special case of that in which numbers of two figures each are mtiltiplied together. The graphic symbols for the operation are | X I . In performing the part of the process denoted by the middle symbol X, the cross products may be united in one operation, if the fractions in the two factors have the same denominators. Thus, to mtiltiply 0| by Of the work represented by X may be done thus: times f + times | = 18 times |, or 12. § 3 PEDAGOGICS OF ARITHMETIC. 51 If the factors were 12f and 0^-, the work would be, 12 times i + 9 times f = V'+V = ¥. ^v Of. A very compact method applicable where the terms of the fractions or the integral parts are large is the following: Example 3.— Multiply 28if by 19|. Also, 234§ by 98?. Solution.— 2 8 if 195 17 2 4 7 = 19 X 13 8 I 140 = 28 X 5 1 4 j\ = 247-^17 1 7 t ' = 140 -H 8 "^ ** ~ ISB 234| 98| 4 9 = 1 6 3 8 = 98 X T) 234 X 7 2 81f = 182 = 29 82 If 490 ~ 1638 -^ 9 3 19 14 Ans. 564 jSj'^, Ans. Explanation. — First multiply the upper nmnerator 13 by the lower whole number li), getting 247. Before this, write the denominator IT as a divisor. Next multiply the lower numerator 5 by the upper integer 28, getting 140. Before 140 write the denominator 8 as a divisor. Perform these divisions and write the results, 14Y"y and \7k, directly under- neath. Multiply 28 by 19 and write the result 532 as shown. Annex to 532 the product of \f by |. Add these numbers, and the sum will be the required product. The second example is solved in exactly the same manner. 43. Canceling in Fractional Work. — Cancelation is one of the most useful expedients in arithmetic, and pupils should be taught to apply it whenever it can be done with a'dvantage. This is more frequently possible, perhaps, in multiplying and dividing fractions than anywhere else, and when these two operations are combined. The following operations will illustrate what is meant: Example 1.— Divide § X H X 7j\ by 4| X 81 X ff- Solution.- (§ X 5| X ^j\) - (4i X 8f X ||) = ^ ^ '^' ^ " 8 X 29 X 84 X 5 X 7 X 33 9 X 5 X 1 1 X 24 X 58 X 28 V V' 1' 6 > V t* X ¥ X = ; = 11 Ans. 52 PEDAGOGICS OF ARITHMETIC. § 2 Explanation. — We first cancel 5 above and below. Then 33 above and 9x11 below are canceled with 3 below as a quotient. This 3 with 28 below will cancel S-l above. Finally, 29 in 58 gives 2 below; this 2 in 8 gives 4 above, and 4 in 24 gives 6 below. Example 3.— Find the value of (§ X f ) -^ (| X W ' also, of (| of |f) -f- ■^\. 1' >' 2 (5 ctf 2i\ .^ 9 — 5 sy 2i \/ H — 2 AnS Y Y 3 Example 3. — Find the value of 11^ -(«^- 2^) -also, of 81X101X171 V S V V V V 69 51 53 5 6 10 Solution. — "s^y^T-^ga-^ss-^so V V V 2 y '^' 2|Xl|-H ' ' 18|Xl4iXB/j, Solution.— \ '%' . ' ^'' = -\°- X A X § X | X f X | = f = U- Ans. 3X0 • 3 T T 1 1 ) Explanation. — f in the numerator is a divisor of -^^ and the result obtained is a divisor of *y^-. This requires what amounts to two inversions of f, which leaves it uninverted. The same is true of ^ in the denominator; it is a divisor of the entire numerator as well as of | of |. = I = 11. Ans. 44. Cancelation Simplified. — If an error is suspected in canceling, it is usually impossible to verify the work without writing the entire solution a second time. This is owing to the fact that the numbers are usually crossed out and quotients written above and below until all legibility is destroyed. These causes of confusion may be avoided partly by using check marks instead of crossing out figures, and partly by writing no imnecessary quotients. This is illus- trated in the following examples showing the two methods: Example 1.— Divide 73 X 56 X 54 X 77 by 33 X 63 X 24 X 43. Solution. — V 8 V V ^ 8 ^ XX 72 X 56 X 54 X 77 _ J^ x ^^ X ^^ X n _ . 33 X 63 X 24 X 43 - °- ^''^- 33 X ^3 X ^^ X 4? ~ § 2 PEDAGOGICS OF ARITHMETIC. 53 Explanation. — The solution on the right illustrates the objectionable method usually employed, while that on the left shows the proposed improvement. Begin by consider- ing the numbers above and below very attentively. Time thus spent is not lost. We see that 24 below is contained in 72 above just 3 times. Check 24 and 72, but do not write the quotient 3 — carry it in your mind. Divide 33 by this quotient 3, placing a check mark under the former. By the quotient 11 divide 77 above, checking as before. The quotient above is now 7. Divide 42 by 7, check 42 ; divide54by 6, and check; divide 63 by 9, and check; divide 56 by 7, and write the quotient 8. The check mark may be omitted where it is necessary to write a quotient. If it should be necessary to verify the work, everything except the original numbers may be easily erased. Example 2.— Find the value of 72x113X168x144x121 divided by 88 X 56 X 126 X 96 X 99. 4 3G V V V V „ 72X112X168X144X121 , . ^°^""'°^"- 88X56X126X96X99 = ^- ^"^- V V y V V Explanation, — Check 56 and 112; quotient 2 above. Check 96; quotient 48 below. Check 144; quotient 3 above. Check 126; quotient 42 below. Check 168; quotient 4 above. Check 88; quotient 22 below. Separate 22 into the factors 2 and 11 ; divide 72 by the 2 and write the quotient 36; with the factor 11 check 121; quotient 11 above. Check 99; quotient 9 below. Check 36; quotient 4 above. Write 4 as the answer. By proceeding with the factors somewhat differently, the entire solution may be finished without writing any quotient except the answer 4. V V 4 V V 72 X 112 X 168 X 144 X 121 88 X 56 X 126 X 96 X 99 V V V V V = 4. Ans. Explanation.— 88x99 = 8x9x11x11. Check 88 and 99. With 8X9 check 72; with 11x11 check 121. Check 56 and 112; quotient 2 above. Check 96; quotient 48 below. 54 PEDAGOGICS OF ARITHMETIC. § 2 Check 144; quotient 3 above. Check 13(3; quotient 42 below. Check 168; quotient 4 above. Write 4 as the answer. If the teacher should wish to use such an example for class work on the blackboard, it would be necessary only to erase the check marks each time the exercise is assigned to another pupil. How the entire work may be done without writing any quotient but the final result may be held before the class as the perfection of operation to be sought. This can- not be done advantageously if the final result is a fraction or a mixed number; nor, indeed, is it desirable. Accuracy should not be sacrificed for performance. 45. Inverting tlie Divisor in Division of Frac- tions. — As long as teachers are examined, one of the stand- ard questions that they will be required to answer will be, " In division of fractions why do you invert the divisor and multiply ? " It is not enough to say that multiplying by the reciprocal of a number is the same as dividing by the num- ber itself. It is one of those questions of which the difficulty lies in the fact that the matter is so simple. Proving the correctness of the rule for division of fractions is very much like proving an axiom. Perhaps there is no way more easy to be understood than the following method by induction: Since 8 dollars divided by 2 dollars gives a quotient of f , or 4 ; and, since 8 days divided by 2 days gives also a quo- tient of f , or 4, we may conclude that 8 things of any kind divided by 2 things of the same kind will give the same quotient 4. Hence, 8 thirds divided by 2 thirds^ or •|-^-|, equals 4; also-V«--^f = 10-^3 = Jt^. Further, 10- ^3 10 — 3 • 9_ _- 8- -9 = f ; 12- -10 = 1 2 TO 5 -— J-"- - .15 — • "If" — 10 ■|2_^01 — 5_^.5 — in_:_15 — lO-^lfi — 10 I3 . ^., — 3 . 2 — -g- . -5- — IW . 1,J _ j^. Now in each of these divisions the result would have been the same if the divisor had been inverted and the operation changed to multiplication. (It must be remembered, how- ever, that any integral quantity may be written as a fraction *o 2 whose denominator is 1. Thus, $5 = -— , 2 = -, etc.) § 2 PEDAGOGICvS OF ARITHMETIC. 55 Taking- in order the foregoing examples, , , „ 8 dollars 8 dollars 1 8 8 dollars -f- 2 dollars = = -r X^i,, =5 = 4; 2 dollars 1 2 dollars 2 8 days 8 days 1 8 8 days -^ 2 days = irzr^ =T X^i i =o = 4; 2 days 1 2 days 2 V U O W •-* Q 8 thirds -r- 2 thirds = '.^ -- ^ = - X [^ = :i = 4 ; V ,„ , 10 7 10 2 3 2 4 8 10_!_3 — V- — • : — — V— — • ■r ■ T - q ^3- s' 'S- 4 3^3~9' . , 4 3 12 ,,' .^, 5 5 5 2 10 5 -3-5^2" 10" ' ' -~3'2 3^5 ~ 15' Since, when the denominators are the same, we divide the numerator of the dividend by the numerator of the divisor in order to divide the dividend by the divisor; and, since the same result is obtained by inverting the terms of the divisor and multiplying, we infer the following by induction : Rule. — Invert the tci'ins of the divisor and proceed as in inultiplieatioji. 46. Greatest Coninion Divisor of Fractions. — In studying the subjects of the Greatest Common Divisor and the Least Common Multiple of whole numbers, pupils are very likely to inquire about the method to be pursued in the case of fractions and mixed numbers. For the teacher to be unable to answer such inquiries satisfactorily is not only embarassing, but it loses him a certain prestige of the highest value. Moreover, there are frequent occasions in practice when the process must be applied. For these reasons the subjects will be explained. It is first important to indicate exactly what is intended by the expression at the head of this article. This may best be done by recalling the matter with respect to integers. Definition. — T/ie greatest conn/ion divisor (G. C. D.) of two or more whole numbers is the greatest wJiole number that will divide each of the numbers and give an integral quotient. Thus, since 12 is the greatest whole number that will exactly divide 36, GO, and OG, it is the greatest common divisor (G. C. D.) of 36, 60, and 96. 56 PEDAGOGICS OF ARITHMETIC. § 2 Definition. — The greatest conivion divisor [G. C. D.) of tivo or more fractional numbers is the greatest fraetional mimber that ivill divide each of the numbers and give an integral qnotioit. Thus, the G. C. D. of 2%, \\, and f f is ■^-^, since if these fractions be in turn divided by /g-, the respective quotients are the whole numbers 2, 3, and 7. If -^^ were not the G. C. D., 2,' 3, and 7 would have a common integral factor greater than 1. It is evident from the foregoing that when several fractions have the same denominator, their G. C. D. is a fraction having the same denominator as the fractions, and a numerator equal to the G. C. D. of the numerators of the fractions. This may be more fully shown by solving some examples. Example 1. — Find the greatest common divisor of |, |, and y'j. ^ 3 3, 12 15 18 ^ ,^ ^ ,12,15,18 „ . Solution.— |, |, ^^ = _, — , _. G. C. D. of ^ = 2%- Ans. Explanation. — The fractions are first changed to equiva- lent fractions having the L. C. D. Then it is evident that the G. C. D. of if, \%, and \\ is also the G. C. D. of f , |, and -^-^. But we know by inspection that the G. C. D. of 12, 15, and 18 twentieths is 3 twentieths. Example 2.— Find the G. C. D. of 6f, 4|, 4i, and 6|. Solution.— 6|, 4i, 4i 6| = ^j^, %, ~, ~. 4' _ 5 5 4 2 5 5 G. C. D. of 27, 9, 21, 33 _ ^ . L. C. M. of 4, 2, 5, 5 ~ 20' "^" Explanation. — Reduce the numbers to improper fractions. Find the G. C. D. of the numerators, and write the result over the L. C. M. of the denominators. To show that there will be an integral quotient when each of the numbers is divided by the G. C. D. , the division may be performed : 6f^^ = 5xf = 45;4i-^^ = |xf = 30; ^6 • 2W - 5 X 3 - -», O5 . ,^ - g X 3 - 44. § 2 PEDAGOGICS OF ARITHMETIC. 57 Now, since these quotients, 45, 30, 28, and 44, have no other integral common divisor greater than 1, it follows that y\ is the (CJ'catcst common divisor of the given numbers. EXAMPLES FOR PRACTICE. 4: < . Find the greatest common divisor of the following: [a) s 5 5' 2 3- {e) 51- 4? ^8' 16|. r(«) 1 T2- (^) (^) 4 5- |. 8 T5- (/) 5 * 101, 12^. Ans. - (^) A- (/) ic) 5 6' 5 5' 1 27- U) 7i 4f, m- (0 5 51- U) {d) 3 6 7' 15 2 8- (/o 3|. si, A\. U^o 3 2 8- (/') 48. Least Common Multiple of Fractions. — Very similar to the process of finding the greatest common divisor of fractions is that of finding their least common multiple. Definition. — The least comuion multiple {L. C. M.) of two or more fraetional Jiumbers is the least fiuviber, integral or fractional, that z^'ill contain each of them a zvhole nninber of times. Example 1. — Find the least common multiple of |, |, |, and |. Solution. — 5 — 2? ' ? — 2? ' g ~ 2? ' 8 — 2^ L. C. M. of 16, 18, 20, 15 = 720. ^ ^ ^^ ^ 16 18 20 15 720 ^^ , L. C. M. of ^^, _, ^, _ = _ = 30. Ans. Explanation, — Reducing the fractions to equivalent fractions having the L. C. D. , we have IG, 18, 20, and 15 twenty-fourths. Now it is evident that the L. C. M. is a number of twenty-fourths equal to the L. C. M. of the numerators. This same result may be obtained by writing the fractions in their simplest forms, and then dividing the L. C. M. of the numerators by the G. C. D. of the denominators. ^, L. C. M. of 2, 3, 5, 5 30 „,, . ^^"^- G.C.D.of3.4,6.8 = T=^'^- ^"^- The former method is to be preferred, for if any of the fractions is not in its simplest form, the result, although it is a common multiple, is not the least common multiple. 58 PEDAGOGICS OF ARITHMETIC. § 2 Suppose, for example, f be written as y\, and the other frac- tions be in simplest form. L. C. M. of 8. 3, 5. 5 _ 120 _ G. C. D. of 12, 4, 6, 8 ~ 2 ~ ' Again, let both | and | be written as twelfths. L. C. M. of 8. 9. 5, 5 _ 360 _ G. C. D. of 12, 12, 6, 8 ~ ^ ~ Example 2. — Find the least common multiple of li, 2g, and 2|. Solution.— l?, = |; 2| = V; 2| = V- AT „C /I 10 ie ,tU 48. Ans. L. C. M. of 4, 12, 16 48 G. C. D. of 3, 5, 7 1 EXAMPLES lOU PRACTICE. 49. Find the least common multiple of the following: (a) g- 15 • ('-) 2 3 8 3' 3' 9- {t>) 8 5' 3 (7) .5 7 14 g- T3' 15- A (0 4',, n- (M) 03 Q5 71 -J. Og, (j. (^0 or, ~8' H- (/o 11 2 fJ2 't' ■^i' "S- ' ('0 311. (^■) 24. ns. "1 1 (0 24. 18. (/') (A-) 231. 79|. 1 L('0 147. (/O 120. DENC)>riX.\TE NUMHERS. 50. ISIattc^rs Important and Unimportant in Denom- inate Xnmbers. — Perhaps more time is wasted in the study of unimportant matters in denominate numbers than in any other arithmetical subject. Some of these are English money, and addition, multiplication, and division of compound num- bers. In business operations, the only use for subtraction of compound numbers is in finding- the difference between dates, but the more exact method now employed by business men obviates the necessity for the plan of twenty years ago. About the only other use for subtraction of compound num- bers is in finding the difference between two angles, in trig'onometrical calculations. For retaining English money in our arithmetics, there is no reason that is not equally good for German, French, or Spanish money. When this country was merely a colony of England and the coinage of the mother country was in use § 2 PEDAGOGICS OF ARITHMETIC. 59 here, our boys and girls had to be taught to count it ; but when we adopted the decimal system and discarded the coinage of England, the subject might have been omitted from our textbooks. Unless one visits Europe, he never has the slightest need to know about pounds, shillings, and pence, and even that event furnishes an equally good argument for studying the coinage of European countries other than England. The retention of the subject in our books illustrates how conservative we are, notwithstanding our boasted progress. For many years the coinage of Spain was in use here, but we never introduced it into our school books. It is difficult to imagine a situation in actual business in which it would be necessary to add, multiply, or divide denom- inate numbers. The same may be said of reduction a,scend- ing, so called, and reduction descending. The important thing is to have the pupil perfectly familiar with the useful tables. In learning them, he should, as far as is possible, see and handle the weights and measures actually used in busi- ness. The measures of length, surface, and volume he can easily and profitably make for himself. The dimensions of the class room, the areas of floors, walls, and ceilings, and the volumes of various rectangular spaces may be found by the pupils themselves, and thus they will become familiar with the most important units of mea.surement. The measures of capacity can be procured without much expense, and after they have been obtained they should last indefinitely. 51. Order. — If any particular order is preferable in pre- senting the tables of denominate numbers, it is perhaps the following : 1. Measures of Length. 2 Measures of Surface. (^? Space. 3. Measures of Volume. 1 Wood. Stone. 4. Measures of Capacity. W^ 'l^> Liquid. Dry. 60 PEDAGOGICS OF ARITHMETIC. S 2 5. Measures of Weight. 'a - b Avoirdupois. Troy. 6. Time. 1 Apothecaries 7. 8. Counting. Stationery. {a Lumber. b Plastering. 9. Practical Measurements. { c Painting-. d Shingling. c Lathing, etc. If reduction involving decimals were excluded from our courses of study, there would be undoubted gain. Nobody has ever been required by the exigencies of business to change .87 of a year to units of lower denomination, or to reduce 17 days 5 hours 31 minutes and 19 seconds to the decimal of a year. There are so many things having a direct and important bearing upon the concerns of life, that it seems a pity to fritter away valuable time with matters of no consequence. 53. Classiflcatioii of tlie Processes of Denominate Numbers. — All the operations in denominate numbers may be referred to two main classes. These are : 1. Reduction. — Of reduction there are two kinds, {a) reduction descending, and (/;") reduction ascending. 2. Fundamental Operations. — The fundamental opera- tions with denominate numbers include {a) addition, {b) subtraction, {c) multiplication, and {d^ division. All these processes are important, and should be thoroughly taught. Especially important is it that the pupil should know the best and briefest methods, and an arrangement of work least likely to lead to error and confusion; for with units of meas- ure that change with each advance from lower to higher, denominate numbers will always be to most pupils a trouble- some subject. On account of this fact, examples with their solution, illustrating every operation likely to be met in denominate numbers will now be given. § 2 PEDAGOGICS OF ARITHMETIC. 61 53. Keduetioii Descending;. — Before entering upon the solution of examples, the student should carefully note the following definitions: Definition. — The reduction of a denominate number is the process of changing its denomination without altering its value. Thus, changing miles to feet, or quarts to bushels is reduc- tion. Definition. — Reduction desceruling is the process of chang- ing a denoini)iate number to an equivalent denominate nundn-r of lower denomifiation. Thus, changing miles to inches, or years to hours or minutes is reduction descending. Definition. — Reduction ascending is the process of chang- ing a denominate number to an equivalent denominate number of higher denomination. Thus, changing pounds to tons, or square feet to acres or square miles is reduction ascending. There are two cases of reduction descending: 1. To reduce a compound denominate number to lower denominations. Example 1. — Change 3 mi. 189 rd. 5 yd. 2 ft. to inches. Solution.— 3 mi. 189 rd. 5 yd. 2 ft. 320 1149 5 1 rd. 5 74 1 5750 " 6 3 2 4 1 3" yd. 18975 1 1 2 ft. 2 2 7 7 6 in. Ans. Explanation. — Change 3 miles 189 rods to rods by mul- tiplying the number of miles by 330 and adding 189 to the product. This should be done in one operation. Change 1,149 rods 5 yards to yards by multiplying the number of 62 PEDAGOGICS OF ARITHMETIC. § 3 rods by 5^ and adding 5 to the product. In doing this mul- tiply first by ^. Change (:;,32-4^ yards 2 feet to feet by multi- plying the number of yards by 3 and adding 2 to the product. Change the feet to inches by multiplying the number of feet by 12. 2. To reduce a doiomiiiate fraction to integers of loiver denouiinatioii. There are two slightly different varieties of this case: [a) when the fraction is a common fraction; (/;) when the fraction is a decimal. These cases are both exemplified below. Example 2. — Reduce f of a mile to integers of lower denomination. Soi-UTioN. — 5 mi. 320 6)1600(266 rd. 4 6)22 ( 3 yd. 4 3 6 ) 1 2 ( 2 ft. Explanation. — f «£ 1 ""^ilc is i of 5 miles. Change 5 miles to rods and divide by (i. Change the remaining 4 rods to yards and divide by 0. Change the remaining 4 yards to feet and divide by 6. In dividing write only quotients and remainders. E.XAMPLE 3.— Reduce .90625 of a gallon to integers of lower denomi- nation. Solution.— .906 2 5 gal. 4 3.62500 qt. 2 1.2 5 pt. 4 1.0 gi. 3 qt. 1 pt. 1 gi. Ans. Explanation. — Since a part of a gallon expressed dec- imally is reduced to quarts in exactly the same way as a whole number of gallons, we multiply by 4, and point off 2 PEDAGOGICS OF ARITHMETIC. 63 5 places in the product. Next, reduce .025 quarts to pints, and finally, .'25 pints to gills. Note that the part of the product falling to the left of the decimal is not multiplied. 54. Reduction Ascending. — There are two well defined cases of reduction ascending, and a third case that may properly be referred to this division. 1. To reduce a deiiouiiiiate number to higJier de)iouii)ia- tions. Example 1. — Change 98,329 inches to higher denominations. Solution. 12 3 5 1 1 320 3 2 9 in. 1 !t 4 ft. 1 in. 2 7 8 1 vd. 1 ft. 5 4 6 2 half -yd. 4 9 6 rd., (j half-yd. = 8 yd. 1 mi. 176 rd. 1 mi. 176 rd. 3 yd. 1 ft. 1 in. Ans. 2. To reduce a denominate fraction, common or decimal, to an equivalent fraction of higher denomination. Example 2. — Change 4^ feet to the fraction of a mile. Also .75 of a pint to the decimal of a gallon. Solution.— ^ -^ 16| -f- 320 = f X u's X sh = Ans. Explanation. — Dividing the feet by 10^ changes to rods, and dividing that result by 320 changes to miles, as required. The steps in the process are obvious. Solution.^ .7 5 pt. .3 7 5 qt. .09375 gal. Ans. Explanation. — The process and the reasons for it are exactly the same as with integers, except that care is required with reference to the decimal point. Note that the second point stands directly under the first, and the third tmder the second. 3. To reduce a compound denouiinate number to a fraction of some other compound denominate )t umber of greater value. 64 PEDAGOGICS OF ARITHMETIC. § 2 Example 3. — What common and what decimal fraction denotes the part that 1 bu. 1 pk. 3 qt. 1 pt. is of 2 bu. ? Solution.— 1 bu. 1 pk. 3 qt. 1 pt. _ 87 pt. 87 2 bu. 128 pt. 128 -V- 128 - .6796875. Ans. Ans. 55, Addition of Coiiii)oiiiid Deiioininate Numbers. The student can have no difficulty with the addition of com- pound denominate numbers, unless it be in examples like the following: Example 1. — Find the sum of 59 mi. 95 rd. 4 yd. 2 ft. 9 in., 97 mi. 200 rd. 3 yd. 1 ft. 8 in., 75 mi. 171 rd. 2 ft. 5 in. Solution. — niL 5 9 rd. 9 5 yd. 4 ft. 2 in. 9 97 200 3 1 8 7 5 1 71 2 5 232 147 3 1 1 1 - = 1 6 23 2 147 3 2 4 Explanation. — The first column = 22 inches, or 1 foot 10 inches. Write 10 inches and carry 1 foot to the next column. The second column = 2 yards feet. Write feet and carry 2 yards to the next column. The column of yards = 9 yards, or 1 rod 3|- yards. Write 3^ yards and carry 1 rod to the next column. The next column = 467 rods, or 1 mile 147 rods. Write 147 rods and carry 1 mile to the next column. The last column = 232 miles, which is to be written under the last column. Finally, ^ yard = 1 foot 6 inches, which must be written under the proper columns and added. 56. Subtraction of Componnd Denominate Num- bers. — The chief interest and use of subtraction of denomi- nate numbers is in finding- the difference between dates. The following method, which counts 12 months of 30 days each as making a year, was exclusively used: Example 2. — A certain man was born February 12, 1822, and died January 5, 1890. How long did he live ? Solution. — yr. mo. da. 1890 1 5 18 2 2 2 12 67 10 23 § 2 PEDAGOGICS OF ARITHMETIC. 65 Explanation. — The second column shows the ntimber or place of the months mentioned. Thus, January is the first month, February is the second month, and so on. Since 12 days cannot be taken from 5 days, it is necessary to bor- row 1 month, 30 days, from the column of months. This is added to the 5 days and 12 days subtracted from the sum, leaving 23 days. The month borrowed reduced the 1 month in the minuend to 0. vSince 2 months cannot be taken from months, we borrow 1 year from 1890 years, leaving- 1889 years. Subtracting, now, the 2 months from 1 year, or 12 months, we have 10 months. Finally, we subtract 1822 years from 1889 years, and write the remainder, 07 years, as the last item of the answer. There are three methods of finding the difference between two dates. One of these is the method shown above. The other two have come into u-se in calculating exact interest, which is now employed by the United States Government and by most banks. This method assumes that there are 365 or 366 days in a year and not 360 days. It is gaining rapidly in favor among business men, and will doubtless be adopted imiversally. To show the three methods together we shall now give the solution of the same example by each method. Example 3. — Find the time from January 29, 1883, to August 15, 1884. Solution. — {a) First method. yr. mo. da. 1884 8 15 1882 1 29 3 6 16 Explanation. — The years, months, and days are written and subtracted as already explained, giving 2 years, 6 months, and 16 days. {b) Second method. Jan. 29, 1883, to Jan. 29, 1884 = 2 yr. \ Jan. 29, 1884, to July 39, 1884 = 6 mo. [ Ans. July 29, 1884, to Aug. 15, 1884 = 17 da. ) Explanation. — The number of whole years is first found — 2 years. Next, the number of whole months included 6G PEDAGOGICvS OF ARITHMETIC. § 2 between January 29, 1884, and August 15, 1884. This is 6 months. Finally, the days from the end of the 6 whole months to the end of the time, August 15, or 17 days. This is 1 day more than the result obtained by the first method. (t) Third tnef/iod. Jan. 29, 1882, to Jan. 29, 1884 = 2 yr. Jan. F'eb. Mar. Apr. May June July Aug. 2 + 29 + 31 + 30 + 31 + 30 + 31 + 15 = 199 da. Explanation. — The number of whole years is first foimd, and then the number of days. In estimating exact interest the third method is usually employed. By this method, 2 years 199 days is regarded as 2^ff years. When, however, the period ends within a leap year, and after February 28, the denominator of the fraction is IJGG. In the case of the foregoing example, since the time ends in August, 1884, a leap year, the result is regarded for the .second method as 2^ years + -^^ years. By the third method it is 2^f years. The following example illustrates a method of solution in which it is sometimes necessary to borrow more than one unit from the next higher denomination : Example 4. — After traveling 20 mi. 400 rd. 10 yd. IT ft. 20 in., how much farther will make a distance of 30 miles ? Solution. — mi. rd. yd. ft. in. 3 20 400 10 17 2 ~8 2^6 5 2 4 Explanation. — First borrow 2 feet, or 24 inches. Then borrow 7 yards, or 21 feet, and subtract 17 feet + 2 feet borrowed. Next, borrow 4 rods, or 22 yards, and subtract 10 yards + 7 yards borrowed. Borrow 2 miles, or 640 rods, and subtract 400 rods + 4 rods borrowed. Finally, subtract 20 miles + 2 miles borrowed. The example might have been solved by reducing the subtrahend to 21 mi. 82 rd. 5 yd. ft. 8 in., and then subtract- ing in the usual way. Or, the minuend might have been written as 28 mi. 636 rd. 15 yd. 19 ft. 24 in. § 2 PEDAGOGICvS OF ARITHMETIC. 07 57. Multiplication of Denominate Xunibers. — Ordinary multiplication of denominate numbers involves no principle of reduction not included in addition of denom- inate numbers; for, as is well known, multiplication is in reality only the process of adding two or more equal nimi- bers. Formerly, however, there was a process employed by artificers in finding areas and volumes when dimensions were given in feet and duodecimal divisions of a foot. This process was called duodecimals, but it is no longer used to any extent. The notation of duodecimals was formerly somewhat dif- ferent from what it is now. The table as found in the old works on mensuration reads as follows: 12 fourths ("") = 1 third, written 1'", 12 thirds = 1 second, " 1", 12 seconds = 1 inch, or prime, " 1 in. or 1', 12 inches = 1 foot. " 1 ft. The only duodecimal divisions now in general use are the foot and iiicJi ; the abbreviations for these are ft. or ', and in. or ". Thus, the dimensions of a joist 20 feet long, 6 inches wide, and 4 inches thick may be written 20'x'Vx4''. In order to show the operation of multiplying duodecimals, the following example will be solved by the method formerly employed and by that used at present. Example. — Find the area of a floor 20 ft. 7 in. long and 16 ft. Sin. wide. Solution. — Explanation. — Beginning at the right, 8'x7' = 5()" = 4' 8". This means that 56 square inches = 4 strips each 12 inches long and 1 inch wide, and 8 square inches besides. We write 8" and carry the 4'. 20 ft. X 8' = 1(30' (strips 12 inches long and 1 inch wide) = 13 square feet 8'. Next we multiply by 10; 10 ft. x7' = 112' = square feet 4'. We write 4' and carry 9 square feet. .sq. ft. + 20 ft. x 10 ft. = 329 square feet. The addition of the partial products is obvious. In this result, 8" = |^, or | = ^ .sq. ft. = ^ sq. ft. 2 ft. 1 6 ft. 7' 8' 1 3 sq. 32 9 •' ft. 8' 4' 8" 3 4 3 sq. ft. 0' 8" G8 PEDAGOGICvS OF ARITHMETIC. §2 Hence, the answer is the same as would be obtained by the ordinary process. Thus, (20 ft. 7 in.) X (16 ft. 8 in.) = 20yV ft. X 16| ft. = 343yV sq. ft. The teacher will remember that, strictly speaking, feet cannot be multiplied by feet or inches by inches. The multiplier is always abstract and the product is of the same denomination as the multiplicand. In finding- areas and volumes we are told to multiply together certain dimensions }. * ittr. H expressed in linear units, such as yards, feet, inches, Area of rectanfile=4 1 sq. i/n. sq.m.x.3=12 sq.in. 1 sq. in. 1 sq.i'H. 1 sq.in. Fig. meters, etc. But we do not, in reality, perform any such multiplication. This fact will be apparent from the diagram. Fig. 7. This represents a rectangle 4"x3". By drawing lines, this rectangle may be divi- ded into three rows each containing 4 square inches. Since one row contains 4 square inches, 3 rows will contain 3 times 4 square inches. When areas, then, seem to be found by multiplying inches by inches, feet by feet, etc., nothing of the kind happens. A similar explanation of the rule for volumes may be made and illus- trated by a drawing. 58. Division of Denominate !N"unibei's. — There are two general cases of division of denominate numbers. 1. To divide a compound denominate number by an abstract number. Example 1.— Divide 17 mi. 189 rd. 4 yd. 3 ft. 9 in. by 13. Solution. — mi, 13)17 rd. 1 89 yd. 4 Explanation. — 17 miles divided by 12 gives 1 mile with 5 miles remaining. 5 miles -j- 189 rods = 1,789 rods. This divided by 12 gives 149 rods with 1 rod remaining. 1 rod + 4 yards = 9|- yards. 9|- yards divided by 12 gives yards with a 149 8 7i § 2 PEDAGOGICS OF ARITHMETIC. 69 remainder of 9.V yards. The sum of 9i yards and 2 feet = 30|- feet. This divided by 12 gives 2 feet with a remain- der of G|- feet. The sum of 6^ feet and inches = 87 inches. Dividing 87 inches by 12 gives a quotient of 7^ inches. 2. 7^0 divide one compound denominate ninnber by another of the same e/ass. Example 2. — In how many weeks at 18s. lid. per week can a person earn £25 10s. 9d. ? £25 10s. 9d. 6129d. ^^ . Solution.— — r^ — jj^ = - ...r.^ - ==2/. Ans. 18s. lid. 227d. Explanation, — The dividend and divisor are both reduced to the same denomination, and the quotient is then found in the ordinary way. Under this case may be included the division of a denomi- nate fraction, common or decimal, by another denominate fraction of the same class. This is substantially the second case under reduction ascending, which has already been exemplified and explained. 59. Abbreviations iii Denominate Numbers. — There is, perhaps, no question relating to the exact sciences that is more unsettled than that concerning the form in which abbreviations for the various denominate numbers should be written. This is shown more in the plural than in the singular forms. A few illustrations will make the matter apparent. The Standard Dictionary gives the following singular and plural forms for barrel : singular, brl. , bl., bar., bbl. ; plural, brls., bis., bbls. Now it is evident that there is no real need for more than two of these seven forms; it is not, however, clear which two are best. The dictionary is supposed to reveal current authorized usage, and, doubtless, it does so; but it is unfortunate that there are so many ways of denoting the same thing when the result is only con- fusion and uncertainty. Every teacher should have a well considered scheme of abbreviations from which he never varies. The Inter- national Correspondence Schools have adopted the rule that 70 PEDAGOGICS OF ARITHMETIC. § 2 "all abbreviations of the names of denominate ninnbers are to be printed in the sing-ular form." The reason for this is that the sing-ular form is usually the simplest, and, if intelli- gible and in general use, the simplest form is always the best. The only dii^iculty arising in the application of this rule is in cases where there are two or more singular abbreviations for the same word. Thus, the word barrel is variously abbreviated in the singular by bar.^ bl., brl., and bbl. In such cases, the student should prefer the simplest form unless there is another having more general currency. Of the four abbreviations given above there is no doubt that bbl. should have the preference. 60. Abbreviations in tbe Metric System. — The sys- tem of abbreviations used for the metric system is a good one; indeed, it would not be easy to imagine how it could be improved. It is very simple and imambiguous. For linear measures, including the millimeter, centimeter, deci- meter, meter, decameter, hectometer, kilometer, and myria- meter, the respective abbreviations are mm., cm., dm., m,, Dm., Hm., Km., and Mm. The abbreviations for square and for ciibic measure are the same, with exponents. Thus, mm"., m^, Hm". , etc., and cm\, ml (stere) denote respect- ively square millimeter, square meter, square hectometer, or hectare, cubic centimeter, and cubic meter. For the measures of weight and capacity, we have the principal units, the gram (g.) and the liter (1.), besides the following : Milli Centi Deci Deca Hecto Kilo Myria The student will note that measures greater than the principal unit in each table begin their abbreviations with capitals and all the others begin with small letters. It will gram: mg., eg., dg., g., Dg., Hg., Kg., Mg. liter: ml., cl., dh, 1., Dl., HI., Kl., Ml. § 2 PEDAGOGICS OF ARITHMETIC. 71 be observed, too, that the names of the measures below and including the principal unit are formed with Latin prefixes, while those that are greater than the pi'lncipal unit have Greek prefixes. The former are inilli, ccnti, and dcci ; the latter are dixa {StKa, deka), hecto {eKarov, hekaton), /:i7o {jiXioi, chilioi), viyria (iivpioi, myrioi). PERCENTAGE. 61. Importance of Percentage. — There is no subject in the whole compass of arithmetic of so much practical value as that of percentage. Its application to every variety of business in which men are engaged renders it imperative that whatever matter is neglected in the education of our children, this must not be one of them. If percentage' be well mastered, it is almost a foregone conclusion that the other subjects will be. The decimal system, which is the basis of percentage, has no more convincing illustration of its value than we find here. Our advice to the teacher would be to review the subject until the pupil is familiar with every phase and modification of it. While a certain incurable con- servatism prevents us from availing ourselves of the incal- culable advantage of a general application of the decimal systein to the concerns of life, we should utilize it in the fullest measure in which it has been accepted. 62. Three Methods in Percentage. — There are three quite distinct methods of solving examples in percentage : (1) the decimal method; (3) the method by covimon frac- tions^ or analysis; (o) the method hy formulas. Each of these methods has its advocates among teachers, and there is little probability that the question of superiority will ever be settled. It is highly probable that they are of nearly equal general importance, while for each particular problem to be solved, one of the three plans is specially suited, and is therefore better for that problem than either of the other two. If this view be correct, then it is clear that all three should be carefully taught, and that the pupil's mastery of 72 PEDAGOGICS OF ARITHMETIC. § 2 each should be so full that he can judge correctly which method is best for each particular problem. There are so many applications of percentage both with and without the element of time that there is abundant opportunity to learn all three of the methods. These three methods will now be explained and exemplified. 63. The Decimal Method of Percentage. — Since the word percentage is derived from the two Latin words, per, " by " or " on, " and ccntiun, ' ' a hundred, " its meaning makes clear that the subject relates to decimal {licccm, "ten") matters. Twenty-five per centiun means no more than 25 on 100, and this expressed in the ordinary decimal notation is .25. vSo that to find any per cent, of a number is merely a case of multiplication of decimals — usually the finding of so many hundredths. A few examples will serve to show exactly what is meant by the decimal method of percentage. Example 1. — A man bought a house for §8,675 and sold it at a gain of 35^. What did he gain by the transaction ? Solution. — 18 6 7 5 Explanation. — A gain of 35^ is a gain •^ ^ of .35 of the amount invested. Multiply- ^ ^ ^ ' ^ ing the investment by 35 resfarded as hun- 26025 dredths, and pointing off two places at the $ 3 3 6.2 5 Ans. • ^ ^ c ^\. a ^ • ^-^ • • j right of the product gives the gam required. Or; a gain of 35^ is a gain of 135 on llOO, equal to a gain of $.35 on each II invested. Since the investment is 8,G7o times $1, the gain will be 8,675 times 1.35, or 13,036.25. Example 2. — If I gain §700 by the sale of a lot for which I paid §4,375, what do I gain per cent.? Solution. — 1 Q — i6«;. Ans. Explanation. — Since on § 4 3 7 5 ) § 7 0.0^ ^^^ 375 there is a gain of 1700, 2 6 2 5 on $1 there is a gain of j-^j-^ of 1700, and on 1100 there is a gain of 100 times ^ ..^ g of 700. This is the same as -^yz of 100 times 1700, or 116. But a gain of |16 on |100 is a gain of 16^. 2 PEDAGOGICvS OF ARITHMETIC. 73 Example 3.— receive for it §1 Solution. — $10 .1 25) §1 264. 1 500 7 50 -By selling my house and lot at a gain of 12J^ I should ,264.50 more than I paid for it. What did I pay for it ? 116 Ans. Explanation. — Since 12^^, or. 125 of the cost of the house is the gain, or 11,204.50, .001 of the cost is yfg- of the gain, or 110.116, and 1,000 times this, or $10,11(3, is the entire cost required. This result is obtained by dividing $1,204.50 by .125, as in ordinary div'ision of decimals. Example 4. — How much will a lathe catalogued at §850 bring if sold at a discount of 40;?:, 20,'?:, and lOf^ ? Solution.— §850 X (1-00 - .40) X (1.00 -.20) X (1.00 -.10) = §850 X .6 X .8 X .9 = §367.20. Ans. Explanation. — If the lathe catalogtied at 1850 were gold at a discount of 40^, it would bring . 6 of $850 ; if this price were reduced 20^, the amount received woitld be ,8 of .6 of $850; and if still another reduction amounting to 10,^ were made, the sum needed to pay for the lathe would be .9 of . 8 of .6 of $850, which amounts to $307.20. It is clear that the operation is only a case of multiplication of decimals. 64, The Method by Common Fractions. — This method has the advantages of being well adapted to oral analysis and of being easy to teach and to understand. The essential condition of using it easily and rapidly is that the student shall be perfectly familiar with all the aliquot parts of 100^ and their value as expressed in equivalent common fractions. These aliquot parts, certain of their multiples, and their equivalents are shown in the following table : 4% = .04 = sV 18|^ = .1875 = ^\ 561/^ = .5625 5% - .05 = ,V 20^ = •3 = i 60;^ = .6 m = .0625 = ,V 25^ = .25 = J 621^ = .625 8Xfo = .081 =,V ^\\i = .3125 = j% 66|^ = .661 10^ = •1 = tV 331^ = .331 = 1 70^ = .7 in% = •IH = \ ?^l\fo = .375 = 1 75:^ = .75 m% = .125 = 1 m = •4 = 1 80;^ = .8 14S^ = .14f = 4 43f^ = .4375 = ,V 831^ = .831 i6k = •16| - \ 50jg = .5 =1 8n% = .875 7-t PEDAGOGICS OF ARITHMETIC. g 2 Some of the parts given above are not much used either in decimal or in fractional form, yet it is of some importance that the teacher, if not the pupil, should be familiar with them. The manner of using them may be seen from the following examples: Example 1. — A man sold a horse for !S130, losing by the transaction iy|^'. What par cent, would he have gained if he had sold it for §180 ? Analysis. — Since he lost 1S^%, or j\r of the cost of the horse, he must have sold it for ^| of the cost. Then $130 is || of the cost; y\ of the cost is yig of §130, or §10, and the cost is 16 times §10, or §160. If he had sold it for §180, he would have gained on §160, the cost, the differ- ence between §180 and §160, or §20. If on §160 there is a gain of §20, on §1 there is a gain of ^i^ of §20, or §^-/^, equal to §J . A gain of | on 1 is a gain of 121%. •ExAMPLK 2. — For how much must a sleigh that cost §275 be sold to gain 20,'? ? Analysis. — A gain of 20$^ is a gain of J of the cost; i of §275 is §55 ; this added to §275, the cost, gives §330, the selling price required. Example 3.-^1 sold my house at a loss of 37^^/, receiving for it only $5,500; find its cost. Analysis. — To lose 371;^ is to lose f of the cost. Hence, I received f of -the cost of the house. This being §5,500, i of the cost is l of §5,500, or $1,100; and the cost is, therefore, 8 times $1,100, or §8,800. Example 4. — A dealer sold two stoves at $30 each; on one he lost 20j?, and on the other he gained 20rf. Did he gain or lose, and how much ? Analysis. — He lost 20;?, or J on one stove; he therefore received for it I of its cost. Hence, $30 was 4 of the cost of that stove ; i of its cost was 1 of $30, or $7i, and its cost, |, was 5 times $7i, or §37i. By selling the other stove for $30 he gained 20^, or ^ of its cost. The amount received for it, §30, was f of its cost ; i of §30, or §5, was i of the cost, and the cost, |, was 5 times §5, or $25. Since he received for them $30 + $30, or $60, and paid for them $37| + §25, or $62i, he lost §621 -$60 or $2 J. These examples are sufficient to show how readily the cases of percentage may be resolved by the method of analysis. § 2 PEDAGOGICS OF ARITHMETIC. 75 65. The Method hy P'orniulas. — This method of per- centage rec[uires only a slight knowledge of the equation, and this knowledge, on account of its extreme value in prac- tical computation, should be acquired as early as possible. In reducing formulated operations to their simplest numer- ical expression, cancelation is almost indispensable. The method of solving examples in percentage by means of formulas has, therefore, the effect of making pupils expert in cancelation, an operation that is too mvich neglected in school work. It is both interesting and instructive to derive from the fundamental formula the formulas covering the other cases. The process is very simple — so much so that the operation is easily within the mental scope of average pupils. From the formula, BxK 100 ' ^^ by multiplying both sides by 100, we have 100/^ = ^XA'; whence, n 1(10 7^ {^) 100 P \ — i'^) and It is scarcely necessary to say that />' = the base, or the sum on which the percentage is reckoned ; P — the percentage ; A' = the rate per hundred. If .^ = B-\-P, and B = B-P, by substituting in (1), xve have A = (I"^ + A)x/>- ^ ^^^ amount, (4) 100 ' \ f and n = (lOO-A)xA^ ^ ^j^^ difference. (5) 100 ' ^ ^ To illustrate the use of these formulas, a few examples will now be solved. 76 PEDAGOGICS OF ARITHMETIC. § 3 Example 1. — A man buys a lot for $900 and sells it at a gain of 15%. Find his gain. 9 900 V 15 Substituting in (1), P = -.Q. = $135. Ans. Example 2. — If I gain §720 by selling a property at an advance of 8%, how much did I pay for it ? 90 Substituting in (2), B = ""^ ^ ^^^ = $9,000. Ans. Example 3. — At how much gain per cent, must I sell a house that cost $8,000 to gain $480 ? 6 Substituting in (3), J^ = ""^o ]^,,f^ = 6j^. Ans. Example 4. — I paid $8,450 for a property and s :)ld it at a loss of 1Q%. What did I receive for it ? Here we use formula (5), JJ = ^- r-- . Substituting. ^^^^ ~ \y ^'^''''^ = .84 X $8,450 = $7,098. Ans. 66. Serial Discounts. — Within recent years it has become customary among business men to allow discounts in series such as 30^, 20fc, and 10^; 20^, 10^, and 5^; etc. The reason for this is that a discount so specified is really less than it seems. Thus, the first serial discount given above is not 30^ + ''^0^ + 10^) oi' QO^; in reality it is only 49.6^. Similarly, the series 40^, 30^, 20 fo, and 10 fc, which seems to be 100^, is only 69.76^. A serial discoimt, say of 20^, dOfc, and 25,^ is interpreted thus: 20^ of the full price, 100^, is first deducted, leaving 80;^ of it. Then, 30^ of this 80^, amounting to 24;^ of the entire price. Subtracting 24^ from 80^ leaves a remainder of 56^. Finally, 25^ of 56^ of the price is 14^ of it; these three reductions, instead of being 20^, 30^, and 25fo, or 75^, are really 20fc, 24^, and 14^, or 58^ of the price. Perhaps the best way to find the cost of an article on which a series of discounts is allowed is to find the continued product of the unreduced price and the remainders obtained by subtracting each of the several discounts from 100^. This may be shown by an example. § 2 PEDAGOGICS OF ARITHMETIC. 77 Example. — What must be paid, after a serial discount of 30$^, 25;?, 20;?, and 10;?;, for a piano of which the " long," or catalogue, price is $800 ? Solution.— §800 X -^ X -75 X -80 X .90 = $302.40. Ans. Or, $800 X t\f X I X t X t'u = $302.40. Explanation. — If the discount were oOfc, the cost would be 70^ of $800; if 25fo of this were thrown off, the remainder would be $800 X. 7 X. 75; if 20;^ of this were deducted, the remainder would be 1800 X . 7 X . 75 X . 8, and so on, as is shown in the solution. In order to find the single per cent, that is equivalent to a serial discount, it is evident that if the several remainders, obtained by subtracting from 1.00 the hundredths expressed by each discount in the series, be multiplied together, the resulting product will denote the hundredths that are to remain after the discount is dediicted. It is necessary, therefore, only to take this product from 1.00, and change the remainder into the corresponding per cent. Thus, let it be required to find the per cent, of discount that is equiv- alent to a serial discount of 30^, 25^, 20^, 10^, and 5^. (1.00 - .3)(1.00 - .25)(1.00 - .2) (1.00- . 1)(1.00 - .05) = .7X.75X.8X.9X. 95 = .3501; 1. 00-. 3591 = .0409 = 64.09^. Ans. 67. Applications of Pei'centag:e. — The applications of percentage are very extensive. This fact is owing to the great convenience of computations on the basis of one hundred. These different applications take many names in textbooks on arithmetic, but notwithstanding the inany names, examples illustrating the various applications may all be solved as cases of pure percentage. Moreover, these applications may all be included under two general classes: 1. Applications not including the clement of time. {a) Profit and Loss. {<-') Brokerage. {l>) Stocks and Bonds. (/) Insurance. {c) Premium and Dis- {g) Taxes. count. {h) Duties and Customs. {d) Commission. (0 Stock Investments. 78 PEDAGOGICS OF ARITHMETIC. § 2 2. Applications including the element of time. Equation of Payments. Averaging of Accounts. Compound Interest. Annuities. No two books can, perhaps, be found that will agree with respect to these names, but most arithmetics contain under some name all the foregoing applications of percentage. ('0 vSimple Interest. (/) (^) Partial Payments. {s) (0 Discount. {h) {d) Banking. (0 (0 Exchange. INTEREST. 68. Formulas. — If, in the formulas of percentage, the element R be resolved into r /, in which r denotes the annual rate and / the time in years, we obtain the formulas for every case in interest. The fundamental formula is Prt ' = w <') Multiplying both sides of this by 100, and dividing as in percentage, we obtain rt ' ^^ 100 / 100/ TV- (3) (4) For A and D, by remembering in ( 1 ) that A — P-\- /, and that D = P— /, we have "^ - — 100 ' ^^^ and D = ^^— — . (6) § 2 PEDAGOGICS OF ARITHMETIC. 70 (>9. Use of tlio Foriuulas. — Example 1. — Find the interest of $:-J,0()0 for 2 years 5 montlis 18 days at 3^. Solution. — 2 years 5 months 18 days = 3 years + -/j year + ._}jj year = 2/5, or f i years. $3,000X3X 37 _ 100 X 15 ~ ■ Example 3. — What principal in 3 years 3 months 15 days will give $790 interest at 8^^ ? 100 X §790 X 34 ^.., ,,,,^ . Solution.— F = ^ — ^ — = $3,000. Ans. 79 X 8 Example 3. — At what rate will §4,000 in 3 years 8 months 34 days give §656 interest ? 100 X §656 X 15 ^ , Solution.— r = ,. r\ ,^ — ^^ — = 6. Ans. §4,000X41 Example 4.— In what time will §800 at 5fi give §90 interest ? „ . 100 X §90 .. ,, .3 ^, . Solution. — / = i^ttt^. ^ = 3| vears = 3 years 3 months. Ans. §800 X 5 ^ ' ^ 70. The Six-Pei'-Cent. Method. — If it were not for its inaccuracy, there could be no more satisfactory method of computing interest than this. In spite of its incorrectness, its adoption originally Avas doubtless owing to its simplicity. But the calculations relative to every form of business are each year becoming more and more exact, and it will proba- bly not be very long until the six-per-cent. method will be dropped from our textbooks. Computations of every kind are being made a simple matter of reference to tables. To ascertain the exact number of days in any period less than a year, and to regard the result as so many 865ths of a common year, or as so many 36()ths of a leap year, will undoubtedly be the method of the early future. The teacher should therefore take particular pains to have the pupils expert in the method employed by the government. When the time is an exact number of years, all methods are alike correct. It is only when the time is expressed in months and days that inaccuracy results. If interest is to be computed for a period 80 PEDAGOGICS OF ARITHMETIC. § 2 extending through February of a leap year, the time should be regarded as part of a leap year. But in spite of the inexactness of the six-per-cent. method, it is yet in very general use, and it should therefore be thor- oughly mastered by pupils. In finding the multiplier there is no better way than to multiply 6 cents by the number of years, 5 mills by the number of months, and i of a mill by the number of days, and then take the sum of the products. This will give the interest at 6^ of II for the given time. It is then necessary only to multiply this sum by the number denoting how many dollars are in the principal. Example 1. — Find the interest at 6^ of $468 for 3 yr. 5 mo. 24 da. Also of $897.87 at the same rate for 5 yr. 11 mo. 29 da. Solution. — $.0(;x3 = $.1 8 .005X5 = .0 2 5 .OOOi X 24 = .004 $.2 9 X 468 = $97,812. Ans. Solution. — $.06X5 = $.3 .005X11 = .0 5 5 .OOOi X 29 = .0 4f $.3 5 9 I X 397.87 = $143.17. Ans. If pupils be exercised in finding these multipliers until they can do it c|uickly and accurately, it is better than that they should be required to find them and use them with some principal. For their first operations in calculating interest will be found to contain many errors, and these will usually occur in the multiplier. They should therefore be at first required to solve many examples like the following: Example 2.— Find the interest of $1 at Q% for 3 yr. 7 mo. 18 da. Also for 1 yr. 4 mo. 14 da. Solution. — $.06X1 = $.0 6 .005 X 4 =.0 2 .0001X14 = .0021 .2 18. Ans. $.0 8 21 Ans. Solution. — $.06 X 3 .005 X 7 = .OOOi X 18 = = $.18 = .0 3 5 = .003 § 2 PEDAGOGICS OF ARITHMETIC. 81 Explanation. — If the interest of II for 1 year is I.OfJ, for 3 years it 3 times $.06, or 1.18. Since the interest of II for 13 months is G cents, or GO mills, for 1 month it is ^ of GO mills, or 1.005, and for 7 months it is 7 times $.005, or 1.03*5. Since the interest for 30 days is 5 mills, for 1 day it is ^^ of 5 mills, or -£-^ mills, equal to |.000-|-. For 18 days the interest is 18 times i of a mill, or $.003. An explanation or analysis like the foregoing should be required until every pupil can give it correctly and without hesitation. After facility has been attained in calculating interest at 6^, interest at rates other than G should be taken up and practiced until rapidity and accuracy have been attained. iMost textbooks direct that in finding the interest at some other rate than G, the student shall divide by G and multiply by the given rate. This is not usually the best order, for fractions are likely to occur that may be avoided if the interest at Qfo is first multiplied by the given rate and the product be then divided by 6. This will appear in the solution of the following example : .Example 3. — By the six-per-cenl. method find the interest of $317.50 for 2 yr. 7 mo. 21 da. at 5h%. Solution. — $.06 X 2 = $.1 2 §.1585X317.5 = §50.32+ .005 X 7= .0 3 5 $50.32h-6 = $8.38| .000^X21= .0035 $8.38f X 51 = §46.13 i (•) $.15 8 5 $50.32 X 5h = $276.76 ( §276.76 H- 6 = §46.13 f ^"' Explanation. — The student will notice that in (1) 150.32 divided by G we obtain a mixed number for a quotient, and that this mixed number must be multiplied by another mixed number. If, however, we first multiply by 5i and afterwards divide by 6, the fractional difficulty is in a large measure avoided. When the multiplier itself is exactly divisible by 6, or when the principal is, it is better to change either the one or the other before finding the required interest. 82 PEDAGOGICS OF ARITHMETIC. § 2 est of $240 for o yr. " """'^Z;// ~ D' whence, A \ B = C : D. Hence, citlicr ratio or both ratios of a simple proportion may be simplified by divieling. Thus, if 8 : 12 = 40 : 60, we may divide the first ratio by 4 and the second by 20, and we obtain 2:3 = 2:3. The ratios of a compound proportion may be simplified in the same manner. In a similar manner it may be shown that Both antecedents or both consequents may be divided — each pair by any number that will exactly divide its terms. § 2 PEDAGOGICS OF ARITHMETIC. 97 Thus, 8 : 12 = 40 : GO. If the antecedents be divided by 8, we shall have 1 : 12 = 5 : GO. If the consequents be divided by 12, we shall have 8 : 1 = 40 : 5. If a proportion contains fractions, they may be removed by multiplication. Thus, 8i : 10 = 31 : 4. Multiplying the antecedents by 3, we have 25 : 10 = 10 : 4. A great variety of transformations is possible with propor- tions without destroying them, and the ingenious teacher can advantageously use them all. If the pupils know something of algebra, they should be required to use it in discovering these transformations. It may here be remarked that the fractional form of stating a proportion is rapidly superseding the extended forin given above. Also, that the double colon, used to separate the two ratios, has been almost entirely discarded in favor of the sign of equality. Both of these changes are to be commended. 82. Cause and Effect. — There is no method of stating a proportion, either simple or compound, in which the cor- rectness of the result may be relied upon with the same degree of certainty as this. It is an easy matter for the pupil to select the causes, and the effects produced by those causes. The exercise addresses itself to the judgment from a new standpoint, and thereby gains additional value. The principle upon which it depends is one of equilibrium. TJie product of tlic fii'st cause and the second effect equals that of the second cause and the first effect. This may be shown as follows: Example. — Let Ci and Ci denote the causes, and Ey and Ei the cor- responding effects. Then, ^ = ^. G E^ Clearing of fractions, dE-^ = C\Ei. 9S PEDAGOGICS OF ARITHMETIC. § 2 There are various forms in which examples are written for solution by this method, but the solution of the following example will serve to illustrate one of the best. The miss- ing term is denoted by x, and the canceling is across the vertical line. Example. — If 12 men dig a trench 40 rods long in 24 days of 10 hours each, how many rods (.r) can 16 men dig in 18 days of 9 hours each ? Here, the men, the days they work, an(J the hours per day are the causes, and the rods dug are the effects. The miss- ing term is the second effect. Solution. — .y = 4 X 9 = 3G days. c, a x^ n 4 u i^ n 9 E^ E, X ^9 EVOIiUTION. 83, Methods of Teaching Evolution.— -There are four methods of presenting this subject to pupils : 1. To teach the process without giving reasons. 2. To illustrate the process by means of geometrical figures. 3. To illustrate by means of developed binomials or by formulas. See Evolution in the arithmetic published by the International Correspondence Schools. 4. To employ both geometrical diagrams and developed binomials. Which of these is best it is perhaps not easy to decide. But the age and proficiency of the pupils should be considered. Our authors have exhausted their skill in presenting evolution so that it may be brought to the level of easy comprehension ; but every teacher, after finishing it with a class, has the feeling that it is seen "as through a glass, darkly." With the process itself there is little more difficulty than in long division, but it is otherwise with the reasons for the process. This naturally starts the question whether there are not many § 2 PEDAGOGICS OF ARITHMETIC. 99 subjects that should at first be taught only so far as the oper- ation is concerned, and the effort to reach a comprehension of the reasons therefor be deferred until greater compass of mind has been attained by the learner. A little reflection will convince the teacher that there are many such subjects. Grammar is full of them. The logic of cause and effect in history is utterly beyond the average intelligence of children in their first work in that subject. Yet we teach both early in the school work. Truths beyond us at first lie in the mind, and by the proc- ess known in pedagogy as apperception, they take their places later in classes to which at first they were not known to belong. The writer remembers that many years ago he learned and quoted, perhaps many hundreds of times, very glibly, " The subject of o. finite verbis put in the nominative case. " The word ' ' finite " had then no meaning to him. What " finite " has to do with verbs never started an inquiry in his mind. Afterward, while studying Latin, he learned that ' ' The subject of the infinitive is in the accusative " (objective). Then, by the apperceptive process, the words _/?;/ //rand infin- itive, with much accompanying knowledge of the subject, became parts of an organized whole, and in proper relation. Every one agrees that it is a good thing to have children memorize poetry, even if it contains thoughts and words they do not understand. A poem ripens as it lies in the mind, and, years afterwards, is perfectly understood, and may be a source of inspiration in the affairs of life, and an element in aesthetic culture. It appears, then, that it is often good pedagogy to teach processes only, even if the pupil is left to his own resources to get possession of the reasons afterward. With pupils of considerable maturity of mind, the explana- tion of evolution by means of the development of a binomial is undoubtedly the best. The second term of each power gives the trial divisor, and the terms that follow enable him to complete the divisor. Moreover, it is no longer necessary to remember the rule — only to write out the development of the binomial to a power equal to the index of the root. A very slight knowledge of algebra makes this an easy matter. b.tr<" 100 PEDAGOGICS OF ARITHMETIC. 2 The only powers of practical importance are two, the second power and the third power. To show the use of these developments, the extraction of the square root and of the cube root by this method is shown below. 84. Square Root. — Suppose that the pupil has forgotten the rule. Square the binomial / -|" ^^ ^^ which / denotes tens and 7/ units. {f + ny = /' + Itu + le - f-^ (2/ + u)u. Example. — Find the square root of 7,569. Solution. — power root P + (3/ + u)u ■=. 7 5'6 9 I 80 + 7 = 87 f = 640 (2/+?^// = 2/ = 1 6 2/+U = 1 6 1169 1169 = {2/+7e)u. Explanation. — The greatest square (/") in the left-hand period is 6,400, and its square root (f) is 80. Taking this square from the power, there rem.ains 1,109, which is {'Zt-\- 7()i(. Of this product we know 2/, or 100, which is the greater part of one of the two factors. Dividing by 160 (2/) gives 7 for //. We now add 7 (//) to 100, and the result, 167, is 2t -\- H. Multiplying 167 by 7 gives the value of {2t -\- 7i)?{. If there were more figures in the root, we should have to regard those so far found as if they were one figure repre- senting units, and proceed as before. 85. Cube Root. — We shall give somewhat more briefly an example in cube root, omitting imnecessary ciphers. Example. — E.xtract the cube root of 405,224. Solution. — P = {Zt- + ZtH + ir)H = 3/^ = 14 7 ^ttt = 8 4 iP ■= 16 power root 4 5'2 2 4 I 74 843 3/2 ^ ^f^^ _^j^-. _ 15 5 5 6 62224 2 2 2 4 = (S/"" + Ztu + uyt. 2 PEDAGOGICS OF ARITHMETIC. 101 86. The Foiirtli Koot. — The fourth root is, of course, found by extracting the square root of the square root; but, to illustrate the above method more fully, let us suppose that it is necessary to do this by one operation, as in cube root. (/ + uy = /' + 4/'// + Qt^u'' + 4.tu' + It' = /' + (4/' + Vyfu + 4/;r + //')//. Example. — Extract the fourth root of 1,500,625. Solution. — power root fi + (4/3 ^_ f^f^i, + 4^fir- + u'')H - 1 5 O'O 6 3 5 1_35 t' =81 4P = 108 000 Gf'u = 2 7 000 A/u' = 3 00 u^ = 12 5 4r + 6/-U + 4//r + «' =: 13 8 12 5 6 9 6 2 5 6 9 6 2 5 = {4P+G/-u+4/u^+uye. 87. Roots of Fractions. — Finding the square root of a fraction is easier if the fraction be first changed to an equiv- alent fraction having a perfect square for its denominator. Thus, " X"3 3X3 l/l = l/i^a = t/h|/5xc = j^. Vl = f1^5 = l4x= = iv^. This reduction may be taught to a class without any diffi- culty. It enables us to avoid extracting two roots and per- forming an awkward operation in division. Besides, it gives a more accurate result. The same method is applicable in finding the cube root of a fraction. Thus, n-i^' 3X9 27 X18 L^18. Vl = ^l;^s = l/rrx3 = ,^a It is a good exercise to make these reductions, but per- haps it is better to change the fraction to a decimal, and then extract the required root of the decimal. 103 PEDAGOGICS OF ARITHMETIC. § 2 88. Geometrical Illustration of Square and Cube Roots. — The writer is satisfied, after many years' experience in the classroom, that it is beyond the ability of pupils, even of those whose intelligence is above the average, to read and understand these illustrations, however skilfully they may be presented. If the teacher is expert with the crayon, and constructs the illustrations piece by piece as the numerical work proceeds, some of the class may be able to follow, though even these will have but an imperfect comprehen- sion of the logical force of the demonstration, and, in a brief time, the whole matter will have so faded as to be valueless. 89. Evolution by Factoring. — It is often necessaiy to extract the square or the cube root of the product of several factors. In such cases the factors may sometimes be rear- ranged so that we may find the required root by inspection. Example 1.— Extract the square root of 50 X '72 X 18 X 162. Solution. — We notice that each factor contains a perfect square. Hence, we may write them thus, 25 X 36 X 9 X 81 X 2 X 2 X 2 X 2. Whence, the square root is 5 X 6 X 3 X 9 X 4 = 3,240. Example 2.— Find the cube root of 24 X 45 X 200 X 448 X 49. Solution. — Recomposing the factors, 24 = 8 X 3 45 = 9 X 5 200 = 25 X 8 448 = 64X7 49 = 49. Hence, the product equals 8 X 27 X 125 X 512 X 343. Whence, the cube root equals 2X3X5X8X7 = 1,680. By preparing a list of such exercises, the teacher can add much interest to the subject of evolution and secure good review work in factoring. The readiest method of so doing is to begin with the indicated product of several cubes or squares, and recompose them so as to conceal the perfect powers. 90. Reduction of Radical Forms. — To reduce to sim- plest form indicated roots of quantities containing a factor § 2 PEDAGOGICS OF ARITHMETIC. 103 that is of the same degree as the root indicated, is another easy and interesting exercise. Thus, 4/50 = |/35 X 3 = 5\/2. -fT93 = feTxa = 4^ 3. The exercise aids in giving the pupil a more exact and discriminating notion of the meaning of evolution. 91. Equal Factoi* Method of Extraetinjj: Roots. — It is important that pupils should fully understand the points of likeness between evolution and division. Many persons that use both processes with ease are unaware of the fact that evolution is only a special case of division just as invo- lution is only a variety of multiplication. Few pupils learn of these likenesses at the time when they study arithmetic, and if they discover them at all, it is later in life and by the merest accident. This should not be, and it will never hap- pen when the teacher himself imderstands in all their rela- tions the subjects he teaches. The usual definitions of division and evolution do not suggest this analogy, but they might easily be so formulated as to do so. Thus, Division is thr process of finding one of fzco /actors of a number x^'Iieu tlieir product and the oti/er factor are given. Evolution is the process of finding one of tioo or more equal factors ivJiose product and the number of factors are given. Square root is the process of finding one of tivo equal fac- tors li'hose product is given. Cube root is the process of finding one of three equal fac- tors ijhose product is given. There are several methods of extracting roots. Perhaps the least useful of these methods are those usually given in the arithmetics. These shall be passed without further notice in this place and a method explained that the writer believes to be much better and more easily tmderstood than any of them. It has the additional advantage of bringing out very clearly the likeness between division and evolution. It is a method derived from Sir Isaac Newton's Method of Approximating the Roots of Higher Equations. 10-i PEDAGOGICS OF ARITHMETIC. § 2 Example 1. — Find the square root of 89, that is, one of its two equal factors. Solution. — We begin by finding two numbers as nearly equal as possible whose product is 89 or nearly so. The numbers 9 and 10 will immediately suggest themselves, since 9 X 10 is 90- The true square root lies between 9 and 10; hence, we take their arithmetical mean, that is, half their sum, as being probably more nearly correct than either 9 or 10. Taking arithmetical mean, (9 +10) -^3 = 9.5. Now, assuming that 89 is the product of two equal factors, one of which is 9.5, we may find the other by division. Dividing, 89-f-9.5 = 9. 868. We find that the factors 9.5 and 9.368 are not equal, but they are more nearly so than 9 and 10. It is evident that by taking the mean of 9.4 and 9.368 and repeating the process, we shall obtain two factors still more nearly equal. Taking mean, (9. 5 + 9. 368) H- 3 = 9.434. Dividing, 89 H- 9.434 = 9.4339633. Taking mean, (9.434+ 9.4339623) H- 3 = 9.4339811. This is the correct square root of 89 as far as it is carried. E.xAMiM.K 3. — Find the approximate square root of 1,971.14. Solution. — A brief inspection would suggest the two factors 50 and 40, since 50 X 40 is 3,000. The mean of these factors is 45, which is too great, since 45 X 45 = 2,035. Hence, we may begin with 44 as the first mean. Dividing (using at first only 1,971), 1,971-4-44 = 44.8, nearly. Taking mean, (44 + 44.8)^-3 = 44.4. Dividing, 1,971.14 -- 44.4 =44.395. Taking mean, (44. 4 + '14. 395) -- 3 = 44.3975. Dividing, 1,971.14 -- 44.8975 = 44.3975449. Taking mean, (44.3975 + 44.3975449) -- 3 = 44.39753245. The exact root corresponds with this to the last figure. Of course, the work is rarely carried so far. The preceding mean is correct to four decimal places, which is quite suffi- cient for ordinary calculations. The important points to be noted in this method are that sets of factors are successively § 2 PEDAGOGICS OF ARITHMETIC. 105 obtained that are more nearly equal than preceding sets, and that, finally, a set is found in which the factors differ so slightly that their mean may be taken as the required root. Example o. — Find the cube root of 937. Solution. — Here we must begin with three factors. Of course, the more nearly equal they are and the more closely their product approaches 937, the more rapidly we shall approximate the correct cube root. A brief inspection leads to the choice of the factors 9.5, 10, and 10, whose continued product is 950. Taking mean, (9.5 + 10 + 10) -- 3 = 9.8, nearly. Dividing, 937 -f- 9.8 = 95.6123; 95.6132 -9.8 = 9.756. Taking mean, (9.8 + 9.8 + 9.756) -- 3 = 9.7853, nearly. This result is correct as far as three decimals ; but let us note the effect of repeating the operation. Dividing, 937 -f- (9.7853)- = 9.785686563. Taking mean, (9.7853 + 9.7853 + 9.785686563) h- 3 = 9.785438854. The cube root of 937 to seven decimal places is 9.7854388. Example 4. — Find the cube root of 61,331. Solution. — A brief inspection shows that the true result is between 39 and 40. Taking the factors 39, 39.5, and 40, the mean of which is 39.5, we proceed to find a new set of factors. Dividing, 61,331 -- (39.5)" = 39.303. Taking mean, (39.5 + 39.5 + 39.303) -- 3 = 39.434. This result is the correct root to three decimal places. Example 5. — Find the fourth root of 1,000. Solution. — The fourth root of a number is best found by taking the square root of its square root ; bt:t the object here is to show the process of equalizing four factors of 1,000. We may separate 1,000 into two nearly equal factors, 31^ and 33. Each of these is then separated into two factors as nearly equal as possible, 5 and 6|^, 5 and 6.4. Taking mean, (5 + 6.35 + 5 + 6.4) -f- 4 = 5.66, nearly. Dividing, 1,000-^(5.66)^ = 5.515066, nearly. Taking mean, (5.66 + 5.66 + 5.66 + 5.515066) -f- 4 = 5.63376+. The correct root to four decimal places is 5.6334. In finding the first factors it is a great advantage that they shall be as nearly equal as possible; for the more nearly they approximate the true root, the greater will be the num- ber of correct decimal places in each successive approxima- tion. To show this an example will now be solved in which, {a) TJie factors are nearly equal ; {b) The factors differ considerably. 10(j PEDAGOGICS OF ARITHMETIC. § 3 Example 6. — Find the cube root of 62. Solution. — (a) It is evident that the true root is very nearly 4. Taking 4 and 4 as two of the three factors, the third is obtained by dividing, 62 --(4X4) = 3.875. Finding mean, (4 + 4 + 3.875) -^ 3 = 3.958+. Dividing, 62 -i- (3.958+)- = 3.957675-. Finding mean, (3. 958 + 3. 958 + 8. 957675) h- 3 = 3. 957891. This result, after only two adjustments of the factors with which the work began, agrees throughout with the true root. {/>) Since 2x6x5^ = 63, let us begin with these factors. Finding mean, (2 + 6 + 5. 16+) -f- 3 = 4.3+. Now, we know that the root is less than 4 ; hence, our work is not so far advanced as the point of starting in ia) above. But. for the sake of the illustration, let us proceed. Dividing, 62 h- (4.3)^ = 3.35+. Taking mean, (4.3 + 4.3 + 3.35) -r- 3 = 3.98+. Dividing, 62 -h (3.98)^ - 3.914. Taking mean, (3.98 + 3.98 + 3.914) -- 3 = 3.958. Here, the mean is exactly the same as the first mean in {a). It is clear, then, that much labor is saved by care in the choice of factors. 93. Finding? Factors Approximately Equal. — A little practice should make the pupil expert in separating any number into a set of factors that are nearly equal. The fol- lowing, however, will be found helpful: Example 1. — Separate 11 into two nearly equal factors. SuLUiiON. — We begin with 3 and 4, the mean of which is 3.5. But since 3.5 X 3.5 is 12.25, it is evident that 3.5 is considerably too great. We take 3.3, and dividing 11 by it, obtain 3.3333+ for the other factor. These two factors are so nearly equal that their mean is the square root of 11 correct to four decimal places. Example 2. — Separate 11 into a set of three nearly equal factors; also into a set of four such factors. Solution.— Since 2X2X2 = 8, and 2.4x2.4x2.4 = 13.824, it is clear that the factors desired lie between 2 and 2.4. Let us try 2.2. Dividing 11 by (2.2)^ we obtain 2.27+. Hence, 11 = 2.2 X 2.2 X 2.27, nearly. To find four such factors we may first find two factors of 11 as nearly equal as possible, and then separate each of these factors into two others. We know from example 1 that 3.3x3.33 = 11, very nearly. If now 3. 30 and 3.33 be each separated into two factors nearly equal, the problem is solved. Since 3.3 is less than 2 X 2 we know that the first § 2 PEDAGOGICS OF ARITHMETIC. 107 pair of factors are slightly less than 2. Now, since 1.8 X 1-8 = 3.24, we shall not be much astray if we take 3.3 = 1.8 X 1-84. In a similar way we inspect 3.33 and find it exactly equal to 1.8 X 1-85. Hence, our four factors are 1.8, 1.84, 1.8, and 1.85, and their mean is 1.8225—, very nearly the fourth root of 11. Example 3. — Find five factors, nearly equal, of 3,827,963. Solution. — -Pointing this number into periods, as in finding the fifth root, 38'27963, we see that the required factors must have two integral places. Since 20' = 3,200,000 and 2P = 4,084,101, it is evident that the required factors are not much different from 20.7. Dividing, therefore, by 20. 7^ we obtain the fifth factor, 20.85, nearly. Hence, 3,827,963 = 20.7^ X 20.85. Example 4. — Separate .0823 into three approximately equal factors. Solution. — Dividing .0823 into periods as if for finding the cube root, we have .082'300. This may be for the time regarded as a whole number 82,300; of this the cube root is between 40 and 45, say 43. Dividing 82,300 by 43^ we obtain 44.51, nearly. Hence, 82,300 = 43- X 44.51. Returning now to the consideration of the decimal point, we see that .0823 = .43'^ X -4451. EXAMPLES FOR PRACTICE. 93. Solve the following: 1. Separate each of these numbers into two nearly equal factors and find the mean of each pair: (a) 187; (i) 2,449; (r)7; (--O-^l; {^')-085. 2. Separate each of the following numbers into three factors, as above: ((?)700: (/;) .0715; (r) 387,496; (r/).0067; 0') 50.07. 3. In finding the square root of 4,137, if 64.2 is chosen as the first factor, what is the other, and what is the first mean? 64.44+. 64.32. 4. Use 7.1 and 7.25 as two of the factors in finding the cube root of 376, and then find the other and their mean. A 5 ''•^+- Ans. I ^ 2^,__ 5. By the foregoing method find the following correct to four deci- mal places: Ans. I {a) i/i;079; {d) ^1,428; (<;) ^1,541; (^/) ^559; (c) -^^3,000. ' (a) 32.8481. {l>) 11.2609. Ans.osition in its vari- ous forms of letter luriting, business forms, essays, etc. § 3 PEDAGOGICS OF GRAMMAR. 9 Involved not only with composition, but also with its con- stituent, the sentence, are arrangement, style, etc. — cover- ing the entire domain of rlietoric*. Prosody with its many varieties of feet and their combi- nations into the numerous forms of metrical compositions, belongs, at least partially, in the domain of syntax. Rhetoric, with its figures of speech that owe their existence to poetry, is indispensable io prosody. Eloeution, or " the art of correct intonation, inflection, and gesture in public speaking and reading," belongs also in language study. It might be shown that the scope of language study is much wider than is indicated above, but enough has been given to make it clear that to decide what should be omitted from a work on grammar is by no means easy. Still more difficult is it to determine what should be found in a work on grammar and language. The student may be convinced of the truth of these observations by examining a numl^er of the grammars issued during the last fifty years. While it is perhaps impossible to sa.y what sul^jccts should be omitted from a work of this kind, and very difficult to decide what it should contain, yet in this task we may wisely permit ourselves to be guided, in a general way, by eminent writers on language, such as Professors Bain, Whitney, and others of their class. We have, besides, examples of books lately written by educators that have evidently studied the matter carefully, and have practical acquaintance with the demands of the times and the needs of the classroom. 0. AVliat a Textliook on Language and Grammar Sliotild Contain. — We may take, as a criterion of selection, Mr. Spencer's dictum that the end sought for in any study is twofold : 1. Mental discipline. 2. The acquirement of practical knowledge — knowledge that will be of use in gaining a livelihood. As an additional help, we shall perhaps not err in assuming the truth of what is urged by the authorities mentioned just 10 PEDAGOGICS OF GRAMMAR. § 3 above, that in g'ramniar the scnsi' and the sciitoicc are the main thing's to be considered. If these criteria be assumed, it follows, almost inevitably, what such a work should contain. If, besides, we find that the latest and most approved textbooks exemplify these requirements, we may be reasonably sure of our ground. Every matter proposed for admission t(^ a textbook must satisfactorily answer the test, qui bono? — what is it good for ? — or be rejected. Excluding the histo7-y and a)itiqnitics of the language, curious and interesting though they be, and orthography — the Ictlcr — with its vozvcls, its cojisonants, its phonics, from all of which we suffered in childhood, w^e come to etyniol- og-y — tlie Avoi'cl. The subject of etymology should be found in every rational work on grammar. That its treatment should occur first in the arrangement of topics does not fol- low, but stripped of all its curiosities of Saxon, French, Latin, and other derivations, its classifications should be made familiar to the pupil by all the available devices that have been proved to be valuable. By similar means, its inilections must be taught and emphasized by appropriate exercises, until they are perfectly familiar to the student. This is especially true of the irregular verb, which in nearly all European languages is the verb most commonly used. Our w^orks on grammar are singularly deficient in the sug- gestion of means of freeing the conversation of students from errors in the use of these verbs. It is only one person in a thousand that discriminates between " don't " and ' ' doesn't, " and we are constantly hearing "I had went," "We have saw," "The bell has rang," and so on. 10. Syntax. — The word syntax is derived from syntaxis, a Greek military term meaning to draw up into line a body of soldiers. In a similar manner words are arranged, each word in its proper place, to form a sentence expressing in the best possible manner a complete thought. The sentence, being the unit of thought and language, should be fully treated, not only in the ideal textbook on grammar and § 3 PEDAGOGICS OF GRAMMAR. 11 language, but also in every other work on the same subject. By varieties of construction, and by component elements, one author's work may be distinguished from that of another. The field for the student is here a large one. It unites the two uses of a study as they are indicated by Mr. Spencer — discipline and practical utility. With respect to the value of the study of the sentence as furnishing the most excellent mental discipline, there is, among educators, no longer any material difference of opinion. Not even psychology or the higher mathematics can yield better results. Moreover, in dealing with the question of best arrangement of the elements of a sentence, to the end of securing the greatest smoothness, and the maximum of force and clearness, literary taste is developed. This is a side of the mind that is not addressed by the studies men- tioned above. The possible varieties of sentence structure are infinite ; hence, the fascination the study of it yields to a mind that delights in generalization and classification — as all normal minds do. If any phase of the study of grammar does really teach the pupil "to speak and write the English language coiTectly, " and, it may be added, to read and u)idcr stand it with keener perception, it is the study of the sentence. Professor Bain speaks of the extraordinary profit that accrues to the student from exercises in rearranging the parts of an involved sen- tence, the aim being to secure the best possible disposition of its constituent words, phrases, and clauses. If, besides, the student be required to give reasons for his various arrange- ments, the practice will surely, sooner or later, affect for the better his own sentences, render his choice of words more discriminating, and the action of his mind more logical and deliberate. A training of this kind has a market value, and may be placed ainong the practical utilities — the things that go to enhance the student's chances of success in life. For there is perhaps no way in which a man may be so accurately gauged as by his choice and arrangement of words, and by the matter and logical sequence of his thought. So that, in 12 PEDAGOGICvS OF GRAMMAR. § 3 its best development, the study of grammar and language realizes the double purpose of mental discipline and practi- cal utility, and it is, therefore, a subject that ranks very high in educational value. 1 1 . Sentences Comblnecl in Composition.^ — Clearness, ease, force, smoothness, and logical sequence are most easily acquired by practice in the construction and arrangement of sentences in the various forms of composition. Of course there are many conditions — some of mind or idiosyncrasy, others of training — requisite to excellence in speaking and writing our mother tongue. But, given that one has thoughts, their effective expression is much enhanced by a previous training in the rationale of the sentence. It is generally conceded that any one whose vocal organs are normal may, by persistent practice, gain at least a fair pro- ficiency in vocal music. So also may one learn to express himself well, either in speech or writing, even if nature has withheld from him what the phrenologists call the faculty of language — provided, only, that he is capable of consecutive thought. Unfortunately — or fortunately — he that lacks nat- lu-al aptitudes in any direction is always reluctant to labor for excellence in that direction. 12. Rlietoric. — It is particularly when we come to com- bine sentences into extended composition that rhetoric in its completeness enters into consideration. With the sentence, incidental questions relating to rhetoric occur, but in the paragraph, the poem, and other combinations of sentences, the sway of rhetoric becomes paramount. Even if grammar should stop short with the sentence, it is difficult to see how rhetoric can be banished from grammar. Again, the teacher can scarcely find justification for send- ing pupils out into the world with no knowledge of letter writing and business forms, and there seems to be no good reason why composition teaching should not be extended so as to comprehend some of their more elaborate and difficult varieties. § 3 PEDAGOGICS OF GRAMMAR. 13 With pupils in advanced grammar there should be no special difficulty in recognizing the various qualities of style, and the more common and useful figures of speech. They can easily appreciate the difference between the jerky style of Carlyle and the majestic sonorousness of Johnson, Addi- son, and Irving; between the prose-poetry of Dickens, say, in his Christmas Stories, his Death of Paul Dombey, and of Little Nell, and the matter-of-fact, straightforward, but elegant narrative of Scott. Access to the works of English classical writers is so easy that there need be no lack of mate- rial upon which to exercise the judgment of students. 13. Prosody. — For exercises in grammar, selections from the poets are so commonly made by teachers that metrical considerations with reference to them can scarcely be passed over without attention. There are, however, so many varieties of feet and meter, and most of them occur in English verse so infrequently, that only those most used need be given. In the matter of the poetical feet found in many of our works on grammar, there is a striking illustra- tion of the influence of the Latin and the Greek grammars in shaping the grammar of our "grammarless tongue." For there is scarcely a poetical foot found in Horace or Pindar that is not found in the prosody of our English grammars, although many of them it is impossible to exemplify by quotations from our own poets. Only a few of them are in common use, and with these the student should be made familiar. Of these, particular attention should be given to the trochee, tambiis, spondee, dactyl, and aiiapest. With these few feet, it is wonderful what a striking and excel- lent variety of English verse has been constructed. No one M^ould, without examination, suspect that, with the excep- tion of a single long syllable at the end of an occasional line, poems so apparently unlike metrically as Poe's "Raven" and his " Bells " are both entirely trochaic. Pupils should be required to indicate the feet in poetical selections and should be exercised in scansion. They should mark, also, the place of cesural pauses, especially in blank 14 PEDAGOGICS OF GRAMMAR. § 3 verse; and it is worth the time and pains to have them understand what is meant by sonnet, satire, epigram, epic, ode, drama, comedy, tragedy, etc. Illustrations of these are easily found, and by knowing their form and name, added interest is given to their study. The conversion of metaphors into similes and the reverse, and other exercises with the figures of rhetoric, are all in line with the ordinary work in advanced grammar ; they are, besides, a means of cultivating a taste for elegant literature. This extension of the work of prosody, it may be said, belongs to the subject of rhetoric; but so few pupils in our common schools ever study that division of language work, that so much of it as is indicated above should be included in our textbooks on grammar. Besides, this will be much less in extent than the matter that is usually given under the subject of prosody. 14. Capitals and PiinetTiation. — It is self-evident that no work on grammar should fail to note the rules for the use of capitals and punctuation. Capitals are not mere embel- lishments of printed and written language. While they add to the appearance of the printed page, — that being their principal function, — they often exert subtle effects upon the sense of a passage. The rules for their use are few and defi- nite. How to use them, therefore, is a matter easy of acquisition, though carelessness has intruded them into many places where they do not belong. For example, our text- books, our general literature, our newspapers, print the word state, and many others, with initial capitals. The following is taken " from a copy of the Constitution of the United States as printed in one of our school textbooks on history: " Section IV. — The United States shall guarantee to every State in this Union a republican form of government, and shall protect each of them against invasion, and on application of the Legislature, or of the executive (when the Legislature cannot be convened) against domestic violence." There is no good reason why state and legislature, as used in this place, should begin with capitals. The §3 PEDAGOGICS OF GRAMMAR. 15 student will notice, in the foregoing, that while legislature begins with a capital, it is otherwise with executive. A good rule might be added to those ordinarily given : When there is doubt wJiether or not a capital letter should be used, a small letter should be preferred. The German language formerly distinguished all nouns by beginning them with capital letters, but in German books lately printed, this practice has, in general, been abandoned. There is no doubt that modern usage is drifting away from the use of unnecessary capitals. In the matter of punctuation it must not be imagined by the student that there is a code of hard-and-fast rules about which all the English-speaking world is agreed. Such, imfortunately, is not the case. Innumerable treatises on punctuation have been wn^itten, but while they agree in the main, in many respects they show striking differences. Thus, some authorities would punctuate a series with a comma before the and that precedes the last item in the series; others omit the comma. " Milk, cream, cheese, and butter are sold in this dairy." In this utilitarian age it has been discovered that punctua- tion is solely and simply for the purpose of making the sense more certain. In consonance with this purpose, in the books issued by those publishers whose usage is regarded as authority, we find punctuation omitted from title pages, heads of chapters, running titles at the tops of pages, and, in short, from everything the meaning of which is sufficiently definite without it. This practice has been growing for only a very few years, but it is doubtless one that has come to stay. If the student will note carefully the punctuation by dift'erent authors, he will find that each writer has his own notions about it. Even the same author differs in the punctuation of his own books written a few years apart. It looks as if, after writing one book, he had been studying the subject in a manual composed by some one having views at variance with his own. For example, Dickens, in some of his books, uses the colon incessantly; in others, 16 PEDAGOGICS OF GRAMMAR. § 3 it is rarely found. Sir Walter Scott is perhaps the most careful and consistent, in this matter, among classical writers. It may be remarked, moreover, that nearly all writers overpunctuate, and that most of them place punctuation marks not by rule, but by ear. That is to say, they are placed where pauses should occur if the matter were read aloiid. Some one has formulated the following excellent rule for the comma — the most abused of all marks of punctuation : If in doubt ivlictJicr to use a couima or not, omit it. 15. Slight Need for the Mark of lilxelaniation. — Among the various marks of punctuation there is none that would be less missed, if its use were discontinued, than the exclamation point — the wonder mark, as some one calls it. Just as bodily repose is regarded in good society as an indi- cation of culture and refinement, so mental repose — the absence of emotion and wonder— {■& deemed a sign of mental refinement. The child, in his first attempts at spoken lan- guage, uses interjectional expressions almost exclusively. Gradually, as his intelligence increases, he expresses his thought in categorical sentences, empty of emotion. What should we think of the charge of a judge if it were punctu- ated with interjections ? The judicial and the philosophical mind does not need the interjection. Most of the sentences with which it is used are better if punctuated with the period or the interrogation point. The gentleman expresses his thought as a gentleman, in passionless, well balanced sentences; the prize fighter and the street Arab require the interjection; and the school girl cannot get along without her Oh my's! and her Dear me's! As civilization advances, the interjection is less and less used. Many of our best authors rarely employ it. AH of our hopes and fears, our passions and compassions, our loves and hates should be formulated and dominated by the intel- lect; if this were done, the emotion involved would not need to be marked by the exclamation. PEDAGOGICS OF GRAMMAR. 17 THE se:n^tekce. GENERAIi C0]V8IDERATI0:NS. 16. The Unit of Tlioxiglit. — It has already been said that the sentence is the nnit of thought, just as the word is the unit of the sentence. Every composition can be resolved into distinct sentences, each of which expresses a complete thought. The thought expressed in a sentence may be true or false, but if the sentence is constructed in accordance with the laws of language, it is none the less a sentence. Some of our authors insist that the sentence must make "complete sense. " A sentence may make complete nonsense^ and yet be a proper sentence. The circle is square is just as much a sentence as if it expressed a truth. Indeed, if the works of at least some of our authors were judged from the standpoint of "complete sense," there would be very few sentences found in them. Truth and falsehood have nothing whatever to do with the question whether a group of related words does or does not form a sentence. 17. Saxon Words. — We frequently hear that the prefer- ence is to be given to Saxon words rather than to those derived from the Latin and the Greek languages, and to those of Norman-French origin. The Bible, Shakespeare, and Bunyan are cited as examples in which the vSaxon element predomi- nates. But since those works came into existence, the world has been advancing. Its requirements now in the matter of language are different from what they were at that time. The vSaxon is homely and roundabout; and while it is the best for pathos, it lacks the precision and definiteness of the language generally employed by writers of today. Shake- speare, when he rises highest, draws most freely from Latin and Norman-French. The truth is that language is constantly imdergoing a process of evolution, and that our vocabulary of a century or two ago would not meet the requirements of 18 PEDAGOGICS OF GRAMMAR. § 3 today. And then, too, we are apt to exaggerate the excel- lence of that which bears upon it the impress of age. As we grow old, we take our places in the ranks of those whom Horace refers to as Laiidatorcs tciiiporis acti — the eulogists of time gone by. Our language today is better than it was when Shakespeare wrote, and if he were with us now, to do again the work that made his name immortal, he would undoubtedly do it better. As the race evolves, everything keeps pace with its progress — science, invention, education, language. We must not forget what .some one calls "the perspective of history. " Crime seems to have increased in the world. It is only because there are more people in the world, and because our means of information are better. A good rule for composing English sentences might be given as follows: Put jour tliougJit in such ivords asiuill exact Iv express your iiicaiiiug. Don't trouble yourself about the origin of the words, so long as they are of good repute. Let them be Latin, Greek, French, Teutonic, anything, provided only that they have the warrant of good usage and meet the requirement of your thought. Thought must not be subordinated to words. 18. Classification of Sentences Witli Respect to Use. — With respect to use or function, sentences a:e usu- ally classified as declarative, interrogative, imperative, and exclamatory. However they may be punctuated, exclama- tory sentences are declarative, interrogative, or imperative. " How sweet the moonlight sleeps upon this bank ! " (Declarative.) " What are the wild waves saying!" (Interrogative.) " Build thee more stately mansions, O, my soul!" (Imperative.) The foregoing sentences, although expressive of strong emotion, and, therefore, exclamatory, are in fact, respect- ively, declarative, interrogative, and imperative. That is to say, when the element of strong feeling is added to the thought expressed in a sentence, it becomes exclamatory, § 3 PEDAGOGICS OF GRAMMAR. 19 but it is none the less to be classified as declarative, interrog- ative, or imperative. The division of sentences into four classes is absurd. The three forms mentioned above, plus emotion, give three others. We have, therefore, six varieties of sentences when they are classified with respect to use or function : 1. Declarative. 1 a. Declarative-exclamatory. 2. Interrogative. 2 a. Interrogative-exclamatory. 3. Imperative. 3 a. Imperative-exclamatory. 19. Exclamatory Sentences to Be Avoided. — The g'radations of emotion are so various and uncertain, however, that it is by no means easy to determine when we should use the exclamation point. Remembering what has already been said concerning the exclamation, we are warranted in formulating' and observing the following rule : Ulicii tJicrc is doubt wJicthcr the cxclainaiioii point should or should not be used, do not use it. It was formerly the custom among writers to make much use of this point, but in later years there is a pronounced drift away from its employment. Another consideration of much weight in deciding this question is the fact that a sentence as rendered by different persons and under different circumstances may be devoid of emotion or it may be surcharged with it. If we are setting type so as to render faithfully the utterance of a professional elocutionist, we must punctuate in one way, but if a passage is thought of as read when hearers and reader are in perfect repose, the punctuation must be different. In other words, cold type and human utterance are greatly different, and if it were possible, they should be differently punctuated. And since repose — absence of passion — is in the direction of cul- ture, refinement, education, let us avoid as much as may be, the signs of emotional disturbance and excitement. Shake- speare, in his instruction to the players, anticipated the quietness and absence of demonstration that come in the slow evolution of the race. " Speak the speech, I pray you, as I pronounced it to you. 20 PEDAGOGICS OF GRAMMAR. § 3 trippingly on the tongue : but if you mouth it, as many of your players do, I had as lief the town crier spoke my lines. Nor do not saw the air too much with your hand, thus; but use all gently: for in the very torrent, tempest, and, as I may say, the whirlwind of passion, you must acquire and beget a temperance that may give it smoothness. O, it offends me to the soul to hear a robustious, periwig-pated fellow tear a passion to tatters, to very rags, to split the ears of the groundlings; who, for the most part, are capable of nothing but inexplicable dumb shows and noise. I would have such a fellow whipped for o'erdoing Termagant ; it out- herods Herod: pray you avoid it." The form of sentence that in Greek is called the optative, — the wishing sentence, — is in English only the declarative. ' ' Would that I were a boy again ! " means only, ' ' I wish that I were a boy again." Sentences expressing a wish are usually followed by the exclamation point, though a period would be better. In concluding this paragraph, the writer would insist on the correctness of the classification of sen- tences as declarative, i)iterrogative, and imperative. 30. Classiflcatioii of Sentences AVitli Respect to Form. — There is perhaps no subject in which grammarians differ so much as in what is a simple, a complex, and a com- pound sentence. If a sentence be judged by exactly what it contains, the matter, although still difficult, is much sim- plified. But our grammarians insist upon supplying what they call ellipses. Thus, "John, Henry, and William go to school," means, they say, "John goes to school, Henry goes to school, and William goes to school. " The writer thinks that no such thing is true. The former is a good English sentence, but the latter is not. Why not take our authors as we find them? If their sentences are faulty, they are not worthy of notice as specimens of English; if they are fault- less, do not mutilate them by supplying ellipses. "Jane swept the floor and washed the dishes " is the proper form in which this sentence should be written. But many authors insist that, for grammatical treatment, it should read, "Jane § 3 PEDAGOGICvS OF GRAMMAR. 21 swept the floor and {Jaiic or sJic) washed the dishes." In this form, they say that it is a compoiDid sentence. Others prefer to call it a simple sentence with a contracted or compound predicate. To illustrate, we quote from Pro- fessor Meiklejohn, one of our most scholarly writers on grammar: ' ' There are three kinds of sentences : Simijle, Coiu- l><)iiiid, and Coiniilex. ' ' A simple sentence is a sentence which consists of one subject and one predicate. "A simple sentence contains, and can contain, only one finite verb. "If we say, 'James and John ran off,' the sentence = ' James ran off ' + ' John ran off. ' Hence it is called a contracted coniijonnd sentence — contracted in tiie predicate. " If we say, 'John jumped up and ran off,' the sentence = ' John jumped up ' + ' John ran off.' " The objection to all this is that it is the for 7 n and not the meaning of which the grammarian must take cognizance. These awkward and mutilated forms are not what we ask our pupils to classify, but we submit to them the correct and approved forms chosen by the authors. Much difficulty is added by the fact that we must include in our classifications the imperative and the interrogative sentence. The imperative sentence rarely contains an ex- pressed subject. Thus, "Study your lesson," "Sit erect, and keep your eyes on the blackboard." These are impera- tive sentences, but in both the subjects are missing. Again, when the subject of an imperativ^e sentence .seems to be expressed, it is generally not the subject, but the nomina- tive case by address. Thus, "John, go to school," "Go, thou, and do likewise," "Go, you, and light those hay ricks." If, therefore, sentences are classified in accordance with what they really contain, and not with regard to what may possibly be supplied, the difficulty is much diminished. A declarative or an interrogative sentence regularly contains 22 PEDAGOGICS OF GRAMMAR. § 3 a subject and a predicate verb. A normal imperative sentence omits the subject, and if the omitted subject be supplied, the sentence becomes at once awkward and un-English. The writer ventures to offer the following classification, which is dominated by the principle that sentences must be classified in accordance zvith their expressed contents : 1. A simple sentence is a sentence in which an action or a state of being is predicated of a subject. If the subject be represented by a short horizontal line, and the predicate by a roimded oblong, the varieties among sentences may be clearly indicated. An imperative sentence may be denoted by a cross through the subject line, thus denoting that the subject word is regularly omitted. The fact that a sentence is strongly exclamatory may be shown by an exclamation mark; that it is declarative, by a period; and that it is interrogative, by a question mark. " The earth moves." " The boy is sick." ( ) • "Go home." " Be quiet." — X — C ) . " Build thee more stately mansions, O, my soul!" — x — ( ) ) " Who goes there ?" " When is it to be ?" 2. A simple soitence tvitli a compound subject is a sentence in which an action or a state of being is predicated of two or more subjects, or of any one of two or more subjects. " Butter, eggs, and vegetables are sold in this market." "Horses, sheep, and poultry are unknown in the island." " Was Arthur, his sister, or their friend at the picnic ? " El ;} § 3 PEDAGOGICS OF GRAMMAR. 23 3. A simple sentence with a eoinpoiind predicate is a sen- tence in which two or more actions or states of being are predicated of the same subject, or in which any one of two or more actions or states is so predicated. " The boy rose and offered his excuses." — " Wh)^ do men so envy, distrust, and fear one another ? " " He works, sleeps, or plays." "Be still, sad heart, and cease repining." — > It will be noticed that the last sentence is griven as a sim- ple sentence. It has already been stated that the imperative sentence regularly omits its subject. When several predica- tions are thus made of the same subject in an imperative sen- tence, it shotild be regarded as simple. 4. A simple sentence with subject and predicate compouud is a .sentence having two or more subjects connected by con- junctions expressed or understood, and two or more predi- cates connected in the same way. 'The boy, his sister, and tlieir cousin go to 1 C ) \ school and recite their lessons." J C ) J ' 5. A compound sentence is a sentence composed of two or more simple sentences of equal rank, and capable of making complete sense when they stand alone. vSttch simple sen- tences are connected by a coordinate conjunction, expressed or understood, and when so united these simple .sentences are called clauses. "The teacher gave out a difficult example, but the well trained class solved it very readily." " One sows, another reaps." " The sun went down, and the moon soon rose round and beautiful." The teacher will see that the varieties of compound sen- tences are practically inexhaustible. It must be ob.served that a compound sentence may contain one or more subordinate 24 PEDAGOGICS OF GRAMMAR. § 3 clauses. But to be compound, a sentence must contain at least two principal clauses; that is, clauses that make com- plete sense when standing alone. 6. A complex sentence is a sentence in which there is one principal clause accompanied by one or more subordinate modifying- clauses. " I will pay you when my ship comes in." " Who are you that build your gay palaces on my margin ? " In these sentences, the principal clauses are ' ' I will pay yovi, " and " Who are you." The subordinate, dependent, or modifying clauses are " when my ship comes in," and " that build your gay palaces on my margin. " These inferior clauses serve only as modifiers of the verbs in their respect- ive principal clauses. The following are other examples of complex sentences: "The raindrops stereotyped themselves on my beaches before a living creature left his footprints here." " Build thee more stately mansions, O, my soul, As the swift seasons roll." " Meanwhile, I was thinking of my hrst love As I had not been thinking of aught for years ; Till over my eyes there began to move Something that felt like tears." 31. Mapi^ing' Coinpoiiiirt and Complex Sentences. In the mapping of compound and complex sentences nothing more should be attempted than to show their structure by clauses and to denote the connectives expressed or implied between the clauses. Such mapping may be made of great value and interest in the classroom. The writer believes that the following scheme will meet the approval of most teachers : 1. Principal clauses should have a sign of equality at the beginning and the end of a heavy line indicating the clause; thus = i =: T/ie sun set and the nioo7i rose. § 3 PEDAGOGICS OF GRAMMAR. 25 2. Subordinate clauses should be denoted by lighter lines, and should be separated from independent clauses and from one another by the sig;i of inequality, the opening of which is towards the clause of which the dependent clause is a modifier. If a subordinate clause modifies a mere word or phrase, the sign of inequality should be turned towards the line representing the clause that contains such word or phrase. = = -f-> Tlie iiioou rose bcj07-c the sun set. i-^ < = = If the day is fine, ^ve shall go. f+> + Before I leave I shall see yoii, if > — — you are at leisure and wish me to come. == — ■ — =; y^ 1 kiio%v a bank 70 hereon the ivild thyme gr07ijs. 3. If a principal clause is broken by one or more con- tained subordinate clauses, the fact should be shown as follows : — 1-> < = The house that Jack bid it stood by the sea. +> hieh the school house stood had a trout stream flo^ving through it. <-l — < ^ h> — — < = When 7ve said that ice had lost our 7vay, the farmer's Avife, Avith a smile that made us feel at home, invited us to stay to dinner. 4. If a clause is used in apposition, or for any other reason is out of grammatical relation to the other clauses of a sentence, the fact is indicated by a wavy line. Clauses so used commonly have the value of subordinate clauses, for 26 PEDAGOGICS OF GRAMMAR. § 3 their use is to explain the meaning of some word or phrase or clause. They are said to be used independently. = = >^'--'^~ "They asked the old doctor the very trouble- some question, ' Where did Cain get his wife ?' ' "In the serene expression of her face he read the divine beatitude, 'Blessed are t lie pure in heart.' " = +> 1-= = " Whence did we come? whither are we going?: these are questions that are continually asked, but no person has ever been found able to answer them satisfactorily." 33. Subject and Predicate. — No grammarian has thus far been able to give a satisfactory definition of the subject or the predicate of a sentence. The difficulty is chiefly owing to the fact that we have three forms of sentences — the declarative, the interrogative., and the imperative. The first states, or declares; the second expresses an inquiry; the third consists of a command or an entreaty. No device of language can be foimd that will include all these. One author says: " The subject of a sentence 7S wliat we speak about.'' "John saws wood." But we speak about ivood\\QXQ just as much as we do about John. And then, too, accord- ing to the definition, it is the person John, and not the ivord John, that is the subject. The teacher cannot emphasize too much the fact that the subject of a sentence consists of one or more ivords denoting a thing. Hold up a book in your class and ask your pupils to say what part of speech it is, and they will invariably call it a noun. But they are not to be blamed when it is the " Pro- fessor of the Theory, History, and Practice of Education " in one of the greatest universities of Scotland that gives us the definition quoted above — " TJie subject of a sentence is what %ve speak about. " The same author says: " The predicate in a sentence is §3 PEDAGOGICvS OF GRAMMAR. 27 zvhat zve say about the subject.''' Now, a little reflection will make it clear that in a declarative sentence we say, but in the interrogative and the imperative sentence, we do nothing of the kind. Moreover, it takes all the zvords in a sentence to say anything of a subject. The predicate has no more important part in saying things than the subject. In short, subject and predicate, in grammar, never have been, and perhaps never can be, defined. The best way out of the difficulty is to have our pupils know which words in a sentence make up the subject, and which the predicate. One of our late writers on g. ammar and language, recog- nizing, apparently, the utter futility of attempting to define subject QXid predicate, resorts to a plan like the following in order to have pupils understand what these words mean: subjects: Birds Good boys The "Mill on the Floss" " A bird in the hand The house that Jack built predicates: fly. obey their parents. was written by George Eliot, is worth two in the bush." was a house of the imagination. a:n^ai.ysis of sextexces. 33. Distinction Between Mapi)inj>; and Analysis. — The foregoing scheme considers only the large parts that make up a sentence. For the simple sentence, these parts are the subject and predicate ; for the complex and the com- pound sentences, it is their clause structure that is indicated by mapping. This general analysis is perhaps of more value to the student than the more elaborate and detailed methods that are given in nearly all grammars published in recent years. In mappings sentences nothing more need be attempted than is indicated above. The three kinds of simple sen- tences — declarative, interrogative, and imperative — can be sufficiently distinguislied by using, at the end of their out- line, a period, a question mark, or an exclamation point. If 28 PEDAGOGICS OF GRAMMAR. § 3 strong emotion is to be superadded, an exclamation point, in addition to the ordinary mark, may indicate it. Declarative sentence. CZD. Declarative sentence, plus emotion. - — ( ) i Interrogative sentence. ■ ■ ( ) ? Interrogative sentence, plus emotion. ( ) ?l Imperative sentence. x ( ) Imperative sentence, plus emotion. — )f- ( )[ A cross denotes that the subject is not expressed. The analysis of a sentence requires not only that the use, or function, and the relation of its larger elements — its phrases and clauses — should be clearly indicated, but also that the oiSce of every word should be denoted. This may be done entirely in written or spoken language ; but during the last few years many systems of diagrams have been devised for this piirpose. 34. Analysis by Diagrams. — Professor Bain, in his " Education as a Science," argues, not with much force, the writer thinks, against the employment of the terms analysis and synthesis. "To express," he says, "the conduct of any school lesson under either of the terms anal3^sis and [or?] synthesis, is to produce the utmost confusion in the mind of a young teacher, as everything that the words cover is con- veyed by other names, more expressive and more intelligible. Such are description, explanation, abstraction, induction, deduction." The writer thinks that the contrary is true. Very rarely are the words that Mr. Bain would substitute for those in question well imderstood by young teachers. " Take down a watch, analysis ; put it up, synthesis," says Lord Brougham. Among the teachers of the United States, it is in precisely this sense that these words are understood and employed. To take a sentence apart, an example in arithmetic or an argument, is analysis. Nearly every author of a work on graiumar or language lessons has a scheme of picturing minutely the relations that exist among the words, phrases, and clauses that are united § 3 PEDAGOGICS OF GRAMMAR. 29 to form sentences. Almost all of these schemes are open to objection, and the difficulties that beset the subject are n(;t easy to remedy. Sentences should not be dismembered in analysis, but should be preserved just as their authors left them. Moreover, the scheme of analysis should le .'■•o simple as to be easily intelligible. The author ventures to offer the following method of sentential analysis — examples first and explanation afterwards. It may be accompanied, or not, by the general mapping of sentences, as already explained. Examples sufficiently numerous are given to indicate fully the method of analyzing sentences without dismembering them. Several eminent writers on education insist that this should be realized in every system of diagrams. Doubtless some better method of doing this may be found later; but, for the present, the writer knows of nothing better. !25. Models of Analysis. — ir 1. The (earth) [is] round. 2. [Was] (Barrabas) a robber? CZ3- JI 1 3. (Paul), the apostle, [preached] upon Mars Hill. t 220 t I — + -< IV 4. (That the (earth) [is] round) [is] no longer [disputed]. 30 PEDAGOGICS OF GRAMMAR. = +>- + _£ 1 I IL_ 5. (He) [died] 'when the (tide) [went] out. CD. 6. (To be), [contents] his natural desire. The object of a transitive verb— in this sentence, desire— may be connected to the verb to show that it has on the verb a modifying efeect. Example 10 shows how the con- nection is made. 7. + _L 4 If the (sky) [fall], ; (we) [shall catch] sparrows. 1 T — l( ) 8. Seventeen hundred, (it) [came] and [found] 111 + The deacon's masterpiece strong and sound. .....< ^.,.. 9. 1 i _L 1 ^ (I) [met] a traveler from an antique land t f 1 + 1 1 1 1 i '>(Who) [said] : Two vast and trunkless (legs) of stone t 1 [Stand] in the desert. t 1 PEDAGOGICS OF GRAMMAR. 31 4- 10, A little (learning) [is] a dangerous thing; T -^ t T I I + I 1] L I ^ [Drink] deep, or [touch] not the Pierian spring. t =r- t ^r= 11. =Milton, (thou) [shouldst be living] at this hour; I t J 1 r^ =(England) [hath] need of thee: ^=( she) [is] a fen J 1 + Of stagnant waters :=( altar, sword, and pen, 1 t I I I 4- Fireside, the heroic wealth of hall and bower, ) [Have forfeited] their ancient English dower _J Of inward happiness, zz I t This sentence consists of four clauses of equal rank sepa- rated in the diagram by signs of equality. 12. - }+> ^ +> JT V The (world) [will] little [note] nor long [remember] what (we) [say] here; + + i — Zl_ but (it) [can] never [forget] what (they) [did] here. 32 PEDAGOGICS OF GRAMMAR. The first wJiat is the object of say—ive say what; the second is the object of did — tJicy did iv/iat. In like manner, luhat ii'e say here is the object of reiiiembcr, and if J ^y the well at the home of my the old oaken, iron-bound i j childhood the old oaken, iron-bound, | | that hung by the well at the moss-covered J I home of my childhood 38 PEDAGOGICS OF GRAMMAR. § 3 On the contrary, qualities detached from a notion extend the list of objects to which it applies, but each such exten- sion in number makes the picture less vivid and definite by diminishing the number of characterizing- marks or qualities. In the one case, we have a picture in merest outline with no details; in the other, the picture has life and color and motion and relation of parts. These opposite spheres of notions constitute what in logic is known as I'xtciision and coinprcJioisioii — the former refer- ring to the number of objects to which a term applies, the latter to the number of attributes or qualities associated with it. Hence, we have the well known law of the inverse ratio between the extension and the comprehension of common terms, viz., Tlic greater the extension^ the less the coinpre- heusioji, and viee versa. 30. The Word '' Qualify."— The word qualify is another term much used in grammar. It should be exactly understood and carefully explained by the teacher. Being derived from the Latin qualis — of what kind ? — it is not of so wide or general meaning as modify. All words modify that qualify, but not all modifying words qualify. Thus, in the expressions, red apples, some apples, five apples, all the adjectives modify, but, as used by most grammarians, only the first qualifies — denotes some quality that appeals directly to one or more of the senses. The term is synonymous with deseriptive as employed by most grammarians. Modify and modifying are generally used to indicate adjectival and adverbial functions of words, while the noun modification is restricted to those changes of form denoted by number, gender, case, declension, comparison, and conjugation. Of the words that contain the Latin qualts, qualify and qual- ifying are the only forms usually found with a technical meaning in the grammars. 31. The Word *' Jjiniit.'"' — The \word limit is derived from the Latin limes, the root of which is limit. The literal meaning of the word is a cross-path. The Romans usually § 3 PEDAGOGICS OF GRAMMAR. 39 had in their fields two broad and two narrower paths cross- ing- at right angles. These were limitcs, but each had a special name. So they came to use the term in the sense of boundary or margin. As applied to concepts, it has refer- ence to anything that restricts their extension, using this word in its logical sense. The terms limit and modify are, therefore, almost exactly synonymous, but the latter has come to be the more generally used word. When we say seven men, we limit the men with reference to number; that is, we establish, a boundary or path that must not be crossed from without or from within. In a similar manner, in the expression good girls, the word good has the effect of inclu- ding — shutting in — all girls of that class, and excluding — shutting out — all others. To limit, therefore, is to establish boundaries. The writer has dwelt upon these terms, not only because of their extreme usefulness in grammar, but also because he has noticed that very few teachers employ them with dis- crimination; and when the teacher does not understand, tlie pupils will always be in the same condition, or in a worse one. 32. Geiiei'al Modificatiou. — Again, it should be observed that ei'cry word in a sentence modifies the meaning of all the rest taken collectively and separately. When, for example, the ear hears the word runs, there is at once formed in the mind a picture of something — anything — performing the act of running. In the absence of informa- tion, the mind may supply a man, a horse, a dog, a loco- motive. This tendency of the mind to complete, in some way, imperfect mental pictures, is irresistible. If, now, the boy be prefixed to runs, the mental picture is inodified — its comprehension is widened and its extension is narrowed; man, horse, dog, locomotive — everything- but boy — is shut out. If rapidly be added, the act of running is limited to a certain man- ner of running by a boy ; and along the street again changes or modifies the mental picture. Similarly, the meaning of the expression / zvrite is modified — its extension is narrowed 40 PEDAGOGICS OF GRAMMAR. § 3 and its comprehension or definiteness is widened — when an object is added, / zvrite a letter. The transitive verb ivrite is just as really modified by the object letter as it would be by an adverbial modifier. And not only is ivritc modified by a letter, but the entire expression / ivrite as well. In grammar, however, we say that certain words modify certain other words, and not entire sentences. But in reality the subject modifies the predicate, and the object modifies both, and is itself modified both by the subject and the verb, taken separately or together. A word does not need to be an adjective or an adverb to be a modifier. In other words, the law of the inverse ratio between the extension and the comprehension of common terms applies to all sentential elements. Eveiy word added to a sentence makes the mental image more definite and diminishes the extent of its application. 33. Value of Exactness and Tlioroiijifliness. — It would be difficult to overestimate the importance to the teacher of being exact and thorough; and, indeed, of know- ing thoroughly every subject he teaches, and the precise meaning of every term he uses. The' writer remembers hearing one of the world's greatest linguists say that it is better to know all about one page of a foreign language than to know vaguely a great many pages. One of the great objections to the reading of novels and newspapers is that a habit of skimming the surface of the meaning is formed ; and this habit dominates us when we should read with attention and intensity. Make sure, therefore, that your pupils know the exact meaning of the language they use, and especially the meaning of technical terms. Equally important is it that the teacher shall know exactly what the language means that he uses. Incomplete and imperfect concepts are characteristic of nearly all human knowledge. Another source of vagueness is the uncertain interpretations that different minds put upon the words we use to express our thought. No two persons get exactly the same idea from a given combination of words. Some one says that we learn § 3 PEDAGOGICS OF GRAMMAR. 41 the meaning of words not so much from the dictionary as by noting their context — the way in which they are used. The first time we meet a given word, we assume a meaning for it that seems to suit the use made of it. Our assumed mean- ing may be very different from its real meaning. Then a process of approximation and cliininatioii begins. We meet the word again, and our first notion must be corrected; and so time after time we ehminate elements of our first notion, and approximate moi'e and more nearly to the true meaning. If this view is correct, it follows that the best way to study a foreign language is to read a book in the language without the help of a dictionary. The first time it is read, we get a very imperfect notion of its contents. If we read it again, something is added to our previous knowledge; and after several readings, there will remain some words that caiaiot be understood from the context. Then the dictionary becomes useful and necessary. Having learned the meaning of those words, we read the book as if it were our mother tongue. This is an illustration of the process of approximation and elimination. AMBIGUITY. 34. Ambifyuity From Restrictive and Coordinate Clauses. — In the classification of sentences, the teacher is often in doubt as to whether a given clause is restrictive or coordinate. A restrictive clause is one that merely modifies^ while a coordinate clause is one of equal rank with a princi- pal clause. " The temple tliat Solomon built stood upon Mount Zion. " The clause that Solomon built modifies tem- ple, and is therefore restrictive. This fact renders the sen- tence complex. But take the sentence, "The dog, ivhicJi is man's best friend anuvig the lower animals, is a relative of the wolf." The two clauses composing this sentence are coordinate, that is, of equal rank. The word which is equivalent to and he. The sentence is, therefore, compound. Clauses denoting tiine, place, manner, and inference are nearly always restrictive ; in general, clauses introduced by 42 PEDAGOGICvS OF GRAMMAR. § 3 conjunctive adverbs are commonly restrictive. Clauses introduced by the relative pronouns ivJio and tvJiicJi and their compounds with ever, so, soever, are nearly always coordi- nate; but the relative t/iat is properly used to introduce restrictive clauses. It is necessary, therefore, to consider more fully the latest authorized use of these relatives. 35. Wlio, Wliieli, and That. — In the use of no words in our language do writers exercise less care than \\\i\\ those forming the title of this paragraph. Formerly, no serious attempt was made to employ them with discrimination. It was said that who and that should be used to relate to per- sons, or to things personified, and wJiieJito young cJiildr en, to the hnver animals, and to inanimate objects. Many of our later writers have adopted the following ride with reference to the use of these words : Use avIio and Avliich. as coordi- nating relative pronouns, and tliat as a restrictive relative pronoun. The sentences that follow will illustrate this important distinction : "The house, which cost me five thousand dollars, was destroyed by fire." {zuhich = and it) The sentence is com- pound, vsince it means, ' ' The house was destroyed by fire, a)id it cost me five thousand dollars." " The house that my father owned stood by the seashore." This sentence is complex. The clause that my father oivned is an adjective modifier of house. It is an exact eqiiivalent of my fat J 1 07'' s. "The relatives that zverc invited were at the wedding." The relatives tliat ivere invited = The invited relatives. vSentence is complex. "The children, who' were ver}" obedient, were allowed to go to the picnic. " {ivJio = and they) Compound sentence. They were all allowed to go to the picnic. "The children that are very obedient .shall have a half holiday. " A promise to such only as are obedient ; a complex sentence. "He that soweth the wind shall reap the whirlwind." Restrictive clause ; sentence complex. § 3 PEDAGOGICS OF GRAMMAR. 43 " He, who showed nie all the depths and shoals of honor, died yesterday. " {(ivJio = and he) Coordinate clause; com- pound sentence. " Those that live in glasshouses should not throw stones." Restrictive clause; complex sentence. ' ' Those books, which I bought a year ago, have not yet been read." Coordinate clause, (ivliich — and thciii) "The books that are on the lower shelf were written by Dickens." Restrictive; complex sentence. "The boy, who had done no wrong, was punished." Here wlio = altliongh he. Compound sentence. "The members, who disliked their pastor, asked for his resignation." This means all the members. Compound. "The members that disliked their pastor left the church." Only some of the members are included. Complex. The writer believes that sufficient has been g-iven above to make clear the sharp distinction that should be observed in the use of the relative pronouns. This distinction, too, con- forms to the latest usage. Unless it is observed, a writer finds it scarcely possible to avoid ambiguity. Indeed, nearly all of the uncertainty of meaning that we find in our litera- ture comes from the use of pronouns. In the writings of Robert Louis Stevenson, it is scarcely possible to find a sen- tence where these relative pronouns are misused. One of our critics, speaking of the works of this writer, says: "No better English has been written by any other author since the pen fell from the tired hand of Thackeray. " If the stu- dent will examine vStevenson's writings, he will notice the almost entire exclusion of the coordinating relative pronouns, and will be struck with the sparing use of the restrictive relative pronoun. To illustrate, we quote from his beautiful prose poem, " Will o' the Mill." "That divine unrest, that old stinging trouble of humanity that malce all high achievement and all miserable failure, the same t/iat spread wings with Icarus, the same that sent Columbus into the desolate Atlantic " Here it would be difficult to omit the relative pronoun. " He felt as if his eyesight would be purged and 44 PEDAGOGICS OF GRAMMAR. § 3 clarified, as if his hearing would grow more delicate, and his breath would come and go with luxury." In this quotation we have as if for tJiat, used as a con- junction. Even when tJiat loses in some measure its pro- nominal value and becomes a mere subordinate conjunction, it is still used with something of the office of a pronoun. Thus, "He felt that etc." = "He felt this, namely, that etc." When, as here, tliat is used as a subordinate con- junction, there is an implied antecedent of the pronominal function that has not entirely vanished froin the Avord. " It was no wonder he was unhappy." The coordinating use of %uho and wJiicJi is illustrated in the following three quotations: "The shepherd, who makes so pretty a picture carrymg home the lamb, is only carrying it home for dinner." " I feel tongue-tied myself, who am not used to it. ' "He tried to prove that this was no more than a true lovers' tiff, which would pass off before night." 36. Care Required in the Use of tlie Relative Pronoun. — It may be inferred from what has been said tmder the preceding topic that pronouns of every kind should be used sparingly, and that, when used, there should be no uncertainty abotit their antecedents. When there is only one possible antecedent, no ambiguity can result from the use of pronouns; but, when there are several words in a sentence, any one of which may be the antecedent of a sub- sequent pronoun, the meaning generally becomes a matter of conjecture. The teacher cannot overestimate the impor- tance of this matter. Exercises should be prepared that contain pronouns used ambiguously, and the pupils should be required to clear up the uncertainties. A relative should be as close as possible to its antecedent, and no word should be introduced between them that is likely to be mistaken for the antecedent. " Let me introduce the son of my friend, who formerly resided in this city." The antecedent of ivJio may be either son or friend. If S 'J PEDAGOGICvS OF GRAMxMAR. 45 son is the antecedent, the ambiguity is removed by chang- ing to 111)' fn'i'/h/'s so//, 7i'//o etc.; \i friend, we should say tJic son of i/iy f/-icnd that etc. It would be still better to separate the descriptiv^e part: '' Let me introduce the son of my friend — my friend that formerly etc." Very frequently the predicate is improperly interposed between the relative and its antecedent. ''He is well paid tliat is satisfied." ''He should not blame another man that himself has erred." Better: "He that is satisfied is well paid." "Ife that has erred should not blame another." The following are some other examples of ambiguity from uncertain antecedents: " This way will direct you to a ge//t/e///a//'s ho//se that hath skill to take off these burdens." Should be "to the house of 3. gei/tle/iia// that etc." "Nor better was the//- lot that fled" = " the lot of thei/i that fled." "All is not gold that glitters." Better, "Not all that glitters is gold." "Cats catch no mice that wear gloves." Write instead, " Cats that wear gloves catch no mice. " 37. Exercise. — Both by means of maps and diagrams analyze the following sentences, being careful to distinguish between restrict- ive and subordinate clauses: 1. " All that tread the earth are but a handful to the tribes that slumber in its bosom." 2. " The Romans were the best soldiers and the wisest lawgivers that the world has ever seen." 3. " The first Napoleon, whom tlie English banished to St. Helena, died there in the year 1821." 4. "... a lie which is all a lie may be met and fought with outright, But a lie which is part a truth is a harder matter to fight." ( T/iat would be better than lohich here in both places.) 5. " The saddest thing that can befall a soul is when it loses faith in God and woman." fi. " It is alwavs right that a man should be able to render a reason for the faith that is within him." 46 PEDAGOGICS OF GRAMMAR. § 3 7. " He that does one fault at first and lies to hide it makes it two." 8. "It left a sting behind that wrought him endless pain." 9. " There were the vast lips, which, if they could have spoken, would have rolled their thunder accents from one end of the valley to the other." 10. " How can a country whose very name suggests to us move- ment and progress be governed by a system and under an instrument which remains the same from year to year and from century to cen- tury ?" SYNTHESIS. 38. Synthesis of Sentential Elements. — In teaching the structure of sentences, synthesis is just as important and just as interesting as analysis. Professor Bain, indeed, objects to the use, in grammar, of the term synthesis, although it is pretty clear that his protest is based upon nothing stronger than the fact of its metaphysical use. But, in the United States, at least, a work on language that should omit exercises in synthesis would have but little chance of success against competitors. As has been said, the meaning of the word is the opposite of the word analy- sis. It is derived from two Greek words: syn, together, and thesis, a placing or putting — a putting together. If the parts of a watch or a locomotive were all at hand, but disar- ranged, and one were to arrange them — put them together — the operation would illustrate what is meant by synthesis. Any arranging of sentential elements — words, phrases, and clauses — so as properly to express thought, is synthesis. Hence, any composition in which the writer properly arranges the elements of thought is an exercise in synthe- sis. The same is true when the teacher finds the thought, or the disarranged sentential elements that, properly put together, will express a thought. There is a form of puzzle, much delighted in by children. It is known as the dissected pieture. A picture on a large piece of cardboard is cut into pieces of different shapes, and the child is required to arrange the parts so as to show the picture as it was at first. This suggests a valuable exercise in verbal synthesis. The writer once knew a very intelligent teacher that provided herself § 3 PEDAGOGICS OF GRAMMAR. 47 with as many small paper boxes as there were pupils in her class; in each box she put the words and phrases of a sen- tence, together with the proper punctuation marks. The sentential elements were neatly written upon bristol board. The boxes having been distributed, each pupil was required to arrange the contents of his box so as to form a sentence. The work of preparing the boxes and their contents was one not involving the expenditure of much time or money, and the enjoyment and profit to the children were of the highest. Of course the teacher will see in this a scheme that can be carried down to the lowest primary grade, and used as an adjunct in teaching reading and in furnishing a vocabulary. In these exercises the sentential elements may be given as words, or the phrases may be entire — a matter to be governed by the grade of the class. For the lowest grades "Mother Goose " or other similar classic for children is a good source from which to get the material for this exercise. Of course, for higher grades, more difficult selections may be made. After the various sentences formed during an exer- cise have been examined and approved by the teadier, a writing lesson may follow, and in it the sentences may be i;sed as copies. Two such sets of 50 each should last 100 days. 39. Syiitlietic Kxercise for Increasinj>" tlie Vocabu- laries of I'lipils. — Again, take not more than five new words daily for four days a week. They should be assigned the day before they are to be used. Of course the children will talk about their meaning, and so the process of approxima- tion and elimination will begin. The words are written upon the board and numbered. The teacher directs that the pupils in the first row of desks shall take the first word and introduce it in sentences so as to show that they have learned the meaning of the word — and write the sentences. To the other rows in turn are assigned the other words, with the same directions, until the pupils have heard all the words used many times. If there are more than five rows of pupils, any of the words may be given a second time. Then the sentences are read and criticized — but not bv the teacher 48 PEDAGOGICS OF GRAMMAR. § :^ until after the pupils have been heard and have critieized one another's work. This exercise may be extended to include, in one sentence, f7i'o of the given words, or a// of them in two or more sentences relating- to the same subject. In the Friday review the pupils may be required to write a brief essay on a subject assigned by the teacher or chosen by the pupil, and to introduce into it all the words studied dur- ing the week, underscoring them. If this work is faithfully done and properly reviewed, there is no better means of having children get a knowledge of the exact meaning of words, and of how to use them. The words assigned should, of course, be useful in every- body's vocabulary. Another synthetic exercise of somewhat greater difficulty is to reproduce orally, and later in writing, the reading lesson, or something read by the teacher. To tell in prose the story of a narrative poem, or of one that is descriptive, is also an excellent exercise. Such a poem as Eugene Field's exquisite "Little Boy Blue," or many of the poems in Robert Louis Stevenson's "Child's Garden of Verses" are suitable for this exercise. Many others that are usable for this purpose might be mentioned, such as Cowper's "An Adjudged Case," and others of his poems, Leigh Hunt's " Abou ben Adhem," Wordsworth's "We Are Seven," and innumerable other poems that will readily suggest themselves. Besides, there are many waifs that float about in the papers and magazines, which tho teacher can cut out and paste in a "Language Note Book. " 40. " Sentence Bnilcling:.''' — The exercise known as ^'■sentence building'' is another example of synthesis. It consists in the pupil's supplying and properly placing- one or more indicated sentential elements. Thus, the teacher may supply : 1. A list of subjects, and require the pupil to find appro- priate predicates; and the reverse. 2. A subject and a predicate, and require an attribute, an object, or a predicate noun. § 3 PEDAGOGICvS OF GRAMMAR. 49 3. A subject modified or unmodified, and require a variety of modified or unmodified predicates. 4. A single word subject and predicate, and require the addition to each of several modifiers, one at a time. 5. A list of subjects modified or unmodified, and a list of suitable predicates disarranged with respect to the subjects, and separated from them by a vertical line. Here the pupil is required to tmite subjects with suitable predicates. 6. The same exercise as 5, with object, attribute, or predi- cate noun added. 41. Anotlier Kxercise in Synthesis. — A very interest- ing exercise in synthesis — one that pupils enjoy very much — ■ is to restore to the best possible order the disarranged ele- ments of sentences. This closely resembles the exercise already described, which is suggested by the game of " Dis- sected Pictures." The teacher may write on the board or dictate the disarranged elements of any good sentence — its important words and its phrases — and require the pupils to embody them all in a written sentence as free from faults as possible. A few examples will illustrate. Suppose that the following fragments of a sentence are dictated to the pupils, and that they are to arrange them so as best to express the hinted thought : are dressed, of the year, in colors, iit the fall, the most beautiful, everywhere, the woods. Some such results as the following may be expected: " Everywhere in the fall of the year the woods are dressed in colors the most beautiful." "The woods everywhere are dressed in the fall of the year in colors the most beautiful." "In the fall of the year the woods are everywhere dressed in the most beautiful colors." " The woods in the fall of the year are dressed in the most beautiful colors everywhere." Many other arrangements are possible, and the very instructive matter for the pupils to consider is which arrangement is the best and the reasons why it is the best. 50 PEDAGOGICS OF GRAMMAR. § 3 The difficulty of the exercise may be increased or diminished by using long or short sentences. Simple and familiar poems may be thus dissected by the teacher and restored by the pupils. The exercise that follows will make the student familiar with the details. 43. Exercise. — Arrange each of the following in a good sen- tence : 1. a few, for the dismission, the signal, of school, in minutes, usual, will be given, without doul:)t. 2. out of them, the child, yellow, to get gold, poor, for her mother, simple, buttercups, beloved, boiled. 3. down the middle, there, a little girl, that hung, of her forehead, a little curl, was, who had. 4. of the village, the rain, the mist, and, and, a feeling of sadness, see, comes, gleam, my soul, resist, through, cannot, I, the lights, o'er me, that. 5. in shallow water, into the small streams, of the year, up the riv-ers, of fish, go, many kinds, to lay, in the spring, their eggs. 43. The Iniprovement of Method. — The exercises above will indicate what is meant by sentence building, and the teacher fertile in devices will invent many more to emphasize the particular phase of the subject imder consid- eration. Such of these devices as are found to have good working value should be carefully preserved for future use. The teacher that means to grow in his profession must not be content to do his work in the same way year after year, using the same material. That is to get into a rut, than which nothing can be worse. What he has should serve to suggest something new and better, or at least improvements upon the old devices. He should realize that no life is long enough to reach the goal of perfect teaching. Each year should reveal imperfections in the work and methods of the last. The last stanza of Oliver Wendell Holmes' ' ' Chambered Nautilus" should serve as an inspiration to the teacher not only in mental and spiritual, but also in professional, growth. We make no apology for quoting it here, for nothing more noble, inspiring, and intrinsically beautiful was ever written. § 3 PEDAGOGICS OF GRAMMAR. 51 " Build thee more stately mansions, O, my soul, As the swift seasons roll! Leave thy low-vaulted past ! Let each new temple, nobler than the last, Shut thee from heaven with a dome more vast, Till thou at length art free. Leaving thine outgrown cell by life's unresting sea." 44. Order of Sentential Elements. — In the construc- tion of a sentence the main object to be attained is such an arrangement of its elements as shall occasion the least possi- ble mental effort in understanding the meaning. The great masters in the art of composition have accomplished this, and hence the pleasure we find in reading their works. For the mind to build up, all in perfect logical sequence, the thought expressed by sentential elements, produces an emo- tion of pleasure; but, when the arrangement is illogical and out of sequence, a sense of confusion results, and, in conse- quence, pain. In most sentences, notably in long and com- plicated ones, a great variety of arrangement of the elements is possible. Obviously, there must be one arrangement easier of comprehension and more forcible than any other. Moreover, there must be some general principles dominating the order of elements. The importance of this subject to the teacher is very great. Professor Bain insists that, in the teaching of English, no exercise is so valuable as training the pupils in discriminating various arrangements with respect to their force, smoothness, clearness, and intelligibility. Mr. Herbert Spencer, in his "Philosophy of Style," intro- duces this general subject by discussing the question : Which is the better order, the French //// cJicval noir, '*a horse black," or the English, a black horse? In the former, upon hearing //;/ clicval, the mind instantly calls up the picture of a horse, — preferably the horse we drive daily, or see often- est, — it may be a white, a bay, a sorrel, or a chestnut horse. When the adjective noir follows, the mind is taken aback ; it must divest itself of the picture already formed, and substitute another. This involves the useless expenditure of mental effort, and is attended by a sense of bafflement that obscures 52 PEDAGOGICvS OF GRAMMAR. § 3 the image and unfits the mind somewhat for the confident interpretation of what may follow. The conclusion of Mr. Spencer's reasoning is that /// general a modifier should pre- cede the eleuient modified. So that, the adjective should pre- cede the element it modifies. Thus, " Great is Diana of the Ephesians." And Tennyson, " . . . . bright, and fierce, and fickle is the South, And dark, and true, and tender is the North." "And brief the sun of summer in the North, And brief the moon of beauty in the South." By inverting these extracts, much of their force and beauty is lost. Thus, " Diana of the Epliesians is great." " The South is bright, and fierce, and fickle,*' etc. Again, " Dctxr as remember'd kisses after death, And sweet as those by hopeless fancy feign' d On lips that are for others ; deep as love. Deep as first love, and 71.'//^/ with all regret; O Death in Life, the days that are n^) more." Here, the beauty of the whole is much enhanced by the precedence of the italicized adjectives which all modify days at the end of the stanza. 45. Coinnion Usage. — Usage, however, requires that, in ordinary prose, and in the conversational style, the predicate adjective and the predicate noun shall follow the subject. Thus, we say, "The sky is red," not, "Red is the sky"; and " He is a gentleman," not, " A gentleman is he." Yet we believe that any one can feel the superior force of the second forms. In like manner the most forcible position of the adverb is before the element it modifies. Thus, " Blandly and sweetly he smiled." — " He smiled blandly and sweetly." The former is clearly the more forcible, but it is the poetical, not the prose, arrangement. § 3 PEDAGOGICS OF GRAMMAR. 53 " the gods, who haunt Tlic lucid interspace of world and world, Where nc7>er creeps a cloud, or moves a wind, Nor ever falls the least white star of snow. Nor ever lowest roll of thunder moans, Nor sound of human sorrow mounts to mar Their sacred, everlasting calm." In the above quotation, not only do the adverbs precede the elements they modify, but the subjects cloud, %vi>id, and star follow their verbs — this being their poetic and most forcible order. " And siueet it was to dream of Fatherland, Of child, and wife, and slave; but evermore Most weary seem'd the sea, weary the oar. Weary the wandering fields of barren foam." In this quotation will be seen the same arrangement of predicate adjective and verb, and of subject and predicate. It is, however, in the formation of compound words that we see best exemplified this law of arrangement. Sidcivalk, steamboat, zuatfr-whecl, ivatcJi-kcy, douni-Jicartcd, short- sighted, trolley-car, overcoat, are examples. Indeed, it would be difficult to find a compound word in which the modified part is not placed last. 46. The General Law of Sequence. — Briefly stated, the law of sequence, not only in the structure of compound words, but also in sentential structure, is from the abstract to the concrete — from the less specific to the more spec fie. If a complicated sentence contains many phrases and clauses that modify, and to carry them all in the mind and hold them in readiness for the main idea becomes burden- some, a judicious distribution of them is often better. Mr. Spencer gives the following as an example; first, with the modifiers of the predicate placed after it: "We came to our journey's end, at last, with no small difficulty, after much fatigue, through deep roads, and bad weather." He qtiotes from Dr. Whately the following arrangement: "At last, after mrich fatigue, through deep roads and bad weather, we came, with no small difficulty, to our journey's end." 54 PEDAGOGICS OF GRAMMAR. § 3 Mr. Spencer suggests as better: "At last, with no small difficulty, and after much fatigue, we came, through deep roads and bad weather, to our journey's end." Of these arrangements it may be observed that the first is extremely awkward and entirely inadmissible. It illustrates very forcibly the weakness that results from putting modifiers last. The second arrangement is better, but its modifiers do not proceed from the less specific to the more specific. J/7/// no small difficulty is less specific — less concrete — than any preceding phrase except <-?/ A?^/. In Mr. vSpencer's rearrange- ment, the modifiers are in the order of increasing concrete- ness, and, besides, they are placed before and after the predicate verb came in such proportion as to make the mental effort in grasping the thought the least possible. The mod- ifiers that follow the verb do not materially change the meaning of the whole, and their effect is easily added. It appears, therefore, that while, in general, modifiers should precede the terms they modify, the task of carrying in the mind conditioning elements may become so great that a judicious distribution of them, such as is indicated in the above sentence, becomes necessary. The fact is that it is only the most vigorous mind that can vividly retain the modifying effect of many phrases. and clauses, and apply them with their full force to the modified part. For ordi- nary minds, it is better to distribute the modifiers, placing some before, and some after, the main statement. In doing this, care should be taken to arrange them in accordance with the law already indicated: To produce the greatest pos- sible mental effect, modifiers should proceed in order from the abstract to the concrete, from the less specif c to the more spe- cific, and, if numerous, they should be placed, some before and some after, the predicate. 47. Syntliesis of Complex Sentences. — In complex sentences the subordinate clause should, in general, precede the principal clause; but when there are two .subordinate clauses, it may be better to place one of them, usually, the more specific, after the main clause. § 3 PEDAGOGICS OF GRAMMAR. 55 " When the tide turns we shall set sail." " If you wish to govern wisely, learn to govern yourself." " If I mistake not, I met him when we made the charge at Gettys- burg." In this .sentence, If I mistake not is less specific than ivJien wc, etc., and the arrangement is better than to put both subordinate clauses before the principal clause. Of the six possible arrang-ements of the three clauses in the sentence above, the order given is undoubtedly the best. Even in poetry and highly emotional prose, the principle of tJic least mental resista)iee may make necessary a sequence of sentential elements different from that dictated by theory. In other words, there is in language work no exercise requir- ing better judgment and nicer discrimination than the dis- position of the words, phrases, and clauses that make up a complicated sentence. Moreover, no exercise yields better resitlts than that so much insisted upon by Mr. Bain — trying the ear and the mind upon all possible arrangements of a sentence, the end in view being to determine which is mo.st forcible, clear, smooth, and easy of comprehension. The ultimate object of such exercises is the acquirement of a taste — an automatic mental action that shall at once select the best sequence of sentential elements. As soon, therefore, as the mental maturity of the pupil is sufficient for the exercise, the teacher should, during the reading lesson, start questions as to the best possible sentential arrange- ment. He will find his reading book full of faulty sentences that even comparatively young children can rearrange and improve. Clauses may often be condensed into phrases, or even into single words. On the principle that force is gained by brevity, this will generally be a means of bettering the sentence. The exercise of expanding words into phrases and clauses, and phrases into clauses, is almost equally valuable; for in the manipulation of language it furnishes much needed skill, and is perhaps the best method of enlar- ging the pupil's vocabulary, and of rendering more precise his notion of the meaning of words. 50 PEDAGOGICS OF GRAMMAR. SUMMARY. 48. Tabular Classification of Heiiteiices. — The fore- going general treatment of the sentence would be incom- plete without a synoptical classification as to form and use. The writer believes that the following tabular view will be found by the teacher to be helpful: r 1'. Exclamatory- "] I declarative. I + strong ) _ J 2'. Exclamatory- emotion f interrogative. 3'. Exclamatory- imperative. 'A As to Use 1. Declarative 2. Interrogative I 3. Imperative 1. vSimple r Subject and Predicate Simple. j .Subject Compound, Prediciite Simple. I Subject Simple, Predicate Compound. 1 [ Subject and Predicate Compound. f One Principal, one Subordinate Clause. As to ^^ _, I ^ Form > ''^' ^*^™Pl^^ ^ One Principal Clause, two or more Sub- [ ordinate Clauses. ( Two Coordinate Clauses. Two Principal Clauses, one or more Sub- ^ 3. Compound J ordinate Clauses. More than two Principal Clauses, one or more Subordinate Clauses. 49. Remarks on the Table. — The teacher must not assume that every possible variety of .sentence is included in the six forms that, in the table, are classified with respect to use. A declarative clause may be combined with an interrogative clause to form a complex or a compound sen- tence. In like manner, a declarative clause may be united with an imperative clause. Moreover, either combination may be exclamatory, and either may be accompanied by clause modifiers. Many other varieties of union are pos- sible. In classifying such sentences, the character of the § 3 PEDAGOGICS OF GRAMMAR. 57 successive clauses should determine the order of the terms indicating the classification. Some illustrations follow: A Coiiipouiid Impcrativc-Dcclarativc-Exclamatory Sen- tence: " Stand ! the ground's your own, my braves ! " " Come one, come all; this rock shall fly Fi'om its firm base as soon as I ! " A Complex Imperative- Deelarative-Exelainatory Sentence : " Flee, if you value your lives 1 " A Compound Deeletrat ive- Lit errogat ive Sentence : " Death is the end of life; then \\\\\ should life all labor be?" 50. Couuectives in the Classification of Sentences. The presence of a connective between clauses is not neces- sary to indicate that they are to be taken together. Indeed, where the element of strong emotion enters, connectives are usually omitted. Their absence denotes incntal turmoil and excitement; their presence, repose and mental balance. The degree of connection must be determined from the context and from the meaning. 51. Pnnctnation in tlie Classification of Sentences. Neither should the punctuation determine whether the clauses are to be taken separately, as sentences, or together, as parts of a compound or a complex sentence. Few teach- ers, for example, would hesitate about treating the following stanza, however it might be pimctuated, as one compound sentence : " Woodman, spare that tree! Touch not a single bough ! In youth it sheltered me, And I'll protect it now." Here, again, is an opportimity for the discipline of the judginent and the powers of discrimination; for it would be almost impossible to find tw^o writers that would punctuate in the same way a long, complicated paragraph, to say nothing of a poem, a letter, or a magazine article. As has been said, most authors pimctuate their composition in accordance with their notion of the manner in which it 58 PEDAGOGICS OF GRAMMAR. § 3 should be read ; but, since an author is likely to feel more strongly than others the meaning he intends, it follows that his punctuation will differ from that of his reader, who is not influenced by the "white heat of composition." Again, it would be difticult to find two readers of an emotional pas- sage whose conceptions of its rendition would agree. No two actors have ever rendered Hamlet in the same manner; the words they used were the same, but the pauses, the inflections, the gestures, were different. The teacher, therefore, in determining the closeness in the sequence of the elements of a paragraph must be guided, not by the punctuation alone, but also by the degree of earnestness intended to be expressed, by the emphasis used in reading it, by the length of the elements themselves, and by many other considerations. SPECIAL COIS^STRUCTIOXS. 53. Pleonasm. — In classifying sentences, the teacher will frequently meet a very puzzling construction that gram- marians have called pleonasm. The word is derived from the Greek v^ord p Icon, more. It signifies the employment of more words to express a thought than are really necessary. The term tautology is often used in much the same sense; but pleonasm is the generic term of which tautology, rediin- daney, prolixitxy, and verbosity are species. The treatment of this subject properly belongs to rhetoric, but its importance in the classification of sentences is the writer's excuse for briefly referring to it in this place, and exemplifying it. Tyndall, in one of his books, quotes the following passage, saying of it that a subject seems to be "left floating in the air. " " He that hath ears to hear, let him hear." The subject meant is lu\ which has no accompanying verb. That hath ears to hear modifies both he and Jiim. The Jie is superfluous; for, rearranging the sentence, we have, Let him hear that hath ears to hear. He, in this case, is said to be § 3 PEDAGOGICS OF GRAMMAR. 59 "in the nominative case by pleonasm." The construction is a very common one, and is frequently found in the best authors. " The boy, O, where was he ?" "The sweet babe," said the king, "she shall be cared for by the queen herself." " A human cry; methought I heard a human cry." The effect of simply moitioiiiiig the matter that is to be the principal content of a sentence to follow is to concen- trate the attention upon that idea. It is an effective rhetor- ical device. Perhaps to suggest, by means of an elliptical question, the subject matter of a following sentence should be regarded as another form of pleonasm. " The woman's cause? The woman's cause is man's; they rise or fall together." "A healthy body? It is an indispensable condition to a healthy mind." " The sea ? God bless us ! The sea ? It is the greatest thing God ever made." It is a cjuestion whether, in the last sentence, everything as far as // were not better treated as independent by pleo- nasm. It is certain that there is no grammatical relation between the sentence and the exclamatory matter; yet the latter cannot be regarded as composed entirely of interjec- tional matter. Sentences preceded by such matter, therefore, should be classified as if they stood alone. The effort to fill up the supposed ellipses simply results in changing the meaning of the whole, and in spoiling the rhetorical effect. The point aimed at in our system of diagrams is to avoid the dismem- berment of sentences. They should be taken with the idioms they contain, withoitt supplying ellipses never contemplated by the author. 53. Otlier Forms of Pleonasm. — There are other varie- ties of pleonasm, such as saying the same thing more than once in the body of a sentence ; as, " He told me the very, (iU PEDAGOGICS OF GRAMxMAR. § 3 identical, same thing," for "He told me the same thing." This is usually called tautology or redundancy. If an idea differently expressed is repeated in two or more successive sentences, or in two or more clauses of a sentence, it is a form of pleonasm called //W/>//j/. But the only variety that needs to be noted here is the one explained above, where the pleonasin consists simply in mentioning the subject matter of a sentence to follow. This is good, strong, idiomatic English; the other forms are always blemishes, and should be carefully avoided. FALSE SYNTAX. 54. Error as Example. — Some of our educators insist that, so far as the teacher can accomplish it, error of every kind should be kept from the mind of the pupil. He should never be permitted to see or to hear a word wrongly spelled, lest, later, it might displace in his mind the correct form. These educators say also that the pupil should never be required to rectify errors in grammar, but should be exer- cised solely in classically correct English. In reply to all this it may be said that the pupil hears bad English con- stantly. The air is full of it. If he goes out to play, he hears it from his playmates ; if he goes to school, he hears it from his classmates — and from his teacher. He hears it in nine out of ten of our homes ; he meets it in the books he reads and in the grammar he studies. Who, indeed, always speaks correctly ? Not the teacher, the school principal, or the school superintendent ; not the minister, not the lawyer. It is granted that a very few people blunder but rarely, but the number of such is not one-tenth of one per cent, of our population ; and there is perhaps no one that a/ways speaks classically pure and otherwise correct English. It is doubt- ful whether any one can be found that invariably writes so as to be above fair criticism. Only today one of my children came home from the High School and told of an impressive lecture upon the beauty and importance of speaking good English. This was followed by the question, " Now is there § 3 PEDAGOGICS OF GRAMMAR. 61 anythin^^- in this lesson that anybody don't understand ?" It is generally assumed that in conversation a certain margin of incorrect speech should be allowed, even to teachers, on the same principle that a moderate license is granted to poets. If it is human to err, it would seem to follow that to be always right should be accepted as evidence of divinity. The reasoning of those educators that would keep from the pupil all incorrect forms would prevent us from indicating the meaning of a word by giving an approximate synonym, for the authorities tell us that no two words of exactly the same meaning can be found. To the writer this contention seems utterly indefensible. We learn perhaps more from bad example than from good — more from unlikeness than from likeness. Nothing is qiiite .so emphatic as contrast. 55. Some Illustrations. — False syntax, therefore, is proper matter upon which to exerci.se the judgments of our pupils. The likelihood of their retaining the incorrect form and of confusing it with the correct, is purely imaginary. As long as we hear cultivated people saying " I feel badly," " vShe looks nicely," "prettily," etc., exercises in the correc- tion of false syntax seem to be, in ohr schemes of education, very much in order. The writer, not long ago, overheard the superintendent of schools of one of the largest cities in the United States answer the questions of a friend: " How are you today?" "Nicely, thank you." "And Mrs. — — , is she well?" "No; she complained of feeling badly this morning. " The writer was asked a short time ago whether one should say "The package arrived safe,'' or "The package arrived safely. " The inquiry was made by a gentleman that has for many years been a writer of books, and yet he had not learned to discriminate betw^een the case where the action expressed by the verb is to be modified by an adverb and that where the state of the subject is modified by a predicate adjective. In this example, a little reflection makes evident that it is not the act of arriving that is safely performed, but that it is the state or condition of the package after the 62 PEDAGOGICS OF GRAMMAR. § 3 act is finished. The package is safe after the act of arriving is complete. There is a long list of what soiPie grammarians call neuter verbs that must be followed by adjectives expressing a state or condition of the subject. Some of them are the forms be, seem, feel, appear, get, beeome, look, etc. Besides these, innumerable active verbs are used in the same way. Ope?i your eyes tvide. Shut the door tight. The general sat erect upon his horse. Do not aet silly. Sometimes it is difficult to tell whether it is the meaning of the verb or of the subject that should be modified. But, if the adjective is used, it is the subject to which the attention is directed ; if the adverb, we must think of the action expressed by the verb. " The citizens stood firm for their rights." "The citizens stood firmly for their rights." " Quick as a flash the man sprang to his feet." "The man quickly sprang to his feet." This subject will be treated more fully in another place. It has been introduced here only as an illustration of the need for exercises in correcting false syntax. 56. Collections . for Correction. — The teacher should be provided with a note book in which should be arranged a well classified list — 1. Of local errors in speech — those frequently heard in the neighborhood where he teaches. The writer knows of a large city in this country where the expressions "quite some," "quite a few," and "quite a little " are imiversally current. Even the clergymen of the city use them in the pulpits, and nobody seems to know that they are gross errors of speech. In a conversation with one of the clergymen of the place, the writer mentioned the fact that these errors were in general use in the city. " I think that I do not use them," he said. "Constantly; yon use them constantly, " was the answer. "I really did not kriow it, and I shall try to avoid them in fttture." But he continued to say "quite some," and, if he is still alive, he probably commits the same blunder. § 3 PEDAGOGICS OF GRAMMAR. G3 2. Of errors that ma}- be heard elsewhere, or found in books, ma^'azines, and newspapers. In the course of a few terms, a large variety of examples illustrating errors can be accumulated, even if they are sought for in our best authors. The object to be attained is, primarily, to exercise and sharpen in the pupil the power of discrimination, and, secondarily, to make him careful of his own speech. If the teacher expects to add materially to the correctness with which his pupils speak the mother tongue, he will be disap- pointed. It is only when we have learned the difficult art of listening critically to onr ozvn language Wxa.X. rapid improve- ment in speech begins. This is almost as difficult as the task the stenographer must master — -that of writing one sen- tence and of accurately hearing and remembering the next. In the correction of false syntax, after the teacher and pupils have gone over the examples orally, and have dis- cussed the principles involved, the corrections should be made in writing, with or without reasons, as the teacher may direct. This work should be done, not on slates, but on paper; it is good practice in composition. ACQI IRIXC; A TOCAIil LARY. 57. Tlie ?^atiii"e of our KuoAvletlge of Words. — Every person knows the meaning of hundreds, perhaps thousands, of words he never uses. His failure to use known words does not come from the fact that they are iiseless and would not embellish his speech. Indeed, the best measure of a man's culture is the abundance and variety of his stock of words, and the precision and discrimination with which he uses them. A large vocabulary is, therefore, something worth laboring to acquire. But why, when we know the exact meaning of a term, is it not ours for daily use ever afterward? Oliver Wendell Holmes says: "My thoughts flow in layers, or strata, at least three deep. I follow a slow person's thought, and keep a perfectly clear undercur- rent of my own beneath it. Under both runs obscurely a 64 PEDAGOGICS OF GRAMMAR. § 3 consciousness belonging to a third train of reflections, inde- pendent of the other two." Sometliing akin to this is true of the words we know. They are in layers. The top layer consists of the words we learned in childhood, increased by a slow accumulation since. These words call up the most vivid images that the mind is capable of forming. It is our ordinary, daily, working vocab- ulary. We use it in our home conversations, wath wife and children, and with our oldest and dearest friends. In society, with those whose life environment has been different from our own, we draw largely from a second stratum of words, using at the same time many from the first layer. But here our conversation fakes on a certain hesitancy and artificiality not found in our familiar talk at home. We are conscious of a want of promptness in the words getting into proper place and relation in our sen- tences. The home talk is almost perfectl}^ automatic; this costs us an effort, and is, therefore, less pleasurable and much less forcible. And so, all the world is agreed that "old friends are best," and this arises partly from the fact that they have many memories in common with us, and partly because they use, in the main, the same vocabulary that we use; it is easier to converse with them. Lower still is a stratum containing many technical terms, and Latin and Greek derivatives. In our miscellaneous reading we have met these words once or twice a year for many years, until we know from the various contexts, or from the dictionary, exactly, or nearly, what they mean. But as the memory is called upon for words in which to express our thought, these words show no tendency to take their places in our sentences. Rarely, one of them will, so to speak, stir or turn over, indicating that an impulse was felt, but it was not strong enough to dislodge it from its place. 58. Method of Ijearning Words. — But, how do new words get into our working vocabulary ? The primary con- dition is, that we shall hear them daily and for a considera- ble time. It is reiteration — repetition — that does it. Years § 3 PEDAGOGICS OF GRAMMAR. 65 ago I stopped for a time in a family where the word appre- hend was constantly used. It was a synonym for thifik, sup- pose, believe, imagine, fear, conjecture, and many other words. Of course, I noticed the excessive use of the word, and I noticed, too, that the wife and a son and daughter employed the term with almost the same frequency as the father. I observed later that the w^ord began to offer its services in my own sentences — an offer that I steadily declined. But even to this day the word will come and cause me a momen- tary delay in finding a substitute. This necessity for reiteration, repetition, review, is the one indispensable condition of success, not only in making permanent and useful additions to the pupil's vocabulary, but also in giving him a firm, lasting, and usable hold upon, anything that he studies. Teachers constantly complain of the fact that their pupils forget so soon the things that have been so carefully taught. Reviews, and more reviews — that is the remedy. The brain tissue of growing children changes rapidly, and old things pass away or fade into a general con- fusion of images. They must be renewed again and again. 59. Getting- Rid of Objectionable Words. — The cor- rectness of the method of acquiring words as described above is confirmed by the experience we find in the effort to get rid of an objectionable word. Have you, my reader, managed to get the word nice into your vocabulary ? Do you say, ' ' It was a nice speech," "a ///rt'day," '^ nice soup," "■nice sleighing," " nice singing, " " a nice house " ? Is she a nice lady on a nice horse riding along a nice road to a nice town in the distance, where there is a nice store, full of nice attendants, that will sell her all manner of nice things ? Try to expunge the word from your vocabulary, and learn to use terms that dis- criminate these many different nice things. You will find that the word is in the upper layer, zealous to be serviceable as a sign of the absence of mental activity. It is a tenant having a lease in perpetiiity, who refuses to be dispossessed. Without knowing that you have used the word, you find it in your sentences, its presence demonstrating the tyranny of 6Q PEDAGOGICS OF GRAMMAR. § 3 habit. Even if you do learn practically to construct your sentences before you speak them, the task of finding a sub- stitute for the offensive little intruder is so onerous that you give up the struggle from sheer weariness. We are reminded by all this of the comment that Cassius makes on Brutus after he had consented to join the conspiracy against Csesar. "Well, Brutus, thou art noble; yet, I see, Thy honorable metal may be wrought From that it is disposed; therefore 'tis meet That noble minds keep ever with their likes; For who .so firm that cannot be seduced ?" A new word that every person should avoid seems to gain a wide currency Avith a facility and rapidity that no word of good lineage can show; and the difficulty of getting rid of a word appears' to become greater as its offensiveness increases. 60. Enlarg'ing the Pupils' Vocabularies. — It is clear, then, that if the teacher would enlarge the vocabulary of his pupils, he must expect to do it slowly. Twenty new words per week have been suggested in a former paragraph as a sufficient number. It may be added here that the teacher actually able to put so many good and useful words weekly into the working vocabulary of his pupils, — into the " outer layer,'' where their response to the mind's demand for signs for its thought is automatic, — mitst be an artist in the teach- ing of language. Yet this is the goal for which he should strive. Words that we know but do not use, have a value in enabling us to imderstand what we hear or read ; but only when we use them without conscious effort, do they change our personality and transform us before the world. It should be observed that learned, technical, and pedantic terms, even if they respond promptly to the mind's call for words, should be avoided in ordinary conversation. The reasons for this avoidance are so obvious as to require no statement. 61. General Remarks. — In the preceding pages the sentence has been taken as the "ttnit of thought," and stich general considerations have been discussed as it was believed § 3 PEDAGOGICS OF GRAMMAR. 67 would be helpful to teaehers of language and grammar. No attempt was made, however, to suggest an orderly method of procedure in teaching these subjects. That will be found in any good modern textbook. We come now to a treatment of U'onh. Just as the unit of thought is the sentence, so the sentence unit is the word. The sentence is here treated before any attention is given to the words that compose it. This is in accordance with the opinions of our best authorities on education, and it is in the same order as the development of speech. As we learn to recognize faces before we notice attentively the features that make them up, so the child learns to express his thought in sentences, giving no special attention to the words of which they are composed. It is impossible, however, entirely to separate syntax from etymology, and in what follows no effort shall be made to do so. The treatment of the sentence, so far, is of the wider kind that includes not so much what the teacher must introduce among the things he teaches, as matters that every teacher of language should know and think about. No one is competent to teach a subject familiar to him no further than he is required to teach it. Every teacher should have a large fund of general information, and besides, he should know very thoroughly, at least all the subjects he is required to teach; or, as some one has said, "The teacher should know something of everything and everything of something. ' ETYMOLOGY ^JST> SYNTAX. PRELIMINARV REMARKS. '^ ^. IMeaning' of TCtyniolo^^'y, — The word etymology is I i" e 1 from the Greek w^ords t:TVjiog, ctymos^ "real," "sure," "true," and "koyoc, logos, "aword, " " a discourse. " P-imarily, therefore, it should treat of the triic meaning of words as determined by their histor}^ derivation, and 68 PEDAGOGICS OF GRAMMAR. § 3 inflection. Thus, from love we have loved, 'lover, loves, loving, lovely, etc. These variations of form are for the sake of denoting" that the root idea in the word love is to be conceived of under various conditions of time, niiiiibei', action, etc. As a purely grammatical term, the word etymology, in its modern use and sense, means, " The branch of grammar that treats of the parts of speech and their inflections; the science of the elements of the sentence." It is with this meaning that the term is here used. Although the study of the origin and the history of words — etymology in its literal sense — is very fascinating and profitable, and a study that the teacher can scarcely afl'ord to neglect, yet the task of teaching it to immature pupils is one that yields but a poor return for the labor involved. It is rather a subject for the scholar in his library. It is conceded, however, that in the later stages of grammar work, the study of prefixes and suffixes can be made a source of much profit and interest to the pupil. But, in view of the inultitude of subjects that have a direct and vital bearing upon the questions of success in life and of human progress, we are not wise to consume our time in the study of a subject for no better reason than that it is interest- ing, and, to a degree, profitable. More and more, educators, in arranging the subject matter in which our children are to be educated, are taking into accoimt the probable life environ- ment of those children. How should they be trained so as to be fitted to do life's work most effectively for their own advan- tage and in the interest of the progress of the race ? That is the crucial question for the teacher and the educator. We must not, in this life so full of needs to be satis'fied — physical as well as aesthetical and spiritual — allow ourselves to be the- orized into an educational Utopia. We owe something — much more indeed than is generally suspected — to the house we live in — the body. It must be fed and clothed, of course; but, besides this, the repose, comfort, and health of its tenant are worthy of the most careful attention and forethought. (>8. Method of Treatment. — Professor Bain and some others insist that the parts of speech should be taught before § 3 PEDAGOGICvS OF GRAMMAR. 69 their properties or inflections are taken up. There is good reason for this, for a child can learn to distinguish nouns, adjectives, verbs, etc. long before he can understand what is medinthy person, ease, degree, mode, or tense. There is, per- haps, equally good reason for departing from the usual order in which the parts of speech are presented in our textbooks. If the sentence is to be regarded as the "unit of thought," it is obvious that its elements — words — should be treated in the order of their relative importance in the sentence. 64. Etymology and Syntax Sliould Be Treated Tog:etlier. — To study words as used in speech they must be treated with reference to their office in the sentence, and their relations there to one another. For it is only by these relations that we can tell an adjective from a noim, or a verb from a preposition or an adverb. It follows, therefore, that etymology and syntax ought not to be separated in the study of language, although imtil recently this has usually been done. In this work, the main concern with respect to any matter, will not be whether it is a question belonging to etymology or to syntax, but whether it belongs to the sub- ject of grammar and language. 65. Comparative Importance of Sentential Ele- ments. — In the simple sentence, the subject noun or pro- noun, and the predicate verb are the centers about which everything else clusters. They are, besides, the easiest parts of speech to recognize. With these will follow, in logical order, the word modifiers of the subject — adjectives, nouns in the possessive case, and the various pronouns that modify — then word modifiers of the predicate verb ; and, finally, connectives, including prepositions, conjunctive adverbs, relative pronouns, and conjunctions proper. Then should follow complex and compound sentences with phrase and clause modifiers. After thus going over the parts of speech with the object of becoming familiar with their classification as determined by their use or function in sentence structure, their inflections 70 PEDAGOGICS OF GRAMMAR. § 3 may be studied. The interjection naturally belongs with the independent constructions, the nominative case abso- lute, by address, and by pleonasm. Peculiar and idiomatic constructions may receive separate treatment, or they may be taken in connection with the parts of speech to which they are most closely related. With reference to the order of treatment indicated above, it may be remarked that it is one specially suited to the graded schools of our cities, large towns, and villages. A teacher beginning the study of grammar and language in the higher primary grades will find Mr. Bain's suggestion, referred to above, a good one. In higher grades, when the subject is to be completed and reviewed, no harm can come from following the 'Latin and Greek order that most of our writers have copied. Still, logical arrangement and logical methods of procedure are always b^st. C6. Terms Used by AVriters on Oramniar. — Before beginning the treatment of the several parts of speech, it should be observed that in their treatment of etymology there is much diversit)^ among authors in the use of terms — a fact especially noticeable in the case of the- verb. These diversities will be noted in their proper places. THE IsOUX. G7. Introductory. — The word noun is derived through the French from the Latin nonien^ a name. A noim is, there- fore, a liavic of anything. Tins definition follows so natur- ally from the original term, and is so simple that one might easily infer that all grammarians would be content with it; but it will be shown in a later paragraph how our authors have endeavored to differ from one another in defining the term. 68. Gradation of Treatment. — One of the errors most likely to be made by an inexperienced teacher is the failure to observe grades of difficulty in recognizing the noun, and to §3 PEDAGOGICvS OF GRAMMAR. 71 arrange his work in accordance therewith. Nouns may be conveniently taught in four groups: 1. Names of material objects denoted by single words; as, boy, horse, slate, book, etc. 2. Names of immaterial objects denoted by single words ; as, thought, memory, wisdom, plan, etc. o. Names of material things denoted by several words; as, '^A piece of rock broken fr-om tJic mount aiii rolled down into the valley. " 4. Names of immaterial things expressed by several words; as, "■ Livi)ig in a city is expensive." ^^The search for the north pole has not yet been successful. " It is extremely easy for the pupil to recognize nouns of the first class, and to be taught to put them into sentences as subjects, predicate norms, and as objects of verbs or of prepo- sitions. The special value of the norms included under 3 and 4 is to teach that a noun, or substantive, does not neces- sarily consist of one word, and that it is use or function that determines etymological classification. After the pupil has clearly seen that a certain phrase or clause is used as a noun, he may be required, when the proper time arrives, to clas- sify its several components. 09. The Noun Witli Modiflei's. — Before passing to the second class, the pupils should be trained in finding for a given noun all possible appropriate modifiers. The reverse exercise of finding a noun forgiven modifiers would naturally suggest itself to the teacher. In these exercises the brace should be constantly used. Devices like the following will be found useful: A obedient careless truthful An bov. A or An J pretty studious amiable 1 - girl. While in these exercises the pupil is required to find mod- ifiers for nouns, and nouns for modifiers, thus keeping up his acquaintance with word arrangement, he is not supposed as 72 PEDAGOGICS OF GRAMMAR. § 3 yet to know or use the word adjective. The term "modifier " which he employs, serves a better purpose, for it denotes fu7iction; adjective doe^ noi. The more familiar he becomes with the offices and relations of words in sentences, the more significant to him will be the etymological names when he finally reaches them. 70. Other Matters Connected With the Study of the Noun. — The difference between the pronunciation of the before a consonant (thu) and that of the same word before a vowel (the) may be emphasized by suitable exercises, as may also the distinction in use between a and an. If handled properly, the utmost enthusiasm may be aroused in a class by such exercises, and many others may be invented by the teacher or found in our textbooks. Of course, the teacher will preserve in a note book such devices as are found good in practice. The choosing of suitable predicates for nouns used as sub- jects may be reviewed during the study of the noun. It is extremely important, too, that children should not be left in doubt as to whether it is the word or the tiling that is the noun. After a thorough drill with nouns denoting material things, nouns denoting iimnaterial things may be taken up and treated in the same way ; — a much more difficult exercise. The pupils may be asked to point out the nouns in their reading lesson, and to make sentences in which other parts of speech are, without change of form, used as nouns. vSuch words as zoalk, love, fire, stop, start, etc. are examples. Then should follow those substantives that are composed of several words — phrase and clause nouns. It will be noticed that these divisions of the noim are progressive in difficulty, the last being by much the most formidable. But, if each is thoroughly mastered before passing to the next, the work necessary will be reduced to a minimum. 71. Definitions of the Xonn, — It might be assimied that in a matter so apparently simple as defining the noun, grainmarians would long ago have agreed. But such is not § 3 PEDAGOGICS OF GRAMMAR. 73 the case. Each author seems to regard it as imnerative that his definition shall b'e in some respect different from the definitions of his predecessors. The following will illustrate some of the variations: 1. "A noun is the name of any person, place, or thing." 2. "A noxm is the name of any person, place, or thing that can be known or mentioned." 3. '.'A noun, or name word, is the name of anything existing or conceived by the mind." The author of 3 explains in a note the meaning of thing or anything : " The word 'thing,' or 'anything,' used in its widest sense, as above, signifies whatever we can tJiink about, and applies to persons as well as to inanimate objects." 4. "A iioviii is a word used as the name of something." 5. "A noun is the name of anything." 6. "A nonn is a name, or any word or words used as a name. " 7. "A noim is a word used as the name of a thing, quality, or action existing or conceived by the mind. " Of these definitions it may be observed that the longest seem to be least satisfactory, for the reason that their diffi- culty of being understood by the pupil increa.ses with their length. Moreover, a long definition is more liable to contain tautology than a short one. Thus, the author of 3 explains that thing or anything includes persons; hence, in 1 and 2 the words person and p/acc are superfluous. In 3, the words existing or conceived by the viind add nothing to the thought. Besides, anything, either material or immaterial, that is conceived at all, is conceived by the mind. Definition 3, therefore, would be much better without the last six words. The same kind of objection may be made to 7. Definitions 4 and 5 are, of all that are given above, least open to criti- cism, and, if the words or any word were omitted from 6, it would pei^haps be the best of all. A noun is a name, or laords used as a name. An obvious inference from all this, and one of special importance to the teacher, is: be brief — in your definitions, in your ordinary conversation, in your explanations and 74 PEDAGOGICS OF GRAMMAR. 3 directions. Cultivate the rare art of sa3'ino-, in the fewest words, exactly what you mean. Nearly all teachers talk too much, nearly all definitions are wordy, nearly everybody is guilty of the fault of verbosity. Some one says of a certain author: "He could suspend a thought no larger than the body of a fly between the wings of an eagle." There is something soporific in the monotonous sound of a teacher's voice. Compel your pupils to find for themselves, and for one another, words for the expression of their thought. 73. Classes of !N"oiins. — The same diversity that is found among authors in their definitions of the noun obtains in their classifications of this part of speech. For example, one author divides nouns into two great classes — Proper and Common; another makes three classes — Proper, Common, and Abstract. The outlines shown below will further illus- trate this difference: Proper George, Boston, Nile, Hudson Riv-er. Many regarded as one — Con- gress has passed the law. Many regarded separately— The 23eople are dissatisfied. Abstract — wisdom, truth, hai-dness. Verbal or Participial — To live is to think. The Common -* writing is distinct. Siti gcnc7'is (of its own kind) — This class includes chose nouns that have no qualities in common with other things, and that can- not, therefore, be classified — music, geometry, galvanism, God. f Class names — horse, slate, j Names singular — color, space. Common -| Names material— gold, salt. Collective nouns — senate, army. Becoming proper — Providence, the Park. Strictly proper — John Milton. Becoming common — " a Shakespeare." Abstract — (from adjectives) whiteness, honesty. Abstract \ ,•<-•<.•' i. >~ __ . . ( infinitive — to write. verbal in -ing — writing. NOUNS f Collective — NOITXS Proper Verbals — § ;3 PEDAGOGICS OF GRAMMAR. 'lo Many other classifications might be given, but the effect upon the student would be only to confuse. With regard to common nouns sui generis, it may be observed that a common noun is always the name of a class of things. Thus, horse is the name of a class of animals, rose is the name of a class of flowers, etc. In other words, common nouns are general terms, each applicable to a multitude of things having certain attributes in common. Now, by definition, a noun sui generis never denotes a class, it is never used in the plural; hence, it cannot be a common noun. It is the name of something unique — ■ something unlike anything else. One author says, "The names of the arts and sciences are abstract nouns, because they are the names of processes of thought, considered apart and abstracted from the J^ersons that practice them. Thus, ninsie, painting, grammar, ehemistry, astronomy, are abstract noims. " It is difficult to see how abstract nouns can be abstracted from persons. The same author says, "Abstract nouns are {ii) derived from adjectives, as hardness, dullness, sloth, from hard, dull, and sloi^'; or (b) from verbs, as growth, thought, from grozu and think.'' That is to say, abstract nouns are derived from leords, not from things. If the aim of the author just quoted was to get rid of the noun sni generis,. h.e has not succeeded; for, when we take such nouns as galvanism, magnetism, infinity, eternity, it is obvious that they are not abstract noims. Neither are the}' common nouns, for thc}^ do not belong to classes. It is doubtful whether the word thing includes what is denoted by infinity, eternity, God, etc. If it were not that these terms transcend the power of the human intellect to con- ceive their meaning, they might be classed as proper nouns. The subject is environed with difficulty, but, in teaching it, such refinements are not for the pupil. They have a value for the teacher, however, in that they sharpen his powers of discrimination and classification. From the nature of the case, an exhaustive classification of the noun is not 76 PEDAGOGICS OF GRAMMAR. § 3 possible, and, for ordinary purposes, a division into proper and common is sufficient. Later, the common noun may be distinguished as collective, abstract, and verbal. Nouns siii generis may be called common or abstract, as the teacher prefers. It has been said that the part of speech to which a word belongs must be determined by its use or function in the sentence where it occurs. Hence, any word, sign, or char- acter may be used as a noun. Some examples will iHustrate this : A is always called a vowel and b a consonant. -f is the sign of addition and — the sign of subtraction. Cross your /'s and dot your e's. Alas is commonly an interjection. He answered the question without one if or but. [(6 X 7) + (4 X 3)] was written upon the blackboard. He made 7's that looked like O's. From these examples it will be seen that before a pupil can classify words, he must ascertain what office they fill in each particular case. 73. Inflection of Nouns. — The word inflection is derived from the Latin word inficxis, a bending. It carries with it the idea of a change of for7n in the inflected word, and is, therefore, not a very fortunate term as applied to the noun; for the only changes of form undergone by this part of speech are those that denote the possessive case and those that indicate number. For the same reason the word declen- sion, which denotes the inflection of nouns, pronouns, and adjectives, is no better. The English language has so few inflections that these words, which are indispensable to the grammar of Latin, Greek, and many other languages, are to us more embarrassing than helpful. Relations that in other languages are indicated by endings, prefixes, and root changes, with us are largely determined by use or function. The word modification, if it were not already applied to mean the effect that one word, phrase, or clause has upon the extension or comprehension of another, would serve as a § 3 PEDAGOGICS OF GRAMMAR. 77 substitute for i/ijlcction. Indeed, many authors so use it, and speak oi the niodificatioiis of nouns, meaning their changes of form, use, or relation. 74. Person. — The word person is borrowed from the stage. In Roman plays the actor wore a mask, through an opening in which he spoke. The word is from per, through, and sonns, sounding. In the uttering of a play, a discourse, or a sentence, there is a speaker or reader, one or more listen- ers, and some person or thing referred to, present or absent. Most closely related to the uttered matter is the speaker or the reader, next, the audience, and least closely related are the persons or things discoursed about. The nouns that denote these three are, respectively, in the first person, the second person, and the third person. Fii'st Person. — "I,,AV///, saw these things." Second Person. — '' Come, my boy, let us go." Phird Person. — ''Henry VIII was king of England. " A misconception common among pupils is that by person in grammar is meant a human being — a person — or the name of a human being. The teacher should be careful to have it clearly imderstood that, 1. The name of the person or thing that is represented as speaking, or a substitute for a name denoting the speaker, is in i\\Q Jirst person. 2. The name, or a substitute for the name, of tlie person or thing represented as the hearer is in the second person. o. The name, or a substitute for the name, of that which is spoken of is in the third person. Of course, the speaker may speak of the listener or of him- self in the third person. " The boy that has finished his work may stand." " The 7naH that you have honored has now the pleasure of addressing his constituents." The first .sentence refers to the "boy" as if he were absent, while in fact he is present as a listener. In the second sen- tence, "man" in the third person denotes the speaker, and "constituents," in the same person, denotes the audience. 78 PEDAGOGICS OF GRAMMAR. § 3 The speaker's reference to himself in the third person gives to what he says an air of modesty; and, without viola- ting- good taste, he may be inore complimentary to his audi- ence in the third than in the second person. In all such cases, the person of a noun or a pronoun is determined by its grammatical iisi% and not by what it denotes. Thus, in the sentences above, boy, man, and constituents are all in the third person. 75. Number. — A noun is said to be in the singular number when it denotes only one person or thing, and it is in the ////rrt'/ number when it denotes more than one person or thing. The plurals of nouns are 7-egularly formed by adding i- or cs to the singular; but there are so many exceptional and doubtful cases that, with reference to very many words, the authorities are by no means agreed. The subject is one to be mastered, if, indeed, it can be mastered, by reference to our latest dictionaries and spelling books. Spelling, inclu- ding the formation of plurals, is best learned by long and constant practice. The teacher should prepare a list of rules and words belonging under each rule, and with each rule the exceptions to it, all abundantly illustrated by words in com- mon use. In addition to these, he should have a miscella- neous collection, and require the pupil not only to spell each correctly, but also, when his degree of advancement warrants it, to give the rule applicable. Inasmuch as the Pedagogics of Orthography forms one of our sections, the student is referred to that for further suggestions concerning the for- mation of plurals. 76. Genders. — The subject of genders is a perplexing matter, and one upon which our grammarians are very much at variance. Richard Grant White argues with much heat that English nouns have no such distinction as gender; that we merely use different zvords to denote males and females. Thus, by king we mean a male and by queen a female exer- cising certain functions. In the Anglo-Saxon, the Latin, § 3 PEDAGOGICS OF GRAMMAR. 79 the Greek, and many other languages, gender is determined by endings, without reference to the actual sex of that which the word denotes. Only two gender terminations have descended to us from the Anglo-Saxon. These are en and stcr in vixen, a female fox, and spinster. In changing Lathi and Greek words into English words we have left behind all signs of their gender in the original. Professor Whitney, perhaps the most eminent authority in questions of this kind, says, "The distinctions of gender have been extirpated even in our nouns. To us the name or appellation of a person is masculine or feminine only according as the person is male or female; and of sex in the lower animals we make very small accoimt; while our Anglo- Saxon ancestors were as much under the dominion of that old, artificial grammatical distinction of all objects of thought as masculine, feminine, and neuter, on a basis only in small part coinciding with actual sex, as are the Germans now, or as were the Greeks and Latins of old; it was one of the orig- inal and characteristic features of that language from which all these, and most of the other tongues of Europe, are descended. The French has suffered the same loss only partially, having saved the distinction of masculine from feminine, but confounded neuter and masculine together by the obliteraticm of their respective marks of difference." Again he says, "Once more, man in its distinctive sense indicates a male animal, and we have a different word, wcvnan, for a female of the same kind ; and so all through the list of animals in which sex is a conspicuous or an impor- tant distinction; as, brother and sister, bull and ecn^\ ram and eive ; nor is there a language in the world which does not do the same. Only, as we have alreadv seen, our own family of languages (along with two or three others) has erected the distinction of sex into a universal one, like num- ber, making it a test to be applied in the use of every word ; breaking away from the actual limits of sex, and sexuali- zing, as it were, all objects of thought, on grounds which no mortal has yet been wise enough to discover and point out in detail." 80 PEDAGOGICS OF GRAMMAR. § 3 Some of onr authors, on the gTound that where there is no sex there can be no gender, give us two genders, the mas- culinc and the fcmijiinc; others follow the German, Latin, and Greek in having the masculine^ the feminine^ and the neuter. As to the neuter gender, they argue that the absence of a quality is just as distinctive a feature as its presence — that we make our words and our classifications as well from the negative as from the positive and afBrmative standpoints. A third classification of genders is into four — Diaseiiline, feminine, neuter, and eonunoji. This last is supposed to find justification from the fact that the Greek has a class of words called epieenes neariy equivalent to our common gender. But there is one important difference. The Greek common noun, like the German, is always preceded by an article to show the gender; so that while the sex of that which is denoted by the noun is indeterminate, the gender of the noun itself is known. Thus, the Greek word for fox is pre- ceded by the feminine article, although we cannot know the sex of the animal denoted by the word ; and the Greek word for lynx is used sometimes as masculine and sometimes as feminine. 77. Etymological Parsing. — These unimportant dis- tinctions of gender were introduced into our earliest English grammars from their Greek and Latin models, and they have been retained, perhaps on account of the figure they make in etymological parsing. The more voluminous and minute account a pupil can give of the properties of a word, the more learned and important it seems to the unreflecting. If, however, the distinction of gender is of any real impor- tance, it certainly does not extend farther than to the mas- culine and the feiniiiine. It is important to know that cer- tain words are masculine and feminine correlatives; as, earl and countess, beau and belle, zviteh and zvisard, lord and lady, foal And. filly ; but what practical or disciplinary value^ can come from requiring the pupil to say fha-t fish, sheep, cattle, bird, parent^ advisor are of the comvion gender, and then to § 3 PEDAGOGICvS OF GRAMMAR. 81 add as a reason that what they denote may be either male or female ? The minute etymological parsing of the successive words of a sentence is an indefensible waste of time, and it is done, even at this late da}-, in many of our schools. The etymol- ogy of the words of a sentence can, in most cases, be dis- posed of in a very few words. The educational value that comes from the examination of a sentence grammatically, lies in its syntax and its rhetoric; these furnish discipline for the most important faculties of the mind. 78. Sex and Gender. — The teacher should carefully distinguish between srx and gender. The former applies only to living beings, the latter is a property of ivords. Thus, the word man is of the maseuline gender, but the reality denoted by the word is of the male sex. Gender, as has been said, is a very unimportant property of words. Only the masenline and the feminine have any educational value, and these but rarely. The nenter and the common gender may be omitted from any attention in our grammar work. 79. Cases. — Grammarians are pretty well agreed that case is not an inflection of nouns and pronouns, but a modifi- cation in their relation to other words in a sentence. A few definitions follow to show that relation and not inflection is the doininant basis of classification: 1. " Cases, in grammar, are modifications that distinguish the relations of nouns or pronouns to other words. " 2. " Case is that modification of a noun or pronoun which denotes its oflice in the sentence. " 3. " Case is the _/. Absolute Possessive Pronouns.— These fonns are mine, t/iine, onrs, yonrs, his, hers, theirs. They are ec^uiv- alent to a noun used with an adjective pronoun modifier. ^^ Mine and j'onrs together are worth more than his and hers." If the reference here is to books, for example, the sentence is exactly equivalent to " My books and yonr books together are worth more than Jus books and Jicr books. " These pronouns, although they denote possession, are never used in the possessive case, and they occur in both numbers; " Mi)ic was lost and I took his.'' " His were large, but niine were very small." § 4 PEDAGOGICS OF GRAMMAR. 7 Mine and thi)ic are used also as adjective pronouns before nouns beginning with a vowel, especially in poetry, '•'■Mine eyes have seen the glory of the coming of the Lord." " TJiine ears are open to the cries of the oppressed." 7. Ambiguity From tlie Use of Pronouns. — There is no part of speech requiring more care in its use than the pronoun. If the student will carefully examine the writings of our best authors, he will notice a studied avoidance of this class of words. When a sentence contains but one possible antecedent of a pronoun, no ambiguity is likely to occur; as, " The boy lost /!/jr hat. " But when there are two or more words, any one of which inay be the antecedent, it is certain that the sentence will be ambiguous; as, "William assured John that Jtc should be much pleased if lie could attend his party." The following sentence, quoted by Cobbett from The Rambler^ is notable for want of clearness: " Melissa brought with her an old maid recommended by her mother, luho taught her all tlie arts of domestic management, and was, on every occasion, her chief agent and directress. They soon mvented one reason or [an] other to quarrel with all my servants, and either prevailed on me to turn tlion away, or treated //win so ill that //wy left me of //u';/ist'/7'rs, and a/-a'ays siipp/icd //leir p/accs with some brought from my wife's family." Was it the mother of Melissa that recommended the old maid, or did the old maid's mother do it ? Who was the teacher and who the pupil in " the arts etc."; who was the " chief agent," and whose chief agent was she? The ante- cedents of the pronouns in the next sentence are almost as indefinite as those in the fir.st sentence, but the matter need not be pursued further. The teacher will see the propriety of the following suggestions: 1. Use the pronoun only when you ean do so without ambiguity. 2. See that your pupils are well trained in finding and in correcting errors in the use of pronouns. 8. Compound Pronouns. — Of the five classes of pro- nouns enumerated above, the personal and the relative 8 PEDAGOGICS OF GRAMMAR. § 4 assume compound forms. The simple personals become compound by the addition of self iov the singular and selves for the plural. Thus, myself, ourselves, thyself, yourself yourselves, hijnself herself, itself, themselves. In the first and second persons only the possessive forms, my, our, thy, andjw/r are compounded with self while in the third per- son only the objeetives Jiim, her, it, and tJieui are used in these compounds. The simple relatives, in all their case forms, are com- poiuided by adding ever or soever. Thus, whoever, whoso- ever ; whosesoever ; zvhomever, wJiomsoever ; whichever, whiehsoever ; ivhatever, whatsoever. There is a colloquial use of certain compound forms of the interrogative pronouns ; these, of course, should be avoided. Whoever can it be ? Whatever does he want ? Whoso is frequently used in the Bible, and in some of our poets, notably Whittier, In Carhde we find, " . which whoso wished might come and examine." Whatso is also used by early writers. 9. The Relative ''What.'"' — The pronoun ^vhat is by many grammarians said to be a double relative, equivalent to that whieh or the thing which ; and to illustrate, they give such sentences as "Tell me what you want." "Explain what caused the trouble." In such constructions, they separate zohat into that %vhich or the thing ivhicli, and say that, in the first sentence, that is the object of tell and 7uhich the object of %vant. The second sentence, they expand into " Explain the thing that (or tJiat wliieJi) caused the trouble." Then, thing or that is said to be the object of explain, and that or luhich the subject of caused. To this it may be objected that these writers do not account for what, but for its supposed equivalent, that which or the thing zchich. This use of zi'hat is good idiomatic English, and its double func- tion of object of two different clauses, or of object of one clause and subject of another, with an added connective function in both cases, no more requires its reduction to other terms than does the case of any other word performing § 4 PEDAGOGICS OF GRAMMAR. 9 two offices. Thus, in the sentence, '' His work is neater than hers," it is not considered necessary to explain the grammatical function of hers by accounting for its equiva- lent, her work. Besides, consistency would suggest the same kind of reduction of luho and whom in the following sen- tences: "Tell me who you are." "Mention zvJioin you seek." Such treatment of these sentences would result in, "Tell me the person who you are." ''■Isilention the person ivhoni you seek." In all these cases the unexpressed ante- cedent is revealed by reducing the relatives to other terms, but by so doing we are not disposing of the sentences as they were, but of others that are assumed as equivalent to the original. The relative whieh can be treated in similar fashion. The writer would suggest that tvhat be called a iioublc rehitive, and that its functions with respect to both clauses be pointed out and its connective office mentioned. This is exactly similar to our treatment of tlie eonjunetive aifverb, the adjective pronoun, and the absolute possessive personal pronoun. "He died where he lay." "You have torn my coat." ^^ Mine surpass j'cj;//'.s- in quality." It would manifestly be absurd to change " He died where he lay" to "He died i)i the place in zuhich he lay." We prefer to say that cohere modifies the meaning of both ve:bs and connects the two clauses. It is not amiss to empha.size here what was said before : Do not needlessly dismendnr a good English sentence, or supply imaginary ellipses. Of course, there are many ellipses about which there can be no question. Thus, "Henry ate his supper, and [he] studied his lesson." "The boy went away, and his sister also [went awayj." By "imaginary ellipses " we mean such as, "The sled is zvorth a dollar" = "The sled is worthy of a. dollar" = "The .sled is of the worth ofn dollar." Or, " The interjection," some authors say, "is an entire sentence con- densed into one word." Thus, "vShame!"= "You should be ashamed of yourself." Of course, no one can, with any certainty, expand an interjection into a sentence. 10 PEDAGOGICS OF GRAMMAR. S 4 TA35I^1^ OF THE PROXOI I^. i Simple. 1. Personal J, { Compound. .„, ,2. Relative 3 f^^^P^^" ^ I Classes -; | Compound. 3. Interrogative. I 4. Demonstrative. [ 5. Indefinite. r Gender. [Only certain personal pro- ! Person. nouns intlie singular have j Number. gender.] [Case. Properties THE ADJECTIVE. 10. Derivation and Office. — The word adjective is from the Latin adjectivus, added to. The term implies that the adjective is always joined directly to the noun or pro- noun modified by it, but such is not the case. " Good, sweet, and beautiful though this little g'irl was, etc." " This little girl was g'ood, sweet, and beautiful." The term viodifieation has already been explained as any means of determining the modus or measure in which the meaning of a word, phrase, clause, or proposition is to be taken. The primary and distinctive function of the adjective is to do this with nouns and pronouns. The teacher will, of course, note that words are not modified, but their i/ieauiiigs ; so that an adjective is not, as many say, a word used to modify a noun or a pronoun, but it is a word used to modify the iiieanvig of a noun or a pronoun. It should be noted, however, that for the sake of brevity it is allowable to say that adjectives modify Jiouiis and pronouns, that adverbs modify verbs, etc. The teacher should have a distinct notion of what is meant by the extension, and what by the eomprehension of a term. If a word, say a noun, has no other word joined to it to modify its meaning, its extension is nnliniited, universal, general, and its comprehension is the narrowest possible — § i PEDAGOGICS OF GRAMMAR. 11 mere existence. Thus, apple includes every object in the class that the word denotes. But when the term red is joined to apple, the extension is narrowed, — not so many apples are included, — but the comprehension of the terra is enlarged. We know more exactly what kind of apple is meant. To the notion of mere existence is added that of color. Large red apple comprehends existence, color, and relative size. That is, the extension of a term has reference to the number of objects to which the term may be applied — to the extent of its applicability; the eoviprehension of a term or a collection of terms has reference to qualities expressed — not implied, denoted — not eonnoted. The teacher should here recall the law of the inverse ratio between the extension and the com- prehension of terms. This law may be thus expressed: Each modi fier that is added to a term increases the definitoiess of the mental picture, and diminishes the range of objects to ivJiich the modified term is applicable, and the reverse. It will be obvious, therefore, that adjectives of every class modify the meaning of nouns and pronouns; that is, they limit or narrow their extension and enlarge their comprehension. 11. Definitions of tlie Adjective. — Remembering these general observations, let us examine some of the definitions of the adjective that are found in otir textbooks: 1. "An adjective is a word joined to a noun or a pro- noun to limit or qualify its meaning." 2. " An adjective is a word used to modify a noun or a pronoun." 3. " An adjective is a word used to modify a noun or a pronoun without representing an object." ■1. " An adjective is a word used to qualify or //;//// the meaning of a noun or a pronoun. " 5. "An adjective is a word added to a ncnin or a pro- noun, and generally expresses quality." 6. " An adjective is a word used to limit or qtuilify the application of a noun or a nominal phrase." The student should be able to find much interest and profit in comparing and criticizing these definitions. They 12 PEDAGOGICS OF GRAMMAR. § 4 are all taken from well known authorities, and the surprising thing about them is that they differ so widely. In such exam- ination, the first question likely to occur is as to the precise differences in meaning of hmt^, qualify^ and modify. These terms have been considered at some length in Art. 28, Pedagogics of Grammar, Part 1, which the student is advised to read again with care. As used by most grammarians, it seems to be intended that /////// shall have reference to adjectives denoting num- ber, size, or mass. Such are three, third, some, many, any, every, large, small, vast, immense. This, however, cannot be asserted positively. The truth is that even very careful writers often employ words without considering how niuch is included in, and how much excluded from, their meaning. But strictly, all adjectives /////// — determine the extension of the meaning of nouns and pronotms — and all adjectives also modify. We may, therefore, use the two terms interchange- ably, preferring, however, the word modify on account of the fact that all writers agree in using it in its wide generic sense. Definition 1 is objectionable for three reasons: first, because the adjective is only sometimes "joined to a noun " ; secondly, because of the vagueness of "limit or qualify"; and thirdly, because an adjective modifies, not a noun or a pronoun, but the meaning of a noun or a pronoun. Defini- tion 5 is open to the first of these objections, and is, besides, unfortunate in its last clause. Definitions 1, 4, and 6 contain " limit or qualify," and the last would be better without " or a nominal phrase," by which is meant a substantive or noun phrase. In definition 3, "without representing an object" is intended to exclude from among adjectives the absolute possessive pronouns mine, thine, etc. ; but, unfortunately, it excludes, as well, adjectives denoting material; as steam- hamiuer, r^(7/-shovel, etc. Providing against these objections is not a difficult matter. An adjective is a word used to modify the meaning of a noun or a pronoun. This definition is brief, and it provides for both the exten- sion and the comprehension of the noun's meaning. g 4 PEDAGOGICS OF GRAMMAR. 13 12, Classification of Adjectives. — Equally various are the divisions that different authors have made of adjectives. Many authorities give two classes of adjectives — qualifying and limiting. The diiliculty in this classification lies in the uncertainty of the word qualifying. The logicians and meta- physicians have not yet been able to agree as to the meaning of the term quality; and it is upon this that the meaning of qualifying depends. One authority says, "Quality is an element of anything, and aids in making it distinct from other things; the attributes or characteristics of anything as determining its place, rank, value, etc." This definition seems to cover every function of the adjective, for certainly every adjective aids the mind in making one thing or group of things distinct from other things. The adjective does this by denoting some characteristic of place, rank, value, number, quantity, etc., or of properties that address the mind through the senses. In short, every adjective denotes some quality belonging to the thing named by a noun. But the divi- sion of adjectives into two classes, qualifyinga.nd limit ing.^ or into three, qualifying., limiting., and numeral., is very common. 13. Brown^s Classification. — Remembering, however, the vagueness of the term qualifying., and that all the adjec- tives limit — fix boundaries — let us consider one of the best known classifications — that of Goold Brown. His divisions and definitions are as follows.: common, proper, numeral, pro- nominal, participial, and compound. I. A common adjective is any ordinary epithet, or adjective denoting quality or situation; as, good, peaceful, eastern, outer. II. A propel* adjective is an adjective formed from a proper noun ; as, A merican, English, Mil tonic. III. A nnmeral adjective is an adjective that expresses a definite number; as, one, tzvo, three, four, etc. IV. A pronominal adjective is a definitive word which may either accompany its noun, or represent it understood; as, "^//join to guard what each desires to gain." ^^ All men join to guard what each man desires to gain." 14 PEDAGOGICS OF GRAMMAR. § 4 V. A participial adjective is one that has the form of a participle, but differs from it by rejecting the idea of time ; as, an aumsing story. VI. A compound adjective is one that consists of two or more words joined either by a hyphen or directly; as, nnt-broivn, laughter-loving, four-footed, lovesick. 14. Criticism of Bro^vn's Classes. — Of these classes, it may be remarked that : 1. Most, if not all, compound adjectives are "epithets," though some of them may not be '^ordinary epithets." Hence, VI might better be included under I and II. The Franco-Prussia)i war, a self-made man, a dozvncast look — these are epithets. Some compound adjectives belong among the numerals; as, a six- fingered hand, a five-toed bird, a six-pctaled flower. These also are epithets. Class VI, then, seems to be superfluous. 2. If words are to be classified strictly in accordance with their rise, IV should read, "A pronominal adjective is one having the double function of adjective and pronoun " ; as, my hat, some men, every person. It is nndonbtedly better to call such words pronouns when they have no accompany- ing noun. U.sed to modify a noun, they are adjective pro- nouns or pronominal adjectives. 15. Professor MeiklejohnN Classes.— Another classi- fication, which the student may prefer to Brown's, is that of Professor Meiklejohn. He divides adjectives into four classes, which he defines as follows : I. Qualitative adjectives denote a quality of the sub- ject or thing named by the noun ; such as, blue, sad, big, little. II. Quantitative adjectives denote either quantity or tjtdefinite number; and they can go with either the singular or with the plural of nouns, or with both. The following is a list : any, all, both, certain, divers, enough, feu>, little, many, much, no, several, some, whole. III. Numbering or numeral adjectives express the § 4 PEDAGOGICS OF GRAMMAR. 15 )iuiiihcr of the things or persons indicated by the noun. They are generally divided into 1. Cardinal iiiinierals ; as, onc^ fi'<-'<'\ nine. 2. Ordinal numerals ; as, first., fifth, ninth. IV. Demonstrative adjectives are those used to point out the thing expressed by the noun; and besides indicating a person or thing, they indicate a relation either to the speaker or to something else. Demonstrative adjectives are of three kinds: 1. Articles. 2. AdjectiA'e i^ronovms. 3. Ordinal numerals. Adjective pronouns can be used either as adjectives i^'itJi the noun, or as pronouns for the noun. They are divided into the following classes: 1. DemonstratiA'e adjective prononns ; as, this, these, that, those, yon, yonder. 'I. Interrogative adjective prononns ; as, which ? li'Jiat / whether {of the t7c>o) .^ 3. Distributive adjective pronouns ; as, eaeh, every, either, neither \. Possessive adjective j)ronouns ; as, my, thy, his, her. 16. Articles. — It is not many years since the article was recognized by all grammarians as a separate part of speech. No one thought of classifying it among the adjectives. But later, grammarians came to see that a and an are as much adjective in their function as one, and that tlie and that belong in the same class. Goold Brown, in his "Grammar of English Grammars," argues in favor of retaining a, an, and tJie in a distinct class. His arguments failed, however, for the grammarians of today are of one opinion with refer- ence to this subject. The article is merely an adjective, and it will doubtless continiie to be so regarded. We may expect soon to see a and an placed in the class called by Professor Meiklejohn Quantitative, and tJie is already found with tJiis and tJiat among the Demonstratives. 16 PEDAGOGICS OF GRAMMAR. §4 1 7 . Anotlier Classification. — In the belief that it is pos- sible to improve upon the classification of adjectives hitherto given, the foregoing is submitted, which will perhaps be found more exact and useful for classroom work. Brown's common, proper, participial, and compound adjectives all belong under the general class of Qiialitativcs. His numerals and some of his pronominals are Quant itativcs, and the rest are Demonstratives. Professor Meiklejohn's numerals are more exactly classed as Quantitatives and his ordinals belong in the same class, although he makes some of them numeral and some demon- strative. TABLE OF THE ADJECTIVE. 1. Common M "W eincnt clearly understood. But in the cases of to tliinic, to reflect, to remember, to lilie, to detest, and in an infinite number of [other] cases, the movement is not so easily perceived. Yet these are all verbs, and they do indeed express movemetits that we attribute to the mind, or to the Iieart. But what shall we say in the cases of to sit, to sleep, to rot, and the like ? Still these are all verbs. " Verbs are, then, a class of words, the use of which is to express the actions, the movements, and tlie state or manner of being, of all creatures and things, whether animate or inanimate. In speaking with reference to a man, to figtit is an action ; to reflect is a move- ment; to sit is a state of being." To the foregoing may be added the following from Brown's "Grammar of English Grammars": " So various have been the views of our grammarians respecting this complex and most important part of speech, that almost everything contained in any theory or distribution of the English verbs may be considered a matter of opinion and of dispute. Nay, the essential nature of a verb, in universal grammar, has never yet been determined by any received definition that can be considered unobjectionable. The greatest and most acute philologists confess that a faultless defini- tion of this part of speech is difficult, if not impossible to be formed." 32 PEDAGOGICS OF GRAMMAR. § 4 But while it is, perhaps, impossible to give briefly and exactly a definition of this part of speech, it is easy to rec- ognize the verb when we meet it in a sentence; and when all is said, that is the most important matter. In an exam- ination in gi'ammar, almost any of the definitions that have been formulated would be acceptable, and this is true merely because of their great number and confusing variety. CLASSIFICATION OF VERBS. 30. Ileg:iilai' and Irreg'iilar Verbs. — The simplest form of a verb is that by means of which we ordinarily express present action, being, or state; as, I lovc\ lualk, seem. So far as English verbs can be said to have roots, this is the root form. In other tiine forms, the root or 23resent form is generall}' changed. In some cases the change is a suffix ; in others, an entirely new word is employed. But all verbs are arranged in two classes, 7'egular verbs and irregular verbs. These two classes are determined by the way in which certain time forms are made from the present. The number of these forms, or principal parts, is not the same in all authors; most making three, others /(3//r, and a few, Jive. The three tmie forms or tenses usually given as principal parts are: 1 . The present; as, I see, go, work, skip, sit, sleep, seem, am. 2. The past indefinite; as, I saio, went, worked, skipped, sat, slept, seemed, was. This tense has been variously named imperfect, preterit, past, first past, first preterit, etc. It denotes action, being, or state in the indefinite past — a year, a month, a day, ago. If the student understands the mean- ing intended, the naine is of little consequence. 3. The perfect participle. This is the form used after I Jiave in the following: seen, gone, worked, skipped, I have A , , , sat, slept, seemed, been. A verb is regular if it forms its past indefinite tense and sent Tense. Past Indefinite. Ft -rfeei Partieiplt turn, turned. turned. snap, snap[p]ed, snap[p]ed. . live, lived. lived. steady, steadied. steadied. parley. parleyed. parleyed. § 4 PEDAGOGICS OF GRAMMAR. 33 W.'s, perfect participle by adding -d or -cd to its present or root form. The rules of spelling- must be observed in changing the present tense into the other forms. Principal Parts. The inflection in -ing, called the present, or imperfect, participle, is very cominonly included as the fourth among the principal parts; as, turn, tiiniiitg, turned, turned; sec, seeing, sazi', seen; go, going, luent, gone; etc. A verb is irregular if it forms its principal parts in any other way than by adding -d or -cd to the present. Present. Past Initefinite. Perfect Participle. ( sing, sang, sung. I grow, grew, grown. Priuc-ipal I ^ , '^ , , * 1 - speak, spoke or spake, spoken. Parts. 1 / r / freeze, troze, trozen. [ swim, swam or swum, swum. 31. Verbs ^He^vly Coined Are Always Regular. — The regular verbs comprise nearly all in the language, and their number is constantly increasing. Human progress is marked by new methods, needs, processes, products. For example, the introduction of electricity as an industrial force has created a need for many new verbs. Greater precision in scientific and mechanical processes, increased exactness in classification, — these and many other things are adding to the list of verbs. The additions, however, are all regular verbs. It Avould be difficult to find an irregular verb that has come to us during the last half-century. Another source of increase of the stock of regular verbs is in the fact that we may form verbs from almost any part of speech; as, "Things animate and inanimate are Jid d and slicd in the German language." "They tlicc'd and thou'd me beyond endurance." "After c?/^-///j'?V/^'' about it for some time, she accepted the situation." It is, however, from the noun and the adjective that verbs 34 PEDAGOGICS OF GRAMMAR. § 4 are mostly formed. Thus, from the nouns ;//;'<'^//Arr. They are: Can, Could. Shall, vShould. May, Might. Will, Would. Methinks, Methought. Quoth, Quoth. Must, Must. (?) Wis, Wist. Ought, Ought. (?) Wit, Wot. Whether must and ought can properly be used as past indefinites is disputed. Wis, wist, and icot are old forms and are nearly obsolete. Beware is used only as a present form. 35. Verbs Active-Transitive, .Vctive-Intransitive, and ISTeviter. — Most verbs express action or movement of some kind, real or ideal: physical, mental, moral, emotional, indtistrial, social, political; as, walk, think, sin, hate, iveave, entertain, elect. All such verbs belong to the great class of active verbs, a class comprising perhaps 09 per cent, of all English verbs. In a sense to be explained hereafter, all verbs express action. In any act there may be two principal elements, or there may be three, and even four. When there are two, they denote \.\\Q actor z.\\<\ the act performed; as, "• Snow falls.'' "The boy runs. " "The industrious boy rises early in the morning." If there be three principal elements, they denote the actor, the act performed, and the thing directly affected by the act; 36 PEDAGOGICS OF GRAMMAR. § 4 as, "The sun melts the snoiv.'" " Mai'y %vas]icd Wiq dishes." ^"T\\Q far vier gave food to the hungry traveler." When, as in the first case, the action affects only the actor, the verb is intransitive, from the Latin /;/, not, and transire, to pass over. If the action expressed by the verb passes over from the actor to an object directly affected by the action, the verb is transitive. Transitive verbs are of two kinds, active and passive. In the first, the subject of the verb denotes the actor; as, " John struck William. " In the second class, the subject of the verb denotes the receiver of the action; as, "William was struck by John." These two forms of a transitive verb are called by many authors tlie active voice and the passive voice. In the second form, the subject of the verb denotes the person or the thing- that endures, or suffers from, the action. The word passive is here used in the sense of suffer from the Latin adjective passivus, suffering. 8(5. Omitted Elements. — Strictly speaking, a verb to be transitive should be accompanied by the other two elements, the name of the actor and of the receiver of the action. But sometimes only the verb with one of the other elements, or the verb alone is given. This arises from one of two causes: 1. The missing element inay be clearly implied; as, "John struck (object) and (actor) hurt his playmate;" ia.stead of, "John struck his playmate and he hurt him." 2. The missing element may be unnecessary to the thought. Indeed, this is generally true of the passive form. Active f "(Sub.) Strike (obj.)! till your last armed foe expires." ! " One sows (obj.), another reaps (obj.)." 1 "Mary washed (obj.) and (sub.) combed (obj.)." [ " Men build (obj.) and time destroys (obj.)." " He was struck (actor)." " America was discovered (actor) in 1492." Passive ->, " The story was related (actor) with much effect." I "Many ancient kingdoms were established (actor), but [^ (receiver) were soon destroyed (actor)." § 4 PEDAGOGICS OF GRAMMAR. 87 3T. Otliei* Transitive Forms. — There are several other cases in wliich verbs may be used as active and passive: 1. Where there are four elements,— the three already mentioned and an indirect object. Active. — " They gave him food." Passive. — " Food was given him by them." 2. When an intransitive verb is made transitive by com- ponnding it with a preposition. " He taug/icd c\i her." " She was laughed at by him." 3. When the speaker's own mind seems to be the actor implied. " I am decided to do it." " He was bent on leaving." " I am pleased to learn, etc." "He is inclined {disposed, resoli'cd, deter ruined, gricTed, pained) to make the concession." 38. Wlieii a Verl) Is to lie Tlegarded as Transitive. — There is much difficitlty in deciding when a verb is to be regarded as transitive. If we are to be guided entirely by 7ise, a verb is transitive only when all the elements, actor, verb, and receiver of the action are denoted. When, however, the verb expresses a command, the subject is nearly always missing, and is generally unnecessary. vSuch verbs are clearly transitive if accompanied by an object; if they have no object, the verb is used intransitively. [ " Reap (object) where you have sowed (object)." Intransitive \ " If he would prosper, the farmer must plow, sow, reap, and gather into his barn." Transitive J " Earn money and save it." [" Understand and practice economy. When two or more verbs have the same object, it is u.sually expressed but once, and the verbs are transitive. " The king jaursued, captured, tortured, and then sold, the fugitives into slavery." In cases where the object is unimportant or unknown, the verb should be regfarded as used intransitively. 38 PEDAGOGICS OF GRAMMAR. § 4 " Idleness and inactivity enervate, industry strengthens." "The Romans gained and the Carthaginians lost, in the struggle that followed." If the verb is in the passive, it is transitive, for only transi- tive verbs can have the passive form. "Year after year new stars are discovered, and most of them are catalogued." "The times are changed and we are changed with them." "The Roman Empire was rapidly dismembered and its supremacy among the powers of the woi-ld was utterly destroyed." " The ship was for a time becalmed ; later, she was driven upon a lee shore, where she was wrecked, and the crew was drowned." 39. IVeiiter A'evbs. — The term iiaitcr, as used here, is to characterize such verbs as are //^////^I'r active-transitive nor active-intransitive, or, as many authors intend, neither active nor passive. Of these, there is perhaps none, or there are very few, that do not express some kind of action. Indeed, it may be doubted whether there is any state or condition of being that is wholly without either real or ideal activity; for molecular motion or action is just as real as the motion of sensible masses. The verb be is usually taken as the best type of a neuter verb, and yet life or existence — mere being — is intal activity: when this form of action ceases, the result is death. This is quickly followed by intense chcviical action^ called decay, or dccovipositio)i. Grammarians have tried in vain to draw a hard and fast line between verbs active and verbs neuter. No stich divi- sion can be made — no such line can be drawn. The truth is that all verbs may be separated into three more or less definite groups. 1. Verbs that affirm or deny action real or ideal, — predi- cate action, — and besides, imply a state or condition. In this class, action is the prominent consideration, and the implied state is neglected. Thus, " The earth ;//('T'r.s-." " The man ti'orks." " Cataline hates. " Here there are the acts and the implied states of uiovi)ig\ of icorking, and of hating. We think of the act and neglect the state. These are strictly active verbs. § 4 PEDAGOGICS OF GRAMMAR. 39 2. Verbs that predicate state and imply action. In this class, it is the state that engages the attention, while the implied action may not even be considered. Thus, "He is." "God li7'cs." "The city of Troy was."' "He seems, appears, Aw/\s-, sick." "A'tv/ still." '' Remain (\\x\ei." This class includes verbs that distinctly and imquestion- ably express action, but the action is neglected, and only the state is regarded. Thus, "Open your eyes H'/V/c." " SAut the door //i,'///." "Sit and 7i'a/i erect." "The package arri^'cd safe." "The sun s /lines I) rig /it." " He acts sic/c." " He stands stitt." Here we think of the state of the eyes and the door after the acts of opening and shutting have been finished ; of the state or position of the body rt'?^r//;^ the acts; of tlie condition of the package after the act of arriving; and so on. These are neuter verbs, when thus used, because the action expressed or iinplied is not considered, the attention being wholly devoted to the state or condition of the subject. 3. Verbs in which the action and the state are of nearly equal prominence. With such verbs the speaker may use an adverb to modify the action expressed, or he may use an adjective to show that he is thinking particularly of the .y/rt/r, or he may use both an adverb and an adjective — the one to modify the action and the other to denote the state. " The laoy acts insane." "He ixci'A Jootis/i/y." " The player acts graeefittty." " How sioeet the moonlight sleeps." " He looks anery." " lie ];>;)ks - r - at his ruined hopes." •^ ' ( sa/f \ ^ " We keep (pen all night." " How siceet the moonlight sleeps upon //lis tmn/:." (iii/ivrd) " The sunlight fell /ii>t (upon t/ie soui/iern s/opes)." {adivi-b) "The politician blew /lot and eo/d (in /lis address)." (adverb) " The door is locked -< '' ', \ at nis^/it." \ securely \ i^,,j^„.ri,) 40 PEDAGOGICS OF GRAMMAR. § 4 40. Remarks on the Foregoing Classification. — The student will notice that in the foregoing the impossibility of dividing all verbs into two classes is recognized, and that he is called upon to decide whether, in a doubtful case, it is better to modify by an adverb the meaning of the verb, or by an adjective to denote the state, or to do both. The advantage derivable arises from the fact that a difficulty distinctly for- mulated is often a difficulty mastered. This classification should lead to the banishment from our speech of such mon- strosities as "I feel badly," " She looks sploiduily,'" "The lake \iQS placidlv," "The babe lies iiuioccntly in its cradle," "The boarder sleeps noisy," " I am nicely, thank you." Although, doubtless, all verbs express some greater or less degree of action, it is not intended to formulate a new classi- fication of verbs. The truth is that there are already too many. The object is only to impress upon the student that the grammar of the English verb is a matter for the exercise of his best and most deliberate judgment; that no subject is better for the discipline of his powers of discrimination, and of analysis and classification. The fact that no two authori- ties agree in their treatment of the verb should excuse him for insisting upon thinking for himself. vShould he fail to do this, he will miss, in large measure, the culture derivable from the studjA of grammar, 41. The Term "Active" as Used in Grammar. — Much confusion has arisen in grammar from the twofold sense in which the term active is used. The first meaning is that in which verbs are active and passive — denoting the I'clation of the subject of the verb to the action expressed; the second, where some verbs, whether they are active or passive, are called active because they denote actio)/, in contrast with others called neuter. Active and Passive. — " The sun warms the earth." " The earth is ivari)U'd\)y the sun." Active and Neuter. — " ]o\\n studies^ '• The child ?> pretty." The student will do well, when he meets or uses the word § 4 PEDAGOGICS OF GRAMMAR. 41 active, to decide in which of these two senses it is to be understood. 43. Brill Witli Irrej>uliir Verbs. — It has been stated that most of our errors of speech come from a misuse of the irregular verbs. The best practical way in which to remedy this state of things is by frequent C'nr/ drills ; for it is by Jiearing the correct forms, not once or twice, but many times, that we learn to use them. It is not by studying grammar that we learn to speak in conformity with its rules and principles, but by Jiearing i/iitc/i, reading niucli, and speaking niucli. No teacher should imagine that he has taught the verb well unless his pupils can give the principal parts of all the irregular verbs in common use. In addition, they should be persistently exercised in such drill work as is indicated below: Si(bjccts. Principal Parts. Coinploncnts. I 1 We He -^ r my work carefully, gl^e 1 1^^^ I I the best I can (could). They ' ^1°' ^"^^y have [- done \ my work this morning. I); had I the task yesterday. Henry [the example many times. The girls The foregoing will suggest what should be written on the blackboard for any irregular verb. The pupil should be required to make a complete statement with each subject when the verb form and the complement are indicated by the teacher. Later, the statement may be converted into a q nest ion. Thus, " /do Diy work carefully." " We do our work carefully." " Hr does /lis work carefully." Etc. " Do I do my work carefully ?" " Do we do our work carefully ?" " Does he etc.?" The progressive statement and the progressive question may constitute a third and a fotirth variety of exercise. Thus, " I am doing etc." " We are doing etc." " Am I doing the best I can ?" Etc. 42 PEDAGOGICS OF GRAMMAR. § 4 By turning- the same drills into the negative form and abbreviating, we get a much needed drill with /';// not doing, I don't do, He doesn't do, He isn't doing. The question with not naturally follows. Thus, " Am (not ain't) I not doing ?" " Don't I do ?" " Doesn't he do ?" Etc. "Didn't he do ?" " Hasn't he done ?" " Haven't they done ?" The drill with is and is not, isn't, aren't, and that with the confusing varieties of the verb to be, furni.sh excellent and profitable discipline. Of course the teacher will change the complements and the verbs as occasion demands. Another drill that should not be neglected is that with pronouns in the predicate. It is as follows: I call. It 1 is, be, was, were, ( I, we, he, "1 „ )■ < V that •! calls. If it J had been \ she, it, they j ^^^^ ^ called. Here the sentences in full will be : " It is I that calls," "It was we that called," "If it had been she that called," etc. The same drill may be made negative, and either declara- tive or interrogative — with and without abbreviation. 43, A Daily Work. — The foregoing drills should find a place in every day's work; they may, with proper modi- fication, be introduced early in the school history of pupils; and with profit be made to cover several years. By actual trial in the classroom, they have proved to be a source of unfailing delight to the pupils. One of the notable results of their use is that the children soon introduce addi- tional verb forms from their drills into their daily conversa- tion. If the student will notice closely the tenses used by children and uneducated people, he will be surprised at their limited number. If there is 2i practical ^\de of grammar, if in addition to its disciplinary value, it is to teach us "how to speak and write the English language correctly, " or at least, more correctly than formerly, it is realized by these drills, and others that may be devised by the ingenious teacher. § 4 PEDAGOGICS OF GRAMMAR. 43 MOBES OF VERBS. 44. Preliminary Remarks. — There are several modes or ways in which verbs may be used in predicating. By predication is meant every form or use of the verb in asserting or denying action or state, in making inquiries^ in expressing eoniniands or entreaties^ and in merely assuming action or state. Authorities differ much, and doubtless will continue to differ, about the number of modes and their definitions. The number generally given is five; the indica- tive, the potential, the imperative, the suhjuneti-ve, and the infinitive. Many authors insist that the English verb has only three modes; the indicative, the imperative, and the subjunctive. The reasons usually given for rejecting the potential and the infinitive modes will be noticed later, but, in teaching the subject of modes, no great harm can come from regarding them as five in number. 45. Predicatiiis' Action or Merely Assiimino- It. — Before entering upon the consideration of the several modes, it is necessary that the student should imderstand exactly what is meant by the terms predicating and assuming with respect to the action or the state expressed by verbs. The word from which predicate is derived is prcedicarc, and the meaning of this Latin word is to cry out in public, to proclaim. As used in grammar, predicate includes all the functions of the verb and its various complements. These uses are for the purposes of affirming ox denying, questioning, commanding, wishing, etc. Such uses constitute only par- tially what we mean hy predication. Another form of predi- cation arises when the action or the state is only taken for granted or assumed. Thus, we may .say The boy escaped by running. Here there are two forms of action, one asserted — escaped — and one assumed — running. We do not assert, say, declare, that the boy ran ; biit we use language from which the act of running is implied — it must be understood or assumed. Even when a word derived from a verb is used as an 44 PEDAGOGICS OF GRAMMAR. § 4 adjective to modify a noun, there is an obvious assumption of action, although grammarians content themselves with calling it a verbal adjective. Thus, a ritimiug brook, a sleeping child. Some other forms of the verb predicate by assuming the action. These will be considered later. 4:6. The Indicative Mode. — ^The form or use of a verb by means of which we affirm or deny a simple fact or ask a question, is the indicative mode of the verb. This word indicate really means to point out, show, or declare, although it is applied to the use of qnestioning or inquiring; and in grammar we often find that the use of a term is thus carried beyond its exact meaning. Examples to illustrate the indic- ative mode are the following: " James ^<7^^ to school." " Z><;t'jr James ^^t^ to school?" "James is not a studious boy." "Harry went to the brook." '' Ha^'c the birds not gone south?" " Will you not visit tis? " 47. The Potential Mode.— There are some short verb forms called auxiliary or helping verb.s. These are much ■used with other verbs, and they help to make what many grammarians call verb phrases. The student will notice that, in the sentences given above, several of the verbs have double forms; as, does go, have gone, etc. These compound forms are verb phrases. They may be taken apart, and each part considered separately with respect to its functions; or, as most grammarians prefer, they may be treated as if they were simple forms. The different forms regarded as being in the potential mode are all verb phrases. The auxiliary words by means of which we may recognize this mode are may, can, must, might, could., tvould, and should. When we meet verb phrases containing any of these words, we may be sure that they are in the potential mode. The indicative and the potential modes are the only modes by means of which we are able to express questions; but § 4 PEDAGOGICS OF GRAMMAR. 45 while the indicative mode, used for this purpose, inquires only about mere facts, the potential is employed to make statements and to ask questions about the ability, necessity, duty, etc. of some person or thing to do or be something or other. Thus, He can read. She may go. Should he obey ? Must he recite ? He might be late. The name potential is derived from the Latin word potentia, which denotes power or ability. Among the auxiliaries given above, can and could are the only ones that have this meaning; so that the mode is named from these two words, and its meaning is made to include all the other help- ing words of this mode of the verb ; as, may, must, might, etc. 48. Fuuctions of the Several Modes. — Every mode has some prominent function or use, and it is of great importance to the student that he shall know in each case what this function is. For the indicative mode, the act itself and the time of its performance are the matters of leading import. "The sun shines." "The sun shone.''' "Spring has come.'" " The day w/// soon dazun." '■'■Have the enemy retreated f " Here the form of the verb makes the time of the act very distinct. In the potential mode, the time of the act is of little concern — indeed, it is scarcely taken into account. For the times denoted by He may come and He might come differ scarcely at all, and the same may be said of He may Jiave come and He might have come. In all these cases the time of the action expressed by the verb is very vague and uncertain. It is what is intended by the word potential that is to be thought of as prominent — the probability, etc. of the act. The first forms, so far as they denote any time, point to the future, and the others to the past; and with this limitation, all are wholly indefinite as to time. He can read predicates only ability that may have extended far into the past, and may extend into the indefinite future. Having premised this, we give the following: Definition.— The potential mode is tliat form or use of a verb by which action is predicated as possible, necessary, permitted, or obligatory. 46 PEDAGOGICvS OF GRAMMAR. § 4 It should be added that many authors reject this mode, and regard the auxiharies as principal verbs in the indica- tive mode, followed by infinitives; as, I can (to) go. I might (to) come. I may (to) have come. This view would make can, might, and may transitive, each having as its object an infinitive used as a verbal noun. 49. The Imperative Mode. — The imperative mode is that form or use of a verb in which the predication takes the form of a command, an entreaty, or an earnest request; as, ^'Go thou and do likewise." ^'■Remember thy Creator." Since the person commanded is generally addressed directly, this fonn of the verb has its subject in the second person singular or plural, and usually omits it. There are, however, instances in which this is not so; as, "Now tread %ve a measure. " Now move %ue on." "Come wc that are loyal to the king." " Laugh tJiose who can, weep tliose who may," If the student will read again what is given a few para- graphs back to the effect that each mode has some leadhig function or use, and if he will examine the use of the verb in the imperative luode, he will see that the time of the action is entirely indefinite, unless denoted by the context. It is the command that is most important. If it is desired that the time at which the action is to be performed shall be known, adverbial modifiers must be added to the predicate. "Honor thy father and thy mother." (Constantly.) (While you live.) It may be added that since commanded action can be obeyed only after the command has been given, the time of the imperative reaches from the early to the far fttture. 50. The Stihjtinctive Mode, — The treatment of the subjunctive mode is difficult, not merely on account of the nice points involved, but also because grammarians have failed to agree upon what the mode includes. This mode gets its name from snbjiinctivus, subjoined— joined in an inferior or subordinate relation to something else. The implication § 4 PEDAGOGICS OF GRAMMAR. 47 is that the subjunctive mode is used in subordinate clauses. We cannot, therefore, with this kind of clause alone, make a complete statement, or express a question or a command. Thus, " Were the earth as heavy as the sun, etc." " If a man 'ii>c7-c twenty- feet in stature, etc." " Unless the moon be utterly destroyed, etc." When we read such clauses, the mind demands something to be added that may complete the sense. This something is, in each case, a main or principal clatise. Thus, " Were the earth as /leai'y as t/ie su/i, a man could not stand erect." The fact is that we may find in subordinate clauses all the tense forms of the indicative and potential modes, and some other forms not belonging to either of these modes. The subordinate character of such clauses is generally shown by, certain conjunctions denoting doubt, condition, uncertainty, contingency; as, if, though, idi/css, providing, save, except, etc. To illustrate, we may say, If I am, be, was, were, sJiall be, Jun'e been, had been, shall have been, etc. Unless I may be, might be, may have been, might have been, etc. E.xccpt lie go, goes, went, were going, may go, may be going, etc. The foregoing forms are only a small part of those that may be met with in subordinate clauses. This fact has led to a great variety of opinion as to the forms that shotild be called subjunctive. What tense forms should be excluded as not subjunctive, and what admitted ? No one has so far been able to answer acceptably, or to construct a definition of this mode that will clear away doubt. Undoubtedly the easiest solution would be to call them all subjunctive if they occur in subordinate clauses, or else banish the mode from our grammars. But to this choice of the one or the other extreme few will accede, and no one has found a satisfactory mean. 51. Definition of tlie Siibjnnetive Mode. — A defini- tion of this mode as formerly used — as we meet it in reading the old writers — would run nearly as follows: 48 PEDAGOGICS OF GRAMMAR. § 4 Definition. — The subjunctive mode of a verb is the form or use of it that, in subordinate predication, expresses doubt ^ contingencj', zoish. or a mere supposiiioii that may or inay not end in fact. Doubt. — ''If he be a gentleman, he will remove his hat when he enters." Contingency. — "If I were he, I should obey the order." Wish. — " I would my daughter were dead at my foot, and the jewels in her ear." " Would she were mine." Supposition.— "//"///t- sky fat t, we shall catch sparrows." Professor Meiklejohn says, "The subjunctive mode has for some years been gradually dying out. Few writers, and still fewer speakers, use it. ***** g^^^ ^ knowledge of the uses of the subjunctive mode is necessary to enable us to understand English prose and verse [written] anterior to the present generation. Even so late as the year 1817, Jane Austen, one of the best prose writers of this century, used the subjunctive mode in almost every dependent clause. Not only does she use it after z/and though, but after such conjunctions as ////, until, because, and others." The writer believes, however, that this mode is still much in use, especially in our best newspapers and magazines, but in speech much less than formerly. It would be a pity if the many nice distinctions and shades of meaning, and the added variety of sentential structure made possible by the subjunc- tive mode, should be lost from our language. 53. Kno>vledge of the Subjunctive Mode That Teachers Should Have. — In the classroom the materials dealt with in teaching grammar are: 1. Current speech. 2. Extracts from early aud from modern writers. With respect to these two classes of matter, that of current speech is not much considered in grammar work. The same may be said of the works of the latest writers. It is largely with selections from the earlier classical authors that the teacher deals. What is called "the best usage" is largely determined by what these have done. Milton's writings, the § -t PEDAGOGICS OF GRAMMAR. 49 plays of Shakespeare, the tales and poems of Scott, — the works, in short, of nearly all the authors from whom we get our selections for use in teaching- grammar — abound in the subjunctive mode. This mode is, indeed, "dying out," but not from the teacher's work. Moreover, the principal need for grammar in our education is to enable us to understand what we read. And what better reading can we have than the writings that, after the test of time, the world calls classical .^ Hence, the teacher, more than any other person, should know not only what is, but also what was, the usage with regard to this form of the verb. And no harm will follow if the pupil comes to imagine that what was once so commonly used is still current. Even though he should employ it in his own speech, and in what he might write, it is an embellishment the continuance of which should be encouraged rather than otherwise. Its effect is like that of some of the Greek particles that clearly imply whole sentences. 53. Examples of tlie Subjunctive Mode. — For the purpose of illustrating the earlier and the present forms and uses of the subjunctive mode, we give the following quotations : " Unless he /la^w wings, he cannot ascend the peak." " If a man die, shall he live again ?" " Though he slay me, yet will I trust in him." " Would that night or Blucher were come." " O, had I the wings of a dove, How soon would I taste you again." " O, that those lips /z^ZiY language." "What if thine heaven be overcast ? The dark appearance will not last; Expect a brighter sky." " If wishes were horses, beggars might ride." ' ' We could catch fish were the river dried tip." " The world would be better did men hwe as strongly as they hate." " I would we could hear tidings of our jolly chaplain." " 'I were [were = s/unildbe—\n^\c2Cvi\Q mode) right sorry for it,' said the Knight of the Fetterlock, ' if he were lost.' " " If he have been killed, the world will profit." • Unless he act unjustly, my wealth will be restored." • Might he but come, I should be happy." 50 PEDAGOGICS OF GRAMMAR. § 4 " Though this be madness, yet there is method in't." "Yet, though the ebbing of Time's mighty river Leave our young blossoms to die, Let him roll smooth in his current forever, Till the last pebble is dry." "Yet, unless we greatly err, this subject is distasteful to most readers." "If disastrous war should sweep our commerce from the ocean, another generation may renew it; if it exhaust our treasury, future industry may replenish it ; if it desolate and lay waste our fields, still, under a new cultivation, they will grow green again, and ripen to future harvests. It were but a trifle even if the wall of yonder Capitol were to crumble, if its lofty pillars should fall, and its gorgeous decorations be all covered by the dust of the valley." 54. Remarks I'pon tlie Foregoing. — The student should examine and carefully compare the above quotations, and should determine which italicized verbs ought no longer to be considered as in the subjunctive mode. The last example, which is from an oration by Daniel Webster, fur- nishes a striking abundance of subjoined clauses containing verbs in the subjunctive mode. Is there not proof here that this mode is not really dying out ? The student will see that the distinguishing function of the subjunctive mode is to express mere contingencies and conditions that are generally true when taken with their opposite jneanings. Any verb so used is in the subjunctive mode, as it is now understood by the niajority of writers on English grammar. 55. Siilyimctive Mode Has but Vague Reference to Time. — The student should carefully note that it is the con- tingency, the doubt, the mere fiction, that dominates in the subjunctive mode, and that the idea of time is almost entirely neglected. Such indications of time as in any case may happen to be, must be inferred from the sentence as a whole. Thus, in " If it rain, I shall not go," we see that raiii, while present in form is future in fact. Similarly, in the sentence, " If I were he, I should not yield," § 4 PEDAGOGICS OF GRAMMAR. 51 the sense requires lis to regard tvcrc as present, although in parsing we call it past. So that what are called tenses are, in this mode, only varieties of form without much signifi- cance of time. Such as there is, usually points to the future, sometimes to the present or to the past, and often covers all time. 56. Tlie Infinitive Mode. — There is no special diffi- culty in this mode, although it has been treated in a variety of ways. vSome authors, notably during the last twenty years, have classed as infinitives what are usually called participles, because both are unlimited. By this it is meant that they undergo no changes to accommodate themselves to changes in the person and number of subject words. The implication is that the other modes, called _/?////i', are changed in soine or all of their tenses when changes are made in the person and number of their subjects. This, however, happens in only a few cases. Thus, in the indicative pres- ent we have only two changes, or cases in which the form of the verb is limited. 1 1^'ork, thou 7tvr/^est, he luorks^ zee work, you icork., they luork. There was formerly he zcorketh.^ but that is now obsolete. With the infinitive there is no such change; whence its name. Some other authors have called both infinitives and parti- ciples by the name of verbals. But there is really no good reason for thus merging them into one class, for while they are much alike in function they are very different in form. The terms gerund and gerundive, lately imported from the Latin, and complicated with the obsolete distinction between the Anglo-Saxon dative and the infinitive proper, serve only to confuse both pupil and teacher. The writer would urge in this matter that the old method of treatment is the sim- plest and best, and that we should continue to use the terms infinitive Q.n6. participle in their usual senses. 57. Subject of tlie Infinitive. — There is heard much discussion among teachers as to whether or not the infinitive 52 PEDAGOGICS OF GRAMMAR. § 4 has a subject. After all is said, the fact remains that action implies an actor; every verb, in whatever mode, has a sub- ject expressed or implied; even participles, inasmuch as they have the verb function, imply a subject. But infini- tives and participles omit their subjects so frequently, and besides take on so strongly the nature of the other parts of speech that inost grammarians omit notice of a subject. In the sentence. They told him to go, hint is just as much the subject of to go as they is of told. He zcas told to go, really means //r was told {Jiiiii) to go. When Hamlet says, To be or not to be, he is thinking of the desirability of life, and his meaning in full is [Man) to be, or [man) not to be. They /promised me to come is in full, They promised me to come [themselves], or [tJieni) to come. A few grammarians have said that when the action denoted by both an infinitive and a finite verb is performed by the same person or thing, then the subject of the infinitive is in the nominative case. The following are illustrations: " I expected to go to New York." " He was ordered to resign," " They refused to obey the officer." This, however, is clearly erroneous; for, if in the first sentence /is the subject of to go, then it should be correct to Avrite " I expected / to go to New York, " "I expected ^//r to go," " I expected tJicy to go, etc. " But we cannot say " I expected lie to go," " He asked / to go ": in all such cases we must use the objective forms of the pronoun. From the fact, then, that whenever the subject of the infinitive is expressed, it is in the objective case, we must infer that when it is only understood, it must be in the same case also, if it be supplied. The old rule of grammar, " The subject of a finite verb is in the nominative case,'' implies that there are verbs 7iot finite, wnth subjects that are not in the nominative case. The Latin rule, ^'■The subject of an infinitive is in the accu- sative,'' might have as its English equivalent, " The subject of an infinitive is in the objective case," for objective and accusative are equivalent terms. § 4 PEDAGOGICS OF GRAMMAR. 53 5S. Tlie Sign of the Infinitive. — The little word /o is by most writers called the si^yi of the infinitive, although it is often omitted. It is by some authorities regarded as a /yarf of the infinitive, and by others, as merely 2^ prcpositioi. The bulk of authority seems to be in favor of the latter view, but strenuous arguments have been urged on each side. Perhaps no word in the language has been more written about than this so called "sign of the infinitive." It has been called a preposition^ an adverb, a prefix, a particle, an auxiliary, a little u>ord, a sign of the infinitive, a. part of the infi)iitive, etc. These refinements about so small a matter have little practical value, nevertheless the writer is tempted to call attention to the likeness between this use of the word and its more common use as a preposition. It is primarily the function of a preposition to bring into relation words having no obvious connection. the house — the river the horse — the soldier kind — animals walked — water These unrelated words may be brought into relation by inserting between them in order by, near, to, into ; and by a variety of other prepositions the relation may be varied. Thus, we may use beside, ivith, towards, through. Now this is just what is done by to with the infinitive and some other word : ready — oblige orders — leave mean — go Still, the writer thinks it is of little consequence whether to be regarded as a preposition or as a part of the infinitive. The former is perhaps more nearly in consonance with the true function of the word. 59. The Sign ''•'I'o'" llesyarded as a Preposition. — If to is a. preposition^ then the infinitive is always a verbal noun. 54 PEDAGOGICS OF GRAMMAR. § 4 object of the preposition, and the preposition connects it with some other word and brings the two words into rela- tion. Thus, " We desire to excel." Here to connects desire with the verbal noun excel and brings the two words into relation. Excel is the object of to, and to excel is then a }ioiiii pJirase in the objective case after desire. Take another sentence : " He received bread to eat." (Here to cat ^^ for eating.') In this sentence, to connects bread and the verbal noun eat., and forms with it the adjective phrase to eat, and this phrase is a modifier of the noun bread. Again, " He tried to rescue the drowning boy." The phrase to rescue is an adverbial modifier of tried, and, more widely, rescue, with its modified object, forms, with the preposition to, the completed adverbial modifier of tried. Such cases as "To be contents his natural desire," are explained by supplying the missing subject of the infinitive. Thus, {Him) to be, etc. The preposition to, in this construc- tion, connects him and be, and the infinitive be is a verbal noun. 60. The Sign " To " as Part of tlie Influitive.— If to is regarded as a part of the infinitive, and is to be supplied when missing, then the verb with its sign may become, 1. A iioim used in the nominative or the objective case. " To toil is his necessity; his relief is to rest.'' " The enemy decided to retreat." 2. An adjective or an adverb. " He asked for work to do." " The boy is quick to understand." The closeness of the connection between to and the verbal word is evidenced by the dictiiui of the critics that the two words should never be separated by an interposed word. Thus, they insist that we should say to annihilate utterly or utterly to annihilate rather than to utterly annihilate. § 4 PEDAGOGICS OF GRAMMAR. 55 It must be conceded, however, that their contention has not been observed more than it has been ignored, in the practice of good writers, for the "split infinitive," as it is called, is of very frequent occurrence. 61. Complements of tlie lufliiitive. — ^ Although the infinitive is in a large sense an abstract noun, it still retains its character as a verb, and may, therefore, be modified by an adverb, or take adjective, noun, and pronoun comple- ments, just as is the case with verbs in other modes; as, to choose zvisely, to be careful, to appear sick, to act the gentle- man, to deserve punish jneiit, to resemble him. G'^. The Time Denoted 1).t the Infinitive. — In the use of the infinitive, it is not the purpose to denote the time of an action, but simply to speak of action in the abstract. As has been explained above, it is, when considered apart from the preposition to, nothing more than a verbal noun; although, when taken in connection with to, it may become an adjec- tive or adverbial phrase. If the idea of the time of the action is to be added, it must be done by other words. Goold Brown says : ' ' What is called the present infinitive can scarcely be said to express any particular time. It is usually dependent on another verb, and therefore relative in time." Dr. Blair remarks: "The infinitive mode carries neither time nor ai^rmation." THE PARTICIPLES. 63. Similarity of the Participle and the Infinitive. As has been said, the participle is very similar, in some of its fiinctions, to the infinitive. This is especially so when the preposition to is regarded as a part of the infinitive; for then the verb is used as a noun, as an adjective, or as an adverb. The participle is not usually treated as a mode of verbs, although, as we have seen, it is sometimes classed with the infinitive, forming one group called the infinitive mode, and sometimes both forms are called 7'erbals. In the sense that it is not changed on account of any change in the 56 PEDAGOGICvS OF GRAMMAR. § 4 person and number of the subject, it is infinitive — iinlimited. But owing to the fact that the presence of its subject is less frequent and less important than is the case with the infini- tive proper, it is thought better to treat it separately. Like the infinitive, it predicates by assigning, not affirm- ing, action or state ; and, like the infinitive, it may be mod- ified by an adverb, may take a subject or an object, or may be followed by a predicate adjective or by a predicate noun. " Waking car/y, we set out at once to ascend the peak." "The boy, being indolent, gradually fell behind his class." " Horatio, being a scholar, spoke to the ghost." ''Having accumulated a large fortune, he returned home." The participles have been by some authors regarded as forming -a participial mode, but the objection to this is obvi- ous. For if the participle is to be considered as having mode, there seems to be no reason why it cannot be merged in the infinitive mode, as has been done by many grammatical authorities. 64. Classification of Participles. — As is the case with every other form of the verb, there have been innumerable classifications made of the participle. To enumerate even a portion of these, without discussing them, would serve only to confuse the student and to profit him not at all. These classes have tense names, although it must not be understood that the indication of time by the participle is definite or important. As is true of all verb forms except the indicative mode, time must be denoted, if at all, by accoinpanying words. This is exemplified in the following sentences: " Being deceived has the effect of rendering one suspicious." The action expressed by the verbals may be referred to any time whatever. '' Having been defeated, 2iXi able commander should become more wary, indeed, but more determined to win." Here the time of the participle may be present, past, or future. The sentence expresses a universal truth. The following classification is the one most commonly accepted; §i PEDAGOGICS OF GRAMMAR. 57 tabijE of participi^es. Names. Transitive- Active. Transitive- Passive. Intransitive. Neuter. Present. loving. being loved. fly. being. Past. loved. loved. flown. been. Perfect. having loved. having been having flown. having been. Perf. Pro- having been loved. having been gressive. loving. flying. 65. Remarks. — The past participles, active and neuter, are rarely found except in verb phrases, a use that some verbs seem to admit. It would be difficult to construct a sentence containing loved used by itself as a past active par- ticiple, but flown may be so used correctly; as, " Tlie bird, flown from its nest in search of food, never returned." This is an authorized construction, though the perfect participle would be better: "The bird having flozun,"' etc. These participles are generally given by the grammarians, perhaps on account of their occasional occurrence, and because they are used in forming the perfect active participle. Thus, loved is active in having loved. 66. Degrees of Assumed Predication of Partici- ples.— Predication by participles is of very many, but indefi- nite degrees. When they are joined directly to a noun — preceding it^the verbal origin of such modifiers rarely occurs to the mind, and they become mere adjectives; and such they should be called, unless their verbal nature is for some reason interesting. Instances are: a writing pad, running water, a surprising feat, a spoiled child. Similarly, the verbal noun often contains so little predica- tion that it may be regarded simply as an abstract noun. Thus: ''Swimming is easy to learn." "He earned his living by flshing." The predication comes out more distinctly in such uses as the following: "Columbus, fearing that his men might mutiny, made them promises." 68 PEDAGOGICS OF GRAMMAR. § 4 This is nearly equivalent to the predicating form, ' ' Colum- bus /.?«r^. Moreover, when we speak of an act anticipated, or recall it after it has been performed, we speak of it as a luhole. 60 PEDAGOGICS OF GRAMMAR. § 4 The meaning of the v^ord prcsoit in grammar is better seen in what we call the lunvcrsal pi'cscnt X.qw'&q. "The earth revolves. " ' ' The sun shines. " "A triangle /las three sides. " "Jesus is the Savior of men." The present of this use of the verb generally covers all finite time. In the use of the universal present the student should be careful not to employ the past for it. Thus, "Columbus believed that the earth teas round." "He insisted that the product of seven by six was forty-two." "He assured his audience that Jesus was the Savior of men." This error of speech is of extremely common oc(?Virrence. The student should note the distinction between / work and I a7n working. The first denotes habitual or cnstouiary action. It is the universal present applied to ordinary finite action. / avi working denotes vioiuentajy, eontiniioiis^ or temporary action. The former, / zvork, has for its present an extent of time ranging perhaps far into the past and the future, and it is therefore the present indefinite. The latter, I a7)i Ivor king, is called the present progressive, and usually involves but little time on each side of the now. Like the present, the present-perfeet tense is used to denote action of two kinds. / have thought. I have been tJiinktng. The former is called the prese>it -per feet indefi)nte, and it denotes past action completed at the present, — the time of speaking, — or at some time of which the present is a part. The latter denotes past action in progress at the time of speaking, and has been called the present-perfeet progressive. In the sentences, " vSince Virgil wrote, Rome has fallen," " The poems of Homer have been much admired," the shaded part of the diagram must, for the first sentence, be extended so as to include the time when Virgil wrote; for the second sentence, it must go still farther back, so as to begin with the time when Homer's poems were first admired. But the context may make narrow and definite the range of the present. " The clock has y/zj-/ struck." " The year 1899 was pregnant with events that make history. " By the figure of rhetoric called Vision, the present may be carried by imagination into the past or the future, as we § 4 PEDAGOGICS OF GRAMMAR. GI please. Similarly, the past or the future may be conceived as present. "The twenty-first century kas just daivned. Human progress /las been making great strides. The power of steam and electricity has been supplanted by forces hitherto unsuspected. Nature is yielding her secrets less reluctantly and more and more rapidly." " Behold poor old Socrates. He sits undejected in his prison. His friends Iia^'c been with him ever since his conviction and sentence." In such transfers of the present or any other time, the tense names remain imchanged. 70. The Past Tenses. — Very similar to the tenses of the present are those of the past. They are two in number, the past tense or preterit and the past-perfect tense. Each of these has two forms, the i)idefinite and the. progressive. I /ndefi nite. — Active. — " I walked." Preterit i. Passive. — " He was advised." I Pj-ogressi7'e.^-\ci\ye. — " I was walking." { Indefinite. — Active. — "He had walked." Past-Perkec T j Passive. — "He had been advised." I Progressii'e. — Active. — "He had been walking." The following definitions of these tenses may be useful to the student: 1. The past iiidefliiite tcn.se denotes action at some indefinite past time. 2. The past progressive tense denotes action /;/ progress at some indefinite past time. 3. The past-perfeet indefinite tense denotes action completed at some indefinite past time. 4. The past-perfeet progressive tense denotes action in progress at some indefinite past time. It is usual to call 1 and 2 simply the past tense, or the preterit, and 3 and 4 the past-perfect. 71. Tlie FiTture Tenses.— There are two tenses for future time, the future and the future-perfect. As is the case with the tenses of present and of past time, each of the tenses of futm-e time has two forms, one for completed action and one for continuous ox progressive action. 02 PEDAGOGICvS OF GRAMMAR. § 4 Examples illustrating these forms are given below: I Indefinite. — Active. — " He will walk." Future \ Passive. — " He will be advised." [ Progressive. — Active. — "I shall be walking." Future-Perfect Indefinite. — Active. — " I shall have walked." Passive. — "He will havebeen advised." Progressive. — Active. — " He will have been walk- [ ing." It is a fact not generally known that in our conversation we use the future-perfect tense perhaps not a score of times during our lives, and that one may read many books and not meet this form of the verb once in all of them. When the future perfect is required, some equivalent is used. Thus, for "When I reach home, I shall have walked fifty miles," we may say, "When I reach home, it will be fifty miles that I have walked." It is a ten.se that must be sought in books; it occurs almost not at all in conversation. The practical value of this tense, therefore, is slight, and if it were not for the sake of showing completely the relations of tenses, it might be omit- ted as being little more than a curiosity of the English verb. 73. Passive Proj^rressive Forms. — The student will notice the omission of W\q. progressive passive forms. Strictly, there are, and perhaps there should be, no such forms ; but within the last half- century, there have come into more or less general use z. present passive and z. past progressive pas.sive. ' ' The house is being built. " ' ' He is being advised. " ' ' The house was being built." " He was being advised." Of course the.se are the only passive progressives that could be used, for no one would tolerate such forms as "He has been being advised," "He will be being advised," "He should have been being advised," etc. Good writers avoid altogether the use of progressive passive forms. Equally bad, and nearly as common, are the so called passive forms with the active participle in -ing. "The house is building. " "The cellar is digging." "The wood is sawing." § 4 PEDAGOGICS OF GRAMMAR. 63 It is better to employ a few more words, if necessary, than to introduce forms so questionable. We may always say "They [the carpenters, etc.] are building the house." 73. Tlie Enipliatic Present and Past Tenses. — In addition to the foregoing tense forms, there are two others that are used when we wish to place special emphasis on the action expressed by the verb. These are Iho present and the preterit with do and diei. Present Tense. — " I ih) walk." " He docs think*." Past Tense. — " I did walk." " He did think." The progressive forms also are frequently used when we wish to be emphatic; in this case the stress of voice is put on the first verb element. Thus, " I am walking." " I ivas walking." " He Jias been sleeping.". •74. Siininiary of tlie Tenses of tlie Indicative Mode. It follows from the foregoing that the indicative mode has six tenses, comprehending fourteen tense forms. These tenses are the present and the present-perfeet, the past and t\iQ past-pe7-feet, the future and \\iQ future-perfect. The various tense forms may all be converted into ques- tions by differently arranging the subjects and predicates, and by using do and did when they are needed. Thus, I love. I am loving. Do I love ? Am I loving ? Did I love ? I have been seen. Have I been seen ? I shall have been seeing. Shall I have been seeing ? 75. Synopses of tlie Tenses of All the Modes. ACTIVE VERB. — Regular and Irregular. TENSES. INDICATIVE MODE. Present Indefijiitc. — I walk. He writes. Progressive. — I am walking. He is writing. Perfect indcf. — I have walked. He has written. Perfect prog. — I have been walking. He has been writing. Emphatic. — I do walk. I do write. 64 PEDAGOGICS OF GRAMMAR. Past ' Indefinite. — I walked. He wrote. Progressive. — I was walking. He was writing. Perfect indef. — I had walked. He had written. Perfect prog. — I had been walking. He had been writing. Emphatic. — I did walk. I did write. Future - Indefinite. — I shall walk. He will write. Progressive. — I shall be walking. He will be writing. Perfect indef. — I shall have walked. He will have written. Perfect prog. — I shall have been walking. He will have been writing. Present POTENTIAL MODE. Indefinite. — I may walk. He can write. Progressive. — I may be walking. He can be writing. Perfect indef. — I may have walked. He can have written. Perfect prog. — I may have been walking. He can have been writing. Past Indefinite. — I might walk. He could write. Progressi7>e. — I might be walking. He could be writing. Perfect indef. — I might have walked. He could have written. Perfect prog. — I might have been walking. He could have been writing. Present SUBJUNCTIVE MODE. Indefinite. — If I walk. If thou walk. If he write. Progressive. — If I be walking. If thou be walking. If he be writing. \_Perfect indef. — If I have walked. If he have written.] \_Pe7fcct prog. — If I have been walking. If he have been writing.] Past Indefinite. — If I walked. If thou walked. If he wrote. Progressive. — If I were walking. If he were writing. P effect indef. — If I had walked. If thou had walked. If he had written. Perfect prog. — If I had been walking. If he had been writing. PEDAGOGICS OF GRAMMAR. 65 Present IMPERATIVE MODE. Indefinite. — Walk [thou]. Walk [ye or you]. Write [thou, ye, or you]. Progressive. — Be [thou, ye, or you] walking. Be [thou, ye, or you] writing. Emphatic. — Do [thou, ye, or you] walk. Do [thou, ye, or you] be writing. Present INFIXITIVE MODE. f I)idefinite. — To walk. To write. Progressive. — To be walking. To be writing. Perfect indef. — To have walked. To have written. Perfect prog. — To have been walking. To have been writing. „ ( Walking. Present < „,. .^. ( Writing. PARTICIPLES. I Indefinite. — [Walked. Written. ] Perfect indef. — Having written. Perfect prog. — Having been writing. Indicative Potential PASSIVE VERB.— Irregular. Present. — 1 am seen. Present-perf. — I have been seen. Past. — I was seen. Past-perf. — I had been seen. Future. — I shall be seen. Future-pcrf. — I shall have been seen. Present. — I may be seen. Present-perf. — I may have been seen. Past. — I might be seen. Past-perf. — I might have been seen. Subjunctive. Present. — If I be seen. Past. — If I were seen. Imperative, Be [thou, ye, or you] seen. Infinitive. Present.— To be seen. Present-perf. — To have been seen. PARTICIPLES. Present. — Being seen. Past. — Seen. Present-perf. — Having been seen. 66 PEDAGOGICS OF GRAMMAR. § 4 *7G. Auxiliary Verbs. — The following verbs are used as helping, or auxiliary verbs : Present. — do, have, shall, will, can, may, must, am, is, be. Past. — did, had, should, would, could, might, was. Some of the auxiliaries occur also as principal verbs; as, do, be, have, and ivill. Thus, •' I (/^ my work." "God is." ''Troy was." "John has a book." " When a woman «'///, she will." Besides their use as principal verbs, do and did are auxil- iaries of emphasis and of inquiry. Have, shall, and zvill are tense auxiliaries, in verb phrases the first denotes com- pleted action; the other two denote fjit?ire action. May, might, can, could, should, zuould, and must are mode auxil- iaries, and the several forms of be are by some authors called voice auxiliaries; by their aid, verb phrases are made passive. This is shown below: Active. Passive. He loves. He t's loved. He may love. He may be loved. He might have loved. He might have been loved. To see. To be seen. If I saw. If I luere seen. So far as it can be done, tlie student should write out the auxiliaries in their various modes and tenses, and he should be very familiar with the uses of each. This is especially important in the case of be and have. There are some other words that have been included among the auxiliaries; as, let, ought, going. " Let him go" has been supposed to be " Go he! " a sort of third person imperative present. It is, of course, only "[You] let him [to] go." "He ought to go" has been made into an obligative mode. But ought was originally only the past tense of oive, and it is now a defective verb. This sentence is really a shortened or idiomatic form of " He owes it (is under obligation) to go. " " He is going to write" some authors call the intentional mode; and Professor Melklejohn, as has already been seen, makes a future infini- tive intentional, " To be going, to love," " To be going to be § 4 PEDAGOGICS OF GRAMMAR. 67 loved." But this kind of thing serves no useful purpose, and should not be seriously considered. '7 a, "■ Shall " and " Will." — In no way can one furnish better evidence of being- really cultured in the English lan- guage than by using s/ia// and tfi// always correctly. This, of course, includes also their respective past forms, sJionld and ivonld. It might be well to note that although these are called the past tenses of sliall and zvill^ they usually point to future action. Much has been written upon the correct use of these words; but we continue to hear, and to see in print, blunders with respect to them. The subject is difficult, and we can hope to master it only by constant watchfulness of our own speech, and by careful reflection on the different ways in which, these verb forms are used by speakers and writers. 78. Fundamental Meaning of " Shall " and "Will."" — Will and zvonld originally meant purpose, determination, strong intention. Since all these have reference to fiitiirc action^ the words have come to be used in promising, in threatening, in predicting, and iu announcing mere future action. Moreover, since nearly everything pertaining to the future is involved in more or less uncertainty, the elements of doubt, contingency, conditioji, have served to increase the difficulty. This difficulty is met with especial frequency in the use of shall and should. The sense of shall and should was originally obligation. That was during the early history of our language. / shall go originally meant, therefore, nothing more than / ought to go. But one is expected to do, and is likely to do volunta- rily, what he is under obligation to do; hence, this meaning is now entirely lost from shall and partially lost from should, and they are mainly used to express simple futurity, moral obligation, and often compulsion by a force from without. Both shall and zuill are employed besides in promising and threatening, and in many other ways. In most of these uses, there remains a greater or less degree of determination, resolve, intention. It is obvious that when it devolves upon 68 PEDAGOGICS OF GRAMMAR. § 4 words to express so many cliff cent shades and degrees of thought, one must expect more or less difficulty in using and understanding them, 19. "Shall" and "Will" Denoting Detei-mination. — The rule generally given is that zvill in the first person and shall in the second and tliird persons denote purpose, resolu- tion. To this rule there are many exceptions, some of which will appear later. This element of determination or will may be: 1. The Will of the Speaker.— "I will go, notwithstanding your opposition." "Be sure that we would go if we could." " He shall not enter without permission." " They shall do as they are told." " I ordered that they should not make an attack upon the fort." "Will I do my duty ? Of course I will." " I will drown, and nobody shall help me." (Resolved to drown, and determined to accept no help.) "We promised that we would do the work." "You shall digest the venom of your spleen though it d.o split you." " If I were you, I would not do it." " If he were my boy, he should obey." (On compulsion.) (From choice.) The speaker may desire to weaken the Ti.'/// element, and may finallygetso farinthatdirectionas to indicate nothing stronger Ihaxi preference^ inclination, desire. If preference is indicated by other words in the sentence, we have such cases as: "I &)\o\.\\6. prefer to remain at home." " You would be glad to see him, I have no doubt." " They should be delighted with their pres- ents." " I shall come ivith pleasure." " You would oblige me much by attending to the matter." "I should rather be excused from attending." " I should (or would) as soon live as die." "If I had the power, 1 should compel \i\vs\ to resign." Again, the speaker's will may rest in the statement of obligation or advantage. In this case, the determining will or condition operates from without — it is external compul- sion, opportunity, or favoring conditions. "You should be kind to your mother." " They should make large profits by the transaction." " I should go, but I cannot spare the time." "You should see him at your earliest convenience." "The crops should be unusually good this season." " It should rain today." There is a form of speech, known as the language of offi- cial courtesy.^ employed by officials in conveying orders to § 4 PEDAGOGICS OF GRAMMAR. G9 their subordinates. It relieves the superior from the embar- rassment of seeming to give orders, and the subordinate from that of receiving them. "You 7iiill carry this message to the admiral, and he zuill inform you as to your future movements." " The soldiers of the army will main- tain the strictest vigilance, and they will yield perfect obedience to their officers." 2. The Will of the Hearer. — The usual form in this case is that of inqiiir}' concerning the hearer's judgment or pref- erence, or his will towards the speaker, or towards some third person. It may take the form, also, of a statement concern- ing the will of the hearer. " Shall we go now ? " " Should they be admitted?" " Would you do evil that good may come?" "Will you have him arrested?" " Shall he come into your office ? " "Should I tell him that you are not at home?" "Shall I call tomorrow?" "You promised that they should obey." "You would do it, and must take the conse- quences." " O, you will, you rascal?" "Would you promise to do otherwise ?" The will of anotlier may be inquired about, or a statement made about it, in the third person. " Will Mr. A be good enough to hear what the bearer has to say ? If Mr. A would help in this matter, he siiould not hesitate to ask a similar favor from the writer, his friend." 3. The Will of the Person Mentioned.— " When a woman will she will, and that's the end o't." " He would, but dares not." "How often would they have gone back, but they could not." " Will he do it; dare he do it ? " " Would he do the serv- ice for money ? " This form of willing weakens until finally it is only cus- tomary aetion. " He would lie on his back for hours, watching the clouds." " The swallows would disappear when autumn came." " He would go for a walk every morning before breakfast, and they would lie in bed as long as possible." " They will always fly their kites when there is wind." " Why will he weary the good people with his chatter ?" 4. TJic Will of a Higher Pozcer, or Nature, or Mere Chance. — For the operations of nature or of an imagined higher power, the Latins employed a personal subject where 70 PEDAGOGICS OF GRAMMAR. § 4 we use the pronoun it; as, "Jupiter will rain rain to- morrow." "Jove thunders." "Ceres will increase our harvest." There has been much discussion as to whether we should say, "It should seem, appear, etc.," or "It would seem, appear, etc." Neither expression denotes or implies any of the determination originally in luoiild, or of the obligation in should. Neither does either luoiild or shotild express futu- rity. The meaning of each is very nearly "It seems." After considering all the circumstances of a case we might say either, "It would seem, or "After all, it should seem." Should follows the usage of sJiall^ and zvould of tvill. Now, since it is correct to say, " It will seem best, I think, for you, etc.," and "If it shall seem best, etc.," it must be equally correct to say either, " It would seem," or "If it should seem. " The preference should perhaps be given to the former expres- sion, but when a conjunction denoting doubt, condition, or contingency precedes, should is better than would. "It will rain tomorrow." " If it shall come to pass." "Although it should be late, it would make no difference." " Should oxygen and nitrogen unite as readily as oxygen and hydrogen, all life would be destroyed from the earth." "Although the whale is a mammal and has lungs, it would be impossible for it to live upon land." " The weather should soon change for the better; doubtless it will." " If the clouds would only go away, we should be much more comfortable." " If the clouds should go away, we would be much more comfortable." "If the day should come when you would return, send me word." "I should be sorry if you should fail." "Thy rod and thy staff shall comfort me." " It would be strange if some one should not have visited this island." " How strange it should be that this beautiful snow Should fall on a sinner with nowhere to go ! How strange it luoiild be, when the night comes again, If the snow and the ice struck my desperate brain ! " " If he should come, I would go." " If he would come, I should go." " If he would pay me a fair price, I would do the work." " Unless it should rain, tomorrow should be a fine day for our trip ; for it is the month of Ma}-." 80. "Shall" and " AVill '^ Denoting- Mere Futu- rity. — The announcement of future action may be : § 4 PEDAGOGICS OF GRAMMAR. 71 1. A Merc Predict io)i, or an Inquiry as to Future Action. — " He will come tomorrow." " You will surely be detected." "The time will pass rapidly." "Even though he should apologize, I would (or should) never forgive him." " If he should fail to accomplish the undertaking, he will be disappointed." " He would be disappointed if he should fail to accomplish the undertaking." " I shall be there on time." " When shall we three meet again?" " If you should come to the city, you will call to see me, will you not?" " Shall you go to the theater tonight?" "Will your father go, or shall you go instead?" " He insisted that I should have confidence that, sooner or later, he would pay me." " Shall you not be glad to go ? " "I should be very glad." "Shouldn't we be delighted?" "If they should come, would (or should) 3'ou be glad?" "Shall not my mother depend upon her The student will notice that, in the foregoing' .sentences, while futitre action is the conspicuous element, some of them express in a greater or less measure contingency, ^uill, etc. Indeed, it is difficult to avoid blending these various mean- ings. In this lies the necessity for considering carefully what we would say and how we should say it in each case. Careful consideration is needed in cases where futurity, ivill, and obligation are combined in various measures. The principal difficulty in the use of these attxiliaries is found in such combinations. " What would you do, and what should I do, in such an emergency?" " What should you do, and what would he do, in that case ?" " How shall I repay you for what you will suffer in my behalf ?" " How will (or shall) he repay you for what you will (or shall) suffer by going to the army in his place?" " If he would do such a thing, he should be punished." "If twenty cents will pay for five oranges, how much should be paid for three oranges ?" "At that rate, how much would (or should) iouv oranges cost?" "How many shall I get for eight cents ? " " How much shall I earn in three days, at four dollars a day? " " How much shall I pay for the coat, and what will you charge me for the hat?" 2. A Promise or a Threat. — " He shall be punished." " Come with us and you shall (a proinise merely) have a good time." " Come with us and you will (simple pre- diction) certainly enjoy yourself." " He said that we should share the prize money." " They shall suffer for this." "It shall go hard with him." (The speaker's will.) " It will go hard with him." (Not the 72 PEDAGOGICS OF GRAMMAR. speaker, but some one else will cause it.) "He promised that they should be punished." "It was said that they should be punished." (Ambiguous ; it may mean ought to be, or were going to be, punished.) The same is true of the following sentence. "It was reported that they would be punished." (It may mean wanted to be, or %uere going to be, punished.) " He shall do as he is told; if not, you shall punish him." (The speaker's permission is granted to punish him.) " He shall obey ; otherwise, you will report (you are directed to report — official courtesy) the fact." 81, Collections of Exami^les. — Every student shovild have a note book in which to record all kinds of sentences collected from classical sources. They are valuable not only for reference, but they serve to keep such matters before the mind. This is a condition indispensable to accurate scholar- ship. By readin<^ such collections aloud they sink into the mind throug-h the ear, so to speak, and presently the tongue is rebuked if its utterances are at variance with what the ear demands. Many other instances of the use oi sJiall and ivill might be given here, but the writer believes that the student will be able to supply what may be needed in addition to those above. TABT^E OF THE TERB. H P Action expressed Form . Use r ,r -.-• r Active. I ransitive \ I (^ Passive. j f Active. Intransitive i ^t <. [^ [_ Neuter. Regular — lov^e, walk. Irregular — go, come. Defective — ought. Redundant — dive, dream. Principal Auxiliarv walk, go. walked, went. I walked, gone. r do, may, will, have. j did, might, would, had. j be, can, shall, must. (_ was, could, should, PEDAGOGICS OF GRAMMAR. 73 THE ADVKRI5. 83. Office of tlie Adverb. — In treating of the adjec- tive, it was stated that its function is to narrow the extension and enlarge the comprcluiisioii of the noun's meaning. The same is true of the adverb in its relation primarily to the verb, and secondarily, to the adjective or to another adverb. Thus the verb ;v/;/, used alone, may denote the act in every conceivable p/aee, time, manner, or other limitation — its extension is universal or unlimited. When a modifier is joined to the verb, the extension is narrowed so as to include the act of running only under certain limitations of time, place, manner, etc. today rapidly canjiilly here imviediatcly at once by and by ivitit speed luit/i ease i along t/ie river lohen the signal is gi^'en because he is frightened t/iat lie may escape ivhither he may find help as he ivas iftstrticted to do Any word, phrase, or clause used as above to modify the meaning of a verb, or, in other words, to enlarge its compre- hension and narrow its extension, is an adverb. This is exactly the effect upon an adjective or an adverb, when the meaning of either is modified by an adverb. today always good -> /;/ school for food extremely jrood when his father is at home because he was told where others are bad if he is paid fill- it although he might be bad In a similar way, it may be shown that the meaning of an adverb may be modified by another adverb, or by an adverbial phrase or clause. 83. Adjectives and Adverbs in Tlieir Relation to Verbs. — This matter was treated to some extent in 74 PEDAGOGICS OF GRAMMAR. § 4 connection with the verb, but its importance and its relevancy here require a further consideration. It has been stated that the nature or function of an active verb is twofold. It expresses aetioji and asserts or implies a state of the subject while in that condition of action. The neuter verb docs little more than predicate a state of the subject ; as, James is sick. This verb, however, although it aids in the assertion, which, indeed, coiild not be made without it, is used to bring the subject and the attribute into relation. It is, therefore, a connective. For this reason, grammarians have called the verb is in its various forms a copula^ which is a Latin word meaning a connective. Hence, the neuter verb has two very well marked functions or offices: the predicating or asserting function, and the con- nect i)ig or copn/ative function. It has already been explained that every verb denotes action in some degree, but in this and some other verbs, the action is so obscure that they have been called neuter verbs, — neither active nor passive. Now a neuter verb, or mere copula, can be used in two ways only: 1. To join a subject to an adjective or a participle deno- ting the state of that which the subject represents, or to an expression equivalent to an adjective or a participle. This is the predicate adjective or the participle used in the predicate. "The girl i.s «t-/{'." " The leaves are yrr///;/^^." " The sun is just now going behind the mountains." 2. To connect a subject with a noun, a pronoun, or any substantive expression denoting the same person or thing as the siibject. This is called the predicate noun. "The boy is a. scholar." "It is Jie." "It was i/ic cause of your J ail u re.'" 84. Neuter Verbs Cannot Be ModiflLert. — It appears, then, that the meaning of a pure neuter verb or of a copula cannot be modified by an adverb, for an adverb is used with verbs to denote the time, place, manner, degree, etc., of the action they express. Existence simply or state requires an adjective, not an adverb. Thus, you cannot say, ' ' He is § 4 PEDAGOGICS OF GRAMMAR. To gladly,"' "He looks angrily,'" "He sits erectly."" Hence, where the modifying' word denotes only the place or the time of the being, or the state of the subject, it is really an adjective. For example, in " He is here," " She was there,"' "The hoy is at school,'" "I shall be where I am needed,'" the italicized elements must be taken as adjectives. It may be conceded that many grammarians and the dictionaries call the words here and there adverbs, and such they usually are; but they are sometimes adjectives. Several of our latest and best writers are discriminating attributes of being and mere state from attributes of action, making all of the former, adjectives. 85. A'erbs That Are Botli Active and Xeuter. — Some of the verbs denoting both state and action frequently are accompanied by both adjectives and adverbs; the former denote the state of what the subject names, and the latter modify the meaning of the verb. " John lies in bed sich."' Here /// bed tells where he per- forms the act of lying, and sick denotes his state. "He sat crt'cf on-a-c/ia/r." "He lives rw/Av// in'the-ltoiiic-flf-his- anccsiorsy In the first of these two sentences, erect describes the attitude of the person denoted b\- he, and oii-a-chair is an adverbial phrase pointing out the place where the action was performed. The case is exactly similar in the second sentence. The distinguishing test of a neuter verb is that tJie being or state it denotes cannot be modified by an adverb; and in the case of verbs expressing both action and state, adverbial modifiers can be used only with reference to the actional function of the verb. It is often a nice point to determine whether we wish to modify the action expressed by the verb, or to modify the state. "They landed safe on the shore."" Here on the shore is adverbial, but many would say safely. A little thought, however, will make it clear that we are to think of the 76 PEDAGOGICS OF GRAMMAR. § 4 people or things as being safe after the aet. The sense, therefore,,jrequires an adjective. "He remained quiet, waiting for his father," or, " //^ remained, quietly zvaiting for his father." In the first sen- tence, the word and the phrase are both adjectives; in the second, quietly zvaiting for Jiis father is the predicate adjec- tive. It denotes a state and not a manner of action. More- over, the verbs remained differ in meaning" in the two sen- tences. In the first sentence the meaning is kept quiet, preserved a state of quietness; in the second the meaning of remained is stayed behind. The former is, therefore, more nearly a neuter verb than the latter. "He sat still, watching the birds." "He sat, slill ivatcJdng the birds." adj. adj. adj. " He lay on a rock dreaming of home." adv. adj. " She seemed /;/ every action rational." adv. adj. " The snow lay 07i the nor t Item hill slopes leaking away its life." adv. adj. Sometimes it is uncertain which is required, an adjective or an adverb. In such cases it is usual to give the preference to the latter. "He looked ifidifferent{ly) at the wonderful display." "He walked resoluie{ly) towards his formidable enemy." "My watch runs slo7v{ly)." 86. Classification of Adverbs Accoixling to Their Use. — Many classifications of adverbs have been made, but none of them covers all the functions of this part of speech. The division most commonly made is into four classes, and these classes are determined by their use. 1. Simple. 2. Interrogative. 3. Conjunctive. 4. Modal. 1. A simple adverb is any word used as an ordinary adverb, and having no other function or use than as a modi- fier; as, (jO quickly, extremely careful, quite cautiously, to go promptly, to do his duty thoroughly. 2. An interrogative adverb is an adverb used to ask a question concerning the time, manner, place, or cause of an action or a state. § 4 PEDAGOGICS OF GRAMMAR. 77 "IV/iy do you go?" ''U'/ic/i will he come?" ''Where are they going ? " ''How are you today ? " " IV/icre/ore is he here ? " 3. A conjunctive adverb is an adverb that modifies like an adverb, and, like a conjunction, connects or introduces clauses. " I know a bank whereon the wild thyme grows." " You will behave as good children should, 1 am sure." " W'lien you go, take me with you." " Whither it goeth ye know not." Some authors say that the conjunctive adverb generally modifies an element in each of the connected clauses, and others insist that it is only the verb in the subordinate clause that is modified by the conjunctive adverb. The former view is perhaps the better. In the first sentence given above, bank is modified by all that follows, and groxus by zvhcrcoii. "I was told where he lives. " In this sentence, where he lives is the object of was told, and where is a modifier of lives. 4. A niodiil adverb is an adverb that modifies the mean- ing of an entire sentence, or denotes how or in what degree its sense is to be taken. " He will/;v^/'^i'/''/)' come." " You will not be on time." " Are you going to the city ?" " Sitre/y." " He must, therefore, suffer the con- sequences of his act." " Hence, we may conclude that the sum of the angles of a triangle is equivalent to two right angles." Many grammarians have left it more or less doubtful as to what should be included in the class of modal adverbs. Per- haps the best means of determining whether an adverb is modal or not is to vary its position, and if the meaning of the sentence is not thereby changed, the word may be regarded as belonging in this class. " I ■&\i2ii\ perhaps go to New York." Here the adverb may, withotit affecting the sense, be placed in almost any position, a fact showing that the mean- ing of the entire sentence is modified by it. 87. Resi^onsives. — Among the modal adverbs are placed certain words of affirjiiation ; as, jr*?, yes, surely, certainly, indeed, verily ; also adverbs of negation ; as, no, nay, not, and a few others. Most of these are regarded not as adverbs, 78 PEDAGOGICS OF GRAMMAR. § 4 but as abridged sentences. They resemble in function the interjection, but many authorities deny that such words belong to any part of speech. But whenever they determine the mode in which an entire sentence is to be taken or con- ceived, we should call them modal adverbs. 88. Classification of Adverbs Aecordingf to Their Meaning.— Adverbs are divided into classes that denote time., place., degree, manner, cause, etc. In etymological parsing, the pupil is generally required to classify adverbs with reference to their meaning rather than to their use, but it is more satisfactory to include both func- tions. Thus, in the sentence, ' ' The house is cheerful when the children are at home," ivhen is a conjunctive adverb of time. 89. Adverbial Objectives. — A noim in the objective case is often used as an adverbial modifier denoting time, measure, distance, weight, value, etc. "The clock strikes every half-Iiour." "We shall set out /oinor- row." (Toinorrow = on or during tomorro'iv.) "He was in college iowx years." " The emperor was more than six /t'c/ tall." "I do not care a. Jig for his opinion." "The book is worth, a do// a r." "The train was two liours late." " He looks like his drot/wr." 90. Tlie Position of tlie Adverb. — The adverb should generally be placed immediately before an adjective or another adverb that it modifies, and directly after a verb consisting of one word, and after the first auxiliary of a verb phrase. The position of an adverb that modifies an infinitive has been much disputed about, but the bulk of authority is perhaps opposed to giving any word or words a place between the infinitive and its "sign" to. Whether the adverb should precede the infinitive or follow^ it is a matter largely depending on euphony, and on the influence of other words. "Gaily to burgeon and broadly to grow;" " carefully to observe," "to observe carefully;" "I asked him to decide promptly," " I asked him promptly to decide." In consequence of the careless placing of adverbs, sen- tences are very frequently of uncertain meaning; or they § 4 PEDAGOGICS OF GRAMMAR. 79 often have a sense entirely different from that which the writer intended. Perhaps more errors of this kind arise from the use of the word oily than from that of an}- other word in the language. The following sentences will exemplify the different senses that may be owing to difference in the posi- tion of only : "Only Harry's brother chided him" — No person except Harry's brother etc. "Harry's only brother chided him" = Harry had but one brother, and this brother chided Harry. "Harry's brother only chided him" = Harry's brother did noth- ing more than chide him. f "Harry's brother chided onlv him " 1 ^, , , , , • -, , \ ,T , , , ,.,,,.- ,,,;. = Harrys brother chided I "Harrys brother chided him onlv J -.. ' , , , •-, , ^ ■ ■* Harry, and he chided no one else. A notable authority gives the following rule for placing only ; our reason for quoting it is that it is equally useful as a general rule for placing adverbs: " Place the only next to the word or phrase to be modified by it, arranging the rest of the sentence so that no word or phrase that the only might be regarded as modifying shall adjoin it on the other side." TABLK OF THE ADVERB. ADVERBS 1. SiMPLK.— { Tiinc. — When, then, soon. Place. — Where, there. Manner. — Quickly, kindly, slowly. [ Degree. — Quite, very, nearly. Interrogative. — When? where? how? I 3. Modal. — Perhaps, not, certainly. 4. Conjunctive. — Where, how, why. 1^ 5. Adverbial Objective. — Worth a dune, rest an hour. THE PREPOSITION. 91, Definitioii of the Preposition. — The preposition is almost the only part of speech that has been defined sub- stantially in the same terms by nearly all grammarians. The definition usuallv given is the following: 80 PEDAGOGICS OF GRAMMAR. § 4 " The preposition is used to connect words and show the relation between them." It should be noted, however, that any two words arranged with reference to their reciprocal meaning, are in relation. But the relational function of the preposition does not distin- guish this part of speech from the relative pronoun, the con- junctive adverb, the conjunction, or even from the copula. For example, the word is placed between Henry and zveary estab- lishes between them the relation of subject and attribute, and denotes that relation. Indeed, if a teacher's language be closely noticed, it wall appear that a very common inquiry is in reference to the relation between such and such words. There are perhaps very few words in the English language applied so widely and so vaguely as this word relation. To illustrate the exact function of this part of speech, some pairs of unrelated words are given below, and are then brought into relation by means of interposed prepositions: fly — house going — school f over 1 f into \ kind^ , , J- animals fly ■{ J" y house going { , )■ school i from I \h ' [^ tliroitgh J ytoxvards kind — animals among ^ witti towards \_„. It would, however, be difficult to improve the definition usually given for the preposition. 92. Phrases.— Two or more words properly related, and capable of performing in a sentence the function of a single part of speech, form a phrase. When the phrase is intro- duced by a preposition, it is b. prepositiojial phrase; when by a participle, the phrase \s participial ; Mdien by a verb in the infinitive mode, it is an infinitive phrase. If the office of a phrase is that of an adjective, an adverb, a no7in, or a verb, it is respectively an adjective phrase, an adverbial phrase, a snbstantive or noun phrase, or a verb phrase. §4 PEDAGOGICS OF GRAMMAR. 81 Adjective Phrases. — A cord of ivood, a boy ivith a basket, food for dinner. Adverbial Phrases. — Sorry to go, careful of money, strivey^r success. Substantive Phrase.—" To endure with patience is difficult." Verb Phrase. — "He should liave gone." "He could have been elected." 93. Prepositions Used Adverbially. — In the matter of origin, the prepositions are more recent than the adverb. Professor Whitney says of the former that they were ' ' created a separate part of speech by the swinging away of certain adverbs from apprehended relation to the verb, and their connection in idea with the norm cases which their addition to the verb had caused to be construed with it." Accordingly, the adverbial side of the preposition is very pronounced, and we constantly meet it without an accom- panying object. There is, however, an increasing tendency to give prepositional phrases in full. Thus we are more likely to say, "He has gone aboard the ship," "The boy rode around the town," or "The father walked before the ivagon and his son behind //, " than we are to omit the objects. By this transfer of adverbs the number of preposi- tions is steadily increasing. 94. Governinent by Prepositions. — The term govern- ment has been much used in grammar to denote the power that some parts of speech have to compel words, in certain relation to them, to assume particular case forms. This is not true to any great extent except with regard to the case forms of the personal pronouns. Transitive verbs and prep- ositions are said to "govern the objective case" of these words. But nothing in the form of a noun object of verbs and prepositions reveals that it is in the objective case ; that property must be learned by determining in what relation it stands to the so called "governing" word. In this term govern we have an appropriation from the grammars of those languages that are really inflected. In Richard Grant White's "Words and their Uses," he vigorously insists upon the extreme absurdity of many of the "rules" of syntax, and '^ specially upon the "ridiculous use" we make of the word 82 PEDAGOGICS OF GRAMMAR. govermncnt. He says, "No term was ever more unwisely chosen than governinoit to express the relations of words in sentences. ... In grammar it implies, or seems to imply, a power in one word over another. Now, there is in no language any such power, or any relation which is properly symbolized by such a power " ; and much more in this strain. It is a subject for the student's consideration, who must, however, remember that many eminent authorities are at variance with Mr. White and with one another with respect to this matter. Certainly, a great deal of useless and con- fusing verbiage has been introduced into the treatment of English grammar. 95. JA^t of Prepositions. — The student has already been apprised of the adverbial origin of prepositions. But when adverbs became prepositions, they kept their adverbial character, so that nearly all of them may still be used as adverbs. To employ them as adverbs, we merely omit their object noun or pronoun. The following is a list of the prin- cipal prepositions: aboard, betwixt, past, about, be3'ond. pending, above, by, regarding, across. concerning, respecting. after. down. round, against, during, since, along. ere, tell, amid. except, through. amidst. excepting, throughout. among. for. to. amongst, from. touching. around, in. toward. at. into. towards, athwart, mid, under, bating. midst, underneath. before. notwithi standing, until, behind, of. unto, below. off, tip, beneath, on, upon, beside. out, with, besides. over, within, between, overthw art, without. § 4 PEDAGOGICS OF GRAMMAR. 83 96. Use of Prepositions With. Certain "Words. — Much care is required in the use of prepositions with some other words. Of these words there are so many that only a partial list can be given. The choice is generally deter- mined by the meaning of the prefix of the word associated with the preposition, but often by the meaning of the entire word. Absolve f7-om a promise. Abstract of a legal document. (An outline of its contents.) Abstract /Vtfw, as cash from a drawer. Abhorrenceyi^r a person or thing that one hates intensely. Abhorrence of something we dread ; as, snakes, spiders. A choice hetiveen two, or among many. Accord loith a view or an opinion of another person. Accord in an opinion held by two or more other persons. Accord to some one a privilege or a right. Accomplish by diligence. (As a means.) Accomplish with difficulty. (Any object striven for.) Accomplish tinder hard conditions or terms. Acquit of a. charge, i^otfrom, as formerly.) Acquire by labor. Affinity between friends, ideas. Adapted to, fitted or adjusted to intentionally. Adapted /<^;- grazing, _/<;;' ioo^, for supporting life. (Natural suit- ability for.) Agree with a person. Agree to an arrangement or a stipulation. Changeyiyr, a wagon /"i;;r a horse. Change with, seats with some one at a theater. Change in voice, behavior. Change oo\ifor reference. 84 PEDAGOGICS OF GRAMMAR. § 4 Correspond with a person and to a thing. Dependent on or upon a person's word or promise. Dependent 0/ a king or 0/ any person or thing that supports. Differ 7L'/t/i a person, or from an opinion or a statement. Different in some respects, or from what was thought or expected. Dissenty>(?;;z an opinion or a statement. Die ^V/;-(^?//^/, as-as, as-so, if-then, eithcr-or, neither-nor, whether-or, thongh-yet. 103. Tlie Adverbial Elements in Conjunctions. — The only difficulty of any account with the connectives of various kinds is in classifying them so that they may be kept separate. But this is really of little consequence. There is no impropriety in calling a subordinate conjunction having a decided adverbial quality a conjunctive adverb. The truth is that no one ever has succeeded in drawing a definite line of division between conjunctions and adverbs, and no one may hope to do so. Nearly all conjunctions w^ere originally adverbs, and have, in most cases, manifested a tendency to return when their services are required. Moreover, many subordinate conjunctions and some con- junctive adverbs may be used as prepositions. The student will find no difficulty in verifying this statement. PEDAGOGICS OF GRAMMAR. § 4 tabijE of the conjunction. 1. Coordinate CLASSES \ \^ 2. Sitbo7'dinate { Copulative. — and, also, likewise. I Alternative. — or, nor, either. Adversative. — but, yet, still. Illative. — consequently, therefore. Place. — where, whence. Time. — when, as, until, since. Cause. — why, wherefore, because. I Purpose. — that, so that, in order that. (^ Comparison. — than, so-as. THE INTERJECTION. 103. Interjections Not a Part of Speech. — It has already been said, in substance, that the interjection comes to us from the time of the earliest history of the race. It is found in all languages, and is a sign more of the inability to express thought than otherwise. Its use characterizes the first efforts of children to convey their thought to those about them. Strong feeling of any kind — hatred, fear, bodily sen- sation, earnest desire — leads to the selection of a word signifi- cant of such feeling. This word stands for the words that cultivated people employ to express thought in completeness. Thus, most interjections denote more or less exactly the feeling of the speaker. Any part of speech, therefore, may represent a thought, in the entire expression of which the word would often be conspicuous. Hence, we have such interjections as hush! mum! adieu! shame! soft! behold! welcome ! 104. Interjections Generally Echo the Sense. — There is a figure of rhetoric called onomatopccia applied to words that by their sound more or less clearly indicate their meaning. Such are the sounds made by animals or by some of the forces of nature; as, buzz, bang, baa, crash, hist, soft, roar, hum, etc. If the student will carefully examine the list of interjec- tions commonly given, he will find that they have in large § 4 PEDAGOGICS OF GRAMMAR. 89 measure this quality. Thus, the interjeetions most used to hail some one at a distance contain the long sound of o^ and this sound is prolonged at pleasure. Those that enjoin silence and caution contain the sound of jt and the short sound of i. To denote doubt, contempt, incredulity, the long sound of e is frequent, and this is the sound that is prolonged ; as, indeed! really! ' Most interjections, therefore, have vowel and consonant combinations that can be prolonged at pleasure, or that echo the sense by the sound. One eminent authority calls attention to the fact that "■ all languages contain as an interjection the long sound of c^" In general, the open long vowels are employed in interjections intended to express emotion strongly and without concealment; the short vowels and the liquid or hissing consonants are used when the emotion is to be restrained. Strictly, very many interjections have no meaning other than that denoted by the tones and gestures characterizing their utterance. Thus, ah! oil! may be used to express a great variety of sentiments and emotions, but these must be gathered from the circumstances attending their use, from the inflections and intonations employed in pronoimcing them, and from many other things. This .subject, while curious and interesting, is not one that need long detain the ordinary student. 105. Division of Interjectious Into Classes. — These words have been arranged under various heads ; as, of joy, wonder, sorrow, praise, surprise, disapproval, pain, fear, calling, etc. But to prepare such a list as the various author- ities would regard complete would be impossible, since many words, considered by some as interjections, are by others classed differently. Such, for example, as avaniit ! hist ! hark f bcJioId ! are only verbs in the imperative mode, and good! excellent! sad! etc. are adjectives. PEDAGOGICS OF GEOGRAPHY. IXTT^ODucTIo:^^. EDUCATIOXAT^ VALUES. 1. Of Value in General. — Much has been said and written about educational values. The various theories on the subject, although they are not vitally necessary to the science and art of education, are yet of so much importance that a modern and prog-ressive teacher should give careful attention to the matter. Before proceeding to consider the subject of the various values of the subjects tavight in the schools, it is necessary to inquire what the term value means. The word comes into our language from the Latin. The verb ^^^/rr^' means "to be strong or robust " — to have vigor or efficiency. Like nearly all words from the ancient languages, its original application was to things physical and sensible — to the objects and concerns of cominon life. In process of time, its use was extended to the domain of thought and reflec- tion — from the concrete and material to the abstract and ideal. But in its transfer, the underlying trope or metaphor is retained, and the notion of mere physical strength has been made to include other potencies than those of matter. So the term value is now used with reference to anything that may become an agent or factor in accomplishing a result of any kind — in attaining something that directly or §5 2 PEDAGOGICS OF GEOGRAPHY. § 5 indirectly contributes to the satisfying- of desire or need. Anything helpful as a means to an end has, by virtue of that helpfulness, value with respect to that end. On the other hand, whatever has no such efficacy is without value — worthless. The air, the rain, the sunlight, and the multi- form forces of nature are agencies of value; so also are reading, conversation, study, reflection, investigation, rea- soning, patriotism. J^aluc, then, is the desirability or worth of a tiling, on account of its cffi.cicncy, real or imagined, in securing some- thing desired, or in avoiding the opposite. 3. Value Is Relative, ^NTot Absolute. — Nothing is more difficult to fix than a uniform standard of value. To secure an invariable standard of weights and measures, the French measured, at great expense and with extreme care, the dis- tance from Barcelona to Dunkirk, and from the result they calculated the length of a meridian from the equator to the pole. This quadrant they divided into ten million equal parts and called one of the parts a meter, which they took as a national standard of length. They made of platinum- iridium a rod representing the exact length of a meter, and sent duplicates of it to each other nation, in the expectation of making it a world standard. But the element of human error could not be excluded, for it was afterwards foimd that the quadrant of the earth had not been measured correctly. Even if it had been, the length of the metal rod would change with every variation of temperature. The only other standard of physical length is a pendulum that oscillates in one second in the latitude of Greenwich, England. Such a pendulum is a standard yard, and its length determines the weights and measures used in coun- tries where English is spoken. But the lengths of the yard and the meter are alike variable and uncertain. There can be no such thing in the physical world as an absolutely invariable standard of any kind. The same is true in the ideal world — the domain of immaterial utilities. All values of every kind are relative. Those having reference to human § 5 PEDAGOGICS OF GEOGRAPHY. 3 needs, both physical and ideal, vary iniceasingly. They are affected not only by temperature, but by temperament, by the changeable human measurement of fact and fancy, by the shifting relations among things, and by innumerable other circumstances and uncertainties. A cannon ball has no inherent and constant capacity for destruction. The value of gold is conventional, a matter of agreement merely. Circumstances may arise in which it will be valued no more highly than iron. The coins found by Robinson Crusoe were worthless to him, and it was a matter of indifference to him whether they were gold or silver. In either case, they had for him no value as a means to an end — they could not be instrumental in satisfying any of his numerous wants. The value of a bushel of wheat is neither intrinsic nor con- stant; it changes with demand and supply, and with the use that is made of it. A great sculptor would be less effective and useful as a quarryman than one trained for the work ; the designer of a battle ship or of a great bridge would find his situation in the wilds of Africa more beset w^ith dangers and difficulties than if he were a native savage. A treatise on cuneiform inscriptions or Egyptian hieroglyphics could have no interest or value to an unlearned man, nor would a work on calculus avail anything in the training (jf a child. In the last analysis, all value is relative to human needs, and these are constantly fluctuating, in consequence of changing conditions. Now, hmnan needs are mainly of two kinds, physical and mental, and they vary for different indi- viduals, and change with time and place. Hence, for train- ing the mind and perfecting the physical faculties, the best methods and appliances in one case are by no means so in every other. The ideal education of a boy would be entirely tnisuited, or nearly so, for his sister; and the method to be pursued with a bright boy would not be equally good with a dull boy. It is the old story — what is one man's meat is another man's poison. Value, as well as nearly everything else, is relative and changeable. It follows, therefore, that educational values cannot be fixed and durable. 4 PEDAGOGICS OF GEOGRAPHY. § 5 3. The "^Ne^v^" Education. — In view of the fluctua- tion and uncertainty in value of every item included in our courses of study, it is important that the student should con- sider just what should be understood by the expression, '' The New Education." We are hearing it often, and under circumstances implying that there is an old education, with old methods and old subjects of study making up its curric- ulum. Now, the student should remember that the world furnishes very few examples of sudden and radical change. It is indeed true that " old things pass away, and all things become new"; but this happens not suddenly, but gradually. The history of the introduction of the new is that it is at first sneered at and ridiculed, then argued, with gradually decreasing bitterness, and finally accepted, often after many years. When matches were first offered for general use, our rural grandfathers objected to them for a long time because of the ease with which their barns could be burned. This is an illustration of the first estimate placed on things that finally come to be regarded as indispensable. In the days before railroads and steamboats the horizon of each individual shut in for him the world. A man saw the sun rise at one edge of creation and set at the other. The most capable and scholarly teachers knew nothing of geography. Most of them had never heard the word, which even to pronounce was sufficient evidence of profound and unusual scholarship. No enterprising publishers competed in supplying textbooks on the subject. Indeed, they were beyond the printer's art in this country, as much as they were beyond the power of pur- chase by the average parent. The same is true of every subject of study, with the exception of the "three R's," reading, writing, and arithmetic. Of arithmetic, even, it was not considered important that girls should study it. They would have no use for it; and utility then, as now, was the criterion of value. Each of the many subjects that now overcrowd the courses of study has made a place for itself only after a long struggle through a period of growing need for it. In this gradual way the old passes away after a long period § 5 PEDAGOGICS OF GEOGRAPHY. 5 of diminishing usefulness. Nothing in human progress, if it is really useful, can be or should be sudden. So that, when the advocates of the supposed new educa- tion cry down the old and cry up the new, when the patient, plodding teacher, trying to make the best out of existing conditions, is denounced as an old fogy, and his matter and method are said to be antiquated, he should remember that there is no more a new education than there is an old one. What he is doing and his way of doing it are very probably a little behind the requirements of his immediate surround- ings; but this is in consequence of an unavoidable inertia that belongs with general progress and partakes of the character of a cautious conservatism. The tides are always behind the direct line of the moon's attraction, and the highest tempera- ture of day is not at noon, but a couple of hours later. Be very sure that these things are true: that no one can be found whose training exemplifies a " new education "; that no one can tell you where a teacher that practices it can be found ; that no one can prepare a course of study in accord- ance with it; that there is not, never will be, and never ought to be such a thing as a new education. It is only the watchword of the educational charlatan. Every profession has its humbug, and this perhaps will always be the case; for the average man seems not to be quite happy unless he is regularly imposed upon; he is an easy victim to the alluring advertisements of "yellow" journalism. Lest a wrong impression be left, and that the writer be accused of opposing educational improvement, it is necessary to state here that every true teacher is an advocate of growth and progress. The ambitious and intelligent teacher must keep himself informed with respect to this inevitable and necessary growth in educational method and matter. He must not be deceived and led away after the ' ' strange gods " of the professional reformer. He must remember that, before he lets go the old, he should have good reason to know that what is offered as a substitute is better. If, however, he allows himself to get too far ahead of the natural and orderlv march of the general mass, his power as a worker 6 PEDAGOGICS OF GEOGRAPHY. § 5 will be nearly destroyed by the opposition he must meet. His usefulness will in that case be no greater than that of the teacher too far behind his time. Let the teacher aim to be neither a radical nor a conservative, but to temper the restless yearning of the one for better things with the cau- tious wisdom and persistent plodding of the other, '■^ Prove all things; holdfast that which is good/' 4. Diversity of Oijiiiiou Concerning Educational Values. — In an address on "What Knowledge Is of Most Worth > " delivered at a recent annual meeting of the National Educational Association, by its president, that official, after dwelling on the many unsatisfactory and widely divergent answers that have been made to his query, pro- ceeds to formulate a response as follows: If it be true that spirit and reason rule the universe, then the highest and most enduring knowledge is of the things of the spirit. That sub- tle sense of the beautiful and the sublime which accompanies spiritual insight, and is part of it, is the highest achievement of which humanity is capable. . . . To develop this sense in education is the task of art and literature, to interpret it is the work of philosophy, and to nourish it the function of religion. Because it most fully represents the higher nature of man, it is man's highest possession, and those studies that directly appeal to it and instruct it are beyond compare the most valuable. Most writers on education are guilty of the fault of dealing in poetical and meaningless generalities, that, while very pretty and melodious, are yet vague and of no possible use to the seeker after practical guidance and available help. These flights into the empyrean are, no doubt, very stimu- lating to the "higher nattire " and the "spiritual insight," but they take us nowhere; they fail to furnish any light or help on the practical questions involved in the education of our children. And this light and help are exactly what the teacher wants. He that would wisely and helpfully prescribe the zahat and the hoza in education must forget somewhat the "infinite possibilities of the human soul," " the subtle sense of the beautiful and the sublime," and must remember temporal wants and actual conditions. The thing that man § 5 PEDAGOGICvS OF GEOGRAPHY. 7 is most in need of just now is assuredly not "spiritual insight," "soul culture," "sweetness and light, " or "ears attuned to the higher harmonies," whatever these are; his most pressing necessities are of the earth earthy. He must earn bread for himself and for those dependent on him, he must become an expert and efficient agency in modifying his surroundings and turning them to practical account, he miist equip himself with mental and manual aptitudes that have a market value, he must gain " the wrestling thews that throw the world. " This seems like a humiliating descent from the serene heights whence " spirit and reason rule the universe. " But this is one of the conditions imposed on us by the fact that we live in a world where most of us eat bread that must be earned at the expense of the tis.sue of brain and muscle. Our boys and girls cannot breathe the thin air of those spirit- ual altitudes, and we have learned the hard necessity of moderating our hopes and dreams about the future of our children to the simple wish that we may be able to prepare them to meet with fair success the requirements of the life that awaits them. The writer does not wish to be understood as insisting that life has no place for those finer feelings, those vague, intangible yearnings and hopes and dreams, those soul har- monies and fancies fine, about which we hear so much and really know so little. He insists merely that whoever fails to prepare to do efficiently the practical work that awaits him will make a pitiful failure of the business of living, however thoroughly trained he may be in the transcen- dental culture that is alleged to rule the universe. He that acquits himself up to the fullest measure of his capacity in the duties of practical life is perhaps making the best possi- ble preparation for the conjectural future. Inasmuch, then, as there are so many and such diverse views of values in education, it is important that the teacher should have some standard or criterion by which he may judge for himself the usefulness of the many things that are urged upon him. And this .seems the best and safest — to consider carefully in zv/iat loay and to what extent any subject 8 PEDAGOGICS OF GEOGRAPHY. § 5 or method zvill have real praetieal value in the fiittire life work of his pupils. How and in what measure will arithme- tic help, or geography or drawing or languages or philoso- phy ? You should ask yourself, "Is this new method, or this recent theory better, more helpful,- more in consonance with reason and experience than the method or theory I am now following ? " Insist upon definite reasons for changing your plans before you change them. Your pupils are about to enter a life that is full of importunate realities and impera- tives that cannot be ignored, and your responsibility for properly preparing them for it is great. 5. Educational Values As Affected by Existing Conditions. — The values of the various subjects included in courses of study are much ailected by circumstances of time and place. What is indispensable in a certain place at a given time does not remain so for all times and places. And, as has been already remarked, that which is best for one child or set of children is otherwise for children differ- ently situated. These difficulties become apparent in the attempt to educate children in masses, without regard to home conditions, sex, future employment, and differing degrees of intelligence. It becomes necessary to devise the best possible average course of study. That it should be an average curriculum comes from the obvious fact that no scheme of education for a large number of children together can provide for their individual wants, or give a discrimina- ting treatment to each child. The physician may do this — must do this — with his patients, but it is impossible with the teacher. The boy and the girl, the dull pupil and the bright one, the child from the home of refinement and the child from the home of ignorance and squalor, are all on equal terms with respect to education in the public schools. And yet an ideal training requires the same special treatment of individ- uals that the phj^sician gives his patients. One pupil should receive much mathematics and little science, while these conditions should be reversed in another case. Because their activities in the future are to be unlike, the § 5 PEDAGOGICS OF GEOGRAPHY. 9 needs of our boys differ from those of our girls. As compared with the boy, the girl needs little mathematics and less science, and yet it is impossible to separate the sexes during the primary education beyond which so few go. As density of population increases, the division of labor will doubtless be gradually introduced into the work of teaching and these difficulties will be lessened or removed altogether. The graded schools of our cities and large towns, with their partial specialization of the teacher's work, furnish a hint of better things to come. If education is only adaptation, — the fitting of powers for work to be done, — then the various powers must be trained with constant reference to the work that awaits them. A perfect locomotive engine would have no value whatever for driving an ocean steamer. Even if it were possible to foresee in every case in what exact line of life's activities each of our children is to find his future work, it would clearly be impossible, without great expenditure of thought and money, to educate each for his destined career. No one has the needed foresight. Obviously, then, the question of education resolves itself into one of average adjustment. From the almost limitless field of human knowledge must be selected those studies that will probably furnish the student with the best average preparation for life and its duties. Under existing conditions, this is the best that can be done. 6. Primary and Secondary Education Should Be Parts of One Sclienie. — Another circumstance that has a bearing on educational values is the necessity for continuity of plan from the beginning to the end of educational work. Most of our children leave school at the close of the elemen- tary school course, or even before it is finished. On the other hand, many children continue into or through a secondary course — the academy and high school — and then enter the college and the professional school. To prevent a break involving much loss of time between the primary and the secondary schools, the former should, as far as possible, be 10 PEDAGOGICS OF GEOGRAPHY. § 5 preparatory for the latter, and the latter should be equally well suited as a preparation for college. In other words, our public schools should have in contemplation the fitting of its pupils both for life and for college. This neces.sity, together with the difficulties arising from individual differ- ences, mental, physical, and sexual, added to the varying requirements and imcertainties of life's activities, renders this subject one of the most involved that can confront the educator. This fact is shown in the constantly recurring questions of parents: " How shall I educate my son? What are his natural aptitudes? What can he be trained to do better than he can do anything else?" "And my daughter — what is best for her? " To these important ques- tions each school and each educator has a different answer. One recommends science, another indiistrial training; one commends the classics, or "spiritual insight," and still another tells of the " all-conquering power of thought." In the end, nothing is definitely settled except that our children must do as their parents did — avail themselves of such opportunities of training as they may chance to meet. 7. General Classifleation of Studies. — In an able and thoughtful paper on "Educational Values," our present Commissioner of Education, Dr. William T. Harris, gives a general outline of the subjects in which a man should be educated from first to last, and a logical statement or view of the phases of his nature that are properly related or adapted to each subject or group of subjects. His aim is to present a scheme of education that shall train tJie ivhole man in all the range of his powers, and that shall have unity and cohesion from the lowest primary to the finishing work of the college and the technical or professional school. Such a scheme will give to the course, if broken at any point, a degree of harmony and completeness much to be desired. Of course his plan does not, and cannot, take into account differences among students and their surroundings. P^. Harris considers man as being simply an inhabi'^'^rt o' world, in which he is to play his brief part. Of man's § 5 PEDAGOGICS OF GEOGRAPHY. 11 relation to a sphere wider than the earth he takes no account. Training for that sphere he leaves to the care of religion. Considering man apart and in himself, and afterwards in relation to immediate surroundings, Dr, Harris proceeds to classify the various subjects of study with respect to the powers that they are instrumental in training. His purpose is simply one of adjustment. He says: The theory of man includes three phases: 1. Man as a practical being, a will power, a moral being acting socially and politically — a history maker. 2. Man as a theoretical being, a thinking power, a rational being giving an account to itself of the world and itself — a science maker. 3. Man as an artist, a being that represents or portrays himself, embodies his ideal in real forms, makes the visible world into his own image — a producer of art and literature. The foregoing are the phases of himself that man presents to be educated. For the cultivation of the whole man the range of studies covers the domain of nature and that of j/ian, or spirit. f ^ ^ ( Mathematics. I. Inorganic. — ■ . . , -,. ^, IN'atiire. - ' Jrhysics, including Chemistry. [^ II. Organic. — Natural History in its widest sense. f III. Theoretical ok Thinking Power. — Logic, Phi- losophy, Linguistics. Man, or I Siiirit ' ■ Pi^'^ctical or Will Power. — Civil History, Social and Political Sciences. V. Esthetic or Art Power. — Literature and Art. Answering in the elementary schools to these five general groups, we have the following: I. Xatiii'e Inorganic. — Arithmetic, the mastery of number. II. Nature Orj^aiiio. — GcograpJty, the mastery of place. III. 3Iaii Tlieoi'ctical. — Graiiimar, the mastery of letters. IV. Man Practical. — History, the mastery over time. V. Mail Estlietic. — Reodiiiir and Literature. 12 PEDAGOGICS OF GEOGRAPHY. § 5 The studies given above for these five subdivisions of culture are those that should be found in the curriculum of the elementary schools. In the high school and academy each subject is extended. Arithmetic is continued, but to it are added, in the domain of mathematics, algebra, geometry and trigonojn- etry, analytical geometry, natural philosophy, and chem- istry. Geograpliy, belonging under the division of organic nature, takes on physical geography, astronomy, botany, physiology, and zoology. Graminar, the science evolved by man as a thinking power, and most useful in developing in him the power of abstract thought, is extended into the domains oi philology, ancient and modern languages, linguistics in general, and mental and moral science. Civil History, a science that owes its existence to man, considered as a will power working in national masses, becomes, in the secondary schools, universal and comparative history, civics, and the constitution of the student's own state and country. And, finally, Heading- and Tjiterature, the studies appropriate to esthetic man, include the history of tJie literature of his language, the study of its best typical examples, rhetoric and drazi'ing, with other suitable art work. In the college and the professional and technical schools, the field is still further widened, with special emphasis along lines directly concerned in particular professions. 8. Completeness of tlie Foreg'oinjif Classification. With the exception of the spiritual side of man's nature — a part of him that is believed to share in another existence beyond the present — provision is made in the scheme indi- cated above for his ciilture in every aspect of his being. His religious or spiritual training is left to be the care of the church. No attention is given to the perfecting and main- taining of his mere physical powers, but none is required. The necessary and usual employment of those powers is § 5 PEDAGOGICS OF GEOGRAPHY. 13 generally sufficient to preserve their vigor; if more is for any reason needed, it is easily found. The zvorld, in every aspect in which it stands related to man, is made a matter of special concern and systematic study; man himself, regarded both as a power operating on nature for his own support and advantage, and as a being capable of improvement and happiness, is to be thoroughly and symmetrically trained. The development and culture contemplated are all-sided, and every subject included is indispensable to an ideally complete education. It is evident, therefore, that it is a narrow and incomplete view of education that prompts men to go about with the various and conflicting cries: "Know thyself"; "Study science, for science is all in all"; "Seek after spiritual insight, for spirit and reason rule the universe"; "Mathe- matics is the skeleton of God's plan of the universe; there- fore, study mathematics." The adjuration should be rather: "Know thyself and nature also; study science, and seek after spiritual insight; but with all thy seeking, neglect not matliematics. " The student must remember, however, that a scheme of education like this, or any other that may be proposed, can- not be realized in completeness. Our limitations of every kind are too many; circumstances constantly interfere with our plans, and compel us to change or abandon them. The merit of this plan of education is, that, if at any point it is interrupted, the zvork is all-sided, Jiarnionious, and complete 7ip to that point. However far man's education may be car- ried, it is never finished, since he is capable of indefinite advancement. 9. Specialization in Education. — vSomewhere in the course of the general training indicated above, special prep- aration for some particular activity in life must begin. If one wishes to become a lawyer, a physician, an engineer, or a teacher, he must take up, at the close of his college course, those studies the mastery of which will make him proficient in his chosen profession. He cannot expect to become 14 PEDAGOGICS OF GEOGRAPHY. § 5 expert as a specialist by mastering a general curriculum alone. Hence, it is easily apparent that, if he is to become a physician, for example, there are certain lines in the general-culture course that for him should be emphasized and amplified. Those subjects that should be dwelt on and made prominent are different for each different profession. The engineer finds indispensable a thorough mastery of the laws, properties, and forces of inorganic nature ; the physi- cian should be most familiar with organic nature, in both its animal and its vegetable structures, while of almost equal importance are certain lines of inorganic nature; the clergy- man should be expert in the sciences pertaining to man regarded from the theoretical, practical, and esthetic stand- points — in the third, fourth, and fifth divisions of Dr. Harris's general scheme. It appears, then, that specialization in education is neces- sary if we would attain to the greatest possible efficiency in particular directions. It is equally evident that the earlier this preparation for some selected life work is begun, the more thorough it will be ; but it must be remembered that every gain in this respect will entail a corresponding loss in the general broad culture that we have outlined. It is an important question, therefore, whether the gain on the one hand compensates for the loss on the other. Evidently there is a golden mean to be sought in this matter as in nearly every other. How often we meet professional men that seem to know little beyond their immediate profession; and is there not in such cases a strong suspicion aroused that the specialist is really an incompetent ? Does this physician that knows physic alone really and broadly know even that ? So that those subjects that have special educational value, from the fact that they are indispensable to some profession, lose in value when overattention to them leads to the neglect of some other subject necessary as a preparation for them. For example, it is loss in thoroughness for a pharmacist to give so much attention to the study of the phannacopoeia that he fails to learn chemistry and botany. Thus, these two related necessities in preparing for life — ■ § 5 PEDAGOGICS OF GEOGRAPHY. 15 general culture and professional training" — complicate the question of educational values. As before stated, value is relative and not absolute. Any subject needed in special training' rises in value in proportion to the broadness and thoroughness of culture in him that pursues it. The con- trary of this is true. There should, then, be a wise super- vision in education, to preserve a just balance between study for general culture and that for special training, in order that the former may not be continued too long or extended too widely, and that the latter may not be begun too late or have a range too narrow. 10. The Liiberal and tlio JLiiicrative Sciences.— The Germans have divided all sciences into the liberal and the lucrative. The former are supposed to have no iuimediatc bearing on any bread-winning profession, but to be studies belonging in a scheme of liberal or general education. The latter, called die Brotivissoiscliaften, — "The Bread-and- Butter Sciences, " — include those studies that are immediately preparatory for some lucrative business or profession. From what has been said above, it is evident that, strictly, no such arbitrary division of studies can be made; for culture studies of every kind have a practical material value. Training and discipline, without regard to the study that furnishes them, have the effect of making it easier for a man to earn his living; that is to say, every study belongs in some sense and in some measure among the lucrative sciences, and among the liberal sciences as well. Whatever enlarges a man's mental horizon, whatever gives increased precision and power to his faculties, has value both practical and disci- plinary. It should be noted, however, that the material or lucrative value sought by means of the practical or so called lucrative sciences is more immediate and definite than is aimed at in the case of the liberal sciences. Liberal culture is primarily culture for its own sake; but the training has a remote value in heightening the efficiency of its possessor in meeting the unforeseen and multiform requirements of life. It ecpiips him with 2i general preparedness for life's activities 16 PEDAGOGICS OF GEOGRAPHY. § 5 even more valuable in a money point of view than does pro- fessional training. The man whose powers are all in a con- dition of high development and training can adjust himself to almost any position in life, and by his culture and acquired habits of mastery and easy comprehension, he has a power of adapting himself quickly to new requirements. The strictly professional man cannot do this. If a lawyer is debarred from his practice, he is likely to be ineffective every- w^here else. We have a good example in the destruction of the business of wood engraving by the discovery of the ' ' new-process " engraving. Thousands of persons that spent years in acquiring expertness in the supplanted art find themselves compelled to do something else; and their diffi- culty in adapting themselves to a new work is generally greater in proportion to their skill in their former work. The very best phase of special training is that based on wide general culture. Education, for what Herbert Spencer calls complete living, comprehends not only the widest range of liberal culture of which the faculties are capable under existing circumstances, but also minute and thorough training in some useful art or profession. Now the five general groups of studies mentioned are all indispensable to a liberal educa- tion, and equally so to a profession. Some one says that a lawyer and a teacher should know everything, and the same may be said of pretty nearly every other profession when at its best. In a liberal education, the wider and more com- plete the mastery and coordination of its component subjects of study, the broader and safer will be the substructure it will furnish for a special profession. 11. Educational Tlieovy As Modified by Educa- tional Fact. — Every person that has been engaged in the activities of life has learned that theor}^ and actual practice must differ widely. However complete and plausible a plan may seem, it must be subjected to the test of a trial before it may safely be accepted; and to this fact must be attributed the wise and cautious conservatism of the man of wide experience. The ready acceptance by the ignorant and § 5 PEDAGOGICS OF GEOGRAPHY. 17 inexperienced of each "fad" and "ism" is to be accounted for by the fact of this same condition of ignorance and inex- perience. The alert business man, who has been engaged for years in discriminating between shams and realities, never sends one dollar in answer to an advertisement that promises him for that sum a watch " really worth twenty dollars." He has learned that nobody in this world system- atically gives something for nothing, and that promise is one thing and performance quite another. The old criminal lawyer and the experienced detective are each prepared to doubt appearances and to insist on the test of absolute evidence. In every department of life, ingenious persons are engaged in causing things to seem veiy different from what they are in fact. We are constantly tempted to place value on things without value, and the teacher does not escape the error of putting undue stress on theories that have never been tested. It is comparativel}^ ea.sy to outline a theory of education that seems to be perfect, but to work it out in practice is not so easy. In one place at aparticulai- time it may be satisfactory, excellent, or a failure; elsewhere, or under other circumstances, it may yield results entirelv different. Training in its best sense is not something that has a definite beginning and end; it is a condition of growth that begins before the cradle, and is perhaps not finished at the grave. "When would 3^ou begin the process of educating a child? " is asked of one of our wisest thinkers. "Not less than a century before his birth," he replies. The lines along which individual educational progress is made most rapidly and easily may be laid down so as to accord with average conditions. Dr. Harris has done this, as have also many others; but in attempting to realize these schemes by actually working them out, we are confronted with the fact of "many men, many minds." The native vigor and the functional efficiency of faculties both mental and physical are not the same in those whom we would educate. It is soon discovered that for each kind of growth, the food and excrci.se that are good for one per.son 18 PEDAGOGICS OF GEOGRAPHY. § o are usually hurtful to another. Mental predispositions and aptitudes differ, and must be taken into aecount. Of one pupil we may make a linguist but not an artist; of another, a mathematician but not a scientist. These individual pre- dilections sooner or later determine particular directions of individual culture, and defeat every attempt to make it all-sided. Hence, the educational value of any subject of study depends, among many other things, on the bent or inherited tendency of individual powers. When to these personal likings and aptitudes we add those involved in external cir- cumstances, it becomes clear that educational valuation is a complicated and difficult matter. No one would assert that a course of study could be arranged so as to give the best pos- sible result at once for the savage and the civilized, for the Mohammedan and the Christian, for the peasant and the prince. 13. Appi'oximation in T^dncatioii to Averag'e Requirements. — Obviously, then, it is impossible to estab- lish any general curricuhnn that shall have equal and con- stant value under all circumstances. It is equally clear that methods of teaching are as much dependent on circumstances for their value as are the matters taught. On account of the magnitude of the work, however, some approach to general treatment must be made. When the children of a nation are to be educated, it is impossible to specialize the work of teaching so as to make it accord with the individual wants and aptitudes of pupils. In our public schools, the best that can be done, perhaps, is to meet, as nearly as pos- sible, general or average needs. It follows, therefore, that the determination of approximate educational values is a matter of extreme importance. This is especially the case in the elementary schools, in which the great mass of chil- dren are found, and beyond which only a small percentage of them go. In the secondary school and in the college and university, there has been, within the last decade, an increas- ing specialization, so that nearly all our high schools and § 5 PEDAGOGICS OF GEOGRAPHY. 19 academies have several elective or optional courses, with opportunities of choosing in these courses particular subjects in varying degrees of completeness. In this city, for example, our high school has five courses to choose from. These courses are as follows: Classical, Latin-Scientific, Scientific, English, and Commercial. There is besides a Normal Training course with a department in Kindergarten instruction. So that in our higher — our secondary — schools the predilections of students and the practical end for which a given study is pursued become elements that are available in estimating educational value. Whether this opportunity of choosing the subjects that make up the course pursued by our children will ever be extended to the lower schools, or whether it should be so extended, is doubtful. Indeed, schools below the secondary usually aim to teach but little more than the rudimentary subjects, without which nothing higher can be understood. It is only of late years that this fundamental work has been increased by the addition of drawing, cook- ing, sewing, inventional geometry, manual training, color study, lessons in the elements of various sciences, callisthen- ics, music, the effects of stimulants, and many other matters. Concerning the wisdom of making some or all of these a part of the work in our elementary schools, there are many conflicting opinions, and each subject has its advocate skilled in special pleading. But this is a matter that need not be discussed in this Paper. The thoughtful teacher knows that a wise conservatism is indispensable to steadiness and eifect in working towards any object, and that on the person offer- ing anything new or asking a departure from that w^hich is established, lies the obligation of proving that it is necessary. Many things may be extremely useful, indispensable, indeed, under certain circumstances, and yet, under other conditions, be worthless, nay, even harmful. In education, as in most other matters, there is a place for everything that properly belongs to the subject, and for each item that helps to make up the general scheme there is a due measure and propor- tion of value. In passing, it is important for the student to note that, 20 PEDAGOGICS OF GEOGRAPHY. g 5 almost without exception, the additions that are made from time to time to our school curricula are in the direc- tion of the practical. They belong to the lucrative and not to the liberal studies. Indeed, the present tendency in education is almost wholly towards a greater attention to those studies that are directly concerned in the more rapid accumulation of wealth, and in increasing the output of products that are important to man's physical comfort and well-being. 13. Causes on Wliicli the Value of Geography Deijends. — Three-fourths of a century ago, geographical science was in its infancy. Bryant, in his "Thanatopsis," which he wrote about 1820, has the following expression of geographical remoteness and inaccessibility: Take the wings Of morning, pierce the Barcan wilderness, Or lose thyself in the continuous woods Where rolls the Oregon and hears no sound Save his own dashings The horizon of men in general was then very narrow. The rivers that were navigable for "arks," rafts, and flat- boats were almost the sole avenues for such rudimentary inland commerce as there was in those days. The tribes of ancient Gaul, of whom Caesar speaks in his " Cominen- taries," were nearly as well served by merchants as were our people a century ago. The railway and the locomotive were unknown in this country, for the first locomotive ever con- structed was completed in 1.S24 in England, and the first railway for locomotion by steam power was opened between Stockton and Darlington on September 27, 1825. Every- thing connected with it was crude, and it was for a long time engaged in proving its right to be, and in winning the reluc- tant aid of capital. If, within a week after printing, a news- paper was delivered at a point two hundred miles away, the feat was regarded as an instance of marvelous promptitude and enterprise. The news it contained was local, and not, § 5 PEDAGOGICS OF GEOGRAPHY. 21 as now, fresh from every important place. Timbuctu and Lhasa are less remote now from the resident of interior Pennsylvania than were Philadelphia, New York, or Balti- more in those days. It is useless to dwell on the changes since. vSuffice it to say that the study of g-eography in our schools has been made a necessity. Geography began with the first wanderings of men from the place of their birth, and each added facility for intercommimication has served to heighten mere interest in place knowledge into utility and final necessity. Nation after nation has established bureaus for accurate survey, until now it is difficult to indicate a spot of the habitable globe that has escaped the chartographer. Wherever the commerce of the world has gone, the surveyor and the scientific observer have promptly followed. The importance of geography has become greater with every step in the civilizing- of the world, and it is coming to be a material omission in one's education if he is ignorant of geography. Only about a score of years ago John Stuart Mill wrote of the slight value resulting from the study of geography, and a committee on school studies in one of our largest cities pronounced it a waste of time to study the subject. Nothing of the kind is heard now. Geography has come into our school curricula to stay. It has made for itself a place of importance equal to that of arithmetic, or nearly so. For its increased value it is indebted to many influences — the railroad, steam navigation, electricity, the newspaper, the camera, commerce, with the accompanying efl^orts to colonize, and the labors of civilized nations to remove obstacles from the path of commerce by indicating exactly where and what they are. As the years of development of the earth's resources go by, this interest in geographical science will increase. What intelligent citizen of our country is not now a ready and eager student of every source of information about our newly acquired territory ? 14. Di-. IIari'is''s Estimate of tlie ^'altie of Oeog- rapliy. — In his general survey of educational values. 22 PEDAGOGICS OF GEOGRAPHY. § 5 Dr. Harris assigns an important place to geography — the mas- tery over place. It should be remembered, too, that this was done at a time when educators were still disputing whether geography has any value entitling it to a place among the studies pursued in our public elementary and secondary schools. His estimate in general terms is as follows: Geography localizes. By its mastery, man comes to realize his spatial relation to the rest of the world. As civilized man, the supply of his wants of food, clothing, and shelter is a perpetual geographical process, realized through a division of labor and commercial exchange. By this geographical relation, each individual becomes participant in the entire production of the globe, and in turn contributes to all. In geography, the child learns this fact of interdependence and com- munity, which is, even when known particularly, and not generalized by him, of the greatest possible importance as a category in his view of the world. It is the second window of the mind. Through it he learns of the organic world and its relations to the hiiman race and to himself individually. Climate, surface, plants, animals, man, are the topics to which he is introduced, and these are general categories or tools of thought, the mastery of which gives him great vantage ground. Think of him as not possessed of these distinctions in his mind, and see what imbecility would result in dealing with the world. Shut up the geographical window of the soul, and what darkness ensues. From this study, branch out in higher education the special organic sciences, meteorology, geology, botany, zoology, ethnology, sociology, and to some extent, political and religious forms. 15. Ps.vcliolo;2:ical A'alixe of Geograpliical Study. Beyond the effect of geography in widening and liberalizing man's view of the world and its contents, and in furnishing him with categories of thought, Dr. Harris says nothing of the immediate psychological value of this study. And yet tliis is by no means slight or unimportant. A look out of the "geographical window" always produces many and great changes upon the observer — the mind within. The first and most obvious benefit is that of virmory trai)iing. The physi- cal and political features of the world pass in review before the mind. The student learns their names and their dis- tinguishing characteristics. It is as if he becomes a traveler — like Ulysses, "a man of many turnings, who suffered much, saw the cities of many men, and understood their minds." § o PEDAGOGICvS OF GEOGRAPHY. 23 All of this he does in iniat^-ination, and so doing strengthens the reproductive faculties — the uicniory and the vision poi^'cr of the mind. This diversity arouses inquiries about causes and effects, and an irresistible desire to classify and reduce to unity. To him the winds blow and the sun shines with new significance; the mountains are no longer merely something that he must cross in his travels; they are obstacles in the march of empire, conservators of the peace of the world ; they temper the winds, modify the rainfall, and ai^e instrumental in determining flora, fauna, the food supply, the climate, and the commerce of nations. In his imaginary travels he becomes cosmopolitan; his T7^'ci'.s- are enlarged and liberalized, his data for intelligent judgment are increased, his taste is refined, he gets out of and away from himself. The distinguishing- colors and lan- guages and manners of men lose their strangeness — their ^^///rt' character — and he learns to think of men as belonging- to one common brotherhood, and learns that, in a sense larger than national, individual happiness is an element in the weal of the world. ]\Ian's mind, like the lever of Archimedes, must have a place where it may rest; as Dr. Harris says, it must have a "mastery of place." If one is confined for life to the village or the farm where he and his ancestors were born, and if there be no means of reaching the summits that enclose him, whence he may "clarify his eyesight," and his soul-sight as well, with a glimpse of the wider realm beyond, his culture will be narrow, his sympathies shrunken. A Gerrnan student is not regarded as fully educated and ready to discharge the duties of actual life until he has traveled. Accompanied by his tutor, he sets out on foot with his alpenstock to see at least a portion of Europe, and some of its activities. What he is to learn, geography teaches, but less vividly. He aims to see the reality, for geography shows him only the reflection — the shadow of things as they are in fact. His travels will give a sense of certainty, of reality, with reference to the actualities of the world, and will put into his theories and his book training the leaven of a rudimentary experience. His judgments 24 PEDAGOGICS OF GEOGRAPHY. § 5 will be corrected, informed, and widened; his material for inductive and deductive reasoning about the world and its contents will be increased, and liis taste refined, by his observations of men and their doings. Indeed, there is scarcel}'' a faculty that is not bettered by the study of geogra- phy. The Committee of Fifteen places its value next to that of arithmetic among the studies of the elementary schools. IG. Estimate by the Conmiittee of Fifteen. — In February, 1893, a committee of fifteen persons eminent in the educational work of this country was appointed by the Department of Superintendence of the National Educational 'Association to consider and report upon the subjects of study and the methods of instruction of the elementary schools. The report of this committee was submitted to the Department of Superintendence at its meeting in Cleve- land in February, 1805. Its report was one of great impor- tance, covering the entire work in the elementary schools with respect to both matter and method. The following is the part of their report that refers particularly to the educa- tional value of geography: The educational value of geography as it is and has been in elemen- tary schools is obviously very great. It makes possible something like accuracy in the picturing of distant places and events, and removes from the mind a large tract of mere superstition. In these days of news- paper reading, one's stock of geographical information is in constant requisition. A war on the opposite side of the globe is followed with more interest in this year than a war near our own borders before the era of the telegraph. The general knowledge of the locations and boun- daries of nations, of their status in civilization, and their natural advantages for contributing to the world market, is of great use to the citizen in forming correct ideas from his daily reading. The educational value of geography is even more apparent if we admit the claims of those that argue that the present epoch is the beginning of an era in which public opinion is organized into a ruling force by the agency of periodicals and books. Certainly neither the newspaper nor the book can influence an illiterate people ; they can do little to form opinions when the readers have no knowledge of geography. As to the psychological value of geography, little need be said. It § 5 PEDAGOGICS OF GEOGRAPHY. 25 exercises, in manifold ways, the memory of forms and the imagination ; it brings into exercise the thinking power in tracing back towaixls unity the various series of causes. What educative value there is in geology, meteorology, zoology, ethnology, economics, history, and politics is to be found in the more profound study of geography, and, to a propor- tionate extent, in the study of its merest elements. Tlie student will of course perceive that the foregoing is a very rapid and general statement of the value of geograph- ical study. There are many phases both practical and psychological that are not touched upon here. The main thing has been accomplished, however, in stating the wide and growing usefulness of geography, and in urging the strong imperative that rests upon the teacher of knowing the subject thoroughly and of teaching it skilfully. He must be familiar not only with the names and locations of capes and bays and rivers and cities, — the mastery of place,— but he must be expert also in the philosophy of geography. Not as one stitdies Homer's " Catalogue of the Ships " must geography be sttidied; it must be understood and taught in its causes and effects, its inductions and relations, its changes and developments. It is not a study for the memory merely, but for the betterment of every faculty, and for enhancing the chances of practical success in the struggle for place and opportunity in life. Moreover, it is a subject that will gain in value from year to year as the resources of the world are gradually developed, and as its products become more and more widely necessary in supplying human wants. Every improvement in the means of intercommunication, every line of steamers added to the commerce-bearing fleets of the world, every extension of railroad into new regions or partially developed areas, eveiy invention, scientific dis- covery, and exploration; the conflicts of civilization with savage or semisavage races, every newly developed need of progressing man, together with every device for meeting it — all these and innumerable other matters not now dreamed of will give additional impetus, importance, and educational value to the study of geography. 26 PEDAGOGICS OF GEOGRAPHY. § 5 GEOGRAPHICAL MATTER. D1VI8IOXS a:nd definitions. 1 7. Tlie Term •■'■ Geog-raphy." — -The Greek word y^ugc, meaning' "the earth," is compounded with other Greek words to form the names of various sciences. Each of these treats of the earth considered in some one of its many aspects. Thus, yi] with da/w, data, "to divide," forms geodesy; with Xoyo^, logos, "a discourse," we get geology; yrj compounded with voiioq, nojiios, "a law" or "rule," gives geonomy; the same word with yi'wafc, g/n>sis, "knowledge," yields geognosy; f^tsTQov, metroii, "a measure," and ygdcpi,), grapho, " I write " or " describe," when combined with the word for earth, form, respectively, geometry and geography. The literal meanings of these terms do not indicate with any degree of exactness the distinct field covered by each science. Thus, there is nothing in the literal meaning of geology and geography to show that the former takes account of the constitution and structure of the whole earth without noticing its organic products, and that the latter is con- cerned only with certain phenomena on the earth's surface. Of all these terms, geometry is the oldest. It was first used among the early Greeks in the sense of a ineasurenie)it of land; a geometer was, therefore, a mere surveyor as we now imderstand it. The word did not take on its exclusively mathematical sense until within a comparatively recent period. In the middle ages, what we now call geography was regarded as a part of geometry. What was then meant by geometry was an abridgment of Pliny's geography ; and this was supplemented by definitions of some of the most common geometrical forms. The subject matter of each of the sciences mentioned above is determined, when determined at all, by convention — a kind of vagiie general agreement — something that does not remain constant for any considerable time. As the § 5 PEDAGOGICS OF GEOGRAPHY. 27 domain of a science is enlarged by new investigations and discoveries, it is usually subdivided into more definite and less comprehensive branches, for which new names are devised. Something similar to what in human industry is called " division of labor " takes place here; and it is impor- tant that the teacher of a particular subject should know its scope and comprehension. He should be familiar also with the relations of each subject that he teaches, to every other subject considered as belonging to his professional work. He should know its time and place in a general scheme of culture, and should have definite notions of its educational value. Such knowledge should pi"event him from emphasizing too much or too little any subject in the curriculum that he follows in his work. 18. Definition of (;e«),i»rai)li.v. — In its literal or etymo- logical sense, geography is a description of tJic earth. But there are many aspects in which the earth may be described; and of these, some are recognized as properly belonging in the textbooks intended for use in our schools, and others are not so recognized. It has, therefore, been necessary to narrow this wide generic meaning of the word geographv, and to include only those phases of the subject that have been found to have general value either in practical affairs or for purposes of discipline. In this restriction of geograph- ical matter, the earth as a luhole does not usually receive much attention, at least in textbooks intended for elementary and secondary schools. That phase of the subject, compre- hended under the division of uiathematieal or astroiiomieal geography, is made prominent in navigation, astronomy, geodesy., and some other sciences. With the exception of such limited consideration of the earth as a planet as is required in order to understand latitude and longitude, the seasons, day and night, the tides, and some of the phenomena of meteorology, it is the surfaee of the earth that engages the attention in our works on geography. In seeking for a satisfactory definition of geography, it soon becomes apparent that the task is not easy. The old 28 PEDAGOGICS OF GEOGRAPHY. § 5 definition, " Geography is a description of the surface of the earth," is faulty because it is so extremely general. It is a mere translation of the Greek words that compose the term. When, however, the attempt is made to be more explicit, and to indicate just what should, and what should not, be treated in the science, and thus to meet the requirements of a perfect definition, it is seen that what is true of many other sciences is true also of geography — it cannot be adequately defined. One of our latest and best authorities gives the following definition, or description : ' ' Geography is the science that describes the surface of the earth, with its various peoples, animals, and natural products. " This is in no respect better than the old definition quoted above, if, indeed, it is so good. We have here an example of an attempt to define that which, while incapable of exact definition, may nevertheless be imderstood well enough for all requirements in teaching and studying it. And the fact is that most of the latest and best geographical textbooks make no attempt to define the science. 19. Tlie Element of Place hi Geograpliy. — At first sight, geography seems to be a confused mass of incoherent details — an inextricable tangle of facts without sequence or relation. In the confusion of history, events maybe con- sidered in the order of time, and in the relation of cause and effect ; but neither these principles nor orderly arrangement and classification furnish much help in dealing with the facts of geography. Here the conspicuous category \s place ; but this is the case with every science that deals with material things or their relations. Indeed, for everything of which we can think, the mind demands that there shall be definite location. All the natural sciences, as well as the industrial, political, and social sciences, owe their divisions, subdivisions, 'classifications, and their chief interest to place and environ- ment. Place is one of the most important of Aristotle's ten categories of thought — one of the conditions necessary in order that we may predicate. § 5 PEDAGOGICS OF GEOGRAPHY. 2'.) Every science, therefore, involves something of geography — something of the mastery of place — but each should have some other dominating interest in order to give it scientific unity and logical order. And the fact is that every science does have some such principle of interest and arrangement. In geography, however, place is so conspicuous and so impor- tunate as to obscure every other element of order. Neither the textbook on geography nor the teacher of the subject can easily escape from the thraldom of mere location. And, worst of all, the results to the student are the study and remembrance of mere names and markings on maps instead of the acquirement of correct concepts of real earth features. 30. Abuse of the Idea of Place. — The answer to the question Where ? is undoubtedly of much importance in the study of geography; but while this is true, the predominance of mere place in our conception of things has led to a great deal of unsatisfactory work in our schools. It has resulted in a kind of teaching in which the highest aim consists in a fixing in the mind of mere position on maps, and in the memorizing of accompanying names. To bound political divisions, locate capitals and chief cities, and mention in some prescribed order the natural features of land and water, came to be the chief requirements of place geography. The teacher that could rapidly and certainly secure glibness on the part of his pupils in such requirements was assumed to have done his work well. There were, in the days of this kind of teaching, few pedagogical critics of matter and method to raise awkward questions of educational values or to inquire too closely into the real nature of the geographical concepts produced by this kind of teaching. Those were the innocent days of the golden age of geographical teaching, vvdien the facts of the science were expressed in lines such as might be adapted more or less easily to some familiar tune that the students could sing. Capital of Maine, Augusta, On the Kennebec River; New Hampshire, Concord, On the Mcrrimac River. 30 PEDAGOGICvS OF GEOGRAPHY. § o This kind of thing" extended so as to include all the states then composing the Union, the countries and capitals of Europe, and the principal rivers of the grand divisions; these, with many other items of equal' importance to success' in life, formed a large part of geographical teaching not so very many years ago. For a student to be able to sing all the geography that had been tortured into a shape partially rhythmical, was evidence of scholarship as generally recog- nized and respected as was the ability to spell all the hard words in the extant spelling books. There were in those days no impracticable examiners or county superintendents that insisted upon knowing exactly what a capital is; none that persisted in questioning about it until they left the stu- dents in doubt as to whether a capital is something good to eat or is only a kind of mineral dug from the earth. This is the geography that some of our fathers learned, and, from some evidences, it is not unknown even now in the actual work of many of our schools. This conception of geography owes its wide prevalence and its long endurance to the fact that place is so obvious and constant an element of all data in the study of the earth. 31. The TJelatiou of Science to ITiinian IN"eecls. Few of the sciences are studied for their own sakes and without some ulterior purpose. The various branches of mathematics, for example, are pursued partly because of the excellent mental discipline they furnish, but chiefly because of the power they give man over his environment. They furnish him with the lever with which he moves the world. History, by revealing to him the wonders that men have done, suggests the wonders that man may do here- after; and this is one of its highest claims to a place among the sciences. The physical sciences, like the mathe- matics, are valuable, not merely for training- the mind, but in that they lay bare for human advantage the secrets of nature, converting her forces from agencies of malevolence into such as make for our weal. Natural phenomena no longer suggest the impending and unappeasable hostility of §5 PEDAGOGICS OF GEOGRAPHY. 31 some concealed malevolent divinity ; but, rightly under- stood, they are the manifestations of forces that may be made to contribute in rendering easier man's struggle for existence. The lamp of science has its gcnic whose service to man is hurtful or helpful according to the intelligence with which its potencies are directed and understood. This same helpfulness should characterize in some measure every science that can engage the attention. They should all have as a primary object the enhancement of human wel- fare. And the fact is that any science worthy of the name does have this relation to the wants of the race. On the earth, man is the object of central interest. His needs of every kind — physical, mental, moral, esthetic, and spiritual — are clamorous for their appropriate means of satisfaction; and the overshadowing purpose of every science is to indicate the line of least resistance to the attainment of this satisfac- tion. As man's wants increase in variety and complexity, the sciences increase in munber and scope, and each one addresses itself to the task of furnishing a definite answer as to the best and easiest way of satisfying human desire for something better and higher. Any science, therefore, or any phase of a science that does not have this object in con- templation is deservedly neglected. The old question of cui bono .^ — what is it good for ? — is asked with respect to every subject propo.sed for investigation; and unless it can be .shown to be of probable and not too remote value toman, it is passed over or rejected. This requirement is especially insisted upon in the case of every subject offered for incor- poration in a course of study; for here its purpose is to train our children for the ■ places they will probably occupy in actual life. 33. Test of ^"aliie in Geograpliical Matter. — It would appear, then, that the educational value of every science depends upon the measure of its usefulness to man, and not upon anything inherent in the science itself. This criterion of value has been steadilv gaining in recognition during the last score of years, until now we constantly speak of this as a 32 PEDAGOGICS OF GEOGRAPHY. § 5 utilitariaji age — an age when the right of any science even to be, is determined by its possible usefulness. Usefulness for what ? For man, " the sum and crown of things." Any subject possessing nothing more than mere scientific or doc- trinaire interest, with no other particular value or useful application, commands no serious attention. The application of this test to the subject matter of geog- raphy was made long ago by Ritter, von Humboldt, and other scientists. They believed that "on earth there is nothing great but man," and it was an easy inference that those aspects of the science that are most helpful in perfect- ing the totality of man's powers are the aspects that should have greatest prominence in any scheme for man's culture. Moreover, it is not man as a thinking being alone that was consideredin this adjustment of culture to actual need, but man as an inhabitant of the planet, man in the sum of his various powers and relations. These scientists had in mind man's "complete living," and their aim was to omit nothing that would contribute to human efficiency, man being regarded as a force acting upon the world about him. It will be observed, therefore, that in selecting and arranging the materials to make up a course in geography that shall be the best possible — ^rational, coherent, and defen- sible — this is the test of value — available usefulness to the student in his probable future enviroinne)it. Hence, the inquiries that the teacher should address to himself concern- ing any subject he proposes to teach are: "Just what good in the future will a knowledge of this subject do for my pupils ? In what way will it effect this good ? Can the same object be attained as well or better in some other way ? Will the proposed attention to this subject involve the entire or the partial neglect of something still more important ? " He should insist upon a due proportion of parts in his work, a definite end to be reached by each separate item, and a clear vinderstanding of why such end should be sought. Moreover, he should fix upon a distinct plan of procedure, making very sure that it is the best, and then he should work steadily and persistently along the easiest lines leading § 5 PEDAGOGlCvS OF GEOGRAPHY. ;;:, to his preconceived object. Mnch of the poor work done in teaching is owing to its desultory haphazard character, and to an absence of proportion in estimating educational value. The principle of selection indicated above is general. It is applicable not onl}' to geographical .science, but to every other subject worthy of a place in any scheme of human cul- ture. One of the ancient schools of philosophy taught that '' man is tJic incasurc of the universe ^^ — that things finite arc to each man what the}' sccui to him. In other words, every- thing is relative to our faculties, and is not a fixed reality, having an independent existence. However this may be, it is certain that, in a similar sense, there is no such thing as value except that which is owing to the mediate or immedi- ate fitness of things for the gratification of our wants. This criterion of educational- i;tility should be very distinct in the mind of the teacher, and should regulate his professional work in every subject that he teaches. 33. General Divisions of Geograpliy. — There are many divisions and subdivisions of geographical science. These arise chiefiy from the manifold relations of man to the world about him, and from the many possible stand- points or bases of classification. These various phases of the subject are usually indicated by adjectives prefixed to the generic term geography. The following are some of the most important of these specific terms: mathematical, astronomical, physical, political, historical, ancient, com- mercial, botanical, industrial, zoological, geological, mag- netic, descriptive, topical, comparative, etc. From all this confusion it is necessary for the teacher to organize a coher- ent outline of the science; for such a general view is indis- pensable as a guide in teaching any subject. Without it, all sense of proportion and comparative value and importance will be ab.sent from the work of instruction; for, while the science has many phases, each of paramount concern with respect to some particular standpoint, not every branch of the subject is vital as part of a course for general training in geography. In arranging such, an outline, it must not be U PEDAGOGICvS OF GEOGRAPHY. g 5 forgotten that ///a// is the object of primary interest in the science; his wants and welfare, his relations and activities should determine the suljstance and propcjrtion of the parts as well as their arrangement. Now, there are two general aspects in which the earth may be studied. These are : 1. T/w cartJi as a ^^'hoU\ or in itself. 2. The car til as tlic abode of life. 34. The Kartk ^V.s ji Whole. — These two aspects of the study of the earth include under them all the subdivisions of the subject that are referred to above. Out of the first, which regards the earth merely as a planet having a certain shape and surface structure, and certain positions and motions wdth respect to the sun and moon, arise mathematical or astronomical geography, physiography, or a description of its surface features {(jivaic, pliysis, "nature"), and physical geog- raphy. This last is based npon physiography, of which it is the scientific extension, and its province is to note and give a scientific account of the phenomena and the changes upon the surface of the earth. This distinction between physiography and physical geography is one of importance to the teacher, and should be distinctly and exactly under- stood. It is analogous to the difference between anatomy and physiology, the first of which deals with mere structure, while the latter is concerned with function^ purpose, and laios. Physiography regards the natural features of the earth — the variety, arrangement, and relations of its land and water features, its relief, its coast lines, and its systems of mountains, plains, and valleys. It considers 'only what is, not what Jiappciis. Physical geography continues the study by considering the earth as an (n\ganism in which change is going on, where life resides, and forces are oper- ating in accordance with physical laws. It investigates those changes in their causes and eft'ects, notes the relation of that resident life to those varied forces and physical con- ditions, and formulates the laws by which the whole complex oreanism is controlled. §5 PEDA(U)(;iCvS OF GEOGRAPHY. 35 25. The Karlli As the Abode of Lile.— It is from regarding the earth as the abode of man that seientists have been led to make most of the subordinate branches of geog- raphy. Nearly all of these are, however, mere si:bdivi- sions of physical geography. The human requirement for food, clothing, shelter, education, progress, government, and social intercourse has led to the development of a separate branch of geography, and out of all these must be gathered the material of which to construct a course that shall be suitable for a curriculum for general use. The task is indeed not easy, and the teacher is called upon constantly to distinguish between the essential and the non-essential. It is difficult to find two authors that agree in their material or arrangement. But the general tendency is towards that kind of geographical knowledge that will be most helpful to man in the effort to supply his various wants. In other words, geography must be regarded as belonging among the lucrative sciences rather than among those denominated the liberal. At any rate, every teacher should have in mind a general outline of the science, as well as a distinct scheme of its subdivisions and the considerations to which they are owing. Peculiarly apropos here is a quotation from the writings of Marcus Aurelius, the Philosopher Emperor of Rome ; Make for thyself a definition or description of the thing that is presented to thee, so as to see distinctly what kind of tiling it is, in its substance, in its nudity, in its entirety ; and tell thyself its proper- name, and the names of the things of which it has been compounded, and into which it will be resolved. For nothing so elevates the mind as to be able to e.\amine w'ith method and truth every object that is presented to thee in life, and to look at things always in such way as to see what kind of universe this is and the use everything performs in it, and what value everything has with respect to the whole and what with reference to man, who is a citizen of the highest city, of which all other cities are like families ; wdiat each thing is, and of what it is composed, and how long it is the nature of this thing to endure. In other words, we should study things both in them- selves — their essence — and in their relations; and this is a special necessit}' with him that would be a teacher. oO PEDAG()(;iCvS OF GEOGRAI'llY. S I. L\ Itself 36. A Fiindamentul Outline of Oeograi>liy. — It is believed that the following" general view of the scope of geographical science will be found useful to the teacher. It does not, however, aim to show all the subdivisions of the subject, nor the details of a course suitable for actual use in the schoolroom. It is merely a comprehensive view such as every teacher should have in his mind as a basis of intelligent work. ' 1. As a JfV/r^A'.— Mathemat- ical Geograph}-. //s Features. — Physiog- raphy : Descriptive or Topical. Its Sia'facc Changes. — Physical Geography. Vegetable Life. — Botan- ical Geography. Annua/ Life. — {a) Ani- mals in General. — Zoo- logical Geography. {b) Man. — Ethnography: Political, Industrial, and Commercial Geography, etc. Tlie Earth II. As AiiODE OF Ln-E 3 7 . Ultimate Basis of Science. — In the teacher's search after a clear notion of the causes that underlie all physical change on the earth — life in all its phases — he can scarcely escape the greatest of all the inductions of science. This induction is that solar energy is the primary and sole cause of motion upon the earth, and, therefore, of all terrestrial life and thought. Physical science, and, in its last analysis, all science, is only an orderly accomit of the enormous and complicated activities produced by the Ave principal forms of energy, gravity^ cJicmical affinity., electricity, magnetism., and Jieat ; and, for our system, the great reservoir and source of these energies is the sun. To these energies are owing all the movements of air and water, the disintegration of rocks and mountains, and the formation from them of the broad plains whose fertility feeds the world. § 5 PEDAGOGICS OF GEOGRAPHY. 37 j\Ir. Tyndall. in his " Heat a JModc of i\I(jtion," shows that heat and motion are only different names for the same thin^i;-; that eoohng is diminution of motion and heating is aeeelera- tion of motion. He and many other scientists have abun- dantly proven the beautiful generalization known as the "Correlation and Conservation of Energy." This doctrine, of which no teacher can afford to be ignorant, maintains that all varieties of energy are interconvertible and indestruc- tible. A certain amount of heat can be converted into a fixed amount of motion, light, electricity, or magnetism ; and, whatever form it may take, it is incapable of increase, diminution, or extinction. And this energy in its myriad forms can all be traced to the sun as its source. In order to give a notion of the vast amount of this solar energy received each day, Mr. Tyndall says that, " if distributed uniformly over the earth's surface, it would be sufficient to liquet}" a layer of ice 100 feet thick covering the whole earth." This enormous contribution reaches the earth and is trans- formed for our welfare into an inconceivable complexity of motion and life. It is translated into song and laughter and life and thought. It is heard in "the complaining brook," in the roar of the cataract, and in the majestic bass of the ocean. 38. Physical Science the Essence of Geography. With the exception of topography — tliat phase of geography in which mere place is the leading consideration — the subject consists almost wholly of the inducti(Mis of physical science and of the facts that have furnished these inductions. This is largely true of physiography, and entirely so of physical geography. Commercial geography, including the statistics of the industries and of commerce, is only the story of the earth's conversion of solar energy into life and motion, into forms available for human needs. The .same is true of every other branch and subdi\'ision of the subject. And every science that deals with li'V, whether vegetable or animal, as well as every science that in\-estigates the causes, modes, and results of the interplay of forces on the earth, is an 38 PEDAGOGICS OF GEOGRAPHY. § 5 element in geographical science. What is known as physical science is the very soul and essence of geography. A wide philosophical grasp of the subject is impossible in the absence of a similar grasp of its component sciences. It follows, therefore, that a comprehensive and thorough knowledge of nature — of her forces, processes, and laws — is a necessary equipment in the teacher of geography. The absence of such knowledge, and the impossibility, imtil quite recently, of obtaining it, are perhaps the causes for the extremely poor work that has been done hitherto in teaching geography. Any one that would excel in this work must know not only the surface of the earth, but also what is occurring there ; he must be familiar with the forces that are operating, with the laws that regulate their action, with the effects produced by these forces, and the uses to which their products may be put. He must be familiar with all the wide generalizations of science — he must be a scholar and a student. This of course is an ideal of excellence that is rarely real- ized; but if the writer has made plain the need for it as a condition to the best work, his object has been attained. If the student has been made to see that the successful teacher of geography must be a persistent student of the physical sciences, and if he has received an effective impulse to such study, there can be little doubt of the results that will follow. Read again and again the works of the great investigators of nature, and especially the works of such of them as have generalized and reduced to scientific form their own work and that of others. Remember, too, that no normal school, and no process of training, ever did or ever can make a great teacher. The great things that have been accomplished in the world have been prepared for by self- effort on the part of those that achieved them. Self-activity, thought, reflection, investigation, experiment — these are indispensable to scholarship in science. 29. Man"* Place in Science. — We have alread}' referred to man's importance in the general scheme of things, and to § 5 PEDAGOGICS OF GEOGRAPHY. 39 the completeness with which his interests and wants over- shadow everything else in all systems of education. Goethe says, " Man is the most interesting study of man, and should perhaps interest him exclusively. Everything that sur- rounds us is either an element in which we live or a tool that we apply." Here we have a brief and forcible statement of the highest criterion of value in education. Alan is " the be all and the end all " in this domain. Whatever in science has bearing or influence directly or remotely upon human welfare or development is educationally \ahuLble; whatever is outside of such relationship is to be passed by as worthless. By coordinating what has already been said, we may see in proper order and relation the entire series of which man is the final and most important element. The sun as the source of energy acts upon the otherwise dead and inert matter of the earth. Vibration, motion, circulation begin, and the outcome is life. This at first is the crudest and simplest animal and vegetable life; but the long geological story begins, and after myriads and myriads of years the culmi- nation is man — a being capable of indefinite improvement, whose needs, increasing with his development, place all science, all art, and all the resources of nature under contri- bution. Between the great solar center from which life and motion and force flow, and the mind of man, which is the high- est expression of life, lies the domain of science. Whence came man, and how ? What is he, and what is his environment ? Whitherdoeshego? When these questions are fully answered, the story of science is fully told. But of these questions, the first and the last are incapable of being answered by finite intelligence; even the second baffles us in our attempts at a complete answer. We see but dimly and partially the mean- ing of it all ; but human progress with its newly born m-gencies is the unceasing force that impels new inquir}' and awakens fresh interest. Man, being the central figure in science, that which will give hini mastery over his surroundings must be the chief object — the most important end — of education. Geography, being the science of man's ]Dhysical environment, is the source and framework of all physical science. 40 PEDAGOGICS OF GEOGRAPHY CONCEPTS IN ELEMENTARY SCIENCE. SENSATION AND PERCEPTION. 30. Tliiiig-s Are Distinguished by Difterences. Almost as soon as the child arrives in the world he begins to observe. This he does by means of the senses — the organs of sensation. Each of these, acted on by its appropriate stimulus, brings to the mmd reports from the external world. The tyes tell of the colors, shapes, sizes, and other ■z^/i'7^^/ qualities of objects without; the ears report the soho- rous phenomena of the world — the chief features in the story of its activities, its motions and forces, its changes, its life. To the knowledge thus gained, each other sense makes its contributions. These phenomena attract the child's attention only by the fact of their differences. If there were only one color; if the shapes, the sizes, and other phases of objects presented no variety; the eyes would be of little use or value, and the disadvantag-e of being born without sight would be much diminished. Or, if only one unchanging sound met the ear during our life upon the earth, we should have no use for the organ of hearing. Such uniform imvarying sound we should never notice; but if it should suddenly cease or should change in some manner, our attention would then be immediately attracted by the change — the dffereiiee. Illus- trating this fact, some one has made the very curious ob.ser- vation that, if one were born with toothache that never varied in intensity, and that, if after a time it should leave him suddenly, he would then for the first time experience pam. Wlien the difference between two objects is very slight, they are said to rescjnble each other; when the resemblance is very close, there is little to engage the attention; and when the likeness is perfect, after a futile attempt to detect some point of difference between the objects, all interest lapses. One of our thinkers asserts that things are known onlv ill /hei/isehes, and i?i their relations to other things. To § PEDAGOGICS OF GEOGRAPHY. 41 know a thing" in itself is to know such of its (jualitics as are impressed upon the mind through the senses; to know it in relation is to know how it is conditioned with respect to other things — its relative weight, size, form, distance, posi- tion, etc. Now, all these forms of knowledge amount, in the last analysis, to a perception or a cotiscioiisncss of differ- ences. 31. Need for Sense Training-. — It might at first thought seem that all persons endowed with the usual organs of sense would reach the same degree of thoroughness in knowledge acquired through the senses. Such, however, is not the case ; on the contrary, there is an art of seeing and of using the other senses of which not even the merest rudi- ments are ever acquired by some persons, while others are soon known as "trained observers." It is not because of superior sense organs that some excel in this matter. Huber, the great observer of bees, was blind ; Beethoven was totally deaf when he composed his wonderful "Requiem." Sense alertness, keenness, and discrimination are partly owing to finer brain fiber, but much, very much, to training. This art, like every other, is perfected by persistent practice. By the long imperative of necessity, development has converted the eye of the eagle into a telescope. Here, as everywhere else in matters of practice and habit, the maxim of Comenius is applicable, " We learn to do by doing." Every teacher should be familiar with Mrs. Barbauld's well known story, " Eyes and No Eyes, or the Art of See- ing. " Read by a child, it furnishes him an unrivaled incen- tive to observe, to reason about what he sees, and to generalize and classify. As a mere boy, I read it many years ago, and I shall never forget the impression it made upon me. Even now the twitter of a bird in a thicket sets me to wondering what " tragedy of the woods" is going forward. A walk in the fields or woods will have the " museum charm and fascination," if one has f)nly learned to. note the little things, to see and interpret tiic oliscure and hidden things. It is surprising what differences there are among school 42 PEDAGOGICS OF GEOGRAPHY. § 5 children in this power of observation. The faculty of intense and habitual observation does not depend so much upon whether pupils are bright or whether they are dull as upon their training, though the power to reason and generalize correctly from what is observed undoubtedly does depend upon superior mental qualities. Among Indians the range of inference is narrow, but the keenness of their observations and the correctness of their interpretations of signs are well known. Much of this acutencss is doubtless inherited, but it is perfected by practice. Success in life will depend largely on the training that our children receive in the art of using their senses. One emi- nent authority says that, of two clever boys, the one with the -tjuicker perception of things around him is more likely to succeed than the other. He adds, however, that the chances of the less clever boy will be vastly improved by early, judicious, and skilful training. Extended argument and insistence are not required to make clear and to emphasize the need for training the senses. Every parent and every teacher is aware of its importance — of the great influence it has in determining one's career in life. 32. Sensation. — The term sciisa/ioii is of so much importance to the teacher, and is in general used so vaguely, that an explanation of its meaning seems to be necessary. Like many other words, it has a common or conversational, and a technical or scientific, use. Its technical sense in the science of psychology will be explained in this place. The word comes from the Latin word sciitirc, "to feel." The human body is so constituted that outward changes of various kinds act upon it, and vibrations result that are carried along suitable nerves to nerve centers within. No one knows exactly what happens at the brain centers where these conducting nerves end, but we do know and interpret the nerve vibration. These vibrations, from the point where they begin to the point where the mind is aware of them, is sensation. A homclv illustration will make the matter clearer. A I § 5 PEDxVGOGICS OF GEOGRAPHY. 43 spider spreads his net and retires to his cyUndrical hiding place, woven at the center, and waits for his expected prey. Every radial strand of his web leads to his place of conceal- ment. Lying in wait here, sensitive, alert, expectant, he typifies the mind. The wind blows over his net and he feels the quiver of the silken nerves against which he rests. A fly alights upon it. He notes a difference in the vibration — the sensation is diiferent. The net can only I'ibratc; it cannot feci. When the watcher — the conscious responsive center in which the vibration ends and is significant — is absent, only a part of the conditions necessary to a completed function is realized. The same is true of the body. When the tenant of the body — the mind — lies imconscious within or is absent, there may still be vibration in response to suitable stimulus, but the consciousness of it necessary to make that vibration a real and completed sensation, is lacking. Another illustration is found in the telephone. At some distant point a vocal distiu'bance affects a receiving instru- ment. Transmitting wires in some mvstericjus way carry the impulse along to the place where the person songht is usually to be found. He is there, awake, perhaps expectant. He hears an alarm. Everything that corresponds to a sensation proper is included between these two extremes — the disturbance com- municated to the transmitting instrument, and the con- sciousness of the listener at the other end that there is an alarm or a call at the receiving instrument. This strict limitation of the meaning of the term sensation is important, and should very frequently be useful to the thoughtful and intelligent teacher. The later investigation concerning what the call at the telephone reveals, illustrates a mental operation that begins where sensation ciuh. This, called perception, will be treated in another paragraph. 33. Sensations Classiflt'd. — vScnsations are divided into three classes, determined by the place where the nerve 44 PEDAGOGICvS OF GEOGRAPHY. § 5 vibrations connected with them begin. As has been explained, certain stimuli, disturbances, or changes affect either the whole body or one of its organs. This disturb- ance is carried along the nerves at the rate of about 200 feet per second, and ends in some brain center suited to receive it and to be affected by it. Just what happens in these nerves, or what the nature of the tremor or vibration at the brain center is, no one knows. We do know, how- ever, that in some mysterious way the mind takes notice of the change and is capable of interpreting it, just as a person is capable of realizing that there is a call at a telephone. We know, too, quite accurately the place where this vibration begins, and it is on this knowledge that the classi- fication is made. This threefold division is as follows: 1. General Sensations. — These are the sensations that with respect to their source are either vaguely localized or are diiTused over the entire wSystem; as, the sensations of zvarnith and eold, of nervous or n\\\&c\\\a.r fat igne, of 7'est and motion, of sleepiness or Juinger or thirst. 2. Organie Sensations.— T\\e organic sensations are those that are recognized as belonging to organs situated in the visceral and the abdominal regions. 3. Sensations of the Special Senses. — The most numerous and useful of these are the sensations having their origin at the eye and the ear. Of less, but of very great importance, are the sensations connected with the nose, the tongue, the nerves of touch or feeling, and the sense of muscular resist- ance, by means of which we are conscious of weight and pressure. 34. Perception, — The derivation of this word does not reveal its meaning very distinctly {per, "by means of," capere, '"to take"). Its signification can be best explained by resuming our former illustration of the telephone. vSitting- in my office, I become aware of an alarm or a call at the instrument. This, as has been stated, illustrates the end of a sensation and the beginning of a pereeption. I am at §5 PEDA(;()GlCvS OF GEOGRAPHY. 45 once conscious of the call; I become aware of it; I begin to perceive it. So far, there is no other consciousness than that there is a disturbance, a summons. As to what the meaning- or purpose of it is, I have no knowledge whatever, I g'o to the instrument aud begin an investigation. From some point outside the office definite information comes along the wire. Item by item this intelligence comes tome, until my knowledge of the cause of the call is complete. When this point is reached, I hang up the receiving instru- ment, ring off the connection, and the matter is ended. This illustrates what is meant by perception, except that in the case of the real mental operation, there is no such break in continuit}^ as the illustration would indicate. When there is an alarm or a call in the brain, say from the optic nerve, the cause of the nerve vibration — the outside reality — is usually known cil o/icc. In other words, the alarm itself is caused by the arrival at the brain center of a report of certain cjualities in the object of sense outside. Suppose, for example, that the external object is an orange. The call or alarm is itself a report of the color, size, shape, and other qualities of the object. There is no interval between the alarm and the investigation that follows. There is nothing corresponding to a distinct call that reveals no more than that it is a call; nothing to correspond to a leisurely stepping to the instrument for the purpose of conducting an investi- gation that proceeds step by step in the orderly fashion of a conversation. In the case of a sensation the reports of color, shape, odor, etc., received from without, come along the vibrating nerves and pour into consciousness, united just as they are in the external cause itself. A distinct examina- tion of each reported quality must be luade before the sen- sation has a complete interpretation by the recipient mind and is worthy to be called a perception. This imion of many nerve vibrations into a simultaneous impulse that becomes in the mind a perception of a single external reality, is aptly typified by the phenomenon of a ray of white light, which is composed of the various colors of the solar spectrum. 40 PEDAGOCilCS OF GEOGRAPHY. §5 'Si>, Use 3Iapopot a i/iiis is no more difficult than horse, provided the animals denoted are dis- tinctly conceived. I shall never forget the astonishment of a lady caller that took a little three-year-old on her lap and began to question him about the pictures. ' ' What's that ? " "A lion. " ' ' And what is that ? " "A tiger. " " Well, you can't tell me what that is." "A giraffe. ' " Goodness! What a bright boy ! What's that ? " "A hippopotamus. " " Dear me! Who would have believed it ? Well, what's that?" "A basilisk." And so the catechizing proceeded until the visitor was 60 PEDAGOGICS OF GEOGRAPHY. § 5 convinced that she had found a boy of extraordinary pre- cocity. There is little doubt of the correctness of the theory that a given word is utterly useless to a person until he knows the concept represented by the word. When he has this, the word becomes inseparably associated with it. And it is equally clear that coherent, discriminating, and comprehen- sive thought activity requires a large store of sharply defined and vivid concepts and a correspondingly large store of words. Hence, the educational value of any means of rapidly accumulating a large stock of words, of which the sense is distinctly and accurately represented by concepts, is very obvious. And of the various methods of increasing a -child's vociibulary, there is perhaps none that will yield better results than the method with pictures. Every teacher of geography should begin, at the very outset of his prepara- tion for the work, to accumulate a collection of these impor- tant helps. They will be found i;seful in many other ways. It would be difficult to find a more suggestive and helpful subject for a composition than a good picture, and for off- hand oral description they are unequaled. Every one kno\A's the importance of a good vocabulary, but not even every teacher fully realizes what a valuable fimd of concepts and the words that denote them may be obtained from a collection of good pictures. cot^i.eictio:n^s ix naturat. scie:n^ce. 41). IN'atiiral Science in TjONver School Grades. During the last twenty years the subject of object lessons in the public schools has developed very decidedly in the direc- tion of natural science. The work has not been well organized, however, nor have its exact place and time in the school curriculum been generally agreed upon and fixed; yet the fact that oral teaching in elementary science has been undertaken in many of the best schools of the country indicates a wide recognition of its usefulness and importance. Many attempts have been made to furnish textbooks that § 5 PEDAGOGICS OF GEOGRAPHY. Gl would enable the teacher to proceed with the work in a manner both orderly and intellii^ent ; but a difficulty that at present seems msuperable is found in a general want among- teachers of an acquaintance with the various elementary sciences. It is evident, however, that the present tendency is strongly in the direction of natural science; for the won- derful advancement that marked the closing years of the nineteenth century was owing almost entirely to man's increasing mastery of nature. And there is not the slightest likelihood that this utilitarian development of science will have a pause; so that knowledge of these subjects and of the best methods and appliances to be employed in teaching them will soon become imperative upon every teacher. The teacher must in the early future be thoroughly familiar with the general principles of science, and it is, these demands that come with advancing civilization, and that cannot be ignored, that are making a real — a learned — pro- fession of teaching. 50. ^Tatural Science in Relation to Geography. — In earlier parts of this work it is clearly shown that every science is correlated with geography — that geography is, so to speak, the "mother lode" of all science. But in the gen- eral subject of olyect lessons, which is almost exclusively scientific, there are only certain phases of it that bear directly iipon geographical teaching. Of these, botany, zoology, geology, and mineralogy are the bost examples. Object teaching did not at first include these sciences, but one by one the natural .sciences have most of them made places for themselves in the oral concrete work of the schools. Of course only very elementary lessons, always illustrated by prepared specimens, or given among- the objects as they occur in the broad field of nature, should be attempted. It would be difficult to find a better method of giving reality to the work of geography proper than we have in expert object teaching. Provided each lesson is properly illustrated by specimens, the work can be made of the most intense and absorbino- interest. G2 PEDAGOGICS OF GEOGRAPHY. §5 Since so few teachers know what to collect and how, no excuse need be made here for introducing' a somewhat detailed treatment of the subject. 51, Botanical Helps. — Man is largely indebted to the vegetable kingdom for his food and his clothing, and for the shelter of home. " What do these people eat ? whence does it come ? and the material of their clothes, what is that ? " These are questions of geography, and the answers to them will be fully intelligible only when the pupil has the prelim- inary preparation necessary to understand them. It is important to know more about coffee than that it is the seed of a certain shrub; that tea is the dried leaf of a bush; that cotton, linen, hemp, and jute are vegetable fiber. The child should, if possible, be enabled to conceive of these things as they are in their native environment. To do this properly is less difficult than is generally supposed. Nearly every natural object illustrates something in science; and, when closely examined, becomes of absorbing interest and rich in instruction. Such objects are about us on every hand, and if they are not, they are usually easy to obtain. Most abundant and accessible of all are botanical specimens, which, when properly mounted, become objects of beauty. Did you ever examine, with eyes open to the beautiful and the various, a collection of woods, of seeds, of vegetable tissue, or- an album of ferns, of mosses, of lichens, or of sea- weeds ? If you have not, you are not aware of the vast resoinxes for diversion and instruction, of the opportunities of studying the signs of intelligent purpose and the adapta- tion of means to ends, that are escaping you. Every teacher of children should have a large botanical collection that he himself has collected. It should be a collection that constantly increases in size and scope, one that he has studied and continues to study thoroughly. For collecting, mounting, and preserving such a collection, almost any standard work on botany will give him minute instruc- tions. As his herbarium grows in size, he will wish to arrange his specimens in accordance with their scientific §5 PEi)A(;()(Ucs OF CxE()(;raimiv. g;3 subdivisions; and as tliis work progresses, he will find how very many desirable specimens he lacks, and his eagerness to obtain them will increase in proportion as his desires are satisfied. I suspect that, if a botanist could get a specimen of every vegetable organism, he would, like Alexander, weep because there is only one world to conquer. 53. The National Museiiiii. — Comparatively few per- sons know of the Avonderful work in science that is going on at Washington. The National Museum has many collectors in every part of the country and the world; and what it has accumulated, classified, arranged, and is caring for, surpasses belief. Every department of art, science, and industry is illustrated in that wonderful collection. Moreover, the hearty and W'illing helpfulness shown to any inquirer by- the corps of scientific men in charge would almost convert on6 to a belief in altruism. I find a natural object of any kind that I cannot identify; they will instruct me at the mere asking. I need the best and latest literature on any given scientific subject; they will make it accessible to me in the easiest and cheapest way possible. They are always ready to exchange duplicate specimens with me on terms that seem always highly advantageous to me. Every teacher should be in close touch \vith this beneficent institution, not, how^ever, for the purpose of being helped only, but with a willingness and a pride in being a helper and a contributoi*. Mann's " Catalogue," which can be obtained at "Washing- ton, contains the post-office addresses of botanists in ever}^ part of the country, who are willing to exchange specimens; and, besides giving a numbered list of all the plants of the country that are known to .science, it contains much other information useful to the botanist. " Check-list.s, " giving the names, localities, chemical composition, etc. of all cata- logued objects in every department of science, may be obtained from the gentleman in charge at the National Museum. As has been said above, it is not the object of this paper to instruct the student in the details of making a herbarium or G4 PEDAGOGICS OF GEOGRAPHY. § 5 other collection, but to emphasize the importance of havin<^ such a collection as a help in the study of geography. 53. Serial Specimens. — Many of the plants that have value in commerce, even if they were of easy access, cannot be included in the teacher's collection. Some of them are large trees; as, the date, the banana, the breadfruit, the orange; others are succulent and perishable; as, the pine- apple, the mango, and most edible fruits. These can be illustrated by pictures showing the plant in different stages, and the history of the commercial product on its way to market. Take, for example, the story of cotton, from its place of growth in the fields of the South, to the finished fabric issuing from the mills in the North. A full series of lessons on this subject can be made almost as • rich in geographical concepts as actual travel, and the incidental cominercial and industrial information is important and ver}' valuable educationally, besides being of extreine interest. These specimens of every kind, when arranged serially, furnish the best possible guide in giving the lessons. Of course the teacher must go to considerable trouble, and some little expense, perhaps, in informing himself thoroughly, and in procuring specimens, pictures, descriptions, etc. The following outline will indicate the general plan of such a course of lessons and the illustrative material required: 1. Cotton. — Its three principal varieties — specimens of each. Call attention to the long silky fiber of the sea-islmid variety, and compare with the others. 2. Its Relatives. — It belongs to the iiialhno family, and is therefore a relative of our common mallows, the hollyhock, the Indian mallow, the hibiscus, the althea ("rose of Sharon "), the marshmallow, etc. Show specimens of these blooins, and coinpare with the bloom of the cotton. (Cotton can be bloomed easily in any part of the United States, but the boll will come to perfection only in the South.) 3. Its Habitat and Cultivation. — Show habitat on maps — pictures of cotton plantations — hoeing — picking. §0 pei)AGu(;k;vS OF (;e()graphy. hj Give some account of the people engaged in this work — the negroes, their homes, amusements, songs, etc. 4. Preparing- for Market. — Picking, ginning, baling, shipping, etc. The cotton gin, sketch of Eli Whitney, etc. Many pictures can be found to illustrate this topic. 5. Manufacture. — The water-power of the rivers of the Atlantic slope in New England — "The mills on the Merri- mac" — spinning-jenny, loom, etc. Manufacturing cities, with explanations why they are so. These materials relating to particular topics should not be allowed to fall into confusion, for in such case they become mere iinpcdimoita without any value whatever. The teacher should ba constantly on the alert to improve them by addi- tions, and should keep them in large envelopes properly labeled, or in any other suitable receptacle. Seeds of various kinds kept in small bottles or in boxes of uniform size, labeled, and arranged in cabinets, make collections of miich u.se in the classroom. Many of these can be arranged in series, and may be used in connection with mounted botan- ical specimens or with pictures and drawings. When properly prepared, the varieties of useful woods make a very pretty collection. If the teacher can afford it, or if he can induce his school authorities to bear the expense, the various woods of the country can be bought prepared in the best possible fashion for educational purposes. Very thin sections cut across the grain, with the grain, and radially are beautifully mounted, fully labeled, and arranged in bound volumes. These are not for decorative purposes merely; — - beautiful adjuncts to the parlor and librar}- — they are in the best sense educational, and are of especial value to the teacher of geography. Every person should know the varie- ties of the useful woods. A note of inquiry to any large book concern will obtain for a teacher all the information needed to procure this collection. 54-. Other Collections. — A well equipped school build- ing should be a museum on a small scale. The ofreat wide GO PEDAGOGICS OF GEOGRAPHY. § 5 world outside should be represented there by collections of many kinds, and these should be cared for and systematically used. For the young, as yet unable to make much use of mere abstractions, they are better than textbooks. Speci- mens illustrating- the rock for Jitat ions shovdd be there: granite in its many varieties, trap, calcite, trachyte, mica, syenite, the protean forms of quartz, and any others that will set pupils to observing; for, unless the teacher is him- self an observer and is able to develop the same instinct in his pupils, his work in the field of nature at least will be in a large sense a failure. A small collection of the ores of metals having industrial value, and of other minerals useful to man, will add much to the interest pupils take in geography. For example, in the case of coal, if the teacher can exhibit to a class all the vari- eties in the series, beginning with peat and lignite and end- ing with anthracite, it will add much to the geography of the subject. Seeing a collection of the butterflies of Brazil, a pupil at once imagines them as one more feature of reality in his conception of the vast woods along the Amazon. The writer once received from a friend some of those beautiful flowers — the edehveiss (" noble-white ") — that grow in the Alps. They were to him not daint}^ white flowers merely, to be prized for their beauty and strangeness, but they served in a way to bring those European mountains into immediate touch with his own personality — they became, as it were, a symbol or representation of the mountains them- selves. Nor is this mere sentiment. Underlying it is the psychological law of association. Nothing not known directly by means of the senses can be satisfactorily conceived except through many and various associations. These are the links that bring it into connection with consciousness, the marks that distinguish it from other things. Not immediately connected with geography, but often giving interest and reality to some of its most important facts, are many other objects suitable for use in school collec- tions. Among these are animal forms that may be pre- served in small space; such as specimens illustrating the § 5 PEDAGOGlCvS OF GEOGRAPHY. 07 important genera of insects, insects that are injurious to the interests of man, and the enemies of these pests, together with many other collections of high educational value. 55. Difficulties. — Many and serious difficulties await him that would be a successful teacher of science in any of its departments, but all of them may be overcome if he is willing to pay the usual price of success — labor, persistent labor, with a well defined, clearly perceived object. Of one thing he may be assured; it is, that in the future the suc- cessful teacher of science will place less reliance on text- books, and will depend more and more on concrete material, which is the substructure of all science. With increasing skill the teacher of the future will learn to direct his pupils in original research. To do this, he must himself be an experimenter, an investigator among the realities and prin- ciples of nature. This is a textbook that never gets old and out of date, but is always full of inspiring newness and fresh- ness, and rich in the suggestion of new discoveries. 56. 8ii' Arcliibald CJeikie's Reniai-ks. — In concluding this important phase of the subject, perhaps nothing more weighty could be given than the following words of Eng- land's Director-General of Geological Survey, Sir Archibald Geikie. vSpeaking of geography, he says: The teacher that would gain the greatest amount of personal enjoy- ment from the cultivation of this subject, and would most successfully use it as a discipline in tlie education of others, should, as far as he can, make himself acquainted with the practical pursuit of at least one department of natural knowledge. The man that has once dissected a plant and has practically studied the mutual relations and functions of its several parts, or has himself traced the connection between the topography of a district and the nature of its underlying rocks, has acquired an experience that gives to his teaching of these subjects a precision and vividness that could never be gained from books. And in proportion as he cultivates the spirit and habit of personal observa- tion and inquiry will his labors among the young be satisfactory to himself. • I do not, of course, mean to imply that good geographical instruction is nnpossible without scientific acquirement on the part of the instructor. But I insist that as geography, though it may not c.s i'i':i)A(;()(;irs ( )!■ ci-.ockAriiN'. §5 (.'laiin to he itself ;i ilistiiiel seiiMiei,', is l);is(.'(l iipDii and wea\TS together tlie work of iiuuu' seieiiees, its lull value as an instiuineut ot" ccUieation eamiot be obtained exeejjl by llii>se that are imbued with the scienlilie s|)irit. *****-x- TIk.' teaehei' uiusl be eontcnt, i)atit'ntl\' and thorou,t;hly, lo master his siibjeet. JIc should bcj^in by diveslinj;' himself ol' the ct)mmou notion that the teiieliinj;' of geography can be taken up by anybody at pleasure. When he has realized what geography in the true sense is, he will reeognize that to make satisfaetory use of it for ])urposes of instruetion demands (lualilieations of no mean or ordinary kind. lie will see that a wide range of reading is absolutely neeessary to him, and that he must e(pii]) himself with sueli a store of illustrations gathered from all dej)artmenls of knowledge as will (.'uabk' him to elueidate eaeh sul)jeet as it arises. 'This is the ideal of geographieal teaehing, and until some approach to it is reached I cannot believe that geography will take the place that it is entitled to hold in our educational s\'stem. GEOCillArJI^ WI IIIDUr A TEXI 15()()K. M>L\vSITRF,S A^iy TIIKIU APl'LK ATIOIS^S. 57. An lOarly IJ(Miiiii'<>m<.Mit . — In the elTort to extend the child's view beyond his immediate siirroiniding"s, the first need is for an exact conception of certain common nnits of nieasiire. 'Phis is a matter of i)rime importance, for, in the al)sence of siicli knowledo^c, inteUigent proo-ress is impos- sible. Cliief amono- these are the commonly used units of leng-th and stirface, without whicli the cliild is certain to find the languas^-e of s^-eot^-raphy nearly meaninoless. Unless he ])ossesses well defined concepts of the linear units he will be utlcrU' unable to oei beyond the environment of home, and with(jut a knowlediic of the surface units — especially the scpiare mile — all cotmtrics will be of practically the samesi^c, antl in comparison, each is only vajafuely lar(>'er than his father's farm or the stirface l)oimded by his visible horizon. More and more witlcly to know the snrface of the o-reat earth, tmtil at last he can take into his mind as a conscious reality the conce])tion rcprescntino' the scientific dcscrii)tion, "The §5 ri<:i)A(;()(;iCvS ()1m;i<:()(;kaimi \'. c'.i carlli is ;i j^rciit liall swiiii^iii,^' in space " — lliis is an indispen- sable condition to a j)i"oper kno\vlcdi;"e of s^eoj^ra])!!)'. With the shorter of these nnits — the incli, tlie foot, and the yard — the youni^" student (juickly j^-ains a fair dcj^rce of familiaritx' ; but it is coniparali\-cl y bite in liis school course when lie i4ets to know with any deiinitencss the rod and llic mile. If he could actually travel, — not on llic i-ailway Irain, behind whose speed the features of tlie landscape vanish like those of a di'cani, but in the manner of oui- anccsloi's, on foot, on horse])ack, or in Ihc slow, lunibci-in^' wai^on, he mi_!4'ht (piii'kb' .L;ain a notion, ciupliasi/.cd and \i\iricd by muscular effort and fatij^'ue, of what is meant by a mile. But U) obtain conce])ts of these lont^-er measures of len^lh by the e.\penditui"e of pci'Sonal ph\-sical force, is a form of practical teachin;..^- that is denied to most of our childien. Tt is clear, then, that children recpiire systematic instruction in units of length, and that this insti'uctiou should bci^in earlw Most people ima_u;'ine their knowlcdt^e of these units to be \'cr\' precise, but the\' ai'c in error. Ask tin; ])cop]e you meet on a counti"\' road how far it is to the ne.xt villa^v. "Oh, about a mile." ^^)U j^o on for a mile and ask ai^'ain. *' Well, it's about two miles." Ask \-our pupils to ,^o one b_\' one to the blackboai'd and tlraw withont measui"cnient a line one foot lon^i:;' or one yard lon^'. iMcasure these lines after- wards, and you will be convinced of the need for this kind of teachinj^-. 'I'he measures of the I'rcnch mcti'ic system are no more vaj4'ue to the average American adult than are oui" common l^^nt^'lish measures to the children in our schools. 'I'hcy would (k'tect no improbability in a statt-'Uient that some one acconi])lished a distance of t\vent)'-fi\'e miles in a walk of two hours before breakfast, and they would nex'cr think of ([Uestionin_<4- a statement that some athlete thi\'W a twelve- pound sledj^'e si.xty-onc rods, or jumped over a bar two and one-half rods hi<4-h. Try it with your pui^ils if you can do so withotit showini^' by your face the absurdity of the ni^ures. 58, ]M(>tlM>(l <>(■ l*ro'iilai' Measiirenieiit. — .Vny point in a plane is located with matliematical precision when just two things are known — its direct io)i and its distance from a fixed point. In a similar way, every place upon the earth is located by giving its distanjc north or soutli of the ecjuator and its dis- tance east or west of a selected ncjrth and south line. But since the eartli is not a plane but a spliere, these distances should be given, not in linear, but in a.igular imits — not in miles, but in degrees, minutes, and seconds. Manifestly, then, early in the work preparatory to geo- graphical study, the circle should be introduced: the terms necessary in talking about it, — diameter, radius, circiiiiifer- ence, arc, igii-\ — should be made perfectly familiar to the student. The subject of angles should be taught very fully and care- fully. Show first the right angle,— the "square corner," — and that this is the same for every circle whether large or small — it is always a square corner. So develop the fact that a given angle may have arcs of every length, according to the size of the circle. Gradually get to the measuring unit of ang-les, the degree. Teach the pupils both to under- stand and use such expressions as "an angle of 1°," "an arc of 1°," " an angle of In''," "an are of 15'"," etc. During this early instruction, nothing, or very little, 74 PEDAGOGICS OF GEOGRAPHY. should be said about minutes and seconds; the important objects to be reached are definite ideas of angles and arcs, especially an angle of 1" and an arc of 1°. Besides, it should be thoroughly taught that every circle is divided into 360 equal angular parts called degrees, and that the arcs corre- spond to arcs varying in length according to the size of the divided circles. In doing this, much use must be made of drawing, both by the teacher and the pupils; for the subject is more difficult than the young teacher would suppose. It is a matter that should be persisted in with a careful avoid- ance of difficulties that might discourage the pupil in the early stages of his work. 02. The Protractor. — One of the most helpful instru- ments in the study of angular measurement is the protractor (Fig. 1). Even quite young pupils can be taught to use it, and very quickly to imderstand its usefulness. These may be obtained at a stationer's, or, better still, they may be made from bristol board by the pupils themselves. For the earliest work a graduation dividing the semicircle at inter- vals of 5° is- all that is required. A protractor of the size shown above will be quite large enough for all ordinary classroom use. Very many and interesting exercises in measuring and constructing angles and arcs maybe had with § 5 PEDAGOGICS (3F GEOGRAPHY. 75 protractors, and in this way the pupil will quickly become familiar with the important and useful circular measure. In connection with the protractor a pair of dividers, or, as they are usually called, compasses, are indispensable. The knowledge obtainable by their use is all in the industrial direction, and in this practical age it would be diiificult to mention a stronger reason for learning early to use such implements. 63. Measuring" and Constructing" Ang-les. — This is an exercise of such general practical utility that it should be introduced quite early into our schools. The fact is, how- ever, that it is almost entirely igncjrcd, and although the subject of circular measure as given in our arithmetics is studied by our pupils, it is never in the slightest degree understood by them unless they are fortunate enough to fall into the hands of a teacher sufficiently intelligent to realize its importance. If the pupils are provided with a protractor, a pair of dividers, a ruler, and a pencil, tlicy have all the implements needed for practice of the most valuable kind. The close connection of the subject with geographical place, time, and distance; with latitude and longitude; and with the changes of season, is the writer's excuse for emphasizing the matter in this place. While the most important appli- cations of the subject belong in the later stages of geograph- ical study, the beginning of its development should be with the primary pupil. B}^ the time a pupil is familiar with denominate numbers, he should be perfectly acquainted with angular measurement, and should be able to estimate an angle of G0°, 45°, 30°, etc. as closely as he can estimate inches, feet, or yards. He should be quick and accurate in measuring angles, and in constructing angles of a given num- ber of degrees. 64. The Mariner^'s Compass. — Among the various matters of general information having special reference to the subsequent study of geography is that of the luar'mer' s compass. This is exactly represented in the engineer's 70 PEDAGOGICvS OF GP:OGRAPHY. § 5 compass and in the ordinary pocket compass now very easily obtainable. If the teacher will obtain a thin piece of steel,' have it tempered very hard, and then magnetized to satura- tion at a d3mamo in some electric plant, he can make it serve as an excellent substitute for a compass. It needs only to be suspended by nueans of a string without torsion, so that it will remain in a horizontal position. Every child in the classroom should be able to point very exactly and without hesitation in any required direction. The pupils should be familiar not only with the four principal directions, but also with the principal intermediate directions; as, northeast, southeast, etc. I was very much surprised to find that in the Far West directions and distances are given very exactly even by young children. "You must go two miles north and one mile west," they will tell you. This arises from the plan of the government survey, but there is no reason wh}- the children in the East should not be trained in this respect. They are not, however, for even well advanced pupils are ignorant of these matters, many of them not knowing with any certainty the places of sunrise and sunset in their own horizon. One of the most intelligent men in this city, who was born here, in giving the direction of north to an inquirer recently, was just about 45° astray. Such information is of the highest practical value, but it is not taught with any system or persistence. Very certain is it that no one can undertake and make a success of the study of geography if he is ignorant of these important preliminary matters. It is a work that should be planned by the teacher in minute detail and carefully adapted in difficulty to the capacity of his pupils. In teaching direction, it is a good plan to have pupils first ascertain from a map the situation of one place with respect to another, and then indicate the air-line direction by actually pointing. Thus, ask the pupils to ascertain frcnn their map the direction from their home to Philadelphia, New York, Washington, Pittsburg, Montreal, and then require them to point with approximate correctness towards these places. § pEi)A(i()(;ics OF gi<:()(;rai'1iv. (i5. Mercjitor's l»r<).j<,'cli<>n. — .Vlthoiigii the ciirth is nearly spherical., the impossibility of showiiiL^" its entire surface at one view has led the chartographers to represent it as "round like a cylinder" instead of " roiuid like a ball " (Fig. 2). Under this assum])tion, its surface, if we imagine Fig. ~>. it removed as indicated in the figure and spread out on a flat surface, is a rectangle. The objection against thus repre- senting tlie earth's surface is that the parts near the poles are much exaggerated; but, inasmuch as commerce and travel are mostly confined to the torrid and temperate zones, this p/ojection is used very extensively. On the ocean especial] V, it is indispensable. 66. Location on a Plane. — As a preparation for the comprehension of latitude and longitude, as well as of ■' vStandard Time," it would perhaps be difTficult to find any- thing in the way of an exercise better than the following: Require the pupils to subdivide on paper a drawing of any plane rectangular surface, say the floor of the classroom (Fig. 3). It may be numbered as shown in the figure, or in any other vSuitable manner. The teacher'will of course notice that the two heavy lines at right angles represent for the floor just what the equator and the prime meridian represent on a globe, a Mercator's projection, or on an ordinary map. This drawing can be placed on a blackboard or on a large sheet of manila paper and used for general class exercise. In using this, the pupils may be required to find very promptly points indicated by the teacher; as, N Id, W 4; vS7, E5; vS 11, W IT); etc. Very soon the teacher should ^8 PEDAGUCUCvS OF GEOGRAl'lIV § ^ introduce the word north, instead of N, cast instead of E, etc. This will tend to make the pupils quick to recognize directions on maps and globes. Interest and variety may be added to the exercises by employing certain fictions, such as imaginary sea voyages, railway travel, vessels sunk by storms, cities located, etc. ««1*SN.«V5'**9**'-1CSC1 =CN.tt'5'^<0*t»>. © Wo - *1 "^l N -1 "^ "S *1 •n "^ *<*<** 5 If, later, lines be drawn to show the tropics and the polar circles, the pupils may be made very familiar with the tem- perature that prevails in different zones, ^s well as with the alternation cf the seasons. Such questions as the following will be quickly answered by the average pupil, if he be taught to understand that his diagi'am represents the earth's surface : "Where should one expect the warmer climate, at S 25 or atN40?" "Why?" " Point out places that have summer in June; places that have winter in June." ' ' There is a city at S 23, W 4 o, and another at N 41 , W 74 ; which should be warmer in simimer? Which has noon first on any given day ? " g5 PliDAGOGlCvS OF GEOGRAPHY. 7'J "A ship was sunk tit vS 50, W 50; point out the place. If the time was August 15, what season was it at that place ? " "I have a friend that lives at N -li, WG'J; indicate the place." " In what month does winter begin in Japan ? in Australia ? in Argentina ? " The usefulness of this, and of every other exercise, will of course depend almost entirely on the teacher. If he knows just what he wishes to accomplish; if he introduces the proper exercises just at the right time, and persists with them sufficiently; if he understands his subject thoroughly, and handles it skilfully, the impressions will be clear, sharp, and lasting, and the benefit very great. Obviously, it would be aside from the purpose of this Paper to do more than indicate some of the objects aimed at in the intelligent teaching of geography, and to suggest a few of the many methods of attaining these objects. The field is so wide, and it contains so many matters of practical educational importance, that the teacher is certain to find confusion in an "embarrassment of riches;" and it requires a wide acquaintance with the requirements of life, as well as careful reflection and judgment, to decide what to omit. 67. Plan of tlie Classroom Di-a^vn to Scale. — Avery interesting variation of the foregoing exercise is to draw a few rectangular surfaces to scale, and to represent in cor- rect position the various objects that occupy those surfaces. For this purpose, no better surface than the floor of the classroom (Fig. 4) could possibly be found. Let us suppose that its dimensions are 24 feet by 30 feet. If we make each i inch in the drawing represent 1 foot in the reality, our plan will be 3 by 3| inches — a convenient size. The various articles of furniture must be located by actual and careful measurement. Thus, if the teacher's desk is 3 feet long and 2 feet wide, its .size in the drawing will be fin. X { in. If it be placed 3 feet from the front of the room, and equally distant from the sides, it will stand as shown in the diaoTam. so i>]':l)AG()GiCvS of geograpuv. ^ ^ There are many exercises of i^reat value that may be had with the drawing- after it is finished. Thiis, the teacher may direct the pupils to find out from their drawing- how far it is from her desk to seat 7, 11, etc., and require that the answers i?^^'j:W\mi?M4i4i^mm^ @ @ @ ® @ @ @ ® @ @ @ ® @ @ @ ® © @ @ @ @ @ @ @ © @ @ o Plaf/crr, Fig. 4. be confirmed by actual, measurement. This is the exact equivalent of finding how far it is from one place to another represented on a map. This work may be profitably continued with outside areas ; as, the school yard, the block, the village, etc. Committees of pupils may be sent to measure the distance to certain specified points, and the work of making a map may be con- tinued from dav to dav until it is finished. The teacher § 5 PEDAGOGICS OF GEOGRAPHY. 81 may have a large sheet of paper suspended against the wall, and on this the work may be done to a larger scale than is used by the pupils. The fascination of this kind of work will grow with marvelous rapidity, and it would be difficult to find any other exercise that is valuable in so many ways as is this. THE MAKIXG AXD RECORDING OF OBSERVATIONS. 68. The Bicycle in Geography. — He must be a far-see- ing man that can accurately gauge the wide and multiform influence of the bicycle on the development of the race. This vehicle has come to stay, and has compelled an aston- ishing readjustment of things to new conditions. Many forms of business long established have been greatly affected by it, and many others have come into existence to meet new demands caused by its advent. The writer recently overheard a conversation between a jeweler and a clothier in which each blamed the bicycle with being the cause of depression in his business. " My trade is nearly ruined by the machine," said the one. "The fathers and mothers that formerly bought watches, rings, and dia- monds for their sons and daug-hters, now give them bicycles instead." "Yes," replied the other, "and thousands of young men and women are expending money for clothes that we do not furnish. The wheel has caused them to lose the art of dressing. Dressing for appearance is being dis- placed by dressing for ease and comfort." The horse, discarded by the electric car, and supplanted by the bicycle and the automobile, is, like the American bison, menaced with extinction. The rapid spread and enduring tenure of the ancient Roman power has been attributed to the fact that wherever they went they caused most excellent roads to be made. The bicycle is causing the same beneficent work to be done. It is possible now, in all kinds of weather, to ride for htmdreds of miles continu- ously on roads that are well nigh perfect. The mission t>f 83 PEDAGOGICS OF GEOGRiVPHY. § 5 the wheel, to compel the making of roads, is being accom- plished with a promptness and a thoroughness of which the Romans were utterly incapable. It is widening oiir actual horizon, and making observers of us ; our knowledge of local geography is no longer con- fined to an area of a few square miles, but in many cases it has been extended beyond the limits of the rider's own county and state. Indeed, it is no longer regarded as a notable feat to make a journey awheel from the Atlantic to the Pacific in our own country, or to explore in the same way all the countries of Europe. 69, Tlie Wlieelmau as a Teaclier of Geography. Every wheelinan must become in some measure both a stu- dent and a teacher of geography and its allied sciences. His membership in the "League of American Wheelmen" or in the "Good Roads Association" enables him to obtain reliable maps covering any tour he may wish to make; and not only he, but his friends as well, become interested stu- dents of the topography of any prospective trip before it is begun. But it is when he returns that he really becomes an enthusiastic teacher of geography. Like the tale of the "Ancient Mariner," his also is one that must be told. It is a vivid tale, and interesting, for he knows whereof he speaks. His map is no longer a mere map; it is rich in sug'gestions of personal experiences of every kind; it is, so to speak, a chapter of condensed autobiograph}^, and a sight of it at any future time will recall the most delightful memories. He cannot, then, avoid being an earnest and eloquent teacher, and he has no difficulty in finding and holding his audience. Ulysses, when he returned from his ten years of wandering, could scarcely have been more entertaining than the wheel- man after one of his long, delightful trips. He spreads the contagion of travel; he is not content until he has induced his friends to go with him and see what he lias seen. And just here is an important principle in pedagogics; No one can teach geograpliy so well as an observant and intelli- gent traveler. His teachings have an interest that is strongly § 5 PEDAGOGiCvS OF GEOGRAPHY. 83 human; he deals miieh with man and tlie matters that strongly affect human welfare. How delighted we are to listen to one that has actually seen the myriad sights of travel, — has "been a part of that wdiereof he tells." When Othello finishes his tale to Desdemona concerning the wonders he had seen, she thanks him. Remarking further on the effect of his story, Othello says, " She thanked me, and bade me, if I had a friend that loved her, I should but teach him how to tell my story, and that would woo her." What an admirable teacher ol the natural sciences in general, and of geography in particular, would von Hvmi- boldt have been, or Darwin or Baker or Layard or Living- stone or any others among those learned "globe trotters" whose writings we find so charming. TO. 8uTve.viii^" AVitli ]>ieycle and Cyclometer. — In an admirable article with the foregoing title a cycling friend of the writer gives, in a late number of the " Mechanic Arts Magazine," a minute and systematic account of what maybe done in the way of recording the facts of a trip on a bicycle. The author has kindly permitted the use of his article in any way that may bt- deemed helpful to the students of this Paper. Its length is the only reason for not inserting it entire. The article gives the notes recorded and the details of scenery observed during a trip froin Wilkes Barre to Shawnese lake, in Luzerne county, Pennsylvania, and it shows the maps constructed from those notes. 71. Tlie Cyclometer. — "Now, let its consider," says the author, " the method of procedure by which the bicyclist may become a surveyor and thereby able to convert the results of each trip over a new road into a permanent record for future use. In the first place, a word about the cyclom- eter and its value as a surveying instrument. ' ' A cyclometer is not what mathematicians would call an instrument of precision like the transit, the level, or even 84 PEDAGOGICS OF GEOGRAPHY. § o the surveyor's compass. It will record with an error of about 1 per cent, when working at its best, and under certain circumstances the error will be increased to 3 per cent. This error is due to the relation between the bicycle wheel and the number of revolutions that will cause the cyclometer to record 1 mile. The usual cyclometer requires 720 revolu- tions of a 28-inch wheel, in order to record 1 mile; but owing to the deflation of the tire and the weight of the rider, the wheel may be but 27.5 inches in effective diameter, and the cyclometer will record 1.019 miles for each mile ridden, or 101.9 miles for each 100 miles. In addition to this error, the bicycle actually travels farther than the true length of the road itself, owing to the fact that the rider continually crosses and recrosses the road in order to select the best parts for cycling; and this error, varying as it does accord- ing to the character of the road, will amount to about 2 or 3, per cent. more. Therefore, before we start on our survey, we w411 assume that our cyclometer measurements will all be 5 per cent, in excess of the actual distances traveled. If the bicycle surveyor be an experienced rider, his map may be so plotted that grades and conditions of road may be readily expressed, and other information never found on the most accurate of maps may be added as a guide to the future traveler. " 73. The jS"ote Book. — "The next detail to consider is the note book. This should be long and narrow, with two parallel lines ruled down the center of the page to represent the road. Stenographers note books serve the purpose admirably ; these are about 44- inches wide and 8 inches long, and are ruled across the page with lines about ^ inch apart; the two parallel lines down the center of each page can be ruled with either pencil or pen, and the book is then ready for the trip. A piece of board, the same size as the book, should be secured to the handle bars, and the book laid on and bound fast with rubber bands. A bicycle watch on the handle bar is also a great convenience, but by no means a necessitv. § 5 PEDAGOGICvS OF GEOGRAPHY. 85 "The arrangement will now look somewhat as in Fig. o. At a is the cyclometer, the record of which should be easily read by leaning over the handle bars ; at I? is the note book; and at c is the watch, which will act as a check on the cyclometer and grade notes. Now, we will assume that the bicylist is out on a trip with a number of other enthusiasts, and, therefore, will be imable to stop and make any individual meas- urements of the roads and landmarks which he passes. All notes must be made awheel, and inforiuation recorded without slacken- ing speed. Before he starts, the register of the cyclometer is observed, and written on the lowest line of the note book and is found to be :2,388.8 miles, as shown in Fig. G. In recording subsequent cyclometer readings it will not be necessary to note the thousands and hundreds of miles, except when these, figures change." Fio. 5. 73. Tlie jVotes. — " The surveyor starts out through the main street of Wilkes Barre, and as he crosses the river he notes that his cyclometer reads 2,389.05 miles, and on the second line from the bottom he marks this record, as shown in Fig. (i, and at the same time draws two wavy lines across the road to indicate that it was while crossing the river that he recorded this reading. Soon he arrives at the Kingston cross-roads, and there turns to the right; his cyclometer reading is recorded as 00. '24, and, branching from the nght of the central column of his. note book, he indicates the road he takes with an arrowhead as shown, while on the left he 86 PEDAGOGICS OF GEOGRAPHY S-'d<-v^ , DAGOGICvS OP GEOGRAPHY N Tropic of Cancer. June 21 r Solstice. <, ^ «^ Equator. ,, „, Sept. m . — [ — I — Ma r. 21 Equinox. Eq It i n ox. to be ours six months later. Ask them to imagine and describe what the people of those countries are doing, and have them realize the facts about the length of day and night there and here. If this work be continued from day to day and the records carefully made, a very satisfactory analcniina., as it is called, may be made, and a drawing in cor- rect scale may be constructed by the pupils. Such a drawing with inter- mediate markings omitted is shown below. It should be observed that the mark- ings made on the floor must be reversed in drawing an analemma; for when the sun is farthest south, the shadow limit is farthest north, and the reverse. This kind of observation may be made from the shadow of a pole ten or more feet high planted erect in the school yard. Its shadow at noon will point north, and from this the other points of direction may be fixed in such way as to make them very famil- iar to every pupil. Moreover, a fairly accurate sun dial may be marked around such a pole by indicating the hour lines. This will soon lead to the discovery that such lines are variable, changing somewhat from month to month. When the children learn that this is true, their inquiries will lead naturally and directly to the methods of constructing sun dials that .shall be accurate for all seasons. Very valuable information wall be elicited, provided the teacher will properly direct their curiosity. Very exact details on the subject of "dialing" can be found in any good cyclopedia, and by pursuing this matter, the teacher will be able to benefit very greatly, not only the pupils but himself. Solstice. -Dec. SI. Dec 21t Tropic of Capricorn . S Fig. 0. PEDAGOGICvS OF GEOGRAPHY. Do (JRAPIIIC GEOGRAPHY. 78. Tlie flaking of Maps. — All authorities on the methods of teaching geography seem to be agreed as to the great value of map-drawing. It is regarded as a very useful and important, nay, an indispensable featiu'e. They are not, however, tmanimous about its purpose and methods. Some advocate the teaching of map-drawing for the sake, in large measure, of the training in drawing; and their limit of excellence is the finished elegance and accuracy of the expert chartographer. During the writer's visits among the large graded schools of some of our great cities, he has seen hundreds of maps of marvelous excellence and exactness made by the pupils. Principals and teachers are invariably very proud to show such work, and they seem to believe that such maps are evidence of good work in the teaching of geography. Anunig these maps were to l)e found represen- tations of great land masses, as vSouth America, in all sizes down to less than a scpiareinch. Hours and even days were required to finisli them; and both to execute them and to see them properly a magnifying glass was needed. In them were shown details in bewildering minuteness. Any one that saw the educational exhibit at the Centennial Exposi- tion in 18T0 at Philadelphia, or that at the World's Fair in 1893 at Chicago, will doubtless remember having examined similar work and doubted whether it could possibly have been done by ordinary school children. Other authorities advise against work of this kind, and insist that it furnishes little help in the real teaching of geography. They say that a pupil may be taught to make such maps in the utmost perfection and escape learning any- thing of value in practical geographical knowledge; very much as one may copy in admirable fashion the words of a treatise on any learned subject, and yet not get a single idea that he did not have before he began. In the opinion of these authorities map-drawing should be practiced for the purpose of illustrating geographical facts and principles, and the drawing itself may be rude and rapid, provided it effects 90 • PEDAGOGICvS OF GEOGRAPHY. § 5 the purpose eoiitemplated. For example, a teacher may wish to show the commercial advantages that arise from the fact that any great city is situated where it is, or the reasons why a certain railroad should follow a particular course through a country. In doing this, it is necessary to indi- cate only the means of exit for the commerce of the city tinder consideration, the mineral, agricultural, and lumber- ing fields around it, and the needs of neighboring market centers. In the other case, the relief of the cotmtiy trav- ersed, the centers of industry and population reached, the productive areas and undeveloped resources provided for, may be rapidly sketched, and thus the pedagogic purpose of the drawing is fully accomplished. Another argument in favor of this view is that few pupils and fewer teachers can make an elaborate map, while any one can construct maps of the kind just indicated. 71). The Intermediate Tiew. — As is the case with nearly all other subjects, there is with respect to map-draw- ing a "golden mean" that is better than either extreme. Undoubtedly there are good reasons for cultivating an ability to make finished and accurate drawings of every kind, maps included. But it is to be remembered that the educational usefulness of maps as a help in geographical teaching is not very great, although in some other respects they may be of the very highest value. On the other hand, the skctcJiing of maps is an indispensa- ble aid, and should be much practiced at every point in the geographical work in school. It is the kind of map-drawing that is to be employed in actual later life. 80. The Resolutions of the German Geographical Congress. — In consonance with the foregoing view, the following resolutions adopted by a late German Geograph- ical Congress may be helpful as a guide to the teacher of geography. They were the outcome from an animated and thorough discussion. 1. The German Geographical Congress recommends drawing in geographical instruction as an indispensable means to the promotion § 5 PEDAGOGICS OF GEOGRAPHY. %' of clear intuitions, and :is a powerful aid to iiwakening' the self-activity of pupils. 2. It declares itself most positively against the widespread evil of setting pupils to draw maps as a home task without fitting them for the work by a gradually progressive training. 3. It condemns the use of straight lines to express the lines of a map (Lohse's method), since this plan is not adapted to develop the pupd's sense of form, but rather debases his taste in regard to map representations. 4. It most positively condemns the systematic carrying out of the so called " constructive method," since it requires a system of artificial aids (lines and points), the knowledge of which is in the main of no value to the pupil, and heavily burdens his memory in a useless way. 5. It condemns special preliminary courses in topographical draw- ing as aside from the purposes of the common school. 6. It recommends the method of free sketches of single terrestrial spaces as reproductions of typical relations studied from the map, since these can be adapted in amount of detail and mode of execution to the capacity and skill of the pupils. The student will observe that by these resolutions map- drawing" is regarded as indispensable as an aid in g-eograph- ical teaching, bitt the pupil should not be sent away from the classroom with a task in drawing" to complete by himself. On the contrary, the work should be made a class exercise, in which the map is made only as fast as the ideas to be repre- sented are developed by the cpiestions and answers of the pupils and teacher. No map should be drawn in which reli- ance is placed upon straight guide lines or geometrical skeletons in measured straight lines. The reason for this prohibition is that it defeats the most important object sought in the exercise, that of developing the ptipil's sense of form. By the fifth resolution, it is clear that the Con- gress would discourage any striving after chartographic per- fection, since it advises against any preparatory course of drawing in which skill in the art for its own sake is the object; and by the last resolution, the student is advised to make sketches of parts of a country or state merely as a means of illustrating some point or principle of importance. 81. Vie^vs of the Teacliers and Inspectors at Vienna. — In confirmation and support of the foregoing !»8 PEDAGOGICS OF GEOGRAPHY. § 5 views, the student should eoinpare llie eonelusions reached at a meeting of the teachers and school inspectors in the capital of Austria, a country second to none in Europe for the excellence of its geographical teaching. Among other matters, it was there decided: That a moderate application of drawini^- in teaching geography is pedagogically valuable, Ijut is not indispensable as a means to the right apprehension and memorizing oE the map. That drawing is only a means, never an end in itself. That the geographical drawings of jnipils should not be tirged beyond their acquired skill in general drawing. That the representability of geographical ideas and the special aim or purpose of the instruction in geography should determine the kind of drawing required. That the drawing should be restricted to geographical specialties, such as single rivers, relative positions of places, mountains, slopes, plains, basins, etc. That political boundaries, drawn as mere outlines, and without ref- erence to the position of enclosed places, commercial and industrial activities, or natural resources, should be excluded. The same prohi- bition is made against drawing entire coast lines, countries, and grand divisions. That the requirement should not be made that, at the end of a term, a year, or any other period, the pupils should by way of review be aljle to draw from memory the maps studied during the period. The student will notice that somewhat less insistence is here placed upon the value of map-drawing than is the case with the German Congress; but that is one of the things that must be expected with regard to all matters of opinion. It should be remembered, too, that the Germans, being the map-makers of the world, would naturally emphasize the importance of that in which they excel all other people. And on the other hand, we may safely assume that the Austrian educators would be disposed to disparage some- what an art in which some other nation surpasses them. Here, as everywhere el.se, the thoughtful student will seek the truth between the extreme views of rivals. Let ns hope that our teachers may before many years carry the same degree of enthusiasm and excellence into this work that the American people habitually do into other matters that are §5 PEDAGOGICS OF (tEOGRAPHV. '.)9 in process of development. In the natural search after models that we may imitate, we can j^et what we require nowhere so well as in the practice of the schools of Central Europe. They have approached scientific precision in teaching' geography and the other natural sciences more closely than any other people in tlie world. S2, Map-Ske telling : Dimensions, Area, and Relief. In order to illustrate the manner in which map-sketching should be used as an aid in teaching geography, let us sup- pose that a class is engaged in studying the state of Penn- sylvania. Naturally, the first thing to consider would be its outline, its dimensions, its area, and its relief. A free- hand drawing should therefore be made of its boundaries, and their lengths may be written along the several lines that represent these boundaries. The inountains and rivers may then be sketched in, and as the work pro- gresses, names and important facts should be given. These mountains and rivers will reveal the slopes, the highlands, and the valleys, and the pupils may be called upon to trace the "divides," or watersheds, that separate contiguous basins. If there are regions favorable to agri- culture, lumbeiing, manufacture, mining, or commerce, the slopes, valleys, and mountains will show where they prob- ably are, arid the pupils may be called on to .say where these several features are to be sought. Tliis will introduce the elements of cause and effect, without which geography as well as the other natural sciences cannot be well taught. vSuch a map, with nothing more on it than what is indicated above, may be made the basis of several very interesting and valuable lessons, provided the teacher thoroughly understands his subject and has properly pre- pared himself for the lessons. For example, the pupils may be asked to find out how many days it will take an army, marching at the rate of 130 miles a day, to cross the state from east to west, and how many, from north to south. How many farms of 100 acres each the state contains is a matter eas^^ to find out when it is known that KM) PEDACOCllCS Ol- (;E()GRAPIIV. ^5 four such farms occupy a square mile, and that the laud area of the state is about 45,000 square miles. The population of the state and its area being given, the population per square mile may be found, and later, a table may be made showing the comparative density of population of Pennsyl- vania and various other states; and these figures may then be compared with that of certain indicated foreign countries. This is the only w^ay to interest children in statistics, some varieties of wdiich are of extremely high value in education. A few of the higher and lower points of surface may be marked on the map, although this is not a matter of the greatest importance. In the absence of such marked points, the pupils can find them by observing the direction in which the rivers flow, and by knowing that they must be sought in the lowest valley levels, and that rivers are least elevated at the point w^here they enter the ocean or other large body of water. Our map so far is all the more instructive in being empty of confusing details. This confusion is one of the w^orst features of modern textbooks. Most people are prompt to condemn a geography if it happens not to contain a map showing the little country village where they were born. But a map that does this has no value as a means of teach- ing philosophical geography. 83. liater Ijessons. — Within an outline sketch of the state other important geographical facts may be indicated and discussed, and the necessary drawing may be done by the pupils in turn. Thus, the location of the various species of mineral wealth, — coal, iron, mineral oil, etc., — the tim- bered and agricultural areas, the situation of deposits of iron with respect to their neighborhood to the coal used in smelt- ing them, the means of exit to market for the products of the lumber regions, the inland waterways available for commerce, and the nature of the products carried, the trunk lines of -rail- way and their tributaries, the location of the chief manufac- turing cities and their various industrial activities — these and many other matters of importance may be the subjects of a § 5 PEDAGOGICS OF GEOGRAPHY. lol series of lessons for which textbooks should be used merely as books of reference. In preparin>^- for them, one pupil should be required to obtain from certain sources indicated by the teacher the information bearing- upon some particular part of the subject, and other phases of it may be assigned to differ- ent other pupils. These composite lessons may be made extremely interesting by means of skilfully conducted recita- tions, the purpose of which is to combine into an orderly whole the contributions of the several pupils. The text- book matter may afterwards be studied for the purposes of review, and of organizing many lessons into continuous and logical unity. 84:. Stencil Maps. — Every teacher of geography should know how to prepare stencil maps and sketches of various kinds. These may be bought from almost any educational publishing house. Catalogues may be obtained giving lists of stencil outlines of maps, plants, animals, insects, portraits, etc., and their prices. These stencils consist of sheets of thin paper in which minute perforations represent the correct outlines and the necessary details of the objects to ba repre- sented. They are of a size suitable for blackboard drawings. To use them, it is necessary only to place them against a blackboard and go over them gently with a felt black- board rubber that has been rubbed full of crayon dust. Upon removing the stencil, it will be found that a faint out- line of the drawing has been transferred to the board. This may then be lined in with crayon of any required color, and such other details may be added as the drawing requires. Of course, if the teacher is skilful in drawing, these sten- cils will not be required; but the fact is that few teachers are possessed of this very valuable accomplishment. It is stated above that these stencils may be bought, but better still, each teacher may make them himself or have his pupils make them. A satisfactory method of doing so is as follows: With a lead pencil make on a sheet of thin paper an out- line sketch of the map or other object of which a stencil is 102 PEDAGOGICvS OF GEOGRAPHY. required. Then place a couple of sheets of thin paper under this, and pin the whole together at the corners. Put a fine needle into a sewing machine and follow the traced lines of the drawing. In order to prevent a burr from forming on the under side of the pierced holes, the sheets should be placed upon a piece of manila paper while the perforations are made. These stencils should be preserved; for they may be used a great many times, and they will be found extremely useful, not in teaching geography only, but in connection with nearly every other school subject. Indeed, the teacher gifted with resourcefulness will continually find the means of devising helpful appliances for giving interest and vividness to his work. 85. Pictured Comparisons. — The graphic representa- tion of facts, relations, processes, and principles, as shown in U.S. Elsewhere. Fig. 10. U. S. Elsewhere. Figs. 10, 11, 12, 13, and 14, has come to be indispensable in the best phases of modern teaching. What teacher now could expect to succeed in teaching grammar, for example, Elsewhere. U. S. Elsewhere. Fig. 11. if he were debarred from using a good scheme of diagrams ? Could any one teach physics, astronomy, chemistry, botany, or any other of the natural sciences without the aid of graphic representation ? The same kind of help is required §5 pedagcXjICS of geography. 1U3 in geography. As has been remarked, statistics relating to many subjects are of great importance, especially if it be desired to introduce the principles of cause and effect, and '■*T r^i ^^ 11^ Elbe^\he^e L s Fig. 1-,'. U & U. S. Elsewhere. considerations involving comparison. Our late textbooks are beginning to make much use of the graphic method of representation, and it is easy to see that this is a tendency in Elsewhere the right direction; for any one can understand how much more forcibly such truths as the above can be shown by pictures than if they are merely stated in words. It is not necessary that a teacher should be able to draw skilfully in order to use the graphic method. Stencils of figures in outline are easily made or obtained, and they are available ever afterwards. Even if a teacher has no skill whatever in drawing he is almost certain to have in his class one or more pupils that can do well what may be required. The accompanying cuts are only a few of the innumerable illustrations that may be used advantageously in this work. They all represent activities in which those of the United States are compared with the rest of the world ; but equally instructive would be those cases in which the reverse is true. The illustrations above were suggested by cuts of a similar kind in "The Natural Advanced Geography " of Redway and Hinman, a late and very admirable work published by the American Book Company of New York. 104 PEDAGOGICS OF GEOGRAPHY. § d 86. Graphic Geoiuetrical Forms. — A method of illustration requiring- no skill whatever in drawing is that involving the use of certain geometrical forms. Among the most suitable of these are the square, the rectangle, the cir- cle, and rectangular solids, variously grouped and subdivided. A method used very extensively in European schools consists in parallel straight lines of unequal length. These furnish a very convenient means of showing comparative heights and distances, as well as areas, products, wealth, commerce, etc. The following is an example : J{// Jid il roads. ^^tKtKM Atlantic Ocean and Cr^ii If of Mexico. immmtm Great Lakes, ^mm Mississip'pi and its Tributaries. ■■ Canals. mm J^aci fie Ocean. Comparative Transportation of the Commerce of the United States. Fig. 14. To illustrate further the manner of using these graphic devices, let us suppose that the area of Texas is to be compared with the areas of certain European countries. If these areas are to be compared by //ucs of imequal length, we know that the lines mi;st vary in length as the (rrcas ; but if we wish to represent comparative areas by surfaces, as, for example, by squares, then we must make their sides proportional to the square roots of those areas. Moreover, if so/ids, such as cubes, were used, their edges must be proportional to the cube roots of the areas. In case these dimensions are not great enough or small enough, we may multiply or divide them by any suitable number, provided we use the same multiplier or divisor for all of the dimensions. A very good way to prepare for the actual representation is to construct a table beforehand, and require the pupils to make all the calculations. In such tables, the areas of coun- tries should be given in square miles to the nearest thousand. S PEDAGOGICS OF GEOGRAPHY lO.j Such a table, for representing" graphically the areas of the countries named in it, is shown below. The accompanying- cut is somewhat reduced from the dimensions of the drawing; indicated in the table. Covintrv. Area in square miles. Area 1,000. .Side (if Square. Texas 266,000 210,000 207,000 192,000 126,000 121,000 116,000 111,000 266 210 207 192 126 121 116 HI 14/266 = 16.3 H- 4 = 4.08 ^4/210 =: 14.5-4 = 3.63 i|/207 = 14.4 --4 = 3.60 1^/192 = 13.9-^4 = 3.50 ^|/T26 = 11.2 --4 = 2.80 1V'121 = 11.0-4 = 2.75 14/116 = 10.8H-4 = 2.70 ^4/111 = 10.5H-4 = 2.63 German Empire h ranee Spain Hunijary Great Britain and Ire- land Austria Italy, Sicily, and Sar- dinia . dirjIKUl >J -Spu iji _Iii: Britain .Ualij Fig. l.j. •106 PEDAGOGICS OF GEOGRAPHY. § 5 87. Clay, Sand, or Pasteboard for Modeling. — Clay or sand modeling has come to be regarded by the best authorities as indispensable in the earliest geographical teaching. In every classroom where the first lessons in geography are given, there should be a modeling board about 48 in.x CO in., and this should have around it an edge raised about H inches. This board may be attached by hinges to a table, and in some convenient receptacle there should be a generous supply of sand. The sand may be obtained from any foundry, or ordinary beach or builder's sand may be used, although it is not quite so good. Mois- tened occasionally, and kept covered with a cloth, it is always ready for use. Each pupil should be provided with a shallow pan 12 in. X 20 in., as well as with a piece of thin wood or metal similar in shape to a spatula or a paper knife. For more advanced pupils, modeling clay or putty may be substituted for sand. A supply of either of these, if properly cared for, will last a long time, and their cost is inconsiderable. The work of modeling has lately received so great an impetus in our schools that many of our large cities are now furnishing clay for the use of pupils, just as they supply books and stationery. In the town and country schools this is not done, biit a teacher with proper enter- prise and enthusiasm in his work will find a remedy for the omission. When maps showing contours representing elevations can be obtained, very, much more accurate models may be made by using pasteboard of uniform thickness. Since contour lines usually represent elevations by differences of 100 feet, one layer of pasteboard may be taken as representing this height. Before cutting the pasteboard, each contour Ime should be sketched in proper scale on its surface, and the several pieces may then be cut and firmly pasted on one another. The result will show for each elevation a series of terraces, which, indeed, are not true to the fact, but this is a matter of slight consequence. It is always possible to obviate this difficulty by filling in the terraces with plaster § 5 PEDAGOGICS OF GEOGRAPHY. lOT or other suitable material. From these models casts may be made, and these in turn may be used as molds from which plaster casts may be obtained. Of course, this elaborate work, with pasteboard to show relief forms with approxi- mate exactness, is suitabL> only for advanced pupils that have aptitude and taste for it, but the study of their work by other pupils is in a very higli degree beneficial. 88. Maps of the Governiiieiit Survey. — Every teacher should be provided with specimens of the maps that are made by the United States Geological Survey. They are very complete, showing on larg-e scales every variety of topographical and geological features — every stream, road, lake, swamp, hill, mountain, church, schoolhouse, village, etc. The object of the government is ultimately to have a complete and minute survey of all the states and territories that make up the vast possessions of the country. At pres- ent, somewhat more than one-fifth of this work has been accomplished, but something- has been done in every state and territory, and in a few of the more populous, the survey and mapping have been nearly or quite finished. These maps are perfect aids in teaching home geography. With them, the teacher can get for his rude blackboard maps every fact required to give interest to his teaching. The wonderful perfection of these maps will surprise the teacher, and they furnish the means of indefinite improvement in the teaching of geography. 89. Description of tlie Topographic Map of the United States. — The waiter is convinced that it will be help- ful to the teacher of geography to give him exact informa- tion about the maps of the United States Geological Survey, and to let him know exactly how they are to be obtained. The following description is therefore copied from the back of one of these maps : The United States Geological Survey is making a topographic map of the United States. Tliis work has been in progress since 1882, and about one-fifth of the area of the country, including Alaska, has been mapped. The mapped areas arc widely scattered, nearly every state 108 PEDAGOGICS OF GEOGRAPHY. § o being represented, as shown on the progress maji accompanying each annual report of the Director. This great map is being published in atlas sheets of convenient size, which are bounded by parallels and meridians. The four-cornered division of land, corresponding to an atlas sheet, is called a qitad- raiigle. The sheets are approximately of the same size: the paper dimen- sions are 21| by 18} inches; the map occupies about Yi\ inches in height and 11), to 16 inches in width, the latter varying with latitude. Three scales, however, are employed. The largest scale is 1 : 62,500, or very nearly one mile to an inch ; that is, one linear mile on the ground is represented by one linear inch on the map. This scale is u.sed for the thickly settled or industrially important parts of the coun- try. For the greater part of the country an intermediate scale of 1 : 135,000, or about two miles to one inch, is employed. A third and still smaller scale of 1 : 250,000, or about four mil«s to one inch, has been used for the desert regions of the far West. A few special maps on larger scales are made of limited areas in mining districts. The sheets on the largest scale cover 15' of latitude by 15' of longitude; those on the intermediate scale, 30' of latitude by 30' of longitude ; and those on the smallest scale, 1° of latitude by 1° of longitude. The sheets are sold at five cents each when fewer than 100 copies are purchased, but when they are ordered in lots of 100 or more copies, whether of the same sheet or different sheets, the price is two cents each. ■;:- ■::- * * * * Applications for the separate topographic maps or for folios of the Geologic Atlas, accompanied by the cash or by post-office money order (not jjostage stamps), should be addressed to The Director, Iniited States Geological Survey, Washington, D. C. MATTER A:XD METHOD IX GEOaEAPHY. 90. The Important and tlie Trivial. — Soine one has defined a weed as " a plant out of place. " For example, if a stalk of maize should appear in a field of wheat, it would be a mere weed. It is an intruder; is part of no g-eneral scheme; its presence is not helpftil but hiu'tful ; the natural prompting is to uproot it and cast it aside. So, also, in education, it does not follow that, because anything- happens to be true, it §5 PEDAGOGICvS OF GK()(;RAPHY. Kid has value and should therefore be taught. "A faet, " says SchelHng-j '-is in itself nothing." Unless it is a necessary part of a coordinated whole, — is a link in a chain of sequence, — it should usually have no consideration. "United we stand, divided we fall" is an axiom in science as well as in politics. There is no virtue or value in isola- tion. For the teacher to have in his mind a distinct general scheme of the subject he is teaching; to keep this scheme in constant view while developing its details from day to day and from week to week; to present to his class all these details in proper relation and order, guarding always against irrelevancies, until he has put his pupils in possession of the same clear, sharply outlined conception of the subject that he himself has, is not easy, but it is indispensable to the best results in teaching. A great poet seeking the highest eiTect must know how to discriminate between the important and the trivial, between that which is relevant and essential to the effect he would produce and that which adds to it nothing. In this respect his work resembles that of the teacher, but it is perhaps less difhcult. The teacher is continually impor- tuned to notice and emphasize facts that have no other claim on his attention than that they are curious, striking, fantas- tic, or wonderful. And herein lies the chief fault in the teaching of geography; its continuity is broken and its sci- entific character is lost by an almost unavoidable instinct to make tlie geographical story like that told by Othello, wherein he spoke * * of antres vast and deserts idle, Rough quarries, rocks and hills whose heads toncli heaven. And of the Cannibals that each other eat, The Anthropophagi and men whose heads Do grow beneath their shoulders. This kind of thing is very interesting, but it is not in any proper sense geography. 91, Sailoi' Geog-rapliy. — The report of the Committee of Fifteen, by describing what is called "sailor geography," illustrates what is said just above. liU PEDAGOGICS OF GEOGRAPHY. § 5 At first there prevailed what miglit be named sailor geography. The pupil was compelled to memorize all the (names of) capes and headlands, bays and harbors, mouths of rivers, islands, sounds, and straits around the world. He enlivened this, to some extent, by brief mention of the curiosities and oddities in the way of cataracts, water- gaps, caves ("antres" of Shakespeare), strange animals, public buildings, picturesque costumes, national exaggerations, and such matte7-s as wojild furnish good i hemes for sailors' yarns. Little or nothing was taught to give unity to the isolated details furnished in endless number. In many of our schools there is yet a strong- leaning towards tmdtily emphasizing the curious and abnormal thing's that are found in the various parts of the earth. This is perhaps accounted for by the fact that in the process of the development of the race we have not yet reached the deliberative, philosophical period when principles and laws yield more pleasure than the curious and the incidental; when the sensational, gossiping-, scandal- spreading journal is more widely read and enjoyed than the cleanly edited philosophical paper. Our teaching is perhaps as g-ood as the people expect or deserve, but that is not the inain point to consider. If we are to outgrow and put aside the things that belong to a rudimentary civilization; if, leaving the "yellow" journal and all that it signifies, we are to grow constantly towards that which is higher and nobler, into wider and more refined sentiments and sympathies, we must have something better than sailor geography. And this something better we must get from our teachers more than from any or even from all other influences. 93. The "Capital-and-Botindary" Geograpliy. — Fol- lowing the period of sailor geography, there came a phase of the subject that might be called the " capital-and -boundary " development. If, in addition to the miscellaneous details that were dwelt upon in sailor geography, a pupil could bound and give the capital and mention one or two important cities, his knowledge of geography was regarded as lacking nothing in completeness. But there came Avith this advance some- thing that led rapidly to a higher conception of the best §5 PEL)AGO(tIL\S OF (tEOCtRAPHY. Ill g-eog'raphicul teaching. This was map-drawing. The neces- sity of studying' watersheds and mountains and drainage was speedily followed by attention to industrial centers with their natural resources and their manufactured products, to routes of commerce, and to the causes, conditions, and directions of development. Inevitably, from all these matters there would come and did come a distinct recognition of cause and effect as the most important principle regulating both the choice of matter and the methods of instruction. Or, as it is phrased in the important report already quoted from: Instruction in geography is growing better by the constant introduc- tion of new devices to make plain and intelligible the determining influence of physical causes in producing the elements of difference and the counter-process of industry and commerce by which each difference is rendered of use to the whole world, and each locality made a partici- pator in the productions of all. But this capital-and-boundary method is still widely fol- lowed by teachers that have come down to us from the old regime, as well as by many younger teachers who cling to the methods followed in their own education. Of these two classes the former is almost hopelessly beyond the reach of any influence for change in the direction of growth and improvement, but with the latter this is not so much the case. For there is a contagion for betterment in nearly all the edu- cational influences about us; and these influences are practi- cally irresistible by teachers that have youth and intelligence, and are therefore capable of growth. 93. Need for Discriminating' Among* tlie Facts of a Science. — If there is a subject in which it is more dil^cult than in any other to discriminate between the important, the essential, and that whicli may be passed by, it is geography. As has been remarked, the field of geography is a vast one, covering in some measure nearly all the natural sciences. The chief difficulty lies in organizing from this enormous detail of loosely connected facts a coherent whole of which all the elements are essential to its scientific imity and com- pleteness. There must be nothing lacking and nothing* 112 PEDAGCXilCS OF (xEUGRAl'll V. i5 ■> redundaut. vScarcely any fact that can be construed as belonging to the domain of geography is without interest to somebody at some time in his life, but it does not by any means follow that it is a fact needing to be for that reason introduced into a textbook of geography. A gazetteer or a guide book would perhaps be deficient without it; but, in a geography for school use, it would be irrelevant and imper- tinent. For example, it might be an advantage to know the exact latitude and longitude of every place of any importance in the world, to know the air-line distance from each city to every other city, or to carry in the mind all the important figures of each census made at various times; but no one that studies geography of this kind need hope to get from the study, however prolonged, any knowledge of it as a scien- tific unity. The study of isolated facts is one thing; the mastery of related facts organized into a science is quite another. To illustrate, the following are taken at random from a textbook that was once very much used: Jh-adjo) d has colleges for Baptists, Independents, and Wesleyans, and is the principal seat for the worsted-yarn manufacture. . Dessau is a neat little town on the Mulde. Bernbiirg is a small industrious town on the .Saale. Newbury is celebrated for its serges and shalloons. Szej^eef/ft, on the Theiss, is a place of great trade. The book contains thousands of such statements; these, however, will sufficiently illustrate. The fact that they are put into a textbook implies that they are regarded as of sufficient importance to be studied, but of what value can it be to know that one little town is " neat " and another is "industrious," and that a third produces "shalloons".? These facts may be permitted in a gazetteer, but they are very much out of place in a geography for school use. 94. Evolution of Textbooks. — It is not many decades since all textbooks consisted of an undigested mass of facts, with no suspicion of science or logic or orderly sequence in their matter or arrangement. Maps were of little use except g 5 PEDAGOGICS OF GEOGRAPHY. 113 for playing "hide-and-seek" among geographical names; no hint could be found that great mountain ranges, rivers, ocean currents, or coast indentation have any influence in shaping national activity, development, or history. But little by little, improvements in textbooks have gone on, until now we have in this country some that are admi- rable — textbooks in which the subject appears in the aspect of a science. In some of these works, facts are subordi- nated to the principles and to the laws that they illustrate; effects are traced to their causes, and at every step it is the %vliy not the zvJiat that is emphasized. The student of the subject so presented is compelled to think, to reason, and, in a meas- ure, to philosophize. The result of his study is a nucleus of laws and principles that gathers to itself, from year to year, thousands of facts; and these facts are easily assimilated and remembered because they illustrate these laws and prin- ciples. The advantage that comes from the application of the laws of the association of ideas in teaching is seized in every possible manner, and the correlations of geography with other subjects are constantly utilized. It would of course be invidious to specif}^ in this Paper any of the text- books referred to, and it is really not important that this should be done; for any teacher, after a brief search, can easily find the best for his particular purpose. This process of evolution in textbooks will imdoubtedly continue and keep pace with the wonderful development of the earth's resources that has been so marked in the last two or three decades. The student should note, too, that this growth and progress prevent every presentation of the science from being for any great length of time satisfactory in the classroom. Geography, more than any other subject, very quickly gets out of date. 95. Some Points to Be Observed iu Teacliing Geography. — Whether the textbook used be old or recent, good or bad, there are certain general principles of teaching that may be kept in mind with manifest advantage. 1. Teach map-sketching rather than map-drawing. 114 PEDAGOGICS OF GEOGRAPHY. § 5 Considered as an aid in geographical teaching, elaborate map- drawing, for the time and labor involved, yields a very slight return. The rapid and general sketch is, however, indispen- sable. It shonld be employed constantly — in history as well as in geography. 2. Never teach names for their geographical value alone, for they have none. A name in geography should be a nucleus or center about which many related ideas cluster. The same may be said of facts. To teach a class, for exam- ple, that Chicago is a city of very rapid growth, would be a waste of time and words; but, if the conditions and caiises of such development are pointed out, the pupil will not only remember the fact, but he will have a principle to guide him in investigating the same subject with respect to other cities. In teaching isolated facts, you require him to use his memory alone; in referring to causes and conse- quences, you appeal to his judginent, his reason, his logical faculties in general, as well as to his memory. 3. In geography the object should not be to cover a great expanse, but to do the work very thoroughly. vSome one advises that if you have ten minutes in which to solve an example, you should spend the first eight minutes in thinking about it and planning the solution. So in geogra- phy — spend less time in learning new facts than in consider- ing the relations of the old and in correlating them with the new. Hence, 4. Proceed by the method of constant comparison. It is vastly better to know that the area of California is about three and one-half times as great as that of Pennsylvania or Cuba than it is to know that it has an area of a little more than 158,000 square miles. 5. Be sure that you have definite standards of compari- son. Of these there should be, ((?) A standard of Icngtli — the mile, and its subdivisions. {b) A standard of area — the square mile and the acre; also a larger standard, as the area of Kansas. [c) A standard of arc uieasurcntent — the degree and its subdivisions. §0 PEDAGOGICS OF GEOGRAPHY. 115 (<•/) A standard of altitude. In estimating mountain heights, the standard is feet ; but for great sea depths and lofty peaks use if possible a mountain that the pupils have seen. {e) A standard of population to the square mile. Thus, in 1900 the population of the United States and territo- ries, including Alaska, is about 22 to the square mile; so that each man, woman, and child might have a farm of nearly 30 acres. When the pupil learns that China has about 230, and Belgium more than 530, to the square mile, he has material for many valuable reflections upon the sub- ject of man's distribution and future upon the earth. G. Teach physical and political geography together. The separation is arbitrary and has only a theoretical value. 7. Develop constantly the causes and consequences of geographical facts. Some illustrations of this are foimd in an earlier paragraph of this Paper. 8. The deductive method has many excellent applications in teaching geography. For example, here is a city on the Pacific coast of the United vStates. The warm Japan current strikes the coast and is accompanied by currents of warm air heavily laden with vapor. During the hot summer months the heated air from the mountains that extend north and south blows seaward ; in the winter months the w"ind is in the opposite direction. What should you expect the result to be with reference to rainfall and seasons, and what effect would these varied circumstances have upon the healthfi;l- ness, the industries, the commerce, and the development of that city and its surroundings ? 9. Never require pupils to commit geographical facts to memory. If taught correctly, children cannot avoid remem- bering. If they do forget the facts, they will assuredly remember the principles, and with these in their minds they will be geographical students for life. 9G. Map Reading.— An essential object to be attained in the teaching of geography is the ready and intelligent reading of maps. Even more necessary to the true mastery of the science is the establishment of a habitual tendency to 110 PEDAGOGICS OF GEOGRAPHY. § 5 find in the map a means of sharply conceivini;- tlie reality for which the map stands. In mathematics we quickly get to dealing with quantity and number in the abstract. Very soon many concrete objects are adequately represented to the mind by Arabic numbers or algebraic symbols ; but in geography we must constantly make the transfer from the map that represents to the symbolized reality. If we fail to do this, the great round earth, with its myriad varieties 'of structure and feature, of life and motion, becomes noth- ing more than the flat surface of a paper map. The sight of the map should always be only preliminary to an aerial excursion in imagination, during which we pass over broad plains and real mountains, and trace the. rivers for hundreds or thousands of miles down long slopes and past busy, smoky cities, and quiet villages and farms, until they pour their waters, reenforced by hundreds of lateral streamlets, into the broad bosom of bay or ocean. If we fail to do this, we are studying, not geography, but chartography, we are dealing with shadows, not realities. The pupil that has been thus trained in vividly conceiving the reality from the hints furnished by the map, will indeed be surprised at the vast scale of that reality when he comes to see it, as compared with his previous conception of it; but he will not, as is the case with one that has been allowed to forget that the map is only a symbol, be convinced of the utter futility of the study of geography as a means of making him acquainted with the world before he has actually seen it. Hence, the reading of maps and globes is the crucial test of geographical teaching. When you meet the name of a river, a city, a mountain, do you call up the image of the map and rest with that, or does the mind, guided by what the map has suggested, fly away over mountains and plains and oceans and look down as if from a balloon upon the pres- ent reality? If you do the latter, you have studied geography to valuable purpose; otherwise, your study has been utterly barren. You have been learning mere words and lines and colors. The procedure is identical in futility with the study of words without reference to their meaning. § 5 PEDAGOGICS OF GEOGRAPHY. 117 97. Importance of Wall Mai)s. — Schools should be supplied with wall maps. Of these there are many of vary- ing degrees of usefulness for practical work in the classroom. Some of the essential conditions of value in wall maps are the following: 1. The coloring should not be brilliant, nor should con- trasts be striking. Anything of this kind is calculated to divert the mind from concentrated and continuous attention to the matters that a map should show. It is well known that children are easily attracted by vivid coloring, and many maps are made more for the purpose of pleasing the eye and selling readily, than for instructing the mind. The best maps of the government are almost devoid of color, and the chartographers of Germany, where, confessedly, the most excellent of the world's maps are made, and whose people have a weakness for striking color effects, avoid this common fault in map-making. 2. Wall maps should show general features, but not minute details. A map for reference and a map for teaching should differ very decidedly. The confusion of detail in a reference map renders it almost useless for purposes of instruction. A wall map should be constructed primarily to show physical features, — slopes, drainage, relief, con- tours, — but towns and cities and strongly emphasized politi- cal boundaries and divisions belong in the reference maps. They should reveal strongly and distinctly the phi- losophy of geography, not the temporary changes that are the result of man's political and industrial activity. A wall map should be rich in the suggestion of geographical cause and effect. A late writer on this subject says that such expressions as the following are of frequent occurrence in German and Swiss works on pedagogics: The map, the truest representation of the earth's surface, in which explorers have recorded their observations, is the chief means of geo- graphical instruction. We must see to it that the pupil gives his interpretation to the char- tographic signs ; that he translates into and out of the map the correct 118 PEDAGOGICS OF GEOGRAPHY. g 5 geographical relations. Map reading is the foundation of geographical instruction in the work that follows home geography [/leiiiiaikunde). It was -prepared for in the heimatkunde ; here it must be broadened and deepened. 98. The Map in Recitation. — Even with the advantage of having the very best of wall maps, the teacher may fail to obtain good results by not using them properl}'. Success need not be expected by the old method of requiring pupils to look up and memorize map questions, nor by asking them to recite verbatim a vast mass of descriptive text. The knowledge that is merely pigeonholed in the memory, and has been worked over by no other faculty, is usually more of a hindrance than a help in practical life. It is the logical and orderly reading of what is revealed by the map, and this tmder the teacher's guidance, the tracing of causes and con- sequences that lie implicitly among those facts — the correla- ting and coordinating of facts and principles — it is all of tins that is necessary to the highest siiccess. Every recitation period should be divided into two parts; the first should be employed in a review of the lesson of the preceding day, — emphasizing it and unifying it with other parts of the general subject, — the second in teaching- a new lesson. This lesson should not be assigned as something to be studied, memorized, and recited, but rather it should be developed somewhat after the investigation or laboratory method. In this process the teacher must be the director and guide — himself the most alert of the learners. If the work has been well done, the pupils will carry away from the classroom an impression so vivid, so inspiring, so fi;ll of profitable suggestion, that all subsequent study of geography will be better for it. They will furnish an imperishable picture of the region studied; and with such a picture in his mind, the pupil will ever thereafter feel an irresistible craving for more knowledge to fill in the details of his picture. In this impulse to acquisition that good lessons furnish, lies their chief value and the best argument for the teacher's personal direction while they are being developed. It must not be inferred that the ordinary textbook on § 5 PEDAGOGICS OF GEOGRAPHY. 119 geography is to be banished from the ehiss work. On the contrary, every pupil should have one. It will be found that a lesson under the supervision of the teacher, in the manner described above, will furnish an impetus that will send each pupil to his textbook with his eyesight and mind clarified to see and iinderstand as never before. He will go there for material to complete his picture of the reality, and at the next lesson he should be required in the review to demon- strate that he has really added to it, and that his additions are important and relevant. While the wall map and the globe are the foundation of geographical teaching, the text- book is their most useful adjunct. The best work requires the .second as well as the first. 99. A Model Jjessoii. — The following lesson is intended to suggest the way in which, by the method of question and answ^er, a lesson from the wall map should be conducted. It is the report of a lesson actually listened to by an intelli- gent observer among the schools of Central Europe. The writer says: Let us suppose that the lesson is on the relief map of Europe. In some previous lesson the pupil has read from the wall map the triangu- lar form of the continental mass of Europe, and has noted its west, east, southwest, and southeast angles. It is to the relief of this con- tinental triangle that his attention is now directed. Teacher. Tell me in what part of continental Europe you find the lowland represented, and in what part the highland. Pupu.. The lowland is in the northeast; the highland is in the soiithwest. T. Look at the map again and tell me whether it is all lowland in the northeast. P. Some small highlands are represented there. T. Is the southwest all highland ? P. There are some small lowlands among the highlands of the southwest. T. State what you have learned from the map. P. Northeast continental Europe is mostly lowland. Southwest continental Europe is mostly highland. T. In what direction must I draw a line to separate the lowland from the highland ? P. From northwest to southeast. 120 PEDAGOGICS OF GEOGRAPHY. § 5 T. Some one may point to the northwest part of the highland. What river's mouth is just above it ? P. The Rhine. T. Some one may point to the southeast part of tlie highland. What river's mouth is just above it ? P. The Danube. T. Between what points, then, may my line dividing the lowland from the highland extend ? P. From the mouth of the river Rhine southeast to the mouth of the river Danube. T. This line is called the mountain diagonal of Europe. You may state how the lowland part of continental Europe is separated from the highland part. P. Lowland continental Europe is separated from highland con- tinental Europe by the r^ountain diagonal. It is a line drawn from the mouth of the Rhine to the mouth of the Danube. Northeast of this line the surface is mostly lowland ; southwest, mostly highland. T. We will now attend to the highland part of continental Europe. In what direction must I draw a line from the northwest end of the mountain diagonal to clear the highland on the west side ? P. Southwest. T. In what direction to reach the southeast end of the mountain diagonal ? P. East. T. What, then, is the form of highland continental Europe, and what are its bounding lines ? P. Highland continental Europe has the form of a triangle ; its boundaries are the mountain diagonal on the northeast side, a line drawn southwest from the mouth of the Rhine, and a line drawn east to the mouth of the Danube. T. Look at the map and tell mc which part of the highland is highest. P. The south. T. Of what does this highest part consist ? P. Mountain chains. T. What name do you give to several nunmtain chains extending in one general direction ? P. A mountain system. T. This mountain system is called the Alj^s. You may state what you have learned about the southern part of the highlands. P. The highest part of the highland of continental Europe is in the south. It consists of many mountain chains, forming the mountain system of the Alps. T. Look at the map and tell me how you see the rest of the highland represented. § 5 PEDAGOGICS OF GEOGRAPHY. 121 P. Broad spaces bounded by mountain chains. T. These broad spaces ai-e plateaus and elevated river basins. How do they compare with the Alps as to height ? P. They are lower. T. In what direction from the Alps do they lie ? P. West, north, and east. T. You told me that there were several small lowlands in different parts of the highland. See whether there are any of these between the Alps and the plateaus and river basins, and to what rivers they belong. P. There is one southwest of the Alps and another in the east. The southwest lowland belongs to the Rhone and the east lowland to the Danube. T. Look at the plateau region north of the central part of the Alps and see whether it is joined to them or separated from them. P. It is joined to the Alps. T. This region of plateaus, elevated river basins, and mountains is called the middle mountain and plateau system of Europe. The word juiddlc has reference to its elevation, which is not so high as the Alps and not so low as some other mountains, etc. of continental Europe that lie outside of this region. You may state what you have learned about this part of the highland. P. A region of plateaus, elevated river basins, and mountains lies west, north, and east of the Alps. It is called the middle mountain and plateau system of Europe. It is separated from the Alps in the west by the valley of the Rhone river, in the east by the valley of the Danube, and is joined to the Alps in their center on the north side. 100, Siiniiiiary of Xiessons. — Before any of these les- sons are undertaken, the teacher should prepare a careful summary of what he proposes to develop. He should do this with studied thoroughness, and should plan also the substance and the order of his questions. There is a pretty general impression among teachers that the superiority of their knowledge above that possessed by pupils is suf- ficient warrant for neglecting preparation for lessons. No worse error could possibly be promulgated. Even teachers of the longest experience and the highest attainments can- not afford to be neglectful of this first duty of a teacher. Stippose the le.sson is to be an exercise in reading the con- tour of Farther India. The following, taken from an article by Director Heiland, of the Weimar Seminary, will show such a summarv of an intended lesson. 122 PEDAGOGICvS OF GEOGRAPHY. § 5 Farther India has the form of a triangle ; its base line is the Tropic of Cancer, between 90° and 110*^ east longitude from Greenwich, or between the Ganges-Brahmaputra delta and the meridian of Hainan island. The vertex is Cape Romania, in 1}° north latitude, on the same meridian as Cape Chelyuskin, the northernmost point of Asia. Base is to height as 3 to 4. Length from north to south is (33^° — 1^°) X 60, or 1,335 geographical miles. Length of base line is (110' — 90") X 55, or 1,100 geographical miles. Direction of west coast is from northwest to southeast, interrupted by the gulf of Martaban. It has thi-ee natural divisions: (1) from Ganges-Brahmaputra delta to the Irawadi; (2) to the angle of Malacca; (3) to Cape Romania. Direc- tion of (1) and (3) west-northwest to south-southeast. Lengths equal. The student will of course understand that this kind of work belongs in later geogTaphical study, bttt it should by all means be found there. An exact mental picture of any cotmtry can be attained in no other way than by some such orderly examination. 101. Ciinse and Effect in Teacliiiig' Geog-rapliy. It has already been stated that there is little of educational value in isolated facts. Indeed, one of the conditions essential to the organization of facts into a unified and coherent science is that these facts shall be related among themselves. Now, there are many bonds of relationship possible among facts, but the strongest of these bonds is that of cause and effect; and of all the various sciences, none is so strongly permeated by this principle as is geography. The play of the forces of nature is all in harmony with the laws of cause and effect, and the activities of men and nations cannot be interpreted or anticipated without constant refer- ence to them. Geography, therefore, .should be the most interesting of all sciences and the one most skilfully taught, and it might be, if teachers would avail themselves of the natural and logical method that the subject itself .suggests. It is in this that the schools of Central Europe are giving an instrtictive lesson on pedagogics to the rest of the educa- tional world. The following description of a lesson in a German school, durino- which the teacher observed the cause-and-cffect § 5 PEDAGOGICS OF GEOGRAPHY. 123 method, will enable the student to understand the impor- tance of this principle: A lesson was listened to in a German school where seventy boys sat together like sardines in a box. The teacher had nothing better than a medium-sized wall map made by himself. His mode of marking elevations was very simple and comprehensive — one that is well worth imitating. With pencil or pen he shaded the map by means of lines crossing one another at various angles. Thus he represented the topography of a country in a remarkably accurate manner, and this easy method enabled his pupils to judge at a glance as to the height of the land. They saw icIiy certain r/'c't-rs tool: such a/ui such a course and no other; ix'hy certain countries locre cold, others tvarni. They saw why a river was navigable or not according to the abruptness of the slope; 7uhy certain rivers, flowing from great heights, had a straighter course than rivers that had a more gradual slope or mean- dered through a plain ; \ohy certain lands are blessed uith mild cli- mates when sheltered on the north side by high and steep mountain ranges; why others had a rough climate when exposed on .their northern side. The teacher was well inft)rraed, and he adapted his information to the capacity of his pupils. One part of his lesson, outlined in the following summary, was especially well received : " The Erz-Gebirge (Ore Mountains) were once full of silver mines. At the beginning of the sixteenth century, in the time of Martin Luther, these mines drew a great number of people to vSaxony, and particularly to that range of mountains. When the mines ceased to yield, the population, not being so fluctuating as it is now, was obliged to seize upon other modes of occupation. The slopes of the mountains, being well provided with various kinds of woods, ofi:ered material for a variety of woodworking industries. The slopes being steep, the mountain brooks were turbulent and gave an opportunity to build mills, which were first used for various purposes. Lately, when the textile industry grew, this water-power was used to serve that industry. The woods soon disappeared from the Erz mountains — they were literally used up. So the people had to resort to manufacturing pur- suits almost entirely — agriculture being impossible. Today the popu- lation of the kingdom of Saxony is the densest in Germany, and, aside from that in Belgium, the densest in Europe." It was cause and effect constantl}', and the attention and responsiveness of the boys were truly deliohtful. 102. The Art of Questioning-. — In treating^ of the Catechetical Method in Pedagogics of History, considerable 124 PEDAGOGICS OF GEOGRAPHY. § 5 stress was placed upon its importance as an element of suc- cess in teaching. But to a teacher, the value of skill in this art is so great that it is deemed best to resume the subject in this Paper and present it more fully. A teacher may be scholarl}', have an admirable faculty for illustrating what he would teach, and be gifted with that wonderful magnetic power of securing and holding the attention, but if he is weak in the matter of asking connected, relevant, and sug- gestive questions, he will be unable to obtain the best results. It is a distinctly analytical process, for there must lie in the mind of the questioner a sharp logical outline of the entire subject. Every part must be properly coordi- nated with every other part, and the cjuestioner must be able to make every question tell in just the place and order required. Questioning is called an art on account of its practical use- fulness, but it is at the same time a science, for in its best development its methods of procedure are regulated by a code of principles and laws that are purely scientific. These laws and principles have not, so far as the writer knows, been reduced to scientific form and order. If they were, doubtless they would be found of extreme value to stu- dents of many professions such as law, medicine, and teach- ing. It is not proposed to attempt here anything like a scientific treatment of the subject, but instead, to give such suggestions and illustrations as may seem likely to be of use to the student of pedagogics. 103. Classiflcatioii of Questions. — With reference to their purpose, questions may be divided into three classes: 1. Preliminary or Experimental Questions. — By means of questions the teacher ascertains the condition of the pupil's mind with respect to the subject under considera- tion. This is as necessary as diagnosis is in medical prac- tice, and in many respects resembles it. The pupil may know a subject thoroughly; he may know it partially, but not as a connected whole ; or he may know nothing whatever about it: which of these conditions of mind is the fact is § 5 PEDAGOGICS OF GEOGRAPHY. l^o quickly and certainly ascertained by a few preliminary questions, 2. TJic Didactic, or Iiistrnctioiial Question. — This form of question is intended to lead the pupil on step by step from what he knows of a subject to what he must know in order to fully imderstand the subject. This is in fact a method by which a pupil becomes in a manner his own instructor. He is compelled to consider carefully every step as he is led along by his questioner; and, if he would follow, his inter- est and attention must not flag even for a moment. The teacher must himself know his subject thoroughly, and he must, besides, understand the exact condition of the pupil's mind; otherwise, we shall have an instance of the blind leading the blind. 3. The Question for Testing, or Examination. — When a subject has been carefully and thoroughly taught, it is, cus- tomary in all schools to require that the pupils shall show that they arc actually in possession of a satisfactory knowl- edge of it. This is done by examination questions covering the matter that has been studied. Very frequently it hap- pens that relative rank and subsequent honors are deter- mined and assigned as a result of these examinations. To the pupil, therefore, the examination question is a very seri- ous matter, although its instructional value is very slight indeed. 104. Remarks on the Foregoing Classiflcation. Of these three varieties of questions, the first is very impor- tant indeed. It would be a waste of effort and often perilous for a physician to administer medicine without finding out the exact condition of his patient; but such a proceeding would be exactly paralleled by a teacher that should neglect to ascertain the deficiencies and weaknesses of his pupils before beginning their instruction. To ascertain this, it is obvious that thorough knowledge and a high degree of skill in the teacher are necessary. But it is especially in the didactic questioning that the opportunity occurs for the greatest efficiency in the art of 12r> PEDAGOGICS OF GEOGRAPHY. § 5 asking' questions. It is an art, too, that cannot be acquired by a study of the rules and principles of dialogue. It is con- ditioned on a number of things : 1. As has already been stated, the questioner must have a thorough acquaintance with the matter to be taught. 2. He must know in just what respect the pupil's knowl- edge is defective. 8. He must be able to keep steadily before his own mind the exact matter he wishes to teach. 4. He must be suiSciently expert in the nse of language to formulate questions that will convey to the pupil's mind, clearly and without ambiguity, the exact meaning intended. 0. He must be able to formulate series of questions that are the best for his purpose in matter and order. In short, the teacher that would be successful in the art of didactic questioning, must be a thorough scholar with a very clear head, a strong sense of logical order, and an admirable command of language. The third variety of question — that for examination or testing — is a comparatively simple matter. For examina- tion questions arc usually written ; and, being miscellaneous, they require no logical arrangement, nor is any special scholarship needed in their construction. 105. A Reminiscence. — A good many years ago it was among the duties of the writer to be the teacher of the gradviation class in the high school of one of our large east- ern cities. One of the subjects taught was geometry. It happened that before the pupils reached their graduating year they passed through the hands of a succession of most excellent teachers, and they were, in consequence, admira- bly prepared for the severe work of their last school year. No task could be more delightful than to teach such pupils. They were wonderfully eager to learn, and their mental alertness was remarkable. They, however, were not the only learners; their teacher also learned many things. He learned, for example, the extreme skill required in didactic questioning. That it is incomparably better to question § 5 PEDAGOGICvS OF GEOGRAPHY. 127 than to explain, as teachers do when they say, "Pay atten- tion now, and I will explain this matter"; this was another of the lessons he learned. And again, he found out that there is admirable discipline for the pupil if he himself is required, by asking the questions, to lead his fellow that "sees but dimly." "You have heard John's recitation," the teacher would say; "it shows that he does not quite under- stand why A B C is equal to E F G. Who will imdertake to ask John the series of questions that will make clear to him the missing links in his argument ? " The hands would go up all over the room, and some one would be designated to undertake the task, with the understanding that the rest of the class would criticize the questioner when he was done. The excitement and interest were indescribable. Many of these questioners became extremely skilful by practice ; and, with- out doubt, the training was as valuable as that derived from the study of g-eometry itself — perhaps more so. Another great advantage that came from delegating this work to the pupils was in the fact that the teacher was required to say but little; and this, believe me, is always a great gain in the recitation room. 106. Socrates as a Teaclier. — Socrates has, even yet, after nearly two thousand four hundred years, the reputation of having been the greatest of the world's teachers. He had no great school, like the Lyceum of Aristotle or the Academy of Plato. He taught more as a mere incident of his every- day life than as a business or profession. His pupils paid him nothing except in affectionate devotion. Where he happened to be he taught; and his pupils, who followed him wherever he went, listened to his discussions. His charm as a teacher was purely intellectual, not personal, for physically he was not an Apollo. On the contrary, he was reputed to be the ugliest man in Greece. At the time of Socrates, Athens was the intellectual center of the world ; and it was, moreover, the home of many men of wealth. Attracted by the Athenian love of learning and T)y the large fees that were readily paid by rich men for the 128 PEDAGOGICS OF GEOGRAPHY. § 5 education of their sons, many men of great reputation for skill in teaching' logic, disputation, politics, and other matters, came to Athens and set up schools. Socrates delighted to seek out these men of reputed wisdom and question them about the matters they professed to under- stand. The interview was invariably disastrous to the sophist that met him in dialectics. He had no code of doctrine or opinion to promulgate ; he professed to be only an inquirer — a seeker after truth. He insisted that the greatest impediment to real knowledge is fancied or unreal knowledge, and that the first duty of the teacher is to pre- pare the mind for the reception of knowledge and to convince the pupil of his lack of it ; to awaken him to a keen desire for learning, and to stimulate an earnest search for it. Perhaps the best way of showing his method is to translate one or two portions of Socratic dialogue from the writings of Plato, who was the gTcatest pupil of the old philosopher. 107. The Method of Socrates. — The first specimen of dialogue given here is between Socrates and one of his disciples called Meno. This young man was of the kind having an exaggerated notion of his own wisdom and learning; but he had been probed by his master imtil he began to have an imcomfortable sense that he was less wise than he had supposed himself to be. Smarting under this, he says, ''Why, Socrates, you remind me of that broad fish called the torpedo, which causes a numbness in the person that touches it. For, in truth, I seem benumbed both in mind and mouth, and know not what to reply to you ; and yet, I have often spoken on this subject with great fluency and success. " Socrates does not reply directly to Meno, but calls a young slave boy, an attendant of Meno, and questions him. Draw- ing a square on the ground, he says, " My boy, do yoii know what figure this is ? " "Oh, yes; it is a square." "What do you notice about its lines ? " "That all four of them are equal." § 5 PEDAGOGICvS OF GEOGRAPHY. 120 "Could there be another spaee like this, only larger or smaller ? " "Certainly." "Suppose the side of the square were two feet long" instead of one foot; how many square feet would there be in the figure ? " "Twice two." " How many is that ? " "Four." " Would it be possible to make another square twice as large as this ? " "Yes." " How many square feet would it contain ? " " Eight." "Then how long will the sides of such a square be ? " " It is plain, Socrates, that it will be twice the length, or four feet. " "You see, Meno, that I teach this boy nothing, I only question him. And he thinks that he knows the right answer to my c^uestion; but does he know ? " " Certainly not. " " Let us return to him again." " My boy, you say that on a line four feet long a square, having a space of eight square feet, may be made; is it so ? " "Yes, Socrates, I think so. " " Let us try then. Is this the line you mean ? " " Certainly." (He completes the square.) " How large is the square now ? " " Why, it is four times as large." " How many square feet does it contain ? " " vSixteen." " How many ought double the square to contain ? " "Eight." After some questioning, the boy suggested that the side should be three feet long. " If, then, it should be three feet long, we should add the half of the first line to its own length, should we not ? " "Yes." (Socrates draws the square.) 130 PEDAGOGICvS OF GEOGRAPHY. § 5 " Now, if our first square contained twice two square feet and our second four times four, how many does this contain ? " "Three times three, or nine, Socrates." " But how many should it contain ? " " Only eight, or one less than nine." "Well, now, since this is not the line on which to draw our square, tell me how long it should be." "Indeed, Socrates, I do not know." "Now, Meno, observe what has happened to this boy: you see that he did not know at first, neither does he now know. But he then answered boldly because he fancied that he knew ; now he is quite at a loss, and though still as igno- rant as before, he does not think he knows." "What you say is quite true, Socrate.s. " " Is he not now in a better state with respect to the mat- ter ? " " Most assuredly he is." " In causing him to be thus at a loss, and benumbing him like a torpedo, have we done him any harm ? " " None at all." "We have at least made some progress toward having him know his true position; for now, finding that he knows nothing, he is more likely to inquire and search for himself. " This dialogue illustrates one of the best methods of arous- ing the curiosity that stimulates self-effort and investigation. Before giving a lesson or entering upon a difficult subject, it is often a good plan to cause the pupil to realize his ignorance and to feel the need of your instruction by asking him a series of searching judicious questions. 108, Anotlier Specimen of Soeratic Dialogue. The following is a translation from the " First Alcibiades " of Plato. It gives an imaginary conversation between Socrates and his favorite pupil Alcibiades. Socrates. Hold, now, with whom do you at present con- verse ? Is it not "with me ? Alcibiades. Yes. Socr. And I also with you ? Ale. Yes. Socr. It is vSocrates then that speaks ? Ale. Assuredly. § 5 PEDAGOGICvS OF GEOGRAPHY. 131 Soc!'. And Alcibiadcs that listens ? ^l/c. Yes. Socr. Is it not with language that Socrates speaks ? Ale. What now ? of course. Socr. To converse and to .use language, are not these then the same ? A/c. The very same. Socr. But he that uses a thing, and the thing used — are these not different ? .lie. What do you mean ? Socr. A currier, — does he not use a cutting knife and other instruments? Ale. Yes. Socr. And the man that uses the cutting- knife, — is he different from the instrument he uses ? A/c. Most certainly. Socr. In like manner, the lyrist, — is he not different from the lyre he plays on ? A/c. Undoubtedly. Socr. This, then, was what I asked you just now, — does not he that uses a thing seem to you always different from the thing used ? A/c. Very different. Socr. But the currier, — does he cut with his instruments alone, or also with his hands ? A/c. Also with his hands. Socr. He then uses his hands ? A/c. Yes. Socr. And in his work he i;scs also h!s eyes ? A/c. Yes. Socr. We are agreed, however, that he that uses a thing, and the thing used, are different ? A/c. We are. Socr. The currier and the lyrist are, therefore, different from the hands and the eyes with which they work ? A/c. vSo it seems. Socr. Now, then, does not a man use his whole body ? A/c. Unquestionably. Socr. But we are agreed that the person using a thing is different from the thing used ? A/c. Yes. Socr. A man is, therefore, different from his body .'' A/c. So I think. Socr. What, then, is the man ? A/c. I cannot say. Socr. You can at least say that the man is that which uses the body? A/c. True. Socr. Now, does anything use the body but the mind ? A/c. Nothing. Socr. The mind is, therefore, the man? A/c. The mind alone. 132 PEDAGOGICS OF GEOGRAPHY, BOOKS OF REFEREKCE. 109. Keed foi* Books of Reference. — No teacher can be highly successful in teaching geography, or, indeed, any other subject, without having a good supply of the latest and best books of reference. Books are the tools with which the teacher works, and are just as necessary to him as the appro- priate tools are to the carpenter or the machinist. If his work happens to be in the neighborhood of a public library, he may perhaps borrow all the books he wants, but it is vastly better to own them, just as it is better for the industrial worker to own the tools he uses. These necessary books need not be purchased all at once, but the collection should be systematically increased as means and opportunity offer, and every purchase should be made with extreme care. Of course, no teacher can afford to buy everything that bears upon the subjects he teaches, but with a little finesse he can establish a small school library that may be gradually enlarged at the expense of the school board or by means of money received as the result of any of the various legitimate enter- prises commonly resorted to for such objects. His success will be measured by his ability to invest the otherwise dry matter of the textbook with human interest and reality, and to do this he must have a wider knowledge of his subject than he can possibly get from the book studied by the pupils. 1 10. Reiiiai'ks on tlie rolloAvin^ Tjist. — In the list that follows no attempt is made to include everything of value to the teacher of geography; for a complete list would fill a large volume. Only a limited number of works known to be excellent are given. For more extensive lists the student is referred to the catalogues of the various publishers and to the special works on bibliography. One of the best of the latter publications is Monroe's " Bibliography of Education," edited by our Commissioner of Education, Dr. William T. Harris, and published by D. Appleton & Company, New York Citv. §5 PEDAGOGICS OF GEOGRAPHY. 133 Some of the books in the list are mere stories of imaginary travel and adventure, but they are all valuable, since in their geography and in the manners and customs of the peoples described they are all pretty true to the facts. vSuch books are of great value in developing the "geographical instinct," and they should find a place in every school library. 111. Books of Travel and Adventure. — Children of the Cold. Frederick Schwatka. Casscll &■ Co. A story of the Eskimos met by the author in his Arctic travels. Seven Llltle Sisters. Jane Andrews. Lcc & Shcpard. An admirable preparation for the study of geography. Seven Little vSisters Prove their Sisterhood. Andrews. Lcc & Shcpard. A sequel to the above. Little People of Asia. Olive Thorne Miller. E. P. Duttoii &• Co. Lost in the Jungle. 1 ^ •^ _ j I)u Lhaillu. Harper ^r Jh-otJicrs. vStories of 'i'HE Gorilla Couni Wild Life under the Equator. Great African Travelers. Kingston and Low. Icdicc &" So//s. Roiit- Nclson & So/is. Hale. Roberts Brothers. Heroes of the Desert. Stories of Discoverv. Stories of Adventure. Stories of the Sea. J Boy Travelers in Japan and China. Boy Travelers in vSiam and Java. Boy Travelers in Ceylon and India. Boy Travelers in Egypt and the Holy Land. Boy Travelers through Africa. Boy Travelers in the Russian Empire. Boy Travelers on the Congo. Boy Travelers in Australasia. Boy Travelers in vSouth America. Java, the Pearl of the East. Higginson. Mifflin & Co. Full of information. Knox. Harper & Brothers. These books are richly illustrated and have neces- sary maps. The series is a very valuable one. IlouisJiton. Knox. Harper & Brotlicrs. 134: PEDAGOGICS OF GEOGRAPHY. § 5 NiMROD IN THE North. vSchwatka. Casscll & Co. Hunt- ing and fishing" adventures in the polar regions. Wild Men and Wild Beasts. Gumming. Charles Scrib- iwr's Sons. The Young Nimrods in North America. The Young Nimrods Around the World. The Voyage OF the Vivian to the North Pole. Mutineers of the Bounty. Belcher. Harper & Brothers. In the Wilderness. Charles Dudley Warner. HoiigJiton, Mifflin & Co. Round my House. Hamerton. Roberts Brothers. Along the Florida Reef, Holder. P. Appletoti & Co. Aunt Martha's Corner Cupboard. Kirby. Each and All. Home Studies in Nature. Treat. Harpers. Works of John Burroughs. Two Years Before the Mast. Dana. Mexico. Blake and Sullivan. Lee & Shepard. Captain Bonneville. Famous Travels and Travelers. The Great Navigators of the Eighteenth Century. The- Great Explorers of the Nineteenth Century. Verne. Scribners. 113, Miscellaneous Books on Travel and Geog- raphy. — Comparative Geography. ) „. , . r^ i ^ ^ ^ c Ritter. American hook Co. Geographical vStudies. ) Earth and Man. Guyot. Scribners. The Earth and its Inhabitants. E. Reclus. Apple- ton. (U vols.) Bird's-Eye View of the World. O. Reclus. Ticknor. Brown's Countries of the World. Brown's Peoples of the World. Physiography. Huxley. Appleton. ■ The Earth. Reclus. Harpers. § 5 PEDAGOGICS OF GEOGRAPHY. 135 The Realm of Nature. Mill. Volcanoes. A volume among the "International Scien- tific Series." Applet o)i. Reports of Challenger Expeimtiox. Bird's-Eve View of Central and South America. Bates. Humboldt's Travels. Peru. vSqiiier. Sixteen Years in Chili and Peru. vSutclilTe. Journey in Brazil. Agassiz. Adventures in Trinidad and up the Orinoco. Kingston. On the Banks of the Amazon. Livingston. Between the Amazon and the Andes. Mulhall. Up the i^MAZON AND JHE Madeira Rivers. Mathcws. What Darwin vSaw. Stories of the Nations. Putuam. Sinai and Palestine. Dean vStanley. Spain and the Spaniards. ) ^^ . . . „ -De Amicio. Holland and its People. ) France. Roberts. Greece. Lewis. Siberia in Europe. Seebohm. Iceland. Taylor. Russia. Morfill. The Land of the Midnight Sun. Du Chaillu. The Florence Stories. Abbott. Scotland and the Scotch. The Statesman's Year Book. Keltic. Published annually. Contains much valuable information concerning all the nations of the world. Historical Geography of Europe. Freeman. The Middle Kingdom (China). Williams. The Land of the White Elephant (Eastern Asia). Vincent. Japan. Reiss. A very complete description of Japan. Through Algeria. Crawford. Upper Egypt. Klunzinger. The Nile and Tributaries of Abyssinia. Baker. Life in the Desert. Du Couret. 13G PEDAGOGICvS OF GEOGRAPHY. § 5 African Explorations. Livingstone. Through the Dark Continent. Stanley. Land Journey through Siberia. Travels and Discoveries in Northern and Central Africa. Denham. Among the Huts in Egypt. IsMAiLiA. Baker. How I Found Livingstone. Stanley. The Albert Nyanza. Baker. The Lake Regions of Central Africa. Geddie. Thirty Thousand Miles' Travel in Australia. Vincent. The Country of Dwarfs. ) ^^^ ^j^^.^^^^ My Apingi Kingdom. ) The Congo. Stanley. Voyage of the Vega. Nordenskjold. Arctic Voyages. Intellectual Development of Europe. Draper. Coral and Coral Islands. Dana. The Races of Men and thkir Geographical Distribu- tion. Peschel. The Vegetable World. Figuier. Narrative of Four Voyages to the Antarctic Ocean. B. Morell. Notes of a Naturalist on the Challenger. H. N. Mosely. Voyage of the Beagle Around the World. Charles Darwin. The First Crossing of Greenland. Nansen. Three Years of Arctic Service. A. W. Greely. Structure and Distribution of Coral Reefs. The Glaciers of the Alps. John Tyndall. The Naturalist on the Amazon River. H. W. Bates. New Zealand: its Physical Geography, Geology, and Natural History. Von Hochstetter, translated by E. Sauter. Personal Narrative of Travels in South America. Von Humboldt. New Lands within the Arctic Circle. J. Payer. PEDAGOGICS OF HISTORY. i:nti?oductio:n^. GENERAI. REMARKS. 1. Forms of Wi-itteix Th<)iij>iit. — Extended composi- tion has been divided into four kinds: Dcsr)'iptioii, Narra- tioii, lixpositioii, Argument. Of course, there are many other varieties, but these four are the only forms that are usually found in textbooks on history. To understand the reason why it is so difficult to find a good working manual on the subject of history and what qualities should charac- terize such a manual, it will be necessary to consider briefly these four kinds of composition, ^. Description. — Description may be of posons or of things. A description of anything should present an orderly account of the qualities that belong to the object described. If a description be in terms that are commonly used, it is ordinary or popular ; if it introduces the technical terms employed in some particular science, it is a .yr/tv/Z/^r descrip- tion. 3. Narrative. — Narrative bears the same relation to acts and ci'cnts that description does to persons and things. A narrative, as well as a description, may be either minute 2 PEDAGOGICS OF HISTORY. . § 6 or cursory — it may descend to the smallest particulars, or it may give only the most conspicuous and striking facts in a series of happenings. The items that make up a narrative should follow, first, the order of tunc. It will appear, later, that in this require- ment consists the principal difficulty in historical writing. In the nature of things, events that together make up a com- plex whole succeed one another in time, and an account of them is more vivid and more easily remembered if, in rela- ting them, the orderof their occurrence is observed. Indeed, the most striking excellence in a sentence, a paragraph, or a sustained account of any matter, is this observance of chronological order in the arrangement of its elements. In this respect, more perhaps than in any other, consists the difference between the work of our best writers and that of inferior waiters. Secondly, besides the order of time, a narrative should observe the order of logical sequence or relative iiiiportaiice. In every narrative will be found many passages in which the element of time does not enter. Thus, the explanation of motives, of the purpose, results, or consequences of acts or events, of surrounding or accompanying circumstances — these and many other matters are of this nature. An excel- lent illustration of what is meant by logical sequence in a narrative, is found in the paragraphs introductory to the " Chimes," by Charles Dickens. Edgar A. Poe's prose works furnish some of the best examples of logical arrangement of particulars that can be found in literature. Let the student try the experiment of rearranging the sentences or the para- graphs of that author, and he will feel the force of what is here stated. 4. Exposition.— Exposition is neither more nor less than explanation. Like all explanation, it should be clear ; it should contain nothing intended to arou.se emotion, but should be addressed to the intellect alone. As is the case with narrative and description, it should, in the arrange- ment of its matter, observe the order of time, if time is an § 6 PEDAGOGICS OF HISTORY. 3 clement, and, where the element of time does not enter, of logieal sequence. A definition is the simplest form of exposition. An expla- nation of an example in mathematics, an account of the action of a drug-, or an explanation of a chemical reaction are examples of exposition. In writing a history of the United States, the author would find it necessary to suspend his narrative in order to explain our relations with England, the mutual feeling between the countries, and many other matters neither narrative nor descriptive. 5. Arg'iiiiieiit. — It is no ])art of the work of a hist(.)rian to introduce argument into his writing. He should content himself with the presentation of facts and events; and, accordingly, it is very unusual to find in history anything in the nature of distinctly expressed argument. Occasionally, indeed, we find exposition colored more or less by attempts to convince the reader of the correctness of some view held by the author. Everything of this kind, however, is very much out of place in a history. Other tilings being equal, the excellence of a work on history increases with its impartiality — the absence of any expression of the author's opinion — the absence of argument and of matter intended to appeal to the emotions of the reader. 6. Histoi'.v Consists of the First Thi*ee of These Forms of Coiin>ositioii. — That history should consist almost, if not entirely, of description, )iarrativc, and expo- sition in varying proportions will be evident to the stiident. Anything else should be in the nature of quotation for pur- poses of illustration. It must not be assumed that these three varieties of composition are always, or even often, found separate. They are combined in all proportions, and it is often difficult to determine which predominates in a given paragraph, section, or chapter. In order to render intelligible the narrative of some event, say a battle, a description of the battle field, its surround- ings, and the roads leading to it; or an exposition of some principle of military science, or of the advantages of some 4 PEDAGOGICS OF HISTORY. § G particular formation of the attacked or the attacking forces; or some explanation of how the armies came to meet at that particular time and place — any one or all of these may be necessary. It is clear, therefore, that written history is made up of description^ cxpositio)i^ and explanation in varying propor- tions, and that in all these, chronological order should be followed when time is an element. When considerations of time do not dominate the arrangement of historical matter, as is generally the case in explanation and exposition, then the laws of cause and effect — of logical sequence- — should determine the succession of parts. Historical arrangement in the nature of climax is peculiarly effective. Gibbon, Macaulay, and many others among the writers of history have realized in this fact one of the principal charms of his- torical composition. The writer may be permitted to observe, at this point, that interest is added to a lesson in history, and the opera- tion of the law of association is aided, by having the pupils examine the text for the purpose of determining to which class of composition the several paragraphs belong. This is not to divert attention from the subject matter considered as history, but to illuminate, and add to the interest of, the text. '7. l^nilineal and Miiltilineal AV^riting. — Professor Bain, in speaking of the different kinds of composition, emplo3'S the words iinilincal, lulineal, and vinltilineal. These words contain the Latin word liiunn, "flax," "thread," and very happily characterize the varieties of description, explana- tion, exposition, and argument. If one were required to describe any simple object, or to write a narrative of the doings of any person during an entire period, either of these would be an example of unilineal com- position. The subject is not complicated by any side issues. There are no threads on either side of the main thread of the narrative or the description that are necessary to the com- pleteness. No special literary art or skill is requisite in this §G PEDAG()(;iCS OF HISTORY. 5 kind of composition — only the ability to tell a •'plain nnvar- nished tale." History, however, is not uiiiliiical, but multilincal. Numer- ous threads must be taken up, carried into, and incorpo- rated with, the principal thread; and this must be done in such manner as to g'ive unity to the whole, and preserve its interest and intelligibility. This, it is easy to see, is a very difficult task. The sequence of events with respect to time cannot be observed, for, after tracing the main thread of the narrative through a certain period, the writer is compelled to go back again and again, and follow the minor threads to the point where he broke off. An unavoidable consequence is that the reader is confused by the multitude of extrinsic incidents making up the complete story, the effect upon his inind is weakened, and he is quickly wearied. The multilineal treatment may be likened to a river with its tributaries, or to a tree with its innumerable branches, branchlets, and twigs. Every one has noticed the fact that a tree with an axial trunk, like the pine or the poplar, is much more pleasing to the eye than one with a solvent trunk, and that, when a tree is covered with foliage, hiding its branches and making it a unit to the eye, its beauty as a part of the landscape is much enhanced. It is a general principle, indeed, that simplicity and symmetry are two elements indispensable to the beautiful. This is in accordance with the well known Theory of Pleasure and Pain, that a sense of baffled effort on the part of the mind to comprehend is pain- ful, and that the reverse is pleasurable. Order, simplicity, logical sequence, and symmetry afford us pleasure; while complexity, involvement, and discord hinder and perplex the action of the mind and create an effect that is more or less displeasing or painful. The fact that historical works are necessarily vniltilincal constitutes the chief obstacle to unity, and explains why the world has furnished so few great historians. Some one has remarked that a satisfactory history of the Jesuits has never been written, and perhaps never can be written, the reason being that the Order has been involved and active in the (; PEDAGOGICvS OF HISTORY. § G politics, and has intiuenccd the history, of every country in Europe. A history of this organization would therefore be painfully multilineal. 8. Unsatisfactory Textbooks on History. — From the considerations stated above, it is easily seen that to write an interesting textbook on history is a difficult matter, and it is, in fact, a task that has rarely been accomplished. Many a work of fiction, w^hile vividly conceived and ably written, has failed on account of the introduction of too many characters. When Henry Ward Beecher was writing his novel "Nor- wood " as a serial for the New York Ledger, some one asked him how he meant to dispose of the many people that he had brought into the work. He is said to have replied that he would have them killed in a railroad accident. The novel was wonderfully well written, but no one hears of it now, and this is chiefly owing to its highly multilineal character. How different is the case with the story of Robinson Crusoe. Perhaps no .single fact has contributed so much to make Defoe's story an immortal classic as its wiilincality. The attention is constantly centered on the hero, and even when Friday appears on the scene, there is still but one thread in the narrative. The newcomer falls into the same relation in the narrative as the goats and the parrot sustain to Crusoe. Everything is subordinated to the movements, the hopes, the fears, and the plans of Crusoe. Bunyan's " Pilgrim's Prog- ress " loses much of its interest when the attention of the reader has to be divided between Christian and his wife. The story ceases to be unilineal and becomes biliiieal. The rare art of weaving into a single fabric, elements that seem unrelated and incongruous, must characterize the writer of a good textbook on history. As a consequence of the difficulties mentioned above, our textbooks on history lack unity and interest, and afford but little help to the pupil or the teacher. It follows, of course, that— 9. Children Dislike the Study of History.— It is a fact well known among educators that students of history § 6 PEDAGOGICS OF HISTORY. 7 rarely like the subject. They often delight in the study of grammar, of geography, of mathematics, of language, or of science, but, generally, their feeling about the subject of history is, "I hate it." Occasionally, but not often, a class is found of which the contrary is true. This suggests the question of zvJiy. Is there indeed something in the subject itself that should cause it to be, both to teacher and pupil, a source of weariness and disgust ? We think not. Certainly interest and pleasure ought to be found in the story of what men and nations have done and suffered, of how the slow march of progress has been accomplished, and of what the world's great activities have been. Without hesi- tation, one might assume that ncj subject of study could be of greater human interest, or furnish a more effect- ive stimulus to hopes of high endeavor. Rut, as taught in our schools, history fails, with some rare exceptions, either to inspire the ambition of its students, or even to interest them. 10. A General Principle in Teacliinsf. — As has been remarked, we occasionally find a teacher able to arouse in a class the greatest interest and enthusiasm in the study of history. Another teacher, after greater effort, finds the sub- ject wearisome to himself and hateful to his pupils. The same thing happens with other subjects. The writer has seen entire classes of students extraordinarily interested in geometry — so much so, indeed, that they were disposed to neglect every other study — and he has known the opposite condition of things. Such facts have led educators to the recognition of the principle — Any subject that is 7.'r// taught is interesting to the student. It follows, therefore, that when pupils dislike an}' given study, the teacher is responsible. It is not much in extenua- tion to urge that textbooks are faulty, for teachers of real ability rely little upon them. Tliey themselves are the text- books — living textbooks, instinct with enthusiasm and inter- est — a hundredfold more instructive than books supplied by 8 PEDAGOGICvS OF HISTORY. § (j the publishers. In fact, our best teachers are, in many sub- jects, more hindered than helped by textbooks. It is the contact of mind with mind that is in the best sense effective — not the contact of mind with "cold type." 11. Histoi*y Difflciilt to Teaeli Well. — It is not easy to achieve success in teaching any subject, and this is espe- cially true of the history of the United vStates. Apart from want of skill and experience in the teacher, there are several other causes that contribute to failure. The principal of these are the want of unity in the subject itself, arising from its multilineal character, and the faultiness in textbooks. As has already been stated, for many hundreds of years it has been thought by writers of history that "the king is every- thing and the people are of no account." Hence, during all this time, history has been a record only of battles and the movements of armies, the intrigues of courts, and the rise and fall of kings. The social and political, the commercial and industrial history of the nations ruled by these kings, the interplay of forces affecting the general weal, and the progress and effect of science and invention, are regarded as of no importance. Our histories have told us nothing of the national life at large — its busy activities, its changing opin- ions, with their causes and results; nothing of the nation's industrial and commercial developments, and the means by which they were eff'ected ; nothing of tlie ethical forces operating to create national epochs; only the story of its generals, and the wars in which the}^ figured, of the triumphs and failures of its politicians and its rulers that come and go. The matters relating to the daily life and activities of a nation make up the soul of history, so to speak; but what we reall}^ find in our textbooks is only the body — the mere skeleton of history. The true logic — the correct interpreta- tion — of human happenings is discoverable only from these omitted matters. And, hence, the teacher's opportunity to interest and to instruct truly and rightly is lost, unless he has informed himself by seeking for the whole truth where alone § PEDAGOGICS OF HISTORY. 9 it may be found — in the records of the growth and progress of the nation itself. 13. The Purpose in the Study of History. — In the "study of any subject, there is, or should be, some definite advantage in view. Some gain in discipline of mind or of body, or some practical usefulness, or both, should be clearly proposed as the result of the study; otherwise history should be neglected. In general terms, every subject that we study should aid us in living more completely — physically, mentally, morally, socially, esthetically. When rightly taught, apart from its value for purposes of mental discipline, history primarily enables a man better to understand his duties as a citizen. It instructs him in the causes that have led to the progress and the decadence of nations, and in the best means of assuring the one and of avoiding the other. Not in this respect alone is history of value. It contributes to man's efficiency in every walk of life by extending his horizon, confirming his mental grasp, and liberalizing his opinions. To know the consequences of individual and national action, to be able with greater certainty to infer the laws that govern success and failure among men and nations, to gain the inspiration and stimulus that come from knowing the story of human achievement and progress — these and many more are the ends we should have in the stud)^ of history. The highest patriotism requires that this subject should be retained in the courses of study of all our schools, public and private. More especially is it important for a student to have a thorough knowledge of the history of his own country — nothing so develops and strengthens his sentiment of patri- otism, and makes him willing to fight, and if need be, die, for national liberty and integrity; nothing aids so much to make him not merely a good citizen, ready to obey the laws and to discharge in fullest measure his obligations to the State, but • also to make him understand the nature of those laws, and of his political duties and obligations. Surely, then, it is a most important subject, and is worthy 10 PEDAGOGICvS OF HLSTORY. § 6 of the teacher's highest ambition to guide his pupils wisely and skilfully in its acquirement. 13. The Teaclier Must KnoAV His Subject Tlior- ouglily. — As has been stated elsewhere, if a teacher is to be successful in teaching any subject, he must not only be skil- ful and resourceful in his profession, but he must be perfectly familiar with that subject, both in itself and also in its rela- tions and applications. He should know it so well that no textbook need be in his hand during a recitation. It is not meant by this that he should have committed the lesson to memory so as to know exactly when and to what extent a pupil reciting has departed from the language of the book. The teacher that does this will inevitably bring his class to hate the subject, whether it be history or some other study. The teacher should have in his mind an outline of the topics of the textbook, if one is used by the pupils, and he should be able, besides, to lead the pupil to incorporate the lesson with the whole of which it is, or should be, a part. In other words, history should be taught in such a manner as will exemplify not only logical, but also chronological sequence. Each event is at first an effect or a result of some cause, and later becomes itself a cause. There should be no broken links in the chain of events that make up history — no broken threads shoiild interrupt the operation of the law of associa- tion. Without this law, history becomes only a series of unrelated, isolated incidents. For a teacher to gain this broader view — this knowledge of the philosophy and the logic of history — time, extensive read- ing, reflection, and a keen sense of logical connection are required. He must be willing to devote his best powers to the subject. But no one can teach with success the history of any country if he knows that alone. He miist know the history of other countries. A perfect knowledge of the English language implies a large measure of familiarity with all langiiages, for they are all more or less related to it and to one another. In like manner, the history of each nation of g PEDAGOGICvS OF HLSTORY. 11 the world has been more or less influenced and modified by each other nation. The history of the Roman Empire, for example, cannot be adequately told unless there is related, at the same time, a portion, at least, of the story of all the peoples that came under her domination, and by whom her history was modified. It follows, therefore, that the teacher of history, if he wishes to be successful, must read histoiy extensively. The more comprehensive his reading- the wider will his views become, and the more will they gain in unity. This leads naturally to the question of the teacher's histor- ical reading. 14, .How a Teaelier Should Regulate His Reading;. There is not more than one reader in a score that wisely utilizes his time. This arises from several causes. Chief among these is the fact that only a very small percentage of the works on any subject are really valuable or entirely reliable. Many of the works on history are in large measure fiction, or they are mere garbled compilations of the writings of some other author. The teacher, therefore, that would make the greatest possible progress in informing himself on any subject, should seek the advice of some competent authority as to the books to be read, and the order in which they should be taken up. In the case of history, this order should begin with one or more reliable general compendiums that shall enable him to fix in his mind the principal land- marks of the subject and their relations as parts of a whole. When this has been well done, he is prepared to fill in, more or less completely, the details. To do this, he must " read ill a straight line.'" The reason for this is apparent. If the several steps in an argument, say an algebraic or a geomet- rical demonstration, be disarranged, the force and unity of the whole are destroyed. So, in reading history. The maxi- mum result for the reader is produced only when his order of reading accords with the sequence in logical relation, or in time, of the events narrated. As his reading proceeds, he should make written analyses of each book separately, and, later, he should unite these 12 PEDAGOGICS OF HISTORY. § into a single coherent outline. These synopses should be placed where he may see them often and become familiar with them. The writer remembers calling, many years ago, upon a friend engaged in the study of law. At that partic- ular time Blackstone was the author with whose works the student was engaged. The w^alls of the room were nearly covered with papers pinned together and showing an orderly outline of the contents of the book as far as it had been studied. That friend has since made himself noted for the exactness of his legal learning. In a similar manner the student of any subject should take precautions against anything escaping him that is worth preserving. Such ovitlines are perhaps more useful if preserved in a note book. Other note books, properly labeled, should contain quotations that for any reason are deemed to be of special value. 15. Prose Quotations and Poetry. — The teacher should provide himself also with a collection of poems illus- trating noted historical events, and with celebrated descrip- tions of places, battles, or other matters, for nothing else is so effective in causing the past and the distant to seem like the vivid present. Macaulay's "Lays of Ancient Rome" ; Victor Hugo's description of the Battle of Waterloo; excerpts from Carlyle's "French Revolution" or from Dickens' "Tale of Two Cities" illustrating the horrors of the most dreadful period in French history; Lincoln's Address at Gettysburg; "The Isles of Greece," and many other passages from Byron relating to Greek and Roman history — these and similar quotations can be used with much effect by the teacher of history. The object of all such auxiliaries is to produce vivid impressions; and upon such impressions and upon repetition of effects depends the reten- tiveness of memory. With fine natural aptitudes, such a course of self-training in his art will, in a few years, place the teacher in the rank of experts, and cause him to be sought after as one of those whom the world delights to honor. § 6 PEDAGOGICS OF HISTORY. 13 10. Time Given iu Our Seliools to the Study of History. — Another obstacle in the way of the teacher of his- tory is the shortness of time given to it in our courses of study. In many of our schools no attention whatever is accorded to the study of general history, and one term, or, at the most, two terms, devoted to the history of the United States, are deemed sufficient. One consequence of this is that textbooks are modeled to suit this slight treatment. Some years ago a series of books was prepared, entitled : "Fourteen Weeks in Chemistry," "Fourteen Weeks in Physics," "Fourteen Weeks in United States History," etc. The sale of these books was enormous. Parents, school officers, and even teachers fondly imagined that by using them great strides could be made in accpiring an education. The educated teacher, however, knows that, if a study is begun and ended in so brief a period, it can have no value worth mention. If a subject is to furnish a mental discipline that will change the student from what he was to something stronger and better, it must exert its influence for a longer period than fourteen weeks. The same may be said of the studies that we pursue for the sake of their practical use- fulness. The " vStory of Schcherezade " consumed 1,001 nights, and surely the story of the human race should, in the telling, require more than a brief period twice or three times a week during 70 school days. Textbooks written for the purpose of being completed in such a short time can be nothing better than lifeless and fleshless skeletons, and the "I hate history" of those that study them is inevitable. If history is to have any place at all in our schools, let it be a place worthy of the importance and use- fulness of the subject. Almost all the colleges in this country ignore the subject. It is true that some of these higher institutions are beginning to recognize that history well taught and thoroughly mas- tered is an indispensable element in the education, not alone of the man of liberal culture, but also of the enlightened citizen and the man of affairs. U PEDAGOGICS OF HISTORY. PHEPAT? VTIOX FOR TEACHIKG HISTORY. IT^TRODUCTION. ll'. Method Necessary in Study and Teacliiii^. — - No work is ever well done that is not carefully planned. The engineer that intends to build a ship, a great bridge, or a fort determines the excellence of the ultimate result by the character of his plans. An orator may possibly be eloquent without preparing his address beforehand, but if his thoughts and argument, are carefully considered and arranged before deliver}-, their effect upon his audiences, and their influence upon being read afterwards, will be much greater. Similarly, a teacher whose aim is to do his work in the most thorough manner possible, must make special prep- aration for each lesson. In other words, he must be a stu- dent as long as he is a teacher. Every lesson should be as carefully planned as a sermon, a poem, or a magazine article. There is scarcely a subject that is not capable of scientific arrangement. The same is true of the parts — the lessons — into which the matter in a textbook is separated for the purpose of study and recitation. In the case of history this is true in a marked degree. There is a logic of events, a philosophy of causation and sequence in the occurrences that make up the life of an individual or the history of a people. The rules that should regulate the telling of each, in whole or in part, are the same. The best teacher of his- tory is the one that most accurately discovers and interprets the purpose, the causes, and the consequences of historical action. This, too, must be done not merely by himself; he must lead his pupils to reflection and inferences similar to his own. By being himself a student and an investigator, he must imbue his students with the same spirit of research. 18. The Teacher Must Create Anionjif His Pnpils a Taste for Historical and Bioj^rapliical Keadinj?. — § G PEDAGOGICvS OF HLSTORY. 15 Perhaps no teacher has ever succeeded in arousini^ in a class of pupils a genuine liking and enthusiasm for history by con- fining their attention to a single textbook on the subject. A work, to be suitable for classroom use, must be meager in details. This is necessarily so on account of the vastness of the subject. Such a textbook can, in the nature of the case, be only the merest skeleton account of events. In itself, therefore, it is certain to be dry and tiresome. If, however, the student's reading is so directed as to amplify and give life and reality to its briefly stated contents, it matters little how concisely they are given. The items in the book become mere counters, each significant of a large and interesting area that the student has explored. Just as the name of a city, a river, a mountain, is but a name, a mere combination of letters to one that has never seen them for himself, but becomes rich in significance and fertile in suggestion to him that has seen them, so is it with these mere catchwords of history. How greatly is interest in the history of Germany or France enhanced by reading historical tales such as were written by the woman whose pen-name was Luise Mlihlbach. Dumas' novels have contributed more, perhaps, than any- thing else to make French history intelligible and a source of pleasure. Carlyle's wonderful "French Revolution," Dickens' "Tale of Two Cities," and similar works should be read before any of the histories of France are attempted. An admirable preparation for the history of the United States is found in the historical novels of Sims and the biographies written by James Parton, detailing the lives of noted Americans. A teacher, therefore, must ascertain just what there is in historical, poetical, biographical, and fictional literature that will increase the vividness of effect produced upon the minds of his pupils at any given time in their progress. If he does this part of his work well, he will give an impetus to their love of historical reading that will last throughout life. This part of the duty of a teacher of history is of com- paratively easy accomplishment, if his work is done in a city 10 PEDAGOGICS OF HISTORY. § or in a large town; but if he teaches in a country district or in a small village, he is confronted by a serious obstacle. This is owing to the usual absence, from such places, of libraries large enough to meet the requirements of successful history teaching. 19. Concerning the Supplying of Books of Refer- ence in Country Districts. — To arrange a scheme for dis- tributing- books for general reading in small villages and in country districts, and for having them properly cared for and preserved from loss, is a difhcult problem. About 35 years ago an attempt to do this was made in the state of Ohio. Whether or not the plan is still in operation there the writer does not know. The books, strongly bound in sheep, were furnished by the state, and upon their covers was stamped the statement that they were public property. The custody of a sufficient number to supply a given neighborhood was made the duty of the secretary or the chairman of each local school board. It devolved upon him to keep the records necessary to their proper care and prevention from loss. After a time, when his supply of books had been read by all the people in the district desiring to read them, he would exchange his stock for that in an adjoining district. Owing to the carelessness of some of these custodians of the books, many were lost or quickly destroyed. Only a state having a large fund for educational piu'poses can keep tip such a method of supplying reading matter for the general public. In the densely populated countries of Western Europe, large public libraries are numerous and of easy access. It is no wonder, therefore, that the Germans have been able to surpass us in the quality of their historical teaching. They are the creators of the " Laboratory Method," which some educators have tried, with no marked success thus far, to introduce into the schools of the United States. There can be no doubt that the great success with which history is taught in Germany with this method is largely owing to the density of population and the consequent easy access to books for research and sfeneral reading. § G PEDA(K)GICS OF HISTORY. 17 The man that can devise a g'ood plan for furnishing exten- sive and varied reading matter, not only for the children in country schools, but also for the general rural population, will be doing much for the progress of our country. This is a matter worthy of the most thoughtful attention of the states- man and the educator, and it will become easier of accom- plishment as our country is developed and the density of population increases. 20. IIo^v Ilistoi'.v Liossoiis Are Usually liCarned. — We have all seen the pupils of mediocre teachers prepare history lessons, and to any one knowing how it should be done, the operation has a pathos in it. The pupil, with his book open at the proper place, reads aloud or in a busy whisper, a sen- tence or a paragraph, over and over, again and again. This reading is always accompanied by a busy movement of the lips, an introspective rolling of the eyes, nodding of the head to emphasize important words, and by other bodily move- ments. Many of the words are not understood, but that is a matter of slight consequence to the student, and it never occurs to him that the aid of a dictionary would be valuable. In the highest probability, he does not own one, and very probably the school he attends has no such article among its propsrty. The principal thing, as he tmderstands it, is to fix the exact words of the author in his memory — the author's thoiii^lit and his arrangement of topics are matters of second- ary consideration. If he can get the language into his memory verbatim ct literatim so as to reproduce it before his teacher without varying from tl:e text, he has "no other thought beside.' Now, if words express no thought, every one knows how difficult it is to remember them in a fixed order. It is related of a certain actor having a remarkable mem- ory, that he was boasting on one occasion of his ability to learn quickly and remember anything he chose. A friend suggested that perhaps he could compose something the actor would find difficult, and sul)mitted a series of words having no relation in meaning. Of course, the actor, after 18 PEDAGOGICS OF HISTORY. § (j long study, was compelled to admit his inability to memorize the composition. Our children that study history in which occur words or thoughts they do not understand, are handicapped in much the same way. And if, by sheer force of perseverance, they do succeed in memorizing such matter, it is forgotten just as soon as the recitation, for which alone it was learned, is past. Such lessons do not strengthen the memory; they prostitute and ruin it. The habit of forgetting is learned much more easily than is that of remembering. Moreover, history or any other subject, learned in this way, has absolutely no value for either practical or disciplinary use. It is by methods such as these, that our schools produce so many ca.ses of "arrested development." 21. How History Is Usually Recited. — There are two principal methods of "conducting recitations" that arc thor- oughly and unmitigatedly bad. Each of these has its slight modifications. These methods are : 1 . T/ic Verbatim Recitation. — Let us suppose that the class is ready to recite. The work begins by the teacher asking, "Who can tell me where the lesson today begins and where it ends?" He opens the manual at the place indicated by the pupils, most of whom are not able to answer his question. This preliminary question indicates clearly that the teacher himself is not prepared for the recitation. If he were not provided with a textbook, he would be utterly unable to "hear the recitation." The pupils, too, must have their books under their desks in order to get the cue when they are about to be called to recite. "John, you may begin with Lincoln's Administration," says the teacher. John recites. "Very good, John, except that you said institntion for inauguration, and you left out through Baltimore." While John recited, the teacher fol- lowed the text with his index finger. John is pleased and shows it, for the teacher said, ' ' Very good ! " That miscalled word and the omitted phrase did not count either with John, the class, or the teacher. " Next; tell us about ." And § 6 PEDAGOGICS OF HISTORY. 19 so the pitiful exhibition goes on. John, of cour.se, doesn't know the inferences that may be made from this farce ; nor does his teacher, for if he did, some better way would be found. John and his parents think them.selves fortunate in havint^ a teaclier so exacting, one that compels the "scholars" to study their lessons. The teacher takes occasion to con- gratulate the parents on having so studious a son — and he really means it. 2. The Quest ion-and-Aiisivcr Recitation. — For this species of recitiition, less preparation on the part of the pupil is required than is neces.sary with the method described above. He must learn the dates and the meaning of the text .suf- ficiently to be able to identify the teacher's questions with the several portions of the text. If the teacher is more than usually obliging — or stupid — he will a.sk what the lawyers call "leading" questions. In such case, the pupil does not need to learn even the dates. He will be able to "guess" the answer with sufficient accuracy. Perhaps the textbook is one of those of peculiar peda- gogical excellence that has questions at the bottom of the page. By experience, the pupil knows that he will be asked those questions and no others, and only those are gone over. Not one little wavelet of original thought, or wonder, or curiosity, in the teacher or in his pupils, is started by these questions. In all the foregoing, there is no exaggeration. The writer has before him several late textbooks with lists of questions on each chapter. Many of them require "yes" or "no" for an answer, or they inquire for proper names. It may be asked why intelligent authors will write, and modern pub- lishers — sensible and hard-headed — will print, such books. The answer is that books are made to sell — to meet a "long- felt need." As long as county superintendents, and even those of cities, will go into schools and ask pupils to "give the rule for long division," or will pick up a history and read off such questions as are found printed there, and imagine they are examining or testing the teacher's work by the pupils' ability to answer, so long will books of this kind be found in 20 PEDAGOGICvS OF HISTORY. g G our schools. But the time, let us hope, is not far away when this will be changed. The method of question and answer will be more fully treated under a later topic. 22. Preparing Lessons From a Textbook. — Consider- able has already been said, not only of the teacher's general ecjuipment for teaching history, but also of his preparation for particular lessons. It is the purpose under this topic to treat of the wa}^ in which pupils should be trained to prepare lessons from a textbook. When a lesson is assigned for study it should be read over in the presence of the teacher very much as is done in the case of an ordinary reading lesson. The purposes are mainly two in this exercise — to clear away verbal difficulties, and to bring out the exact m.eaning. Now every subject has, or should have, a logical arrange- ment of parts. Every paragraph should have some leading idea or proposition. In each case, this idea or proposition may generally be denoted by a single word or phrase. A constant inquiry should be made as to the principal subject treated in each paragraph, and the best and briefest expres- sion for it. As these are developed one by one, they may be written upon the blackboard, and after their relative impor- tance as topics, si\btopics, etc. has been determined, they should be copied by the pupils. These outlines serve the double purpose of emphasizing the meaning and of aiding the pupil in memorizing the lesson in the order of topics. The lesson should not be regarded as properly learned until this skeleton or outline, each item in its proper place and relation, as well as the matter to fill up the outline, is firmly fixed in the memory. On the other hand, the teacher is not ready to meet his class for recitation, until he is perfectly familiar with the plan of the lesson and the treatment of each subdivision of it: Then both teacher and pupils may discard the textbook and each is free to take part, not only in recitation, but in a rational and an orderly discussion of it. If, in addition, the teacher is fortified by abundant general §6 PEDAGOGICS OF HISTORY. 21 information covering the lesson, and is, besides, master of the logical considerations involved, the recitation, when it comes, may be made a rare treat to everybody concerned. In case the class in question has access to books relating to the matters treated in the lesson, the teacher should assign to oiie or more of its members the task of preparing to tell the rest of the pupils more particularly about some person or event mentioned. Of course, the teacher should be able to direct the pupils to the books needed for reference. Sup- pose, for example, the lesson were about the treason of Benedict Arnold and the execution of John Andre. One pupil may be asked to prepare himself to give orally or in writing a sketch of the life of Arnold, and another that of Andre. The former pupil should be referred to Sparks' "Life of Benedict Arnold" in his "Library of Anierican Biography," Vol. Ill, and the latter to Sargent's "Life and Career of Major John Andre," or to the "Atlantic Monthly" for December, 18G0. These pupils, if they do their work well, which, under proper management, is likely to be the case, will theniselves be much profited, and will add greatly to the interest of the class in the lesson. Certain is it that, to the members of that class, the names of Arnold and Andre will thereafter be not mere names, but almost living and breathing personages. By this means, too, the memory is aided by the enlistment of the emotions. Pity for the fate of Andre, and respect for him, and horror and loathing for the treason of Arnold, will render it simply impossible for the class ever to forget that lesson. The writer may be permitted to add that no better subject for subsequent composition work can be devised than these matters of special investigation. To use them for this purpose .serves not only the object primarily intended, but also as a review of the history lesson. If a history lesson involves any question of geography, and nearly all do, the pupils should know that every one is expected to be in readi- ness to point out on a map the places where the events hap- pened. Still better is it to require that a map shall be rapidly sketched tipon a blackboard, and the places indicated 22 PEDAGOGICvS OF HISTORY. §6 with respect to other well known and important features. This map-drawing nuist not be elaborate or consume much time. It need not be accurate; a reasonable degree of approximation is all that is required. Anything more con- verts the history exercise into a geography lesson. One or two minutes should suffice in which to do all the map-draw- ing required. It should be added that, as a rule, a mere local map, as of a battle, a settlement, or a fort, is not enough for the purpose. The boundary lines of the state or country in which the locality is included, should be rapidly sketched. If two or more states are concerned, as is the case when armies are marching from one point to another, the boimd- aries should be indicated, and the line of march should be shown. 23. Relics and Mementos. — Another important aid in the study of history, and one that has been much insisted upon, is that of historical relics and mementos. It is sur- prising how many such objects are distributed in any given neighborhood — an old flag of the Civil War, or even of the Revolution, weapons of antique pattern that were used against the Indians or in our wars with Great Britain, arrow- heads, Indian pottery, historic letters, ancient documents, household heirlooms, and many other objects that have come down to us from those distant times. In almost every case, the owners of these things are glad to put them at the tem- porary disposal of the teacher. The following quotation from Mary Sheldon Barnes will illustrate the intense interest that children take in these historical relics: " In response to a request for flags for a special occasion, a little boy of eight years brought me a flag that his father had carried through the Civil War. He recounted the battles in chronological order, told me a little of the geography, and related an incident that I knew to be true. He seemed much interested in the flag, and very proud of the fact that his father had held it when one of the bullet holes w^as made in it. The class of forty boys and girls, seven to nine years old, asked questions eagerly about the flag. ' Where did it come from ? ' ' What makes it so dirty ? ' ' What made the holes in it ? ' ' Were they real bullets out of a gun ? ' ' What did they want to shoot at the flag for ? ' 'Do you § G PEDAGOGICS OF HISTORY. 23 think it was right to have a war ? ' One boy said afterwards, ' Couldn't it tell a lot of stories, though ! ' The children seemed to feel still more interest after I had given them a brief account of it, and several lin- gered to see it more closely, and one wished to touch the old flag." The historic sense with respect to time is perhaps more strono-ly and definitely developed by a study of such relics than by any other means. Every teacher of history should have in his school as large a collection as possible, and should, as thoroughly as possible, understand and know how to use it. The great miiseums of the world expend enor- mous sums annually in making additions to collections illus- trating every department of art and science, and these must be studied by scientific writers, if they would make true to life the state of things they depict. Nothing is more certain than that history can neither be adequately learned nor taught without some assistance other than textbooks. The teacher, therefore, that means to win a place in the first rank of his profession must be willing to give the time and thought, and if need be, incur the expense, necessary to supply himself and liis pupils with every available appli- ance. 34. Historical Use of Poems and Ballads. — All authorities are agreed that of the various aids in teaching history none is more valitable than can be obtained from the use of poems and ballads. "History describes, poetry paints," said W. C. Collar, Head Master of Roxbury Latin School. Continuing, he remarks, "There is nothing like the magic charm, whether of sublimity or pathos, that poetry lends to historical events, persons, and places. ***** At the distance of forty years I recall the emotion, tlie tears, with which I read in our coimtry school reading book a poem that I have never seen since, entitled 'Jugurtha in Prison,' beginning 'Well, is the rack prepared, the pincers heated ?' " I knew nothing of Jugurtha, neither when he lived nor in what part of the world, nor what he had d(nie that he was 24: PEDAGOGICS OF HLSTORY. § to be starved to death in prison. * * * * * * With what a swell of patriotie pride, too, did I as a boy recite, ' Departed spirits of the mighty dead, Ye that at Marathon and Leuctra bled.' "Marathon and Leuctra signified nothing to me. I had not the remotest idea who were the mighty dead that had fallen there, but I felt as if it would have been a joy to have shed my blood wath them." If the development and cultivation of patriotism is one of the important objects of the study of history, and that it is there can be no question, the teacher has in the patriotic poems, ballads, and songs of his country a potent agency for this purpose. " Patil Revere's Ride," and many others of Longfellow's poems, Drake's "American Flag," "The Star- Spangled Banner," " vSheridan's Ride, " " Barbara Frietchie, " " The Bltte and the Gray." vScott's " Breathes There a Man With Soul So Dead," and innumerable others are available. No emotion of which children are capable is deeper, no senti- ment piu'er and finer, than those awakened by a poem describing and idealizing heroic achievement or daring deeds. This subject has already been adverted to, and is resttmed here only on account of its great importance to the teacher of history. 35. Kevie^vs. — Edgar A. Poe in his "Philosophy of Composition " alludes to the value of the refrain as an ele- ment of beauty and force in poetry. The word is derived from the French verb rcfraindrc^ "to repeat. " It is this repe- tition, reiteration, review, that is a primary condition of suc- cess in teaching any subject. No lesson ought ever to be assigned that does not include a review of the preceding- lesson, and as soon as any considerable part of a textbook has been gone over, in review, a "back review" should be begun at the first of the book. And for a fourth time the manual should be covered by a rapid general review. This is in accordance with Mr. Bain's contention that the early work in school should be of limited extent but § (i PEDAGOGICvS OF HISTORY. 25 thoroughly mastered. He insi.sts that little worth speaking of ean be done until the mind has material to work upon. Comparisons cannot be made until there are things to be compared, classifications are impossible until there are in the mind matters that belong in classes, and inferences implied by conditions from which they may be deduced. Many reviews are doubtless more or less wearisome to the teacher and monotonous to the pupils, but much of this may be avoided, and interest and pleasure secured, by new and more comprehensive generalizations and classifications. A teacher's skill may be very accurately gauged by the measure of persistence he can induce in a class in struggling long and patiently with a diflficulty that is to be mastered. At any rate, whether the teacher can make reviews inter- esting or not, the early history work, in order to be valuable, must be thorough. Without thoroughness, there is no proper and certain basis on which to erect later an enduring super- structure. Moreover, the habit of patient persistence until mastery is gained is of incomparable value in all subsequent work. And the opposite is true; if the pupil is permitted to be careless and imperfect in his lessons, it is a habit that is likely never to be overcome. 2G. Historical Recreations. — Every one that went to school three or four decades ago will remember the delight with which the announcement of a "spelling match" was received. Even yet a spelling match is almost as popular in the West as is baseball. This method has been extended to geography. In much the same way as in spelling, the pupils are tested in geographical knowledge. The writer has seen many competitive tests of this same kind in history. Several of our school textbooks contain extensive lists of questions intended to be used for this purpose. They may be given either as a miscellaneous review of an entire class, when any one may answer that can, or as is done in spelling, sides may be chosen and their comparative knowledge ascertained. The following questions for this purpose are copied for the sake of illustration: 26 PEDAGOGICS OF HISTORY. § 6 1. In what battle was "Betty Stark" the watchword ? 2. What battles have resulted in the destruction or surrender of an entire army ? 3. What general rushed into battle without orders and won it ? 4. What trees are celebrated in our history ? 5. What three ex-Presidents died on the 4th of July ? 6. Give the coincidences in the lives of Webster, Clay, and Calhoun. 7. What celebrated philosopher, when a boy, in order to buy books, went without meat ? The teacher must remember that these diversions must not be substituted for serious and genuine work in history. They are useful for creating an interest in, and for breaking the monotony of, the regular lessons; in short, they are used in the same way and for the same purpose as the spelling- matches of years ago. The pleasitre they give and the interest they arouse should suggest a general principle of success in teaching: Do not for long pursue the same method — seek variety, freshness, originality. METHODOLOGT. desciiiptio:n^ of tiif a arioits methods of teaching history. 3*7. Any Method I^sed Exclusively lieoomes Monot- onous. — There is a strong human instinct for variety. We weary of the people that tell us over and over again the same stories, of the musicians whose music is always written in one key, and of the poets that always compose in the same meter. This repugnance to monotony is found also in children. Like their elders, they yearn for novelty. If required to sing at school the same song every morning, they soon become tired of it, however beautiful it may be. Hence, the teacher that wishes to make school a place of constant enjoyment to his pupils, must keep oitt of the ruts; he must be fertile in devices, and able to repeat as often as § 6 PEDAGOGICS OF HISTORY. 27 may be necessary, without becoming" monotonous. If he is content to assign lessons and to hear them recited always in accordance with a fixed method of procedure, he will soon have the mortification of hearing that his pupils like neither liim nor the school, of seeing an increase in their percentage of absenteeism, and of having their number depleted by many leaving school altogether. The fact is, there is no place in the world where a child can experience so much happiness as in a school properly conducted. The teacher of such a school must not only be original, resourceful, schol- arly, sympathetic, genial, and kindly, but he must also be familiar with the best and most approved methods. 38. Many Methods of I'rocediire iii History. — Every school subject is susceptible of various methods of presenta- tion, and the effectiveness of each method depends 'upon many conditions, most of which have been mentioned under preceding topics. One of these conditions is that the teacher must thoroughly know the different methods and devices and be able to decide under what circumstances each should be employed. The writer, therefore, will proceed to explain the several plans that are employed in teaching history, and to make such comments upon them as may seem necessary. In doing this, he will describe with special minuteness the method that has proved so successful in Germany — the Laboratory methocl, which is being introduced more and more widely in the schools of this country. 39. The Catechetical Method. — The oldest and most natural method of conducting a recitation is the Catechetical. In this the teacher asks questions and the -pupil answers them, if he can. This was a favorite method with Socrates, whose practice was to feign ignorance of some matter sup- posed to be thoroughly understood by his antagonist in argument. vSocrates would ask innumerable questions that the person questioned would answer in the unguarded way that comes from the conviction of having perfect knowledge of a subject; and presently the wily old philosopher would 2S PEDAGOGICS OF HLSTORY. § G confront his opponent with a series of answers that were inconsistent with one another and ask him to reconcile them. From this practice of Socrates, there came into the Greek language a noun derived from the verb e'ipsLv, circin^ to speak. This word eironeia, means a dissembling, the asking of ques- tions that involve a snare. From the same source came the noun e'ipcov, e'lroj/, a dissembler, one that affects ignorance and says less than he thinks; finally we have in our own language the word irony. Every teacher has heard of the Socratic method, which is nearly synonymous with the Catecheti- cal method; but perhaps no other person ever employed the method of questioning so skilfully as did that wise old teacher. The catcc/iisj/is that counted for so much in the religious teaching of a half century ago were so called because they were made up of questions with answers. The first notions of what a textbook on history, geography, and many other subjects should be, required that it should take the cate- chetical form; and even yet we find such books in our schools. Many teachers continue to follow the plan of ques- tion and answer in conducting recitations. "■ Who discovered America?" "Columbus." " In what year ? " "In 1-192." Often, too, the question of the teacher is so constructed that it may be answered by jcs or no. Of course, all this is very bad ; so much so, that the Catechetical method has for a long time been practically abandoned in the making of textbooks, and to a degree in the recitations of pupils. And yet the art of skilful questioning is indispensable to the highest success in teaching. It is a practice among teachers to explain points that are not understood. "Sit erect and be attentive while I explain this difficulty," the teacher says, and immediately the class assumes an attitude of respectful attention, with ears for the most part hermet- ically sealed. But if the teacher clears away the difficulty by a series of questions in proper sequence, or, better still, if he delegates to some bright pupil the task of asking the questions necessary to lead a slow pupil to an understanding of the subject, the attention will be real and not feigned. gG PEDAGOGICS OF HISTORY. 21) A skilful lawyer cares less for the direct testimony of a witness than for what can be elicited by cross-examination. Indeed, the eminence of a lawyer is dependent more upon his expertness in the art of questioning than upon anything else. In like manner, no teacher deficient in this art can attain to the highest excellence in his profession. To use the Cate- chetical method with effect in teaching requires that the teacher shall himself thoroughly understand the subject imder consideration, and that he shall know the condition of the pupil's mind with respect to points not entirely com- prehended. The teacher must have, too, a sense of logical order that will enable him to construct a chain of questions in perfect sequence, leading the pupil from those points that he knows to those that he has failed U) grasp. Many books have been written about the art of question- ing, but this is something that cannot be learned from rules. The conditions of expertness in this art are indicated above — a perfect knowledge of the subject, of the end to be attained in any given case, and a strong sense of logical sequence. To these may be added such skill in the use of language as will enable the teacher to frame questions that are brief, suggestive, to the point, and without ambiguity. One of the most effective methods of making a recitation interesting is to require one pupil to ask a series of questions intended to lead another pupil to the comprehension of some point not thoroughly mastered, and to constitute the rest of the class as critics of the questions and their arrangement. The writer has witnessed recitations, the m< st exciting and interesting that could be conceived, conducted in this way, and during them the teacher rarely spoke. It would be difficult to exaggerate the value of skilful questioning as an auxiliary in the management of a recitation. vSuccess in this matter may not attend the first efforts of a teacher, but it will come later as a reward of experiment, patience, and reflection. 30. Tlic Memoi'iteT Metliort of Stiidy and Recita- tion. — In this method the student commits to memorv the :30 PEDAGOGICS OF HISTORY. § G exact text of the author, and in recitation gives it as he learned it. Tlie objections to this are so numerous and so obvious that our best teachers have long ago abandoned it. Even yet, however, one does not need to go far to find this plan in use. In our large cities, where it might be expected that a practice so ruinous and antiquated would not be followed, it is still in vogue, and this will doubtless continue to be the case until all teachers are required to prepare for their work by professional training. It has been argued in favor of the Memoriter method that it cultivates the memory. But this argument is fallacious. When poetry or striking passages of prose are memorized, and are remembered on accoimt of their beauty, the effect is to train the memory; but it is well known that lessons in history are very soon forgotten. However carefully they are learned, they soon run into confusion in the mind and are forgotten. In this method, the words are everything and the thought nothing. It follows, therefore, that when the words are forgotten, nothing remains except a vague sense of half-defined images. Only such matters as are indispensable in our daily employ- ment, and are for that reason of frequent recurrence, are permanently fixed in our minds. The actor remembers his part in a play by virtue of repetition, but he reads the news- papers and speedily forgets what he has read. A poem full of beauty, emotion, and true to nature, is easily remembered, but a magazine article or an item in a newspaper makes but a slight impression upon the mind. The memory is very much like a servant. If discipline is relaxed, the servant becomes negligent and careless. If, on the contrary, he is held strictly to his responsibilities, he becomes more and more exact and painstaking. In like manner, if the memory is rigorously required to reproduce upon demand whatever has been confided to it, and, in case of failure, is punished by the imposition of additional tasks, it will in time become faithful and reliable. It must not be understood that the writer is opposed to verbatim memorizing, for the contrary is true. It is only with respect to the matter that is required to be committed § (i PEDAGOGICS OF HISTORY. 3i to memory that objection is here made. The ideas in a historical textbook, but not the language, should be learned so carefully as never to be forgotten. The teacher, on the day before a lesson is to be recited, should go over it with the class. The objects in view should be to clear away any obscurity in' respect to the meaning, and to get an outline or analysis of the lesson. If it can be done, there should be found for each paragraph a single word that will recall its contents. This outline should be thoroughly fixed in the memory, and later, by way of review, it should be incor- porated with the outlines of preceding lessons, so as to form one continuous whole. During recitations, these outlines singly, and in order collectively, should frequently be called for, so that, when the textbook has been finished, its entire contents may be given by points from memory. Above all, do not permit pupils to give the exact text. One of the best exercises in acquiring and confirming a good stock of words is in the requirement that pupils shall give the author's thought in words of their own choosing. Ideas are easily remembered, but mere words are inevitably for- gotten. 31. The Topical McMiod. — The term topical refers both to the division of the matter in a textbook, and also to one of the best methods of giving that subject matter in recitation. Nearly all school books of the present time have their contents broken up, and the topics indicated by con- .spicuous side heads. This facilitates the work, not only of the pupil, but also of the teacher. Of coin-se the topics should be in close logical connection, and upon this depends greatly the superiority of one maniial over another. The pupil should have these topics in his mind in their order of occurrence, and when called upon to recite, should be required to proceed without help from the teacher. Very frequently, two or more pupils may be designated to recite in turn the portions that make up a topic, if it is long and is divisible into parts. As has been stated above, the aiithor's language should in no case be given by the pupil. An 32 PEDAGOGICS OF HISTORY. § 6 outline of the day's lesson in conjunction with the preceding- lesson should be given by the first pupil that recites. Many teachers cause such an outline or analysis to be given both at the beginning and at the end of the lesson. The practice is a good one, and is worthy of general adoption. One very great advantage of this topical method is that a sense of logical sequence is developed among pupils. More than anything else, it is this art of properly dividing a subject into related parts that gives so great a charm to the writings of Macaulay. He was perhaps the greatest master of para- graphing that ever wrote in any language. Every paragraph is complete in itself and perfect; and the transition from one to another is graceful, and the sequence natural and obvious. It must not be understood that the Topical method pre- vents the employment at the same time of the Catechetical or the Memoriter method. If a teacher desires to analyze motives, or causes, or consequences; in short, if he teaches not history merely, but the philosophy of history, he must ask questions. This may be done as occasion arises during the progress of the recitation, or at its close. Which plan is the better must be determined in any given case by the teacher himself. But while it is sometimes necessary and advantageous to use the method of questioning, the Memori- ter method is invariably and hopelessly bad. When the questions of the teacher lead quickly and naturally to free and earnest discussion on the part of the pupils, the interest and profit will be very great. When the teacher of history can skilfully combine all the various methods and devices for awakening interest and enthusiasm among the pupils, we shall no longer hear it said that pupils hate the subject. No other subject is quite so fascinating as this, if it be well taught, but to teach it so as to secure the best results is very difficult. To prepare and deliver effectively a sermon or an oration is perhaps an easier task. 33. Extension of Meaning' of tire Term "Topical." Although the word topical is usually employed in the sense explained under the preceding- head, there is another § G PEDAGOGICS OF HISTORY. 33 meaning' sometimes attached to it. This can best be illus- trated by a quotation from a brief outline by Professor Tyler of the historical work pursued under his direction at Cornell University : " Perhaps it may be a peculiarity in my work as a teacher of history that I am here permitted to give my whole attention to American history. At any rate, this fact enables me to organize the work of American history so as to cover, more perfectly than I could otherwise do, the whole field, from the prehistoric times of this continent down to the present, with a minuteness of attention var3-ing, of course, as the importance of the particular topic varies. I confess that I adopt for American history the principle which Professor Seeley, of Cambridge, is fond of applying to English history, namel^^ that while history should be thoroughly scientific in its method, its object should be prac- tical. To this extent, I believe in history with a tendency. My inter- est in our own past is derived chiefly from my interest in our own present and future ; and I teach American history, not so much to make historians, as to make citizens and good leaders for the state and nation. From this point of view, I decide upon the selection of liis- torical topics for special study. At present I should describe them as the following: " The Native Races, especially the Mound Builders and the North American Indians. " The alleged Pre-Columbian Discoveries. " The Origin and Enforcement of England's Claim to North America, as against Competing European Nations. "The Motives and Methods of English Colony Planting in America in the Seventeenth and Eighteenth Centuries. " The Development of Ideas and Institutions in the American Col)- nies, with Particular Reference to Religion, Education, Industry, and Civil Freedom. "The Grounds of Intercolonial Isolation and of Intercolonial Fellow- ship. " The History of the Formation of the National Constitution. " The Origin and Growth of Political Parties under the Constitution. "The History of Slavery as a Factor in American Politics, Culmina- ting in the Civil War of 1861-65. " In all these subjects, I try to generate and preserve in myself and my pupils such an anxiety for the truth, that we shall prefer it even to national traditions or the idolatries of party." 33. Ttcmarks on the ?\)i"Cj>:oinj>'. — -The student will perceive that in the sense illustrated above, by the Topical 34 PEDAGOGICS OF HISTORY. § method is meant no more than an arrangement in chrono- logical sequence of the principal items making up the com- plete history of a particular period. With this meaning, the method determines the arrangement of tlie contents of every scientific treatise on history. When the subdivisions are made down to minute epiijodes, the Topical method may be utilized in studying and reciting lessons from day to day, as lias already been explained. When, in the succession of general topics, the order of time is not followed, we have the Laboratory method, which is employed in the lycca and the universities of Germany, and in some of the colleges of the United States. Original researches by this latter method should be dominated by the Topical method, both in generalities and in particulars. i}4. The Ijaboi'ator.v Motliod. — In the teaching of chemistry, physics, mineralogy, metallurgy, botany, or any otiicr of the natural sciences, the need of a well e(iuip])cd laboratory is conceded. These laboratories, when comi)lete, are furni.shed with all necessary scientific instruments, books of reference, specimens, and everything that is re(|uired in the most exhaustive original investigations and experiments. Something of the kind has been proposed in the .study of history. Of cour.se, no instrumental aids are reciuiretl, but the plan contemplates that the student shall have access to all the original authorities, documents, reports, pamphlets, etc., that are resorted to by aiT ;uithor engaged in coni])iling a liistorical work. It is clear, however, that the unaided search of an ordinary student would yield nothing of value. He must have the guidance of a textbook from which he may learn where to find the information that he needs. vSuch books have been made in this country, l)ut they have not been used to any great extent. The plan presui)]:)oses an immense lil)rary accessible to the student. In this coun- try, even imder such circumstances, the method is not a good one. In this busy age, we cannot give to any one subject the time neees.sary to. make any such method successful. No one here desires to make a life work of the study of history, §6 PEDAGOGICS OF HISTORY. 35 as is done in Germany, and in preparing to earn a livelihood, the most profound knowledge of this subject would rarely have any considerable market value in the United States. In Germany much is made of the study of history, and there is a demand for the services of persons specially trained to teach it. The Laboratory method proceeds upon the assumption that no modern writer of history is to be believed, and that every statement must be verified by reference to original sources. This, of course, takes more time than, in justice to other subjects of study, can be granted. Unless the student makes a life work of this subject, the Laboratory method is wholly impracticable as a plaii for the classroom. In the composition of a historical treatise, however, this is the only rational method of doing the work, and it is specially suited to the preparation of a dissertation on some particular historical topic, or controverted point. 35. Historical Clubs. — In Germany especially, and to some extent in France, clubs for historical study are in vogue. They are commonly presided over by a professor or by some one designated for the pur|V)se. He assigns to each member a topic upon which to prepare a paper, and this, at a time specified, the writer reads before the club. Some one is chosen beforehand to criticize the contents of the paper. In order that the critic may be able to do his work thoroughly, he is permitted to examine the dissertation in advance. After the critic selected has been heard, other members follow. In the (ierman Gcscllscliaftcii these criticisms are unsparing, and appear to be made without any regard for the author's feelings. To an American the criti- cisms appear brutally blunt and severe, but they are accepted by the victim with an admirable philosophy and good nature. It is a valuable discipline, for nothing else so effectively enables one to avoid the folly of overestimating his own powers. Of course, it is not history alone that may be studied in this way. In every civilized country, there are innumerable organizations for various purposes, l)ut it is only in Germany 30 PEDAGOGICS OF HISTORY. § since 1830, and in France for about a quarter of a century, that history has been systematically pursued by such societies. Much may be accomplished in this way, and the teacher in our public schools is better situated than any one else to inaugurate and direct the work. The teacher is naturally expected to take the initiative in such matters, particu- larly because he has perfect facilities for reaching parents and others whose cooperation is necessary. Indeed, the teacher's usefulness is not limited to his work in the class- room ; at least it should not be. When it is remembered that man is naturally a gregarious animal, and lends himself gladly to the furtherance of any scheme involving association with his fellows, we can readily see how useful an intelligent teacher, having executive and organizing aptitudes, may be in a community. Such activity greatly helps the teacher in his proper work in the schoolroom. It causes him to be bet- ter known and appreciated by the patrons of his school, and largely increases his influence. If such outside usefulness were generally prepared for in the schools where our teachers are trained, and the methods of its successful realization were carefully considered and systematized, the remrmera- tion and tenure of office of the profession would be speedily advanced. 36. Intei'ost in IlistoTieal Study May Be Increased l>y Public Ijibravians. — An admirable plan of creating among the reading public an interest in historical reading and study has been described by Mr. William E. Foster, the Librarian of the Providence Public Library. The object in view included not only historical reading, but also such geographical, political, economical, and other subjects as are suggested by current events. The method pursued was to post at the library, newspaper clippings referring to impor- tant matters, and then to give below the titles and library numbers of books in which could be found additional infor- mation relating to the subjects so posted. It was immedi- ately found that the plan Avas an excellent one. Increasing numbers of visitors would stop to read the clippings, and, § PEDA(U:)(;iCS OF HISTORY. 37 naturally, they would procure and read the books. Neighbor- ing- educational institutions were invited to send lists of sub- jects in which their students were interested, and the volumes in which these subjects were treated were not only reported back, but the lists were posted at the library. The work was at first done by hectograph, but it was speedily necessary to resort to printing, and lists were finally sent to other cities. These lists were printed in the local newspapers whose read- ers would cut them out, take them along to the library to guide in the selection of books, and preserve them for future reference. Mr. Foster says that the plan developed until, in response to numerous requests, the more extended lists were printed in the " Library Journal " of New York, and that finally, in 1881, was begun the regular issue of the "Monthly Reference Lists." This latter periodical has attained a wide circulation in this country, and it has readers in Europe. He gives, as specimens of current topics, such as: "The Stability of the French Republic." "The German Empire." " European Interests in Egypt." " Indian Tribes in the United vStates." " The Unification of Italy." "The Closing Years of the Roman Republic." "The Plantagenets in England." "Tendencies of Local Self-Government in the United vStates." "Elements of Unity in Southeastern Europe." The foregoing is perhaps the nearest approach to the Laboratory method of Germany that is practicable in this country. Its tendency is to render the reading by the public systematic and orderly, and to turn it more to those subjects that at the time are uppermost in the public mind. It is, moreover, a plan by which intelligent students can be useful to others. There are many newspaper editors that would be glad to print such lists of topics, whether supplied by libra- rians or by well informed general readers. We hear much of altruistic effort; here is a field for persons disposed to exert themselves in behalf of a larger general intelligence. By these and similar means, the teacher may extend his influence and usefulness bevond the classroom. ;3S PEDAGOGICS OF HISTORY. § (5 37. The liectiire Metliod. — This method is much employed in the teaching of a great variety of subjects, particularly in colleges and universities, and in the higher technical institutions. This is more especially the case in the colleges and universities of Europe. During winter, in the United vStatcs, courses of lectures are very commonly arranged in nearly all of our large cities and towns. In these courses, the subjects are usually popular rather than didactic; for, if a lecture is intended to instruct, it is almost certain to be sparsely attended. The people that go to lec- tures expect to be entertained; a fact indicating that the Lecture method in teaching history has, under ordinary conditions, very little value. Unless a lecturer thoroughly knows his subject, and has, besides, rare graces of delivery, he cannot hope to furni.sh his audience any material or last- ing benefit. But there are circumstances imder which this method may be employed with excellent results by the teacher of history. Some of these conditions are as follows: 1. TJic lecturer must be thoroughly master of his subject. — He must know the entire field covered by the lecture; he must know it not merely as a detail of facts — it must lie in his mind as scientific organized knowledge. Its philosophy miist be familiar to him. The laws of cause and effect, of sequence in time, and all the various interdependences must unite this knowledge into (Mie logical structure. Some one says that history is philosophy teaching by example. We can know onl_y facts and their relations ; but a knowledge of facts alone, facts in isolation, is scarcely worthy of being called knowledge. Facts become important only when their relations are fully understood. The voyage of Columl)us, considered merely as a voyage, has no more interest than any other voyage across the Atlantic; but when it is taken in connection with related events before and after, it becomes one of the most momentous occurrences in history. The battle between the Monitor and the Merrimac was a slight affair compared with the battle between the Chinese and the Japanese at the Yalu River, or the destruction of the Spanish fleet by Admiral Dewey in the harbor of Manila, or that of § G PEDAGOGICS OF HLSTORV. 31) Admiral Cervcra at vSantiago clc Cuba. I^ut when that fh-st meeting- between iron vessels is considered in regard not only to its influence in shaping events during our own war, but also as necessitating the remodeling of the navies of the world, its deep significance becomes apparent. The per- formance of the dynamite cruiser "Vesuvius" at Santiago de Cuba, and the late developments in the matter of snbmarine navigation, will doubtless l)e the beginning of striking- readjustments of the world's methods of warfare. The great- ness of events, therefore, depends not so much on themselves as on their relations to other events. It folknvs, theref(n-e, that to employ the Lecture method effectively in teaching history, it is necessary for the lec- turer to have mastered the philosophy of his subject, to have pondered deeply upon the logic of events. His knowledge must be thorough and profound, and it must be organized. He must be able to give in a sentence what may have cost him weeks of reading and reflection. 2. He must not oitcr into details. — If the lecturer intro- duces many particulars, it becomes impossil)le for him to exhibit strongly any logical and connected whole. By the lecturer's matter and manner, his audience should be com- pelled to grasp and remember the general scheme of the lecture. This scheme should be so conceived and presented as to create an impulse on the part of the audience to find the details that will confirm and com])lete it. It should l)e a nucleus aroimd which tlicre shall be a continuous accumu- lation. 3. 'flic stndoit should be supplied toitlt a "vod outline of the lecture. — It is customary for students to take notes of lectiu'es that they deem important. If original research with reference to the matters treated is contciiiplated, these are indispensable. But the task of writing these notes diverts the attention from the main argument, and much of the effect and unity is lost. The best method of meeting this requirement is for the lecturer himself to supply a complete outline of the lecture. By this means he avoids the possi- bility of being misunderstood, and tlie later researches of the 40 PEDAGOGICvS OF HISTORY. § G students are perfectly definite. If reference is made in these notes to authorities where details may be found, the outline of the lecture becomes immensely more valuable. In any case, the notes can be made the ba.sis for subsequent exami- nation into the proficiency of the students. This is the method of procedure in our schools of law and medicine, where the teaching is largely done by means of lectures. 38. Ileiuai'ks on the Ijectvire Metliotl. — ^In teaching history by this method, great care is necessary that the sub- ject and its treatment shall be adapted to the age and intelli- gence of the pupils. This is a matter of difficulty. It requires a tliorough knowledge b}- the lecturer of the mental status of the pupils, and besides, that he shall have the I'ather rare versatility that enables one to make his language, manner, and method suit an audience of children or of cul- tured adults. Tyndall possessed this power of adaptation to a wonderful degree. His Christmas lectures on Light and Electricity were listened to with rapt attention by audi- ences of more than 5,000 children, and in this country he lectured on the same subjects to immense audiences com- posed largely of educated people and specialists. The error into which a lecturer is inost likely to fall will consist, there- fore, in making his subject too little philosophical, or too profoundly so. If a discussion of the lecture is made to follow, directed and supplemented by the lecturer himself, its effect is ampli- fied and deepened, and erroneous impressions corrected. In German)^, this method, with various accompaniments and modifications, and in its most elaborate and philosophical form, is much employed in the Seminar ia or "Training Schools," and in the "Practice Course " of the universities. But it is to be remembered that, in these departments, only comparatively small groups of advanced students are addressed, and that the lecture is intended only to suggest lines of subsequent original research by the students. It is extremely doubtful whether the most accomplished lecturer on history proper could make this method valuable § G PEDAGOGICvS OF HISTORY. 41 below our high schools. Into these, however, and into our colleges, it has been introduced, and in many cases with marked success. But while this method is useful only in the higher study of history, there is a modification of it that may be regarded as indispensable in the historical work in our lower schools. This, on account of its importance, shall be carefully explained in the next topic. 39. The liiograpliical Method. — Before history proper can be studied with any profit from textbooks, the historic sense must be developed; and of all methods for this pur- pose, the Biographical method is the best with beginners. By the historic sense is meant: 1. A demand of the uiind that narratives sJiall be distin- guished as time or as mere myth or story. — To very young children a fairy story is as apparently true as the account of a real occurrence. The tales of the "Arabian Nights" arc just as veracious to them as if the incidents occurred before their own eyes. Dickens strikingly exemplifies this in a beautiful sketch, entitled "The Child's Story": " They had plenty of the finest toys in the world, and the most astonishing picture books — all about simitars and slippers and turbans, and dwarfs and giants, and genii and fairies, and bluebeards and beanstalks, and riches and caverns and forests, and Valentines and Orsons; and all new and all tr-itc." Indeed, it never occurs to children up to about eight years of age to inquire as to the truth of what they hear or read — everything is real, everything true. At this age, questions of probability begin feebly to suggest themselves, and the mind begins to file, but, with slight emphasis, its protests against incongruity. As the result of many tests inade upon children, it has been ascertained that by certain kinds of training this sense of historic truth may be rapidly developed, and thus the child may be prepared for serious historical work. It would be interesting to detail here some of the many tests that have revealed this psychological fact, but the limits assigned for this Paper will not permit it. 42 PEDAGOGICS OF HISTORY. § G 2. A demand of the mind for tlic time of events. — What some one has called t\\Q perspective of In story is absent in young children. The writers of fairy stories have never deemed it necessary to be more specific in this respect than to begin with " Once upon a time," or with " Once upon a time, long, long ago," or with similar vague phrases. To young children, the stories of Columbus and Washington are equally remote, and neither dates farther back or forward than " King Arthur's Round Table," or the myth of " Jason and the Golden Fleece." No such inquir}^ as "When did it all happen ? " is heard from these youthful auditors until after about the age of eight years has been passed. After this time, the demand for the time of events is made with increasing frequency. vStill later, comes the mental require- inent for a definite sequence in regard to time of the several items that make up a single event; and still later, for the relation in time of several independent events. Until this last instinct has become definite, the historic sense with respect to time is incomplete. And it is long after the pupil desires to know the sequence of time in the events of a narrative that he becomes importunate alwut what was at the same time going on in the rest of the world. 3. A mental demand for the cause and the conse- quence of historic action. — Early in the life of children we often hear the inquir)^, "Why did you do that ? " This is one of the first manifestations of an instinct to investigate the causes of action. Such investigations are at first con- fined to the child's actual surroundings, and they generally have reference only to actions that affect his own physical or mental well being, or his personal rights. It is much later when he carries these inquiries outside into the matters of history. In these early years, his instinct deals only with the causes, not the consequences, of personal actions. Long afterwards the tendency asserts itself to trace action to the effect it produces. It is related that a lawyer once advertised for an office boy. On the day indicated, a large number of applicants appeared. The lawyer said, " Boys, before I decide which one of you I § 6 PEDAGOGICS OF HLSTORY. 43 shall select, I wish to tell you a story. " He then very vividly, as some lawyers can, related an incident that may be out- lined as follows : "A farmer one night heard a disturbance near his barn among- his pcoultry — with his gun, he went to the barn — an owl sat on the roof — the farmer shot at it — the wad from his gun lodged among the dry shingles and fired the barn — it burned rapidly — his horses and cows were in the barn — he attempted to save them — his life was lost in the effort — his wife, in trying to rescue her husband, was burned to death — the barn, the farmer, his wife, and all the stock were consumed." The boys listened with suspended breath, and a deep sigh at the close told the story of the intensity of their interest and sympathy. Presently one of them asked, " Mister, did he hit the owl ?" "You are the boy I want," answered the lawyer. In this is an illustration of the fact that the instinct to trace events to their legitimate outcome has a market value. Doubtless the student is familiar with the myth con- cerning Epimetheus and his brother Prometheus. Their names, denoting afterthought and forethought, are indicative of their mental qualities. Most people have Epimetheus, and very few, Prometheus, for their prototype. 4. A;/ iinpnhc to criticize Jiistoric action, and to make inferences from it. — Criticisms of historic events generally have reference to the motives of action, and are based upon the assumption that actions have an ethical quality — right- ness or wrongness; or they concern the expediency of the means employed to accomplish certain ends. 40. Ktliical Criticism. — To illustrate what is meant by ethical criticism, the incident may be cited of the slaughter, by order of Napoleon, of nearly 1,500 Turkish prisoners taken at the storming of Jaffa. His biographers and critics are still disputing whether the exigencies of the situation and the laws of war warranted the act. And the people of our own country are by no means unanimous on the question whether General Grant was right to "fight it out on this line if it takes all summer. " He had to choose between a more dilatory 44 PEDAGOGICvS of HLSTORY. § 6 method with a probable saving of life, and the method that he adopted, that of ending the war quickly by sheer force of superior numbers, and without considering the lives it might cost. Much is to be said on each side of such questions, and it is a part of the teacher's work to develop in his pupils a critical instinct that looks at historical events from all sides. To a child, the ethical quality in human deeds is quite overshadowed by heroic action and daring. The doings of the pirates of the Spanish seas create no sentiment of revolt- ing and horror; they are only fearless freebooters whose legitimate prey is the world. The horrors of battle are quite lost in the glorious exhilaration as he reads or hears of the rush of infantry, the thunder-like roar of artillery, and the magnificent charges of cavalry. There is no room in his young heart for pity of the vanquished, he cannot hear the groans of the wounded, or see the white iipturned faces of the dead. Very slow is the growth of the ethical sense. Even "children of larger growth" have a very rudimentary notion of the right and the wrong in human action. There is gradiially developed in every mind a disposition to predict or infej what is to happen next in any succession of events; or to conjecture the occurrences that have pre- ceded a given state of things. When Robinson Crusoe saw the strange footprint in the. sand, the remains of a fire, and the bones that he recognized as human, his first mental impulse was to seek an explanation of these phenomena. His earliest conclusion was that his island had human inhabitants other than himself. This he investigated and disproved, and thiis established the alternative fact that the island had been visited by cannibals. So far he had been making inferences as to what had already happened. Now he begins to deal with the ////// ;r. " They will return. What has happened is likely to happen again." Such is his thought, and from that time he is in daily expectation of their return. 41. Test of the PoAvei* of Inference. — ^To test the power of inference in young students of history, Mary Sheldon Barnes gives the following as a typical exercise : § G PEDAGOGICS OF HISTORY. 45 " If you were shipwrecked on an island in the middle of the sea, and [if J you found in one corner of the island an old house of logs, and part of an old wooden boat with broken arrows in the bottom of it, what would these things tell you ?" Many children of different ages and degrees of intelligence were required to give their views in writing. Their infer- ences as to what had happened on the island were carefully collated, and some very instructive conclusions were reached regarding the development of the faculty of critical, legiti- mate, and historical inference at different school ages. The stitdent will find her little book, "Studies in Historical Method," to contain much suggestive and valuable help. 4^. Method of Developing: tlie Historic Sense. — Having set forth pretty fully what is meant by the historic sciiSL\ we shall now explain what is generally conceded to be the best method of developing it. Nowhere in the world has history been so successfully , taught as in Germany. The subject is handled there in such a way as to make the student an intelligent and a persistent reader of history during his entire life. His training is such, too, that his subsequent reading is methodical and systematic. He is not taught to " hate history," but it is to him an inspiration and a discipline. With him the period of his- torical study preceding the university work covers about nine years — from the age of nine or ten to about nineteen. It is during the first five years that the Biographical method is employed. This method we now proceed to describe. The first two years of historical work are taken up with stories told by the teacher about the great men and the great events of the world. In this work no dates are given, and times are indicated only approximately. The central pur- pose is to awaken and develop the historic sense, and to this end, the impressions must be the most vivid possible. Only teachers specially trained are employed in this work. Of course no textbooks or books of any kind are used. It is much the same as the entertaining of children by telling them stories in the nursery. These stories occupy a half 46 PEDAGOGICS OF HISTORY. § G hour each, t\\'4ce a week, and, naturally, they are eagerly anticipated by the pupils. They serve to carry the children from their own narrow sphere into the great world of heroic effort and achievement beyond, and to awaken vague ambi- tions and hopes concerning their own future. Every one knows the intense interest and delight that children find in a story well told, and no effect upon the mind endures as does that made during highly wrought emotion. Leonidas, "lion-like," becomes, to the child so taught, a type of heroic and unselfish devotion to country forevermore. Salamis — the heart of the child will beat faster hereafter when he hears the name. Themistocles, Aristides, Demosthenes, Lycurgus, Socrates, Alexander — what a mine of biographical wealth the old Greek race furnishes for the delectation of the stu- dent, and the ideals and aspirations of men are higher and nobler for the lives of such men. In these tales, the teacher naturally begins with his own country, and proceeds in an orderly way with the epoch- making men and events of other countries. Gradually, as the horizon of the pupil widens, he comes to feel the need of greater definiteness as to time and place, cause and effect, ethical fitness, and means and motives. Geography lends its aid. " Here was born this great man; here he did his work; here he died and was buried." "On the banks of this river the battle was fought; here, through a mountain pass the defeated army attempted to escape and was destroyed or captured." Little by little, pity for the vanquished and for the subsequent fate of those whose fiiture was ruined by the defeat, begins to take its place in the child's heart, and questions of right and wrong — the ethical sense — are vaguely outlined in his consciousness. And, thus, slowly indeed, but surely, is built up a mental substructiu-e upon which shall rest later a symmetrical knowledge of history. At the end of two yeans, the same ground is gone over again, but in a different way. The Biographical method is still pursued, but this time the object is to link events into a harmonious outline. The elements of time and place, of § EUATl()XS. 5(5. V^astuess of tlie Subject of History. — In the early years of the present century, it was- possible for a student to become tolerably familiar with almost the entire field of ordinary human learning, at least so far as it had been written in our own language. Comparatively little had been done in the physical sciences and in mathematics. Most of the scholarship of the world was engaged in endless disputes about metaphysics, theology, and other nebulous subjects. It is true that some great historical work had been done, but in all of it, the real, the inner life of the people, was almost completely ignored. Historical investigations were not minute and scientific, as they are now. Kings and courts, and political intrigues, and battles, and military leaders absorbed the attention of historians, to the exclusion of what is now regarded as history. Modern methods of investiga- tion have since been introduced in every quarter, and the domain of all the inductive sciences has been expanded to such an extent that no person can hope to master completely, in our short lifetime, any one subject, even if he neglects every other. In a recent conversation with, perhaps, one of the greatest of living organic chemists, he said to the writer that a perfect (i2 PEDAGOGICS OP^ HISTORY. g i; knowledge of organic chemistry would involve the necessity of remembering at least eight million formulas, processes, combining proportions, affinities, reactions, incompatibles, etc. Discussing the adjustments necessitated in educational methods by the division of labor in scientific investigations, and by the development of specialties, he said that education in the early future will be measured by facility in consulting and understanding books of reference. -However this may be, it is certain that the men that make their mark most indelibly on the scroll of the world's progress — the men whose success in life is the greatest for themselves and the most valuable to the world — are the specialists. These are the men that learn to do some particular thing better than any one else can do it. Such men compel those that seek the best of its kind to come to them. They are not obliged to seek a market for their products. Alvan Clark might have removed to the other side of the earth, but orders for the largest and best lenses that are made would have fol- lowed him, and he coiild have fixed his own price. Steven- son took refuge in far Samoa, but he could not get away from the demand for finished and masterly literary work. With respect to such men as Dickens, Gladstone, Pasteur, Tyndall, Bell, Tesla, Edison, the important thing is that they be alive. Where they may happen to be is of slight importance. The world will find them with its cry for help. This necessity for devoting one's best powers to some specialty is applicable also to the subject of history. He that wishes to become great in understanding, writing, or teaching history must make it a life work. He must, more- over, love his work. And, even if one does not mean to devote his attention to history exclusively, he must, to teach it w^ell, be a persistent student of the subject. 57. Division of Liabor In Teaeliing;. — The assignment to different persons of the several parts of a task consisting of many elements and processes is not confined to science, commerce, and the various industries. Our best schools are doing the same thing. And this is true not only of our § 6 PEDAGOGICS OF HISTORY. 63 colleges with their professors for special subjects, but also of many of our public schools. The best teacher of mathe- matics teaches mathematics, and the same arrangement is made with respect to other subjects. And this is a usage that is growing and has come to stay. It is reaching farther and farther down along the grades in our system of educa- tion. When our population becomes denser the graded system will be introduced even into our country schools, and we shall have different teachers in language, in reading, in writing, in geography, and in history. Even the little folks of the kindergarten will look to one teacher for their knowl- edge of numbers, to another for manual devices and physical expertness, and to still another for language training. No machinist can make equally well the various parts of a loco- motive ; neither can a teacher secure equally good results in every school study. The extension of the division of labor to teaching is .some- thing to be wished for and encouraged. Many of our cities and towns have introduced it, and, wherever this has been done, its great advantage has been demonstrated. Should the introduction of the division of labor in the work of education become general, it will necessitate the training of teachers in special subjects; and, although a generous all-sidedness of culture in a teacher will still be required, the one subject for which he has the greatest liking and aptitude will be emphasized in his preparatory training. 58. Objections to Sijecializatioii in Mental and Physical Training. — Nowhere in the world has devotion to single subjects of study been more general than in Ger- many. Critics of German culture have made the point that such special training in one subject has the effect of dwarfing in every other. They allege that the Germans do not have a single complete history of their own country — only an unorganized collection of brilliant treatises, each of which covers a particular period. This is doubtless true, but is it something to be deprecated ? It may be said, in answer, that if one desires the best possible treatment of almost 64 PEDAGOGICvS OF HISTORY. § 6 any subject, he must go for it to the Germans. The best cyclopedias, the most accurate maps, the most profound mathematical investigations, the ablest works on logic and metaphysics, the highest Greek and Latin scholarship, even the most excellent English grammar, and the most appre- ciative and scholarly edition of Shakespeare — all these are German. And after all is said, is it not perfection in details rather than imperfect general schemes that the world most needs ? If a great bridge is to be built, do we not seek out the greatest engineer available ? He does not, perhaps, know Greek or Sanskrit, he is not an athlete or a chemist, he is unacquainted with whist, and golf, and baseball ; but what of that ? He is great as an engineer, and that is the impor- tant matter. The great military leader cannot be at the same time equally great as the leader of an orchestra; Newton cannot do the work of Mozart, nor can Michael Angelo conduct the investigations of Faraday, Darwin; or Pasteur. "Jack of all trades, but master of none " is a more serious criticism than that urged against the specialization of the Germans. The world will see no more masters of uni- versal learning — no more Scaligers or Admirable Crichtons. It needs rather men eminent in specialties. Moreover, the most effective training is in the direction of inherited tend- ency. It was vastly easier to make of Patti a great singer and of Rosa Bonheur a great painter, than it would have been to make of the former even an ordinary painter and of the latter a mediocre singer. Find out what your boy was born for, and help him to become eminent if he can. Ger- man specialization is the only development that is perfectly rational and perfectly natural. COPtIl>:T^ATIO:N^S OF HISTORY. 59. Interrelation of Subjects of Study. — While, from the foregoing considerations, it is clear that the great- est eminence and usefulness are attainable only by devotion to one subject, it is equally clear that no subject is entirely § 6 PEDAGOGICS OF HISTORY. Go isolated from every other. Perfection in one thing implies a certain degree of acquaintance with many related matters. The great scnlptor must know anatomy, human and com- parative; the eminent engineer must be acquainted with graphics, the strength of materials, the laws of momentum, the effects produced by changes of temperature, and the general properties of matter. Similarly, the subject of his- tory has its related subjects. These are many, and each is extensive enough to constitute a life work for the greatest intellect. The student or teacher of history, therefore, can- not know all these thoroughly. The field is too wide for the brief span of life. He may, however, understand their gen- eral principles and the nature of their connection with his specialty. Before entering upon a consideration of the sub- jects with which history is correlated, it is necessary to understand the meaning of correlation as used in educational science. 60, Meaiiini>' of the Term ''' Correlation/'' — Tlie word correlation has only very recently been introduced into pedagogical writings. The consequence is that its precise signification, when so used, has not yet been settled. The term, as generally used, may be defined as the act of bring- ing into mutual or reciprocal connection, action, or corre- spondence, two or more persons or things, or it is the state of their being in such relation. Applied to the subject mat- ter of education, there is much diversity of meaning attached to the term. By some it is interpreted to mean that all subjects of study are more or less closely related to one another; so that an adequate knowledge of any one implies and necessitates an equal or a partial knowledge of every other. To illustrate, no one can be fully acquainted with the subject of music, if he is ignorant of acoustics and of the mathematical relations of the different wave lengths in the propagation of sound through air; for upon these is depend- ent the entire theory of harmony and discord. 01. Coiiniiittee of Fiftooii. — Others, again, insist that, because such relations exist among subjects of study, none 6G PEDAGOGICvS OF HISTORY. § (i of them should be taught apart from the rest, but all should be taught in conjunction. The extreme advocates of this view insist that some literary work should be taken as a sort of text from which the study of all school subjects should proceed with equal step. In the report of the Committee of Fifteen, and in the discussion that followed, reference is made to the story of Robinson Crusoe as such a center, from which every needful study may be evolved and fully taught. The following quotations from the report of that committee will be instructive : " Your committee would mention another sense in which the expres- sion ' correlation of studies' is sometimes used. It is lield by advocates of an artificial center of the course of study. They use, for example, Defoe's 'Robinson Crusoe' for a reading exercise, and connect with it the lessons in geography and arithmetic. It had been pointed out by critics of this nietliod that there is always danger of covering up the literary features of the reading matter under accessories of mathematics and natural science. If the material for other branches is to be sought for in connection with the literary exercise, it will distract the attention from the poetic unity. On the other hand, arithmetic and geography cannot be unfolded freely and comprehensively if they are to wait for the opportunities afforded in a poem or a novel, for their development. A correlation of this kind * * * * is a shallow and uninteresting kind of correlation, that reminds one of the system of mnemonics, or artificial memory, which neglects the association of facts and events with their causes and the history of their evolution, and looks for unessential quips, puns, or accidental suggestions with a view to strengthening the memory. The effect of this is to weaken the power of systematic think- ing which deals with essential relations, and to substitute for it a chaotic memory that ties things together through false and seeming relations, not of the things and events, but of the words that denote them. "The correlation of geography, and arithmetic, and history, in and through the unity of a work of fiction, is at best an artificial correlation, which will stand in the way of the true objective relation. It is a temporary scaffolding made for school purposes." Farther on the report contains the following: " The story of Robinson Crusoe has intense interest to the child as a lesson in sociology, showing him the helplessness of isolated man and the reenforcement that comes to him through society. It shows the importance of the division of labor. ****** Consequently, the § 6 PEDAGOCxICS OF HISTORY. G7 history of Robinson Crusoe is not a proper center for a \'ear's study in school. It omits cities, governments, the world commerce, the inter- national jDrocess, the church, the newspaper and book from view, and they are not even reflected in it." 6'^. Remarks Upon the Foregoing- Quotations. — The writer believes that the abstirdity and uselessness of the method of correlation described and criticized in the fore- going quotations will be sufficiently obvious to every thoughtful teacher. It appears to be necessary, however, that some additional comments should be submitted. In the first place, then, there seems to be little question that every subject of study should be taught as a distinct entity — as isolated and complete in itself — except in so far as matters belonging to other subjects are used to illustrate and emphasize its principles. These illustrations should, in general, bear a relation to the main subject similar to that in geometry between a demonstrated proposition and a corollary to it. These correlation extremists have a notion that many branches can be successfully studied together, and that the law of association is thus utilized in the best possible manner. As well might one attempt to learn a half dozen trades at the same time. It is not meant that, when we study one subject, its relations to others must be care- fully excluded from consideration; it is intended only that side issues must not be permitted to cloud, and so to divert attention from the main subject as to destroy its unity. And just here the writer may be permitted to remark that teachers especially should endeavor to see matters in proper proportion and with due reference to their relative impor- tance. The world is full of enthusiasts on every subject, of people that have discovered the "much sought kaloii." These people imagine that they can tell us how to do per- fectly what the world has hitherto been able to do only indifferently well. They know an infallible remedy for every disease, and how to perfect every process or method. To them, everything that is, is cankered, and the world has been waiting and yearning for their arrival to set things right. There is something contagious about the enthusiasm 68 PEDAGOGICvS OF HISTORY. § 6 of these evangelists of "fads," and teachers should not permit themselves to be deluded by trivial matters that have been exaggerated out of all proportion to other things. The teacher of music comes to imagine that, in our schools, his speciality is the main thing — that children are created prin- cipally in order that they may sing. Everything else should be subordinated to music. The man employed to super- vise drawing, the teacher of physical training, of sewing, of cooking, of manual training, the instructors, in short, in the various other "educational fringes, " as some one calls them, all labor under a similar hallucination. Their zeal in urging the claims of their several specialties has resulted in crowding into the curriculum of the schools many matters of slight educational value, to the neglect or exclusion of others that are really essential. They smile in a commiserating way when any teacher or educator ventures to protest. "Poor fellow, he is behind the times; he forgets that the world is progressing in educational science, even though he himself makes no advance. " He has to bear the odium of being regarded as an apostle of the " three R's. " The fact is « that all these matters have educational value, but relatively to many others, their value is very slight, and not overshadow- ing, as their advocates actually believe. These subjects are like the quantities known in mathematics as iiifiiiitesiinals, which denote real quantity indeed, but which, in comparison with finite quantity, may be regarded as zero and dropped out of consideration. But this tendency to exaggerate the importance of the subject that one knows best, and can teach best, is general. The teacher that can teach languages best imagines that his specialty is of paramount value, and so on for the others. It would be difficult to overstate the importance of the teacher's having definite and correct views of comparative educational values. Having such views, he will know what amount of time and effort should be given to each branch, and he will preserve a wise conservatism with respect to the new matters that are constantly being urged for a place in the course of study. g (> PEI)A(i()(;iCvS OF HISTORY. (iO G3. Correlation of History Witli (ieog'rapliy. — As has been stated, it is not meant that correlated subjects are to be taught together and finished at the same time. It is intended only that certain facts belonging to one subject have an illustrative bearing upon another, and serve to emphasize it, and give broader and more significant views concerning it. These facts aid in discovering general laws. This is espe- cially the case with physical and political geography as aids in the study of history. The settlement of countries, the development of colonies, the direction and rapidity of this development, the rise and fall of civilizations, the products of the earth and their exchange among nations; all these, and many other factors affecting the history of the world, are not fortuitous — the result of mere chance. They are determined more by the physical features of the earth than by any other influences. River basins, mountain systems affecting rainfall and climate, ocean currents and their accompanying air currents, elevations of surface, and innu- merable other facts of physical geography have dominated the history of the world to such an extent that they must be taken into account in any intelligible view of the progress of the race. All these must be noted in teaching history. For example, in the history of America, why are the great com- mercial centers just where they are ? What gives Chicago, Philadelphia, Duluth, Mobile, New Orleans, Charleston.^ San Francisco, New York, and Boston their importance ? Upon what do the fertility and climate of the Pacific States depend, and why are the states between the Rocky Mountains and the vSicrra Nevada nearly rainless ? Upon what does their prosperity largely depend ? To what are owing the wealth and fertility of the Mississippi Valley and the Atlantic Slope ? Why were the original thirteen colonies all included between the ocean and the Appalachian System ? What influence are railroads, and artificial waterways, and irriga- tion likely to have upon United States history ? What advantages do we derive from our geographical isolation, and what are the chief arguments in favor of and against a policy of colonization ? Such are some of. the questions :(i PEDAGOGICvS OF HISTORY. § having' a bearing upon the study of history. Political geog'- raphy, too, throws a flood of light upon history. The thoughtful teacher, with these side lights, can give unity, coherence, and interest to history to an extent that is possible in no other way. With their aid, laws and principles emerge from confusion and detail, and events take on a new and deep significance. ' History ceases to be a mass of unrelated facts and dates, and its determination by the laws of cause and effect — of necessaiy sequence not in time merely, but in every other important relation — becomes apparent. (54. Correliition of History VYitli Sociology and Political Science. — The term sociology, as the name of a science, is intended to include in its scope "the origin and history of human society and social phenomena, the progress of civilization, and the laws controlling human intercourse." Sociology is not to be regarded as mere history, but as a philosophical study of society. But considerations relating to men as forming society are so closely allied to those relating to men as organized politically and forming states, that the teacher of history is not properly ecjuipped for his work unless he is familiar with the data, the inductions, and the generalizations of sociology. The remarkable work of "Sociology," by Herbert vSpencer, is indispensable to the teacher of history. It will bear reading many times. If, besides, the teacher has access to the same writer's monu- mental work on "Descriptive Sociology," the source from which Mr. vSpenccr largely gathered the material for his " vSociology, " great advantage will be derived. Equally close in correlation with history is political economy, or "that branch of civics that treats of the nature of wealth and the laws of its production and distribution, including all the causes of prosperity and the reverse. It discusses labor, wages, population, capital, money, rent, value, trade, and the relation of government to industry and economic conditions." With a knowledge of the principles and laws of political economy, which are themselves derived from human experience as revealed by history, the teacher § G PEDAGOGICS OF HISTORY. 71 can interpret for himself the canses and consequences of political action, and make them clear to his pupils. The principles that regulate good and bad political action, both in individuals and in nations, are but dimly seen without the guidance of political economy. Many excellent treatises on this subject are of easy access, but perhaps one of the best is Professor Laughlin's abridgment, with notes, of the work by John Stuart Mill. Under the general science of civics is included the subject of international law and usage. This, with reference to ques- tions arising in war, is, at this writing, of especial interest in the United States. Every teacher should be familiar with this subject, particularly if he is a teacher of history. President Woolsey's work, and that by George B. Davis, Judge Advocate of the United vStates Army, will be found interesting and instructive. G5. Correlation of History Witli l^tliios. — Ethics, or "the science of human conduct considered with respect to rightness and wrongness, " includes, in its most general sense, the various branches of political and social science, civil, political, and international law and jurisprudence. In its application to history, it is intended to consider the moral quality of individual and national conduct which, next to cause and effect, is one of the most instructive aids in the teaching of history. Without it, action is divested of that which makes it distinctly human, nations and individuals act without conscience, and history engages only the intellect. " Was it right or was it "wrong ? " "What should he have done under the circumstances ? " "Was the punishment in this case deserved ? " " Did the nation act in this instance as an individual should have acted ? " These, and innumer- able c[uestions like them, should constantly be started with thoughtful pupils. Judiciously employed, they serve rather to emphasize than to destroy the unity of history. The teacher, therefore, should be acquainted with both theoret- ical and practical ethics, and should be skilful in applying their principles to the subject he teaches. Of the sources of n PEDACiOGlCS OF HISTORY. § (1 information, no special mention need be made, for there are innumerable treatises readily available. 6G. Conclusion. — It is hoped and believed that what the writer has herein set forth with much care, and which he has gleaned from many years of personal experience in the classroom, from many other years in supervising the work done by others, and from inuch reading both of writers of our own land and of France and Germany, will prove to be valuable to the student and spur him to higher ambition to excel. However this may be, one thing is certain; he that would succeed in the difficult and useful profession of teaching must himself earn success. . He should form a habit of self-criticism, and aim to do, year after year, better work than ever before. He should not be willing to settle down into routine methods, always doing the same things in the same way. Some one has said that poets and teachers are inade in heaven. Such aphorisms may, many of them, be relegated to the limbo of fancy. wShall we not rather say with Richelieu ? — " In the lexicon of j-outh. which Fate reserves for a bright manliood, there is no such word As—/ai/." PEDAGOGICS OF ORTHOGRAPHY. IXTRODirCTIOX. DEri:N^iTio:N^s and ci^assifications. 1 . Defliiitiou of Orthogi'Jiphy. — The word ortliograpJiy is derived from the Greek dfr^ix;, ortlios, right, and ypdcf)Fiv, graplicin, to write. Its literal meaning is, therefore, ivri- ting correctly. As commonly used, it means "a mode or system of spelling-, especially of spelling correctly or accord- ing to nsag-e." In a usual and wider sense, orthography is the science or art that treats of letters and .spelling, inclu- ding orthoepy, or correct pronunciation, and phonology, or pJioiietics, which is the science of "human vocal sounds, their relations one to another, and their interchanges." Orthography was, until recently, classified as one of the four divisions of grammar, the other three being etymology, syntax, and prosody. It is properly a branch of grammar, but its treatment has been relegated to the spelling- book and the dictionary, just as the subject of pro.sody has been turned over to the works on rhetoric. But the complete separation of orthography from grainmar is not possible, and, perhaps, not desirable. If the student will examine any of our spelling books, he will find that the derivation, the composition, and the meaning of words have in these books much to do with the arrangement and general treat- ment of orthography. But these are questions of etymology^ 2 PEDAGOGICS OF (JRTHOGRAPHY. §7 which has been retained as one of the two general divisions of grammar as now treated. In this Paper, therefore, it will be assumed that orthography includes every considera- tion with respect to words that will aid in mastering their spelling and pronunciation. 3. Alpliabets. — The term alphabet is made up of alpha and beta, the names of the first and the second letter of the Greek alphabet. Of thisw^ord, Max Mliller, the great philol- ogist, says, "The only word that is formed of mere letters is alphabet, the English a-b-e." The invention of the earliest alphabet is lost in the time prior to authentic history. Authorities are mostly agreed that the oldest writings in which letters are combined in words are the Hebrew writings. The earliest letters of the Hebrew and the Phenician alphabet are almost identical in name, form, and sound, and it is impossible to say which alphabet is the older. It is stated in the "Encyclopaedia Britannica " that the Phenician alphal^at w-as the parent of almost every alphabet, properly so called, existing on the earth. Of the Greek alphabet, from which our own is in the main derived, Dr. Raphael Kiihnersays, " The Greeks derived most of their alphabet from the Phenicians. According to the common tradition, letters were brought into Greece by Cadmus, a Phenician. The Phenician alphabet, being nearly the same as the Hebrew, consisted of twenty-two letters. Nineteen letters of the Phenician alphabet were adopted by the Greeks as alphabetic characters. These are the first nineteen letters of the present Greek alphabet. To these the Greeks themselves added the last five letters; viz., npsiloii, phi, cJii, psi, and omega. This seems to be the most rational view of the formation of the Greek alphabet, though somewhat different from the common legendary account." The legendary account referred to above is as follows: Cadmus, a son of Agenor, King of Phenicia, was sent by his father in quest of Europa, who had been carried oif by Jupiter. Ordered not to return without his sister, and having failed to find her, Cadmus settled in Breotia. He introduced § 7 PEDAGOGICvS OF ORTHOGRAPHY. 3 among the Greeks sixteen letters from the Phenieian alpha- bet. To these Palamedes subsequently added four more, thcta, xi, phi, and chi ; and vSimonides, at a still later period, added four others, r.eta, eta, />si, and oiiifga. The alphabets of different nations differ in the number of their letters. According to one of our latest authorities, the Italian alphabet has 31 letters, Hebrew and Syriac 23, Latin 23, Greek 2-i, French 25, English, Dutch, and German 2G, Spanish 27, Arabic 28, Coptic 32, Russian 33, Armenian 3S, Georgian 39, Slavonic 40, Persian 45, Sanskrit 49, etc. The Chinese language has no alphabet, but it has instead about 30,000 arbitrary characters. The language is said to be uicviosyllabic, thougli the word syllabic (from the Greek avv, sj'ii, together, and /iaiiiiavco, lamba)u\ I take) implies separable parts having vocal completeness. It is obyious, therefore, that a good alphabet is an extremely important aid to human learning, and, hence, to civilization and prog- ress. For example, the chief obstacle in the way of the advancement of the Chinese is the fact that they have no alphabet, and, thjrefore, practically no language that can be read and understood by the common people. General cul- ture is, therefore, impossible. To learn to understand and write 20,000 arbitrary characters having nothing in common, and without anything but local agreement to determine their pronunciation, is a life work even for a person above ordi- nary intellectual endowment. Having no letters, they have no established sounds, and, hence, no general code of pro- nunciation. It results, therefore, that, while two learned Chinese are able to read and understand the same book, they may be unable to converse with each other. Most of the common people in China are unable to read and write, and those that can do so have vocabularies limited to a few hun- dred words in daily use. In solving the problem of civilizing such a people, the first requisite is to devise for them an alphabet. Such an inven- tion would necessitate the abandonment of their language, and the learning of a new one. But all human experience in such reforms demonstrates that the total obliteration of 4 PEDAGOGICS OF ORTHOGRAPHY. § 7 an established language, and the substitution of another entirely different, is impossible. In confirmation of this statement, it is necessary only to mention the result of the many attempts to improve our own language. Such changes must not be radical, and mvist be wrought by the slow proc- esses of evolution. These considerations lead to the unavoid- able conclusion that the same fate awaits the Chinese that has overtaken the North American Indian and many other aboriginal races of the world. The superiority of the old Greek civilization was doubtless owing largely to the fact that their language was more nearly perfect than any other that has ever been devised. The "decline and fall" of nations, when face to face with superior civilizations, is owing more to differences in language structure than is generally supposed. It is merely a result of the operation of the law of "the survival of the fittest," involving the obliteration of the unfittest. For further information relative to this curious and inter- esting subject, the student is referred to Isaac Taylor's "The Alphabet." 3. J^ames of tlie Letters and IIo^v to Write Tliem. — In pronouncing the names of the letters of the English alphabet there is general uniformity, but in writing and in pluralizing their names the case is otherwise. Goold Brown says, " The names of the letters, as now commonly spoken and written in English, are A, Bee, Cci\ Dcl\ E, Eff^ Gee, Aitch, I, Jay, Kay, Ell, Evi, En, O, Pee, Kiie, A?', Ess, Tee, U, Vee, Doublc-u, Ex, IVy, Zee I know not whether it has ever been noticed that these names, like those of the days of the week, are worthy of particular dis- tinction, for their own nature. They are words of a very peculiar kind, being nouns that are at once hotli proper and covinnvi Their names, therefore, should always be written with capitals, at least in the singular number; and should form the plural regularly. Thus, A, Aes ; Bee, Bees ; Cee, Cees ; Dee, Dees ; E, Ees ; Eff, Effs ; Gee, Gees ; A it ell, Ait c lies ; I, les ; Jay, Jays ; Kay, Kays ; Ell, Ells; § 7 PEDAGOGICS OF ORTHOGRAPHY. 5 Eui, Ems; Ell, Ens ; O, Ocs ; Pec, Pecs; Kite, Kucs ; Ar, Ars ; Ess, Esses; Tec, Tecs ; U, Ucs ; Vcc, Vers; Doiiblc-u, Doublc-ucs ; Ex, Exes; W'j, IVws ; Zee, Zees." Brown quotes from Shakespeare, " Then comes answer like an A B C book." " Then comes question like an a, b, c, book." Of these he remarks, " Better: ' like an A-Bee-Cee book,' " It will be noted that Brown distingfuishes between the alphabetic characters and their names. But is such a dis- tinction necessary ? The w^riter thinks not. Let the student consider the following, and decide which is better: " Cross your /'s and dot your /'s. " " Cross your Tees and dot your les. " ' ' The word pepper is half /'s. " ' ' The w^ord pepper is half Pees. " " There are two /r's in /itr/i, and two 7i''s in ielie7i>. " " There are two A itches in hah, and two Doiib/e-ues in wlieivS' " How many j"'s and how many j''s in syllable ? " " How many Esses and how many Wies in syllable? " The same reasoning that makes A itch a proper name would make the name of a prefix, a suffix, a root, a word, or of any symbol, a proper noun; but no one thinks of writing any of these as proper nouns. Thus, 5, +, (^, 4/, etc., so far as their written names are concerned, are five, plus, clef, radical sign, and not Five, Plus, etc. In the plural, also, Brown writes the names of the letters wath capitals; now, it is well known that a noun strictly proper cannot take the plural, for it is a name peculiar to an individual. It is true that we have a usage like the following, in which the capi- tal is retained : " There are more Georges than Henrys in this school, and more Marys than Elizabeths.'' "The Shakespeares of the world have done more for its advancement than the Napoleons." But these words so used are class names, and hence, although they are written with capitals, they are common nouns. Besides, in pluralizing such words, we do not u.sually follow the general rule, but add s. Thus, Mary pluralized G PEDAGOGICS OF ORTHOGRAPHY. § 7 is Marys, not Maries, and Henry is Henrys, not Henries. But Brown makes JT/rj- the plural of Wy, Aes the plural of A, and C/es the plural of 6^^, It is extremely doubtful whether any considerable number of people could interpret the fol- lowing sentence, if the meaning of the writer were not indicated by the context: "The vocal values of the JVies are different in sysyg-y, which totally lacks Double-iies.'' But the meaning is perfectly plain when these strange words are written j''s and tl-'s. 4. Symbols and Tlieir Plurals. — It should be noted that, with the exception of letters and Arabic numerals, it is generally better, especially when the plural is required, to write i}i words what is meant by mere symbols. Thus, we should prefer division signs or signs of division to -=-s or -f-'s, G elefs to (^s or ^'s, ratios to :s or :'s, radical sig//s to |/s or j,'"s, etc. But, in textbooks on particular subjects, sym- bols may first be explained, and afterwards used instead of words. Thus, in arithmetic, o-^-d = Jl is better than //le snni of five and six is equal to eleven ; in geometry. As is preferable to triangles; and in chemistry, Fe,fi^ is more satisfactory than sesqnioxide of iron. There are inany exceptions to this, however, and, in general, it is taste that must decide the questions that arise. There is no work in which the subject has been fully treated by a competent authority, but there is usually a way out of every difficulty of the kind. Very frequently a symbol and its explanations are both given, the symbol being generally enclosed in a parenthesis. "The sign of equality (=) denotes that the quantities between which it is written are equal. " " In works on astronomy, the planet Neptune is denoted by a representation of a trident {^), and the planet Venus by the figure of a mirror ( 9 ). " 5. A Perfect Alphabet. — Frequent attempts have been made to modify our alphabet, and the dream of many that § 7 PEDAGOGICS OF ORTHOGRAPHY. 7 have realized its imperfections has been, if not to devise one that is perfect, at least to approacli this ideal as nearly as circumstances will permit. For the difficulties in the way are many, and some of them are insurmountable. It will, therefore, be interesting- to inquire what should be the leading- characteristics of a perfect alphabet. TJie spelling of a x^'ord must denote its proniineiation i^nth mathematical exactness. There is no language in the world that is pronounced precisely as it is spelled. Certainly the English is not. It is scarcely necessary to cite illustrations of this fact. The bewildering series of words containing ongh would suffice. A part of this series includes cough., plough, tough, hough, bough, sough, dough, lough, and this fact may explain why some one has proposed poughteigJiteaux as a "reform spelling" inv potatoes. The German is often mentioned as a language in which the spelling of words indicates their pronunciation, but this is only partially the case. For example,^-,'", d, and.?, when final in words and syllables, are not pronounced as when they are in other positions, and these differences are not uniform throughout Germany. Thus, s in Ihsinarck is sounded like s in sir, and .S" in Sohn is like our z ; g in Ding\^ very nearly our /', and in guter, g is like g in good ; etc. Many other variations in the sounds of particular letters might be noted, but it is not necessar3\ There must be as many different characters as there are elementary sounds. This condition is not realized in the case of any language, and in the nature of things cannot be, for no instance can be found of uniformity of pronunciation in different parts of any given coimtry. In the United States, for example, the authorized sound of a in glass, mass, pass, etc. is very commonly displaced by the short sound of a as heard in mat ; and a short (a) in barrel, marry, etc. are gen- erally pronounced as a in arm. One of our latest and best dictionaries recognizes this divided iisage by an article on "Variant Pronunciation," in the course of which we find, "A few of the most common cc^iditions of variation have been applied, the most important of which are in 8 PEDAGOGICS OF ORTHOGRAPHY. § 7 words colloquial and words technical or scientific. Others occasionally introduced are poetical, devout, hmnorous, in certain old phrases. Pronunciation is really a work of art, one of the fine arts. A great orator or [a] conversationalist deals with varying shades of voice as an artist with the tones of a violin. " Richard Grant White, in "Words and Their Uses," says, " In pronunciation, the usage of the most cultivated people of EnglivSh blood and speech is absolute, as fa?' as their 7isagc itsc/f is fixed. Pronunciation is the most arbitrary, varying, and evanescent trait of language; and it is so exceedingly dilificult to express sound by written characters that to con- vey it upon paper with certainty, in one neighborhood for ten years, and to the world at large for one year, is practi- cally impossible. " Every eoinbiuatioii of sounds in 7uords must eoalesee easily. If the student will pronounce a few words like /ist/essness, />artie7(/ar/y, and stre)igtJie)iedst, and will note the degrees of difficulty in adjusting the tongue, teeth, lips, palate, throat, etc. as he passes from syllable to syllable, and if afterward he will do the same with such words as lullaby., Agameniuou, tintinnabulation., and harmonious., he will understand what constitutes easy and difficult coalescence. Upon easy coales- cence depends not only the music of words, but also the har- mony of language. A perfect alphabet must contain no gutturals and hissing sounds, and no broad vowels like the German a ; and a musical language must abound in liquids and labials — /, ;//, ;/, r, /, b. Some one says, "If Zeus were to visit the earth he would speak only the Greek of Plato," and yet Plato's Greek con- tains one of the most ofifensive of gutturals, % sounded as cJi in loeJi, and has several hissing sounds. The Greek has by no means a perfect alphabet. The student is doubtless familiar with the following: "I would speak Spanish with the gods, Italian with my lady friends, French with my gen- tlemen friends, German with soldiers, Hungarian wnth horses, English with geese, and Norwegian with — His Satanic Majesty." § 7 PEDAGOGICS OF ORTHOGRAPHY. 9 (y. Spelling- Reform. — An eminent writer on grammar says, " Had we a perfect alphabet, containing one symbol, and only one, for each elementary soimd; and a perfect method of spelling, freed from silent letters, and precisely adjusted to the most correct pronunciation of words; the process of learning to read would doubtless be greatly facili- tated. And yet, any attempt toward such a reformation, any change short of the introduction of some entirely new mode of writing, would be both unwise and impracticable. It would involve our laws and literature in utter confusion, because pronunciation is the least permanent part of lan- guage; and, if the orthography of words were conformed entirely to this standard, their origin and meaning would, in many instances, soon be lost. We must therefore content ourselves to learn languages as they are, and to make the best use we can of our present imperfect system of alphabetic characters ; and we may be the better satisfied to do this, because the deficiencies and redundances of this alphabet are not yet so well ascertained as to make it certain what a perfect one would be." Notwithstanding the well known opposition to sudden, arbitrary, and radical change in anything long established, the attempt has many times been made to reform our alpha- betic characters and our spelling. These attempts have imi- formly failed; and this has not been due to the fact that the schemes proposed were less perfect than the method in use, but to the difficulties involved in reforming so important a matter as a language that is read and spoken in every part of the world. No one denies that the English language is faulty — very faulty indeed ; but, as has already been remarked, changes of this kind must be made slowly and gradually, and conformably with the methods of evolution. They must be efiiected by forces acting within rather than by modifying rules imposed from without. Such efforts to improve our English tongue by the influence of high authority and the decisions of learned bodies have never been abandoned. Books with many new characters have been printed, and introduced to a limited extent into 10 PEDAGOGICS OF ORTHOGRAPHY. § 7 our schools, but none of these well meant schemes has suc- ceeded in gaining a permanent foothold. One of the most notable of these attempts took definite shape in 1875 under the auspices and direction of the American Philological Asso- ciation. Professor William D. Whitney was the chairman of a committee whose duty w^as to determine and report a method of improving "the monstrous spelling of the English lan- guage." This committee has been continued from year to year ever since. After much discussion and adverse criti- cism, a change in the spelling of about 3,500 words has been recommended with all the weight of the organization men- tioned above, and approved by other similar associations in the United States and in England. The recommendations have scarcely been heeded or even heard of by the general public, although some of our latest dictionaries have endeav- ored to give them currency. The "Standard Dictionary" is the most conspicuous of these. It gives such spelling as foiuUd, fo)ictii\ sulfur, abnv, bafl, ciiiif, etc., and for their definitions refers the student to the words as commonly spelled. It is careful, moreover, to put "Phil. Soc." in capitals after each new form. The reception by the public of the proposed reform has demonstrated its futility. He would be a brave author or newspaper writer that would imperil his popularity by a book illustrating the reformed spelling. It would be inter- esting to know how "Pickwick Papers" would have been received, if its first edition had been revised before publica- tion by the "Pun.. Soc"; and the average reader would be shocked to see an edition of his favorite author after its ' ' monstrous " spelling had been ' ' reformed. " These attemi)ts serve no purpose cpiite so well as they do to illustrate the impotence of efforts to overcome by authority the inertia of established usage. It may be said, however, that, while proposed reforms, even when they are much needed and perfectly reasonable and moderate, are imiformly ignored, they establish in some measure a direction for the general drift towards a better state of thing-s. For people in national masses refuse to § 7 PEDAGOGICS OF ORTHOGRAPHY. 11 advance in accordance with arbitrary enactments — they will r\.o\.folloxo or be steered^ they insist upon drifting. "7. other Obstacles to a Perfect Alphabet. — Before it is possible for i:s to secure a perfect English alphabet, there are many dilBculties to be overcome besides those indicated above. One of the g'reatest of these is to secure a general agreement as to the exact number and character of the sounds in the language. This difficulty is simply insur- mountable. Take for example the much disputed question whether initial iv and y are to be regarded as vowels or as consonants. If they are consonants, we should have for each a separate alphabetic character; if, as is urged with much show of truth, initial w and y are equivalent respectively to ^"^ and r, each. somewhat shortened, characters for these initials must be identical with those for their equivalents. To illustrate, let us suppose that w represents the sound of do., and y the sound of c\ then 7iv7, boot., yoke, and dap should be written civ/, bivt., yok, and dyp. Again, in order to establish a perfect alphabet it would be absolutely required that variant sounds be eliminated from our lang"uage. But this is manifestly impossible. Even among cultivated people there are widely different degrees of attention paid to the pronunciation of vowels and to the articulations {articiilus, a joint, as at the elbow) of syllables. Thus, if two words, as sufficiently attentive, were pronounced in turn by twenty different persons, no two of them would exactly agree. Unless there were collusion, we should expect to hear many varieties between sflsh'-nt-Ie ten'-tv and suf-fisJi'-ent-le dt-teii'-tiv. This matter of prommciation is one that is determined by many and varying conditions — differences in vocal organs, degrees of rapidity in utterance, conflicting authorities, educational and personal surrormd- ings, geographical differences, changes that come with the lapse of time, etc. In short, there being no imiform prommciation of words, there is no tmiformity in the sounds of letters, either alone or in combination. Hence, a perfect alphabet, if its 12 PEDAGOGICS OF ORTHOGRAPHY. § 7 invention were possible, would have no other value than as an ideal to guide us in bettering our speech — not in perfecting it. Consider the first letter of our alphabet; how many sounds has it ? Nobody knows. Every number from four to seven has been given by different authorities, and there seems to be no way by which these authorities can be brought to an agreement. Briefly, then, a perfect alphabet is only a dream that can never be realized in actual practice. To secure absolute unifomiity in the utterance of the sounds and words of the English language would be no easier, and perhaps no more desirable, than that all men should be in perfect agreement in politics and religion. It is by the discrimination of dif- ferences that the world is slowly led from better to better. The best condition for human advancement is unity in diversity — the fact of "many men, many minds." Pure mathematics is the only science that excludes every element of uncertainty; its results are therefore absolute — unchan- ging. The dream of the bigot is to have all men agree with him ; that of the philosopher, to have all men observe and think. 8. Syllabication. — To every person that speaks or writes our language, its proper division into syllables is important; to the teacher, it is especially so. The objects to be sought by syllabication are variously given by different authors; the confusion, indeed, in which this subject is involved is something almost beyond belief. But, when all is said, the leading object of dividing words into syllables is to determine, as nearly as possible, their correct pronunciation. In general, syllabication is useful in enabling a child to pronounce correctly imfamiliar words, and it guides the writer and the printer in dividing words at the end of lines. In addition to these uses, some authors insist that syllabication should "show the derivation or com- position of words. " But in the attempt to effect this addi- tional purpose or function is found a cause of the confusion § 7 PEDAGOGICS OF ORTHOGRAPHY. 13 that invests the subject. To divide words so as to indicate their pronunciation is one thing; to divide them so as to show their composition is quite another. And these two objects are generally at variance — each defeats the other. Thus, when we divide pJiilosopJiy^ orthograpJiy^ and polysyl- lable so as to show their composition, we have pliilo-sop/iy {(f>iXeiv, to love; aocpia, wisdom), oi'tho-graphy [opdog, right; ypd(peiv, to write), and poly-syl-lablc (ToAvf, many; cn'r, together ; XaiijSdven', to take) ; when we divide them with reference to their pronunciation, we have pJii-los-o-phy, or-thog-ra-phy, and pol-y-syl-la-hlc. By the latter method the composition of the first two is hidden rather than revealed, and in none of them does syllabication indicate the etymology. It is, therefore, clear that we must choose between a syllabication that reveals the composition of words and one that shows their articulations (joints) when we pronounce them properly. Now, it is perfectly clear that only the linguist or philologist is specially inter- ested in the etymology of words, and, in this matter, he needs no help from syllabication. He recognizes the root elements without it. Hence, we arrive at the following principle : \Vo7'ds should bi' divided into syllables ivifh reference to tlieir pronunciation. If, therefore, the correct pronunciation of a word is known, its syllabication is usually evident. 9. Degrees of Difficulty in Syllabication. — The syllabication of most English words is a very simple matter. Thus, no one need hesitate in dividing such words as gram- mar, inscription, prosperity, unprepared, Indianapolis, etc. It is necessary for him to know only how they are pro- nounced. But the problem is not always so simple. This is shown by the fact that there are thousands of words about which the recognized authorities are at variance. Thus, we have warrant equally good for clan-gor and clang-or, for rup-ture and rupt-ure, na-ture and nat-ure, Jin-cr-y and fi-ner-y, ivri-tcr and 7orit-er, cx-ci-ta-ble and ex-cit-a-ble; for sec-ond-a-ry, sec-on-da-ry, and scc-ond-ar-y; etc. U PEDAGOGICS OF ORTHOGRAPHY. § 7 Again, we may find in any standard dictionary many apparent and many real inconsistencies. For example, in one of the latest and most generally esteemed dictionaries occur par-ting and part-ridge; port-age and por-ter; i^<]iis-key and ivJiisk-er; passive, pas-sage, and pass-er; etc. In many examples like the foregoing, the variations may be accounted for by differences in roots, meaning, accent, or termination, or by the liability that one division is more likely than another to lead to mispronunciation. Thus, if the word probity be divided pro-bi-ty it will naturally have the o long; while prob-i-ty will just as naturally make the o short. Such differences, however, as mass-ive and passive, rapt-iire and rup-tiire, naiigJit-y and Jiangh-ty, or-gan-ise and or-ga-non, and others like them, are not so easy to explain. 10. Exercises in Syllalncatioii. — For classroom work, a very excellent and necessary series of exercises may con- sist in the syllabication by the pupils of words in lists of gradually increasing difficulty. In a very short time, there can be developed a nice judgment and a discriminating ear with respect to doubtful words. It is a field in which much desultory work has been done, but, in the way of results, not much of real value has been determined. Such exer- cises, too, have a great influence in indiicing clean, distinct, and accurate articulation and enunciation. It may be added that, notwithstanding the practical value of this subject, it receives almost no attention in the work of our schools. In many of the affairs of life, however, it is of the utmost importance. The person that writes letters, the author of books, the compositor, the proofreader, the private secretary, the public speaker, the singer, and many others, find a knowledge of syllabication indispensable to the best work. We may, therefore, safely assume that very soon it will find a well defined place in our schools. If the student imagines that the proper division of words into syllables is a self-evident, or even an easy, matter, let him copy and syllabicate the following words; and then let PEDAGOGICvS OF ORTHOGRAPHY. 15 him compare his work willi one, dictionaries of standard authority, and, if possible, with two, obligatory onerous absurdity inherent momentary diversity diverting savory vigorous laborious scarcity antipodes modesty perjury jeopardize seniority inaugurate culinary admirable feminine habitable nominative sedentary mutinous mutual fragile fragility versatile comparable combatant educator luminous mythology thousand mischievous naughty haughty contractor refractory refractive 1 1 . llules for Syllabication. — The rule, Syllabicate ivonh so as to indicate their correct pronunciation, requires that we 'shall first kitoto their correct pronunciation. But the dictionaries are at variance in this matter with respect to thousands of words. It follows, then, that, if the diction- aries observe the rule cited above, they must differ in divi- ding- those words; and the fact is that they do differ. Hence, the only method of reaching uniformity in pronouncing and dividing words is for the entire English-speaking world to agree upon some particular dictionary as the final authority from which tliere shall be no appeal. But this is manifestly impossible, for there are many good dictionaries, each of which has its following. Unanimity in the choice of a standard authority in language is no more to he expected than is unanimity in voting for a president of the United States. A congress of learned men might be selected, and the task devolved upon it of adopting a dictionary, but how should its decision be enforced ? Besides, there is no diction- ary that is consistent throughout, and, almost certainly, no dictionary ever will be. And, again, the dictionary that is right today is wrong in a very brief time, for language is constantly undergoing change. This rtile requiring us to divide words so as to show how they are pronounced has innumerable exceptions. Thus, no division of cohvicl, flaccid^ flagitious, propitious, or venison can indicate their pronunciation, neither can these words be rightly pronotmced so as to gttide in their S}'llabication. 16 PEDAGOGICS OF ORTHOGRAPHY. § 7 Many writers have endeavored to devise rules for dividing words into syllables, and the result has been infinite con- fusion, inconsistency, and disputation. Goold Brown, in criticizing one of these codes of rules, says of its author: " He befooled the Legislature of Massachusetts, the School Committee and Common Council of Boston, the professor of elocution at Harvard University, and many other equally wise men of the east He would conduct the learner through the following particulars, and have him remember them all: (1) Fifteen distinctions respecting the classifica- tion and organic formation of the letters. (2) Sixty-three rules for the sounds of the vowels, according to their relative positions. (3) Sixty-four explanations of the different sounds of the diphthongs. (4) Eighty-nine rules for the sounds of the consonants, according to position. (5) Tzventy-three heads, embracing a liundred and fifty-six principles of accent, ('. — Every teacher is aware of the diffiictilty there is in securing, in an oral spelling exercise, uniformity of procedtire on the part of the pupil. Thus, if the teacher requires that before and after spelling a word the pupil shall pronounce it distinctly, the requirement, unless constantly in.sisted upon, is ignored. Finding this to be true, there are three courses, any one of which is open to the teacher: (1) Omit to notice the failure of the pupil to meet the rec[uirement. (2) Call his attention to the require- ment and wait until he has obeyed. (3) Treat it as an error and pass the word to the next pupil. Which of these three courses is usually pursued ? The first, because it is the least troublesome to the teacher. But it is in such trivial matters that general carelessness and want of painstaking find a fostering encouragement. Insistence is the price that a teacher must pay for accuracy, exact scholarship, and prompt obedience among his pupils. Of the other methods, which is the better ? Undoubtedly the last ; for, if the teacher is compelled to say ' ' Pronounce the word," to almost every pupil, the task quickly becomes onerous, and the pupil inevitably comes to wait for the order. In this case, it is the teacher that must be closely attentive, §7 PEDAGOGICS OF ORTHOGRAPII V. 1<) while disci])linc requires that this should be the pupil's duty. Even if a pupil has given the letters and the syllables cor- rectly, and has neglected t(^ pronounce as required, the teacher's unexplained "Next" should be the emphatic com- ment on the pupil's carelessness. In a very short time, the good results of the teacher's insistency will be apparent. The same exactness should be ob.served in written spelling. In school, directions of every kind .should be very brief, very explicit, and very necessary. And then they should be obeyed with military promptness and completeness. 15. Snccess of Any Method I>epeiKleut Upon IIoav It Is Used. — The writer feels justified in amplifying some- what this point. No good teacher is wordy and vacillating. No good teacher issues many and complex orders that are changed from day to day. He makes up his mind very carefully about what requirements are wise, necessary, and defensible; then he insists upon exact compliance. It is not meant that he should be a iiiartiiict ; for the requirements of a martinet are generally luireasonable, oppressive, and inde- fensible. The teacher should be a disciplinarian whose orders are in calculated furtherance of some definite and desirable object. A disciplinarian never issues orders designed only to show that he is in authority; he has no artificial means of making himself heard in spite of the inattention and disorder of his pupils — upon his desk no bell to bang and clatter, no stick with which to pound desks, and, incidentally, pupils ; he talks but little, and then quietly ; he .says less, rather than more, than he means. He never scolds or threatens ; he rarely promises, but if he does, he performs more than he promises. With him, speech is indeed silver, and silence golden. We are not to judge, therefore, of the worth of any par- ticular method of teaching spelling or any other subject, by its success or failure in any given case. A teacher perfectl}^ equipped in every respect can never fail entirely, whatever the method maybe; the teacher having no fitness, natural or acquired, will certainly fail with the best possible of methods. It is to the teacher of no special excellence or 20 PEDAGOGICS OF ORTHOGRAPHY. g 7 want of excellence that modern and improved plans of pro- cedure are valuable. And the fact is that most teachers belong in this class, and herein lie the necessity for, and the value of, professional training of teachers. It needs scarcely to be remarked that the perfectly qualified teacher will be thoroughly informed about everything that is latest and best in the matter and methods of his art. MODIFICATIOX OF WORDS. COMPOITNDIXG OF WORDS. 16. Perplexiiii? Natiii-e of the Subject. — Of the many questions concerning the correct use of English, there is no question quite so perplexing as that having reference to the compounding of words. Two or more words may be so closely associated in their meaning or use as to require their union also in form. This may be done either by wri- ting them together as a single word, called a solid coiiipoiind, or by using hyphens to join them. In this latter case, we have a liypJicncd or hyphenated compound. Solid Compounds. — Mankind, earrings overcoat^ hem- isphere, electrometallnrgy, mnltinii/lionaire. Hyphened Compounds. — Self-respect, ronnd-sJunildered, giant-killer, Jack-d-the-lantern, an P m-xviscr-than-yon expression. Evidently, there are only three ways in which two words maybe written: separately, with a hyphen between them, and as one solid word ; as, cJinrch bell, chnrch-bell, chnrchbell ; post man, post-man, postman. To determine, in any case, which of these forms is best is not by any means a sim- ple matter; for the closeness of association between words used together in speech or writing is of every degree, and does not remain constant. Moreover, when it is determined that any two parts of speech should be written as a solid or a hyphened compound, or that they should not, it does not § 7 PEDAGOGICS OF ORTHOGRAPHY. 21 follow that every two other words belonging to the same parts of speech and used in the same way, should be similarly compounded. This is something that depends upon usage, and usage changes with time and varies with locality. When Fulton brought forward his great invention, then the word steam and boat began to be spoken and written much together, but they were at first regarded and pronounced as two words. By and by, the fact of their very frequent asso- ciation led some one to write them with a hyphen, and the accent fell strongly upon the first element. Later, the hyphen was dropped out, no one knowing just when or by whom, and st cam-boat became steamboat, after which there was no change. This, in general, is the history of the com- pounding of words. Doubtless, if some other means of conveyance shoujd take the place of the steamboat, sooner or later steam-boat would reappear, and finally we should return to steam boat. This is to say, words often have a history very similar to that of men and women. To say nothing of their birth and death — their appearance and disappearance — two words may meet and become acquainted ; then, by means of a hyphen, a bond of union may be established between them — they are engaged ; the hyphen disappears and they are married. After marriage may come, for good reason, separation, and this may be suc- ceeded by divorce. In other words, a living language is constantly going through a process of change, just as is true of almost everything else. What is in accordance with the "best usage " today is displaced in a brief time by something else. And, in the case of two closely associated words, the transition to the hyphened, and finally, to the solid, form — how is any one to know just when it should or does occur ? It was stated above that usage varies with locality. The English spoken and written in England is in many respects different from that of her colonies, and from that of the United States; and, in the United States, there are in the various sections great differences in the language of even cultivated people. What is considered good usage on the Atlantic Slope is not so regarded on the Pacific Slope; and 22 PEDAGOGICvS OF ORTHOGRAPHY. § 7 the language of educated people in the North differs much from that of the same class in the South. 17. Rules for tlie Compounding of AVortls. — Many grammarians and lexicographers have endeavored to for- mulate rules to regulate the compounding of words, but, unfortunately, no uniformity has been reached. Such rules as they have given us have been rendered practically worth- less by a multitude of exceptions such that no person can say with any certainty whether a given case belongs under a rule, or whether it is determined by one of the exceptions. If there were somewhere a literary autocrat from whose decisions no appeal was allowed, or if there were but one dictionary universally regarded as authoritative, and if tliat dictionary were entirely consistent with itself, the trouble would be ended. But there are many autocrats — self -con- stituted — and there are many dictionaries at war with one another and each inconsistent with itself. Each autocrat and each lexicographer believes in his own infallibility, but the confidence of the world is divided among them. One of the latest and best of our dictionaries devotes much attention to the subject of compounding words, and, in the course of a carefully prepared article concerning it, says: "English books contain a large number of compound words — that is, words made by joining two or more simple words into one, either with or without hyphens. The forms in question have never shown any real system. Many terms that have joint forms in some books are printed in others as two or more words, and exactly analogous terms often appear in diflferent forms in the same book. " The author of the article then quotes from "a recent book, published by one of the best-known American houses," such forms as the following: scJiool-roovi, scJioolroovi ; middle-finger, middle finger ; circus-actor, circus actor ; bureaii-drazver, cabin ivindoio ; back-parlor, back windows; and then, from the same book, gives as "compounds with- out reason " such hyphened forms as front-yard, top-seat, tallow-candle, etc. § 7 PEDArxOCxICS OF ORTHOGRAPHY. 23 Continuing, the author says: "Dictionaries profess to be records of the language as found, and not to set forth theoretical opinions; but, with such diversity of treatment in literature, every lexicographer has had to make some choice of form for each word-pair indi- vidually recorded Close examination of the various dictionaries fails to disclose any probable principle of selec- tion Whatever may be said, the fact remains that the dictionaries have given many terms as compounds that are not commonly so printed, and for whose joining no reason is apparent." The author then gives terms culled from the large diction- aries, and intended to illustrate compounds "for whose join- ing no reason is apparent. " Some of them ^.re good-bchavio?', old-maid, Frciicli-ho)icy suckle, through-ticket, clectric-curroit, etc. He attributes the confusion to "neglect to investigate and lay down correct principles and to formulate comprehen- sive and adequate rules." He then proceeds to do this diffi- cult and necessary work. 18. Granimatical Iliiles and Established Usage. — After such an introduction by the editor of the subject of compound words, it might be expected that the dictionary referred to would furnish a system of perfectly definite and comprehensive rules, easy of application by persons of ordi- nary education. But, while it must be conceded that no more careful and painstaking attempt to solve this difficulty has ever been made, it is certain that the result is by no means satisfactory. After "a close study of English litera- ture " by the editor, he gives us "a system constructed /// accordaucc with the rules of grauimar, viodified sou/ezohat by such fully established usag-e as does not follow those rules." His rules are three in number, with numerous, confusing, and arbitrary excepti(jns. Before discussing the results he has reached, it may be well to note the vagueness and imcer- tainty of the " system ' upon which his rules depend. Per- haps the editor would be puzzled to explain with precision 24 PEDAGOGICS OF ORTHOGRAPHY. § 7 what he means by the phrase "in accordance with the rules of grammar" and by "fully established usage." It might easily be shown that many of the best grammati- cal authorities are still disputing as to whether or not there are or should be any "rules of grammar," and, if there are such rules, how many there are, and to what they refer. The following cpiotation wnll exemplify the truth of this statement : " The English language being almost without the former (inflections), and therefore equally without the latter (syntactical construction of sentences), its use must be, in a corresponding degree, untrammeled by the rules of gratiniiai\ and subject only to the laws of reason, which we call logic But the truth of this matter is that, of tlie rules given in the books called English Grammars, some are absurd and the most are superfluous. For example, it can easily be shown that in the English language, with few exceptions, the following simple and informal relations of words prevail: " The verb need not, and generally does not, agree with its nomina- tive case in number and person. " Pronouns do not agree with their antecedent nouns in person, num- ber, and gender. " Active verbs do not govern the objective case, or any other. " Prepositions do not govern the objective case, or any other." — Richard Grant White. And in the same strain this writer continues to question the necessity for grammatical rules, and even the existence of such rules. With regard to the editor's ' ' fully established usage, " it may with much confidence be asserted that there are few English expressions more vague and uncertain than this. What one authority may assert to be "fully established usage" in a particular place and at a certain time, another authority equally good, and differently situated in time and place, will condemn. And again, if it could be definitely determined what is fully established usage, and what is usage not at all established, how shall we decide the innumerable cases between these extremes ? For example, we have authority equally good for torpedo-tubes and torpedo tubes ; readi/ig'- book -And. reading book ; trolley -ear and trolley ear ; map-like and viaplike ; frame loork, fraiite-icork, Andframeii'ork; etc. §7 PEDACtOGICvS OF ORTHOGRAPHY. 25 AVho shall decide which is right? Obviously, no one; or each one for himself. 10. Tlu' IJiiles Formulated. — The editor referred to above gives, as the result of "a close study of English litera- ture," the following three rules: 1. "All words should be separate when used in regular grammatical relation and construction, miless they are jointly applied in some arbitrary way. 2. "Abnormal association of words generally indicates unification in sense, and hence compounding in form. '.). ' ' No expressipn in the language should ever be changed from two or more words into one [word] (either hyphened or solid) without change of sense." 20. Discussion of the I}ules. — Every rule shpuld be definite, easy to be understood and applied, and entirely free from ambiguity. Moreover, it should, if possible, be general ; for, if it is applicable to only a few of many cases, it is not, in full sense, a r^//c\ Now, the rides above are faulty in nearlv all these respects. They leave something with respect to which the judgment, the caprice, the general reading and literary taste, and the locality of each individual, enter as elements in applying the rules. Thus, in the first rule, few people will agree as to exactly what is meant by "regular grammatical relation and con- struction," and "arbitrary Avay " is equally vague. One person will regard as arbitrary that which to another seems regular; and, worse than this, there is no acknowledged final authority to determine which is right. The second rule seems to be nothing more than an exten- sion of the last clause of the first rule ; for, with respect to words, " arbitrary application " and "abnormal association " will not, to the ordinary inquirer, seem very different in meaning. And, again, there are many degrees of abnormal- ity and arbitrariness in the association of words, and it is this " unification in sense " referred to in the .second riile, that by its innumerable grades of closeness makes much of the trouble. 20 PEDAGOGICS OF ORTHOGRAPHY. § 7 Tlie third rule would entirely prevent rail i^'ay, child like, uu'll coiiu\ siDi sliiiic, milk maid, etc., from ever becoming railicay, child-like, childlike, etc. ; for it is certain that the sense of sun shine, sun-shine, and sunshine is, to the ordinary reader, the same in all the forms. Of his first rule, the editor says that it "keeps a regular adverb separate from the adjective it modifies, even when the two express one attribution; as, highly colored loings, recently published book"; and yet the editor has best-kno7un in the second paragraph of his article. (Are colored and published, as here used, adjectives ?) He then says, "The second principle reijuircs compounding, when two adjectives, a noun and an adjective, or any two or more parts of speech are abnormally associated ; as, a %\.'ell- knoion man, the snow is knee-deep, free-trade doctrines, etc." Now, the information would be helpful, if any one could tell why loell-known should differ from highly colored and recently published when each combination is used as an adjective. Besides, it is not clear why, after what the editor says of the necessity of keeping a regular adverb (whatever that may be) separate from the adjective [or participle ?] it modifies, he should give us %vell-educatcd, loell-pleased, ill-treated, ill-supplied, and many similar forms that might be cited. It should be noted, however, that the editor attempts at the close of his article to discount criticism of his work. His words are, "Care has been exercised to make the vocabulary and the text agree throughout ; but, as many compounds are properly written with or without a hyphen, and as this is the first systematic attempt in this direction, it is not at all likely that absolute agreement has been attained." The editor is in error in saying that his "is the first sys- tematic attempt " to reduce the compounding of words to definite rules. There have been many such attempts. Goold Brown devotes a number of pages in his "Grammar of English 'Grammars" (see pages 184-193) to the subject, and at about the same time (1850) John Wilson gave a very careful treatment of compound words in his work on " Punc- tuation." § 7 PEDAGOGICS OF ORTHOGRAPHY. ^7 31. Inconsistent Forms of Conlpo^ln(l AVords. — Not so much to show how the effort discussed above has failed, as to make clear to the student the great difficulty of this subject, the writer gives the following forms from the cHctionary in which the editor's work appears: fooi-bcnch, foot-rest, footstool; foot-ivoni, footsore; foot-pace, foot-path, footfall, footsteps footiuaj'; head-rail, headboard; head-band, headstone, head-note, headlight; hand-lathe, handbreadth, handsereio, handioriting, Iiand-glass, liandbook, handbraee ; candle-power, candle-light, candle-snuffer, candlestick, candleuiold, candle-end. The following are names of ])lants : horse-bane, dogbane, horseradish, horse-bean, horse-nettle, horsebrier, horse-balm, horseniint, horse-thistle, horse vetch, Jiorscivccd; candle-tree, candleberrv, candle-rush, eandlenut ; hobble-bush, rose-bush, feverbush, etc. Doubtless there are, for the editor to whom we are indebted for the foregoing fcjrms, some principles that guided his selections; but, if there are, they are too technical and not sufficiently obvious to be of general practical value. 33. Evolution of Compound Words. — It is stated elsewhere that the changing of two or more words from separateness to a hyphenated or a solid compound is a gradual — an evolutionar}^ — process. The rapidity with which the transition is made depends upon many and vary- ing conditions, and it is not the same for all sections and literary centers. It is a process that is not arbitrarily deter- mined by any known and generally recognized authority. The best dictionaries have much to do with the matter, but. since no two of them agree, and since no single dictionary can be foimd that is self-consistent throughout, other deter- mining forces are operative. Something similar to this is the fashion of various articles of dress. There is no one whose duty or privilege it is to say what shall be the styles for next year. They seem to be the resultant of many forces acting in different directions; or, as is the case with the electric current, they take the path of least resistance. It is certain 2H PEDAGOGICvS OF ORTHOGRAPHY g? that, with words as with fashions, "old things pass away, and all things become new." In the progress of civilization, new articles of luxury or convenience are constantly appear- ing, and are quickly rejected, or they become necessary, and, soon, indispensable. Examples of this are new forms of clothing for greater comfort, means of more rapid com- munication in business and social intercourse, and myri- ads of inventions of every kind. With these come innumer- able new names, some of them consisting of single words, others of two or more associated wcn-ds; as, r a ilii'ay -tele- graph, eottoii-giiij spiiiiniio--Jeii//j\ overeoat, overalls, postage- stamp, siiiokiiig-jaeket, night -goicii, torpedo-tube, ti olley-ear, elothes-Iiorse, baiik-aeeoitut , rubber stamp, lai^'-abidi)ig, ineeuse-breat/iiiig, etc. These terms, which at first arc rarely encountered, soon become familiar to the ear, eye, and tongue of almost every- body-. When they consist of two or more words, a process is begun of concentrating the accent upon one of the ele- ments. Thus, at first, everybody would say steam' boat', rail' road' , lauds' mau', ser'iwrut girl', etc. ; but very soon come steaui'-boat, rail' -road, lauds' -man, ser'vaut-girl, etc. — forms joined l)v a hyphen and having one primary accent. Finally, some of them take the solid form, and which shall do so seems to depend much upon the frequency with which the unaccented element is found in other compounds. Thus, man, fish, iceed, ivort, luay, road, and some others are generally added to the accented part without a hyphen; as, salesman, sunfish, doori^'eed, motherzcort, traun^'ay, etc. "itW, Pi'iniai'y and Secondai\v Accents. — Besides the primary accent of compounds, we usually find at least one secondary accent, which becomes more and mc^re indistinct, and often disappears entirely. In this last case, the com- pound takes the solid form; as, no'blemau, con'gressman, eod'fish, rat'tlesnake, icood' laud, etc. Many compounds have become solid even when the sec- ondary accent is quite noticeable; as, nev" ertheless' , uot"ioitli- stand'iiig, zidien" soev' er, ev' erybod"y, i^'hith" ersoev' er, etc. §T PEDAGO(;iCS OF ORTIKXiRAPHV. 2'.) Some writers on this subject have endeavored to make the compounding of words depend entirely upon accent, and, if their rules were expressed in terms as comprehensive as possible, they would be nearly as follows: 1. If two or more words denote, not several ideas, but one compound idea, and if there remains but one primary accent, either use the hyphen or write them as a solid com- pound; as, for example, a matter -of 'fact' -looking town, an oiit-of-tkc-ioorld' place, a case of didin-kiurw-it-i^'as-load' cd, a sea' side residence, sjiiii mcr-ivard^ cv' cryi^'Iicrc^ etc. ■I. If each element of a compound word retains its own accent, either use a hyphen or write tlie elements sepa- rately; as, an all' -wise' Creator, a self -eonfessed' swindler, a sheep' -raising speculation, a ivell' ed'ueated man, etc. The student will doubtless see the uncertainty attending- the application of tliese rules, and indeed of any others that may be given. It is clearly impossible to devise any rules of general application. This is owing to many circumstances, among which are the varying degrees of closeness of the associated elements of compound words, the distinctness with which the original accents are retained in the compound, the length of the united parts, the nature of the sounds at the united extremities, the grammatical functions performed by the compounds, and many other con.siderations. Thus, we may write ranilnnv and perhaps raindrop, but not raiiiclond or reiinconipeller; nightfall, nighteap, or night-blooming, but not nighttime or night-shade; a bine-eyed girl, or the girl was blue eyed, but not a blneeyed girl, etc. Indeed, since taste determines u.sage, and since taste constantly changes, both in individuals and in societies, there is no fixed usage by means of which doubtful questions may be decided. Everything relating to this matter is in transition. Just at the present time, our literary authorities are divided as to whether we should write today, tomorrow, and tonight with or without hyphens. A usage that seems to be rapidly increasing gives the words without hyphens, but no one can predict with any certainty what form the words will finally assume. :jO PEDAGOGICS OF ()RTlIOGRi\PIlY. §7 ^4. Coiu'liuliii^*' Ileiiitirks on Coiiii)oiiud AVords. — While it seems to be impossible to formulate definite and comprehensive rules for forming compound words, there are some general principles that may, with profit, be observed. Some of them are as folknvs: 1. Uiiiu'ccssarj compounds should be avoided. — The genius of our language is to keep its words separate as far as possi- ble. When the thought can be expressed just as definitely by words as they are, it is not in the best taste to make new compounds. Of course, compounds that have been made familiar by use may, for the most part, be used without hes- itation. The Germans have a method of imiting many words into single adjectives, adverbs, and nouns. In these they use no hyphens. During the last twenty years, our newspapers have contained adjectives made in this way, except that they are formed with hyphens. They are apparently intended to produce a humorous effect, but they are not in good taste, and are a grotesque departure from the English idiom. An illustration follows: " He had an rm-aivfuUy-linnij;rv-hnt-I-caift'Saij-i\.'ood air about him. " •I. When several woi'ds are used to express a compound idea, and usage has not fixed the form, the words written separately are preferable to either the hyphenated or the solid compound. — When the solid form is admissible, it is better than the hyphenated compound. The reason for this is that, when a compound word has acquired a recognized solid form, no further change is possible unless the word is resolved into its elements, and this is very rarely done. 3. Use the hyphen, if to do so is in any ease the only -way in whicJi to avoid ambiguity. — There is, however, usually some other way to make the meaning definite, and the com- pounds may then be avoided. The following are all ambiguous, and the hyphen is not the best remedy: a black bird feather, a sharp pointed tool, silk dress trimming, edible birds' nests, English baby stock- ings, many colored v\hhon.o\([\er, the linen paper box, etc. The foregoing can easily be made unambiguous; thus, a §7 PEDA(iO(TlCS OF ORTIKXiRAPHY. 31 black feather of a bird, a feather of a black bird, a feather of a blackbird, a blackbird's feather; a tool with a sharp point, a sharp tool with a point, a sharp-pointed tool; etc. 4. .{void coinpoiiiids having many icord cliincnts; as, a never -to-be- for got ten experience, a thoronglily-dyed-in-the- ivool democrat, etc. These may generally be avoided by putting' the modified word first; as, an experience never to be forgotten, etc. 5. Do not pnt too nineli stress on any partienlar dietionary; but in each case consider the structure, meaning, and use of the words expressing a compound idea. 6. Greek eonipounds and Latin eonipounds should have the solid form, unless there are imperative reasons otherioise; as, for example, pleuropneumonia, nitroglyeerin, microphotogra- phy, multiaxial, ambidexterity, eireumainbulate; etc., The writer has dwelt with considenible minuteness upon this subject because it is not only difficult, but very impor- tant. It is a subject that shoiild engage the teacher's most careful attention, and he should endeavor to have his pupils acquire a taste and an ability in the discrimination of forms, and in a power of giving definite reasons for preferences in particular cases. They should be taught to scrutinize hyphenated compounds, and to determine whether the sense may not be expressed equally well or even better by their separate elements. They should be trained to a careful conservatism as being the correct attitude when the use of compounds is concerned. While this is a subject that will never be settled, it is one of the best to furnish the extremely valuable discipline that results from careful discrimination. AHBRE>'rArrOX8 AND COXTRACTIOI^S. FOR>r AXT) PlXt TUATIOX OF ABBRE^'rATIOX.*!. 35. General Statement. — It is surprising how many important matters there are that have never been reduced to comprehensive scientific rules. One of these is the subject 32 PEDAGCHtICS OF ORTHOGRAPHY. §7 of abbreviations and contractions— a subject of much prac- tical importance, and one that no alert teacher can afford to ignore. One might expect that the necessity of using these shortened forms would soon lead to uniformity, but such is not the case. Indeed, it would be difficult to mention any- thing in which is found a greater variety of usage. The dictionaries differ in the matter of abbreviations for even the commonest measures employed in business. There is nothing settled about their forms, whether or not certain of them should begin with capitals, and how their singulars and plurals should dift'er. Thus, we find f, ct., c/s., for ciiits; (/., da., das., for day ox days; in., mo., moii., vios., iox nioutJi ox months; ft>, lb., lbs., iox pound ox ponnds; etc. Some authorities insist upon initial capitals for most abbreviations, and upon periods after nearly all contractions. No attempt seems to have been made to formulate general rules, or rules with the fewest possible exceptions ; if there has been any such attempt, it has not been generally known and its results accepted. To realize the truth of the fore- going statements, one has only to observe the hopeless confusion in the treatinent of this subject by the various dictionaries. The person making an examination of the subject will be surprised at the great number of abbrevia- tions that no one uses, and that no one should use. These, of course, should have no recognition. In one of our latest dictionaries we find trans., nni., L., S., s., na., o., O., com.. Com., c, C, etc. To show how indefinite and empty of exact meaning some of these shortened forms are, it may be mentioned that the dictionary from which these are copied makes c. stand for seventeen different words, and C. for sixteen. Without the help of significant surroundings — context — such abbreviations are meaningless; but, with the help of the connection in which they occur, they often become very definite. In such connection, a Hebrew or a Sanskrit character would be just as intelligible; for it is the context that fixes the meaning of the character in such cases, and the character itself has no meaning. This is illustrated by the dashes employed by teachers in grammar exercises, where § 7 PEDAGOGICS OF ORTHOGRAPHY. 33 adjectives, verbs, or other parts of speech are to take the place of the dashes in such a way as to make sense. 26. Use and Abuse of Abbreviations. — It is well understood that in a letter to a friend it is discourteous to employ abbreviations unless they are authorized to such a degree as to be regarded as if they were entire words; as, ////., Sat., Oct., '98, rcsp., etc. Even these are better writ- ten in full. Numbers, also, unless very large, are to bj written in words rather than in figures. Custom, however, has authorized the use of abbreviations that are perfectly definite, in bills, statements, invoices, and business papers generally ; but, even in business letters, abbreviations, if used at all, should be used sparingly. If they occur in social letters, it looks as if the writer is not in reality a friend, and that he grudges the time necessary to say in full what he means. This subject should be carefully impressed upon the atten- tion of pupils until, if they err at all, it will not be in the excessive use of abbreviations. While it is a general rule that we should avoid, as far as possible, the use of abbreviations, there are some that are so definite and so widely known that to avoid them is to be peculiar and pedantic. vSuch are Mr., Dr., Cr., c. o. d., f. 0. b., oz., etc., mdsc, acc't, J/. A., P. O. The man of good taste is a " Roman when he is in Rome." In what every- body is agreed, he acquiesces. He must be indeed a great authority if he can ignore universal usage. But a man of good taste is careful to ascertain what is fully established, and, concerning matters in dispute, to use his best judgment, aided as much as possible by good authority. 2 7 . What Are Abbreviations ? — From the coinposition of the term abbreviate (<'?'c/and brcvis, short), it may be inferred that an abbreviation is a sliortoicdioxxw of a longer expression. It follows, therefore, that a mere s}mibol or arbitrary character is not an abbreviation ; the shortened form must reveal its origin. Hence, |/, -(-, =, G, ^, cf-, 3, etc. are only symbols. 34 PEDAGOGICS OF ORTHOGRAPHY. § 7 But, if the full word or expression is revealed ever so faintly by the briefer character or symbol that represents it, the latter is an abbreviation. Thus, @, aa, ss, lb, £, ^/c, §, ^, m, f, are abbreviations, since, respectively, they denote more or less clearly the words at, ana, semis, librum or libra. Libra, account, United States, per, minim or meter, sitmmum or sunivia. 28. Mixed Abbreviations. — Mixed abbreviations are objectionable ; this is on the same principle that forbids an English word from being composed of elements derived from two or more languages, as is the case with electrocution, talkative, interloper, and many others. But many abbre- viations, although of mixed origin, are so firmly established that they are no longer even criticized. Such are czut, from centum and zueight ; Jfth, 3d, 1st, ironi fourth, third, first ; the enigmatical numerals of the physicians, which are intended to excite wonder and reverence in the uneducated ; Jss for / and semis, one and a half; vijss for ] ^11 and semis, seven and a half; lbs., which is supposed to be the pluralized abbre- viation of the Latin librum — pluralized by adding s, as if it were an English word. Of this it may be remarked that our most careful writers are omitting the s as being unnecessary, since the plural of librum is libra, and lb. is the proper abbre- viation for either. The Spanish onza, ounce, should in like manner have oz. for both the singular and the plural, yet the dictionary referred to above gives the absurd ozs. for its plural. Exactly similar to civt. is divt. for denarius and weight. Denarius, the name of a Roman coin, was finally applied to the English penny ; hence we now have the abbreviation d. to denote penny or pence. The forms 3-cclled, 100-lcgged, 6 footer are often used, although it is much better to write them in full. Perhaps the most ridiculous abbreviation of the mixed variety is dec., but happily it is now out of use. The t(- is intended as an abbreviation of ct, and the c is the initial of cetera in ct cetera. The writer has a textbook on language, used in some of our schotjls, in which he finds t{-ou for etc. § 7 PEDAGOGICS OF ORTHOGRAPHY. 35 The authorof the book is a Germ an -American, and doubtless was seeking our eqiiivalent for u. f. tu. , loid so ivcitcr. Another method of pluralizing abbreviations is to repeat the initial, the final, or some other letter, preferably a con- sonant; as, pp. ior pages, II. for lines., LL. iox laivsxn. LL.D., MSS. for the plural of MS. , gtt. for gittta, drops, and the double plural bbls. This last ought to be bl. but bbl. is well established for both the singular and the plural. Many symbols or mere characters are pluralized by adding 's with no period following; as, 6''s, +'s, A's or A, <^?'s, z's, /'s, ^'s, etc. *^ 39. Contractions. — Nearly all dictionaries distinguish sharply between abbreviations that are, and those that are not, contractions; and it is important that the student Should know exactly what this distinction is, because of the differ- ence in pluralizing and pvmctuating them. As has been said above, any shortened form of an expression that is longer when fully written is an abbreviation ; but an abbreviation formed by omitting intermediate elements and drawing together {con, together, and tractus, a drawing) the remain- ing elements is a contraction. Thus, rce'd, /'//, we're, can't, e'er, Peiina. are contractions. They are also abbreviations, since they are shortened or briefer forms. It is sometimes impossible to tell whether or not an abbreviation is a con- traction, as in such cases as int., Cr., A/a., advt., etc., for interest, creditor, Alabama, advertisement, etc. The missing parts of a contraction are sometimes indicated by apostrophes or dashes, and sometimes not; as, rec'd or reed., indse., J — n Sm — //, aect or acct., zve/l, paynit, etc. 30. The Period With Abbreviations. — We frequently meet the rule. Use a period after every abbreviation ; but this rule has many exceptions. In general usage, we find that Si period is never used after a contraction when apostro- phes or dashes take the place of the missing elements; as, W — m and H — y Sm-th, Ree'd on acc't. In full pay't or paym't, e'er, I'd, etc. lu such cases, the entire word is, on 8IATEUIALS. 32. Spelling- as Taiis>iit Vears A^o. — One of the writer's most vivid recollections of the school work when there were no oi^cial critics of matter and method, and when all teachers were equally good — or equally bad — relates to spelling. There were then no refinements of psychology or considerations of "correlation " to interfere with the teacher's freedom of movement. The first thing in the morning was for the smallest lads and lasses to be summoned, one by one, to the master's knee. With Cobb's or Byerly's spelling book in one hand, and a penknife — there were /^//-knives in those days — in the other, he pointed with a blade at the several letters in turn, and informed the pupil that a particular letter was /', another - Words for Oi'tliograplilcal Work. — In the earliest spelling books published in this eountry, the prineiple of .selection was very simple. After a eertain number of lessons, the leading object of which was to familiarize the pupils with the sound of letters singly and in combination, the transition to words that were merely difficult to spell was very rapid. The probability of meeting or using a word in fiUure was not considered; the only requirement was that its orthography should be abnormal — the more so, the better. Books of this kind have not yet disappeared, and for the purpose of training explained in the preceding paragraph, they are of undoubted value. Most of the books of "Test Words" have been modified, however, by the exclusion of such terms as are rarely or never used in any modern book, but much of the difficulty that characterizes the earliest textbooks has been retained. Hence, for training in mere spelling, they serve the purpose excellently. It is iinneeessary to mention any of these books, for most teachers are familiar with some of them. Better than any one of them, perhaps, for a particular school, grade, or locality, would be a collection made by the teacher or principal of the school where they are to be used. No one can know the needs of a class so well as he that teaches it, if he is thoroughly capable. The writer must not be understood as favoring the dis- carding of all spelling books, and the substituting of words from the geography, the reader, the history, and other text- books. The words in those books are better learned as we § 7 PEDAGOGICS OF ORTHOGRAPHY. (;;) learn the words in general reading;. They do not present the proper degree- of difficnlty for training llie spelling sense, nor are they snfficientl)' practical for a working vocabnlary. It is trne that some of them are suited to these recpiirements, but with the greater ptjrtion of them, this is not the case. The Avriter is eonvinced that a good spelling hook is a neces- sity in our schools. Many books have lately appeared containing hsts of words that are excellent for their practical iiscfulncss. Thev have been cidled with great judgment from many sources, and have been divided into classes according to their spelling, their pronunciation, their meaning, their nse, their relation in sense to other words, the rules that govern their form, the roots they contain, their derivation, composition, etc. An element of much value in some of these books is that they outline many ])edag()gical devices. By their use the teacher may avoid much of the monotony and humdrum of the work in orthography. vSome of these books invade the domain of grammar t(j the extent of treating of pimctuation, parts of speech, the possessive case, pluralizing, capitalizing, paragraphing, and composition work in general. Not much objection can be urged against this, ho^vever; for orthog'- raphy is really a part of grammar, and every consideration bearing upon a correct iise of words is important to the teacher of orthography. 54. The C'()llectinj>' of Devices for Teaching" Orthog- raphy. — If a teacher expects to make the profession his life work, it would be. difficult to overestimate the importance of his lieginning early to preserve in note books the plans of work that he finds successful. When he leaves the normal school he should be well supplied with hints, devices, plans, skeletons of work, methods of procedure, etc. These shoidd be in such form as to be readily accessible and available. A teacher depending upon general psychological principles, and upon pedagogical rules as he remembers them, will very soon become a slave of routine and mechanical methods. If he would have freshness and variety characterize his work, 04 PEDAGOGICS OF ORTHOGRAPHY. § 7 he iiiusL not depend upon his memory to reeall, or upon his instinet to sug-gest, the appropriate method of procedure. H what has been tested and found successful is made a mat- ter of record, the certainty of his handling a given subject or lesson well and wisely is assured. These plans and devices, many of them, will emanate from the teacher's practice, and more of them from his reading of what others have done. One of the characteristics of a good textbook is its richness in suggested methods, and the progressive teacher will therefore welcome every new school book; for, however faulty it may be, it will undoubtedly contain something of value that he can utilize in his work. It makes but little difference where the teacher gets a new plan — from his own experience, from that of other teachers, or even from the successes and failures of his pupils — if it is valuable, he should preserve it; and presently his choice of what is best in matter and method will become involuntary, just as much so as that one having the speller's instinct will spell a word correctly rather than otherwise. 55. Concerning- Rules for Spelling. — Most of the systematic training that our children get in spelling is con- fined to their earlier school years. It is true, however, that expertness in this branch is like skill in piano playing or stenography — it requires constant practice. To become infal- lible in the orthography of our language is a life work. Orthography cannot be generalized under a few comprehen- sive rules, nor under many rules. The fact is that our best spellers know very little about orthographical rules; they simply know how to spell particular words from the fact that they have sir// them one by one with eyes that note what they see. If they happen to know the languages from which most of our English words are derived, so much the better; but upon formal rules they put little dependence. This is owing not merely to the fact that these rules have generally a great man)'- exceptions, but also to the fact that the mental effort necessary to apply a rule and note the exceptions is greater than that required to impress the many words upon the memory. § 7 PEDAGOGICvS OF ORTHOGRAPHY. G5 But, as has been stated above, the formal study of spelling is confined to children of comparative youth, and to them rules are difficult. However simply a rule may be stated, there is an unavoidable abstractness about it that removes it beyond the comprehension of young children. One of the authorities on this subject insists that there arc only two, or, at the most, three, rules that can be used with advantage in teaching spelling. It seems, therefore, to be best that young children should be taught to spell without the aid of rules. Even in more advanced age, it is doubtful whether much is gained by trying to spell by rule. Moreover, there is no unanimity among the various authorities as to the number of rules and their application. Goold Brown, whose atten- tion to this subject was exceptionally careful and thorough, gives fifteen rules, with thirty-one ' 'observations " in fine type. Each of his rules has many exceptions, and these, with his observations dealing for the most part with varieties of spell- ing and with its curiosities, constitute a task more difficult to learn thoroughly than to learn to spelL Some authors have more rules than Mr. Brown, and others fewer, but no two authors can be found that agree. Indeed, this is one of the many .subjects that has never been reduced to a gen- erally acceptable system, and it perhaps never will be. 56. HVecessity for Drill and Ilepetition. — The reten- tive power of tlie mind is facilitated by three circumstances — vividness, rc'f>cfitio/i, and attention. In all these the teacher has a large determining influence. In order to pro- duce the greatest possible vividness of impression upon the mind, he may employ several of the senses. The organs of speech may be required to utter a word while the ear notes the utterance and sits in judgment upon it. The muscles of the hand may fashion it for the criticism and approval of the eyes. The eye, the ear, and the organs of speech unite in strengthening the impression upon the mind. But, however thoroughly this may be done, experience teaches that it should be repeated, and, in most cases, frequently. Indeed, other things being equal, the success of a teacher depends 66 PEDAGOGICS OF ORTHOGRAPHY. § 7 much upon the persistence and thoroughness with which he looks after his reviews. It is not safe to assume that, because a matter has been carefully studied, perfectly understood, and satisfactorily recited, it needs no further attention. Things in the mind have a decided tendency to lose their distinct- ness, and to become confused with other matters. Their frequent disentanglement and rearrangement are necessary. Again, the teacher has much to do with the degree of attention on the part of his pupils. His manner, his tones and emphasis, his personal interest and enthusiasm, the order in which the important elements of a lesson are pre- sented, the pertinency of his remarks and questions, the naturalness of the associations that he establishes, his power of illustration — these, and innumerable other conditions that are scarcely capable of statement, determine whether the pupil's attention shall be steady and intense, or fitful, slight, and wavering. This, however, is certain: if the impression is to be permanent, it must be deep; and, to insure such an impression, the cause upon which it depends must operate vividly, must be frequently repeated, and must command the utmost fixity of the attention. It may here be observed that young children have very little power of voluntary attention; hence, it is almost need- less for a teacher to make a formal verbal demand for the attention of a class. Even with persons of mature mind, that which secures attention is objective, external — not. sub- jective. We never say to ourselves, " Now% I ought to be attentive to what the speaker is about to say, for it is closely related to my own welfare." The same things said by two different speakers affect their audiences differently. One person reads to us a striking poem — it is not striking; another reads it, and stirs our deepest emotions. Similar differences in the power of influencing pupils obtain among teachers. An inattentive class should not be blamed or pun- ished for its inattention. The fault — or rather the misfor- tune — is the teacher's. But every teacher can and should review frequently; for, without this, even the best teacher will fail. § 7 PEDAGOGICS OF ORTHOGRAPHY. 67 57. General Treatment of a T.esson in Ortlioj;?- rapliy. — If all considerations of the meaning and use of words, together with their composition, derivation, and other grammatical properties be excluded, the only remaining objects in view in a spelling lesson are three — pronunciation^ syllabication^ and spelling. In preparing and reciting such a lesson, the work can conveniently be divided into about five distinct stages. 1 . The pupil should pronounce the words, utider supervision and criticism by the teacher.— Th\s is an important exercise, and naturally should be the first. When a lesson is assigned, a few minutes should be devoted to the correct pronunciation of the words composing it. This exercise should be repeated just before the words are spelled orally, and at the time of recitation. During this exercise the various diacritical marks should be observed and commented upon, and any important point connected with composition, suffixes, prefixes, compounding, etc. will add interest and secure attention. 2. The pupil should study the ivords. — This is a work that should generally be done at home, and the teacher should insist that it be done thoroughly. If the pupil has a brother or a sister, he may easily ascertain when the lesson has been mastered. If he can spell for his brother or sister every word correctly, he will probably be able to do the same for his teacher. The object being to familiarize the eye, the ear, and the vocal muscles with the word, no degree of thoroughness in this preliminary study is likely to degen- erate into a waste of time. 3. The teacher should pronounce the words and the pupil spell them. — ^This is a part of the work that should never be omitted, and this is not merely because recitations are impor- tant and valuable in themselves, but because omission of recitations that have been prepared for quickly leads to neglect to make preparation. In giving out the words, there should be such an order of procedure as will discourage any effort to prepare for the recitation by learning certain words that can be predicted as likely to fall to particular 6S PEDAGOGICS OF ORTHOGRAPHY. § 7 pupils. Many ways of defeating such dishonesty as this will occur to the alert teacher. It has already been stated that the pronunciation should not indicate the spelling, unless such pronunciation is correct. Words should be pronounced by the teacher exactly as in correct conversation. Before and after spelling a word the pupil should be required to pronounce it — before, to show that he understands the word ; after, because the pronuncia- tion is a necessary part of the spelling. "Trapping," or any other means of deepening the interest or awaking a desire to excel, will be found of much help. Good results often come from giving a book or some similar sign of success in "the Friday spelling match." •4. T/w pupils should copy the guards. — This exercise is a necessity in familiarizing the eye with word forms. It does for this organ what oral spelling does for the ear, and trains the muscles of the hand to obey easily and rapidly the behests of the mind. This phase of the spelling work is too much neglected by teachers, and, while there are decided objections against making all the school work in orthography consist of written spelling, there can be little doubt that it should have at least as much time as oral spelling. 5. The pupils shojild write the words from die tat ion. — After the words of a lesson have been copied from a book or from a blackboard, they should be wa-itten at dictation. The psychological value of this phase of the spelling work cannot be overrated. By means of the exercise the word is made familiar to the mind through the organ of sight, and a cer- tain musciilar aptitude comes from the act of writing the words. The value of this coordination of mental and mus- cular action is perhaps not generally recognized. When a child first tries to write, he is utterly unable to control the movements of his hand, but his conception of the letter forms is perfectly definite. The failure in mechanical execution is due to the fact that his muscles have not acquired the physical habit of acting in obedience to the mind. This obedience will become involuntary and purely automatic, but to make it so requires much and daily § 7 PEDAGOGICS OF ORTHOGRAPHY. 09 practice. This view is confirmed if we attempt to write with the left hand. This is controlled by the opposite hemisphere of the brain, to which, for this work, the muscles of the unac- customed hand have not yet become subservient. The letter forms required are known just as well as before, but the mus- cular adaptation and cooperation are wanting". The same phenomena are observed when we try for the first time to skate, to swim, to play a musical instrument, or to perform any physical act to which we are not accustomed. It seems clear, therefore, that, in preparing our pupils to use words, a condition of easy, and, if possible, automatic correlated action should be established between the mind and the muscles of speech and of those employed in writing. If the student should have any doubt about the necessity for this in the case of the muscles concerned in speech, let him .make the experiment of reading aloud in German, French, Latin, or any other language that he can read silently with ease. He will discover a very embarrassing and annoying lack of coordination between the mind and the organs of speech. 58. Effect of AVi'iting- the Same AVord Many Times in Succession. — It is an easy inference from the foregoing considerations that persistent practice will just as certainly establish that which is wrong as it will that which is right. If you play a piano exercise incorrectly a few times, especially if the performances are in close succession, it is almost impossible to get rid of the tendency to repeat the error. A chained bear always steps in the same places, and in no others, as he takes his exercise around his post. The milk- man's horse is with much difficulty prevented from stopping at the same places in the same order, morning after morning. If we relate an imagined adventure a few times, it comes at last to seem to us to be true — a part of our actual experience. The French philosopher Thurot says, ' ' Habit is the memory of t lie organs. "" Perhaps no better and briefer definition has ever been formulated, for the organs do certainly acquire an aptitude to do again and again — each time more easily — that which they have done before. This very closely 70 PEDAGOGICS OF ORTHOGRAPHY. § 7 resembles the reproductive power of memory. This same truth, substantially, has been beautifully expressed by another writer: " The mind is a spiritual automaton, and the body is a material automaton. Like two pieces of clock- work, they are so regulated as to mark the same time, but the spring that moves the one is not the spring that moves the other; yet they go exactly together. " This final com- mimity and unison of action is established and perfected only by exercising them together. All of this has been said for the purpose of making clear the extreme harm that results from practices such as the follow- ing, very common among teachers: If the pupil misses some of the words of his spelling lesson, or is disorderly or dis- obedient in any way, and if the teacher deems it necessary to detain him after school, he is generally required to "write words " as a punishment. The requirement generally is that he shall write a limited number of words a great many times. Let us suppose that he is directed to write five or ten words t^venty or fifty times. The task is always long enough to impress him with a sense of the need for haste. The work is generally done upon a slate. For the first few words the writing is hurried, but yet fairly good. But, as the work proceeds, the impression that he must hurry strengthens and becomes more imperative, and presently he is writing very rapidly, but no expert in writing could decipher what he has written. It is surprising how little of this kind of work will suffice to negative the most careful training in penmanship, and still more surprising is it that intelligent and observant teachers do not discover the result- ing damage. This and similar devices constitute a favorite method by indolent teachers of keeping pupils from the mischief that comes from their having nothing to do. It may be laid down as a general principle that a teacher should carefully watch, and, so far as possible, control in pupils the operation of activities that are likely to result in the formation of habits; for it is easier to establish and con- firm ten good habits than to eradicate one bad one. In speaking of habits, Aristotle says, "We should, with all our § 7 PEDAGOGICS OF ORTHOGRAPHY. 71 strength, struggle to the opposite of that to which we are by nature the most inclined, as when we row against a current or straighten the crooked and deformed limbs of a tree. " 59. Wvitiiiji' Beautiful or Strikinj»- Passages at Dictation. — In addition to writing single words at dicta- tion, pupils should be exercised much in copying and writing at dictation sentences, paragraphs, and longer poetical and prose selections. The reason ior this is obvious. In the writing of single words, little or no attention to their mean- ing is recpired, but, if entire sentences or longer quotations are written, some mental accom])animent is necessitated by the thought; and this is a natural preparation for the work of original composition, in which propositions must be formulated and their connections and relations considered. If these excerpts be at the same time instructive and beauti- ful, their value is much greater — so much so that many of them may be committed to memory. They then become a source of mental wealth, and may in later life become an inspiration and a guide to action. Many suitable selections for this purpose have been made, but the teacher will have no difficulty in finding in general literature all of this kind of material that he requires. The pupils should each be provided with books in whicli to copy such selections, and they should be wn-itten with extreme care. On Friday afternoons, a delightful exerci.se may be had by rec[uiring these to be recited from memory by the pupils, and the books should contain nothing that is unworthy of such treatment. Tliis work may be made more profitable by attending care- fully and critically to punctuation, capital letters, paragraph- ing, division of words at the end of lines, indentation of lines in poetry, and, w'ith advanced classes, to grammatical and rhetorical considerations. It should be remarked that these selections are likely to consist entirely of poetry imless the teacher is careful to prevent it. Much of the value that may result will be lost unless prose as well as poetry is used. 72 PEDAGOGICS OF ORTHOGRAPHY. § 7 60. Siglit or "Flasli" Method in Spelling.— Much has been said of late years about the "Flash" method in teaching- spelling. The object of the method is to train pupils in acquiring a power of instant control of the atten- tion, and of concentrating the mind intensely upon one object or upon more than one. An experiment that will exhibit the differences in this respect among several minds is the following: Let several persons walk rapidly past a show window, and afterwards let each write the names of the different objects he noted, with a brief description of each object, its relative position in the window, the number of each kind, etc. A comparison of the various results will be instructive. Again, if a number of marbles or other objects be quickly exhibited and withdrawn, the ability to tell their ntmiber and give a description of each is very different with different people. Or, if several numbers or words, say from four to seven or eight, be pronounced slowly, and it be required that they shall be written correctly and in order, it will surprise the teacher how various the results will be with different pupils. The exercises indicated above have been developed into the "Flash" method of teaching spelling. Its advocates insist upon its extreme value, and some of them would have us abandon every other plan, and employ this exclusively. The plan has several modifications, their difference being that the organ of hearing is addressed at one time, the organ of sight at another, and, at still another, both organs are operative. To illustrate, the teacher may write upon a blackboard one word or several words, erase them quickly, and then rec|uire the pupils to write them correctly and in the same order. Or, the pupils may be allowed to look for one minute at a lesson of, say, twenty words, and then write them at dictation. In all these exercises, the eyes are the chief agents employed in reaching the mind. Similar tasks intended for the ears will occur to the thoughtful teacher ; and others may be devised in which the eye and ear are both addressed. The most obvious objection to the "Flash" method is § 7 PEDAGOGICS OF ORTHOGRAPHY. 73 that impressions made very rapidly upon the mind are gen- erally transient. He that would carry in his mind for a long time a distinct picture of a face, a landscape, or any other object, must see it often, observe it attentively, and note carefully the relation of its component elements. It is stated that the mind is capable of consciously and distinctly perceiving through the eye only about eight separate objects in a second. In other words, the element of time is neces- sary to sense perception; and it would seem that the depth and permanence of a mental impression depend very much upon the amount of time expended in acquiring it. The writer once knew a teacher that regularly each after- noon assigned home work for his pupils, with the under- standing that it should be remembered without writing it, or indicating it in textbooks. Thus, he would give, exam- ples to be divided or multiplied — not more than two or three — and words to be incorporated into sentences and defined. He urged the value of such exercises in cultivating both attention and retention; and doubtless he was correct in his theory. There is no doubt of the value of the "Flash" method, but it is much better to be familiar with all methods and to use those best suited to particular cases ; for every situation differs in some respect from every other, and each has its own requirements. A wise and discriminating eclecticism is more to be commended than a slavish adherence to one or two methods of procedure. The profession of teaching resembles, in many respects, that of medicine. The best teacher, like the best physician, avoids the use of nostrums and cure-alls, and is expert in adapting the best possible treatment to each particular case. Gl. Tlie Deflniiig of Words In Connection Witli Spellinji:. — Many educators believe that the mere spelling of a word is of little con.sequence as compared with its meaning and use. In advocating this view, some of them go to the extreme of insisting that words should be so thoroughly studied that the student shall be able to employ them 74 PEDAGOGICS OF ORTHOGRAPHY. § T afterwards in his ordinary vocabulary. The writer does not consider it necessary to discuss this question here, since his views as to the two standpoints of discipline and utility in the treatment of spelling have already been given. It may be remarked, however, in dismissing the subject, that extreme theories are nearly always bad theories. But, in studying words with the end in view of actually using them, the bast means of making our pupils familiar with their meaning should be carefully considered. Without entering upon the troublesome question of what constitutes a correct logical definition, it may be stated that there are four practical methods by which a knowle&lge of the meaning of words may be acquired : 1. By giving synonyms and by discriminating among them. 2. By giving antonyms, or oppositcs, or terms of approxi- mately opposite meaning. 3. By the method of '^ particular instance.'" 4. By formal definition. 63. Explanation of the Foi*egoingr Methods. — One of the most important of these methods is that of synonyms. In employing this plan, the teacher should avoid defining a word by means of others that are more difficult or in less common usj. Thus, if one were seeking a defining synonym oi fright e)i, he should prefer scare or alarm to intimidate. Since it is extremely difficult to find two words of exactly the same meaning — words that may in every case be used i iterchangeably — the teacher is constantly required to illustrate their differences in sense and use. In no department of the treatment of words can better helps for the student be found than in this. We have many excellent works on " English Synonyms," and some of these should be in the possession of every instructor. By their constant i:se, he will find much valuable training for him- self. His own language will take on greater precision, and his thought also. It would be difficult to say which of these works is best suited to meet the requirements of the § 7 PEDAGOGICvS OF ORTHOGRAPHY. 75 teacher, for each one has its own points of excellence. The writer ventures to recommend Roget's "Thesaurus of English Words," Soule's " Dictionary of English Synonyms, " Whately's "English Synonyms Discriminated," Crabbe's "English Synonyms Explained," and the latest, but by no means the best, James C. Fernald's " English Synonyms, Antonyms, and Prepositions." This work among synonyms must be carefully graded to suit the age and various degrees of intelligence among the pupils, and the judgment with which this is done will be a comparatively correct measure of the teacher's success. The method of defining by opposites is inseparable in practice from that by means of synonyms. The two are psychologically, as well as practically, associated; for it is impossible to conceive of lo/ig except as correlated with shorty or of goodness without badness. Indeed, the mental effejt produced by the contrast of differences is stronger than that derived from resemblances. A child gets a more vivid notion of the meaning of hindci' from knowing that it is the opposite of Jiclp, than he does from oppose, obstrnet^ resist, etc. So that both methods should be used, separately and together, as circumstances indicate. For conveying a notion of the exact meaning of a term, the best possible means is to exhibit the thing denoted by the term; next to this is a good picture of it. The objects with which we are in daily contact require no verbal definition, and any effort to define them in words is worse than time wasted. We merely point to a bool', a door, a ivindoiv; in the same manner we distinguish colors, shapes, sizes, and other attributes; and many actions expressed by verbs, and varieties of actions indicated by adverbs, are thus learned. In short, anything that can appeal to one or more of the senses, either directly or indirectly, by means of pictures, gestures, etc., may be represented in our thought with great exactness without recourse to synonyms, antonyms, or formal definition. ' But this is possible with only a small number of the words that we are required to use. For other words, an effect 7(; PEDAGOGICS OF ORTHOGRAPHY. § 7 approacliing in vividness that derived from the thing itself or a picture of it is obtainable by the method known as "particular instance." To illustrate, suppose that it is desired to convey a precise notion of what is meant by delighted. The teacher or a pupil thinks of a situation in which no other term will so well express the appropriate emotion. ' ' When the little girl found that Santa Glaus had brought her a beautiful doll with large black eyes that could sleep or wake, she was very much delighted. " The inventive power of pupils and their aptness in utili- zing their acquired knowledge may be trained by requiring them to imagine the situation necessary to illustrate the meaning of a word, and to construct a sentence in which the word shall occur. This is an exercise that should be in wri- ting; otherwise, there is likely to be an undesirable colloqui- alism in the sentences. Except with advanced pupils, the formal definition has little value. There is a certain unavoidable abstractness about it that impairs its usefulness in the classroom. Our modern teaching puts by far too much stress upon definition work. Young pupils should never be asked to meuiorize rules., prineiples., or definitions. The pedagogical principle, " From the simple to the complex, from the concrete to the abstract," requires that pupils should first learn what things are. Afterwards, if it be deemed prudent, they may be led to evolve a formal definition from the knowledge they have acquired. The formulating of a good definition involves a high order of classification, abstraction, and generalization. The fact is that few people are able to get from a dictionary a sharp notion of the meaning of an abstract word. 63. What Words Say. — Much effort has been made to bring within the reach of school children the subject of the composition of words. Terms that are made up of Greek and Latin roots, prefixes, and suffixes, generally reveal their meaning by their Composition. But, to get this meaning from them, one must know the exact significance of their elements. § 7 PEDAGOGICS OF ORTHOGRAPHY. 77 The following illustrations, one from the Greek and the other from the Latin, will make this fact clear to the stu- dent : Mon, Mono {Monos) = Flex, Fleet {Fh-ctcrc) = one, sole. to bend, turn. Monareli arclios, ruler. Circxxmflex . . . .circinn, around. Monologue. . . logos, a speaking. Flexible iblc, able. Monody ode, a song. Reflex re, back. Monomania, .mania, madness. Deflect dc, away. Monopoly . . . .polcin, to sell. Reflect re, back. Monotheism .///^<:'.y, a god. Flexure m-e, ing. Monotony . . . .ioiios, a sound. Flexor or, that which. The study of words in this way is very interesting- and fascinating; for the student is constantly meeting with curious instances of words that have wandered far from their original meaning-. Indeed, nearly all of our English words that are derived from Latin and Greek are mo.saics or pictures; and to one acquainted with the languages from which they come, a definition is rarely required. The words themselves carry in their parts the story of their meaning. It is doubtful, however, whether a teacher can sticceed with this method and material if he does not know Greek and Latin. The writer's observation is that teachers and pupils manifest but little interest in words studied in this manner, unless the teacher has rare art and scholarship. G4. Rules of Spellinif . — Rules of spelling have already been briefly referred to, and their variety and doubtful value have been to some extent considered. But perhaps a few rules of widest application may be found useful by tlie teacher. The following arc therefore given : Rtile I. — Final /", /, or s: Monosyllables ending in f, /, or s generally double these finals if they are immediately preceded by a single vowel ; as puff, pass, lull, cell, doff, miss, etc. Some exceptions are if, of, as, lias, was, pus, ks, finis, jws, this^ and a few others. 78 PEDAGOGICS OF ORTHOGRAPHY. § 7 Rule II. — Other Finals: Words ending in any conso- nant other than/", /, or s do not double the final letter; as, r//;-, s/i'r, /ur, kin, pan, don, wJiiz, mix, mad, rob, dog, cat, cap, mum, etc. About a dozen words, with a few proper names, are excep- tions to this rule ; as, add, odd, butt, err, inn, egg, bur^rj, ebb, purr, fuzz, sirjz, Ann, Kidd, Todd, etc. Rule III. — Doubling: Monosyllables and words accented on the last syllable, when they end in a single consonant preceded by a single vowel, or by a vowel after qu, double their final consonant before an additional syllable that begins with a vowel; as, rob, robbed ; sin, sinning; abet, abettor, abetting; intermit, intermittent ; acquit, acquittal ; repel, repelling. Exceptions are generally made to this rule if the accent in the derivative does not remain upon the root. Thus, we have refer and referring, but in reference the accent changes and the final consonant is not doubled. So, in like manner, we have infei'', inference, infer'ring. Final x, being equivalent to ks, is never doubled ; in fact, the rule does not apply to words ending in this letter, for X is really a double consonant. Thus, box, boxing ; mix, mixable, mixed. Rule IV. — No Doubling: A final consonant not preceded by a single vowel, or when the accent of the word is not on the last syllable, is not doubled before an additional syllable ; Q.S, fail, failure, failing ; u)ieq7ial, unequal ed ; real, realize, realist. Exceptions to this rule have in late years been gradu- ally disappearing, so that the derivatives of such words as sJlovcI, rival, marshal, victual, carol, pencil, cavil, etc., are generally preferred without doubling the final con- sonant. Of course, when a word ending in / takes ly, there are two /'s, but this is no exception to the rule; as, really, finally, orally, civilly, cruelly, etc. § 7 PEDAGOGICS OF ORTHOGRAPHY. 70 Kiile v.— Final e: Silent c final of a primitive word must be dropped before the addition of a suffix beginning with a vowel; as, rate, ratable ; true, truism ; debate, de- batable. Some words ending- in ee ox ge are exceptions; i\s,peaeeable, ehaugrable, traeeable, outrageous, aud several others. The e is retained in order to preserve the pronunciation of the root. This is the reason also for the retention of the e in shoeing, and, by analogy, in hoeing. The rule does not apply to comp(junds or to prefixes; ^'^, firearms, forearm, vieeagent ; final cc, also, is retained ; as, agreeing, fleeing, etc. Rule VI. — Final e: Final e of a primitive word is usuallv retained before a suffix beg^inning with a consonant ; a,;, state- ness, cdgcless, houseless, changeful. Some exceptions to this rule are duly, truly, aief'ul, argu- ment, judgment, aeknowledgmeiit, abridgment, loholly. Rule \"II. — Final J': When final y of a primitive word is preceded by a consonant, the y is usually changed into i before a suffix not beginning with /; as, merry, merriment : cheery, cheerier ; arbitrary, arbitrarily ; pity, pitiful, pitiless. This rule applies to derivatives, but not to compounds; as, lonely, lonelier ; mercy, merciful, mercy-sister. The follow- ing are some of the exceptions: ladyship, babyhood, secretary- ship, suretyship. Rule A^III. — Final J': When final j' of a primitive word is preceded by a vowel, the y is generally retained before an additional termination ; as, pays, keys, guyed, chimneys, cloying, annoyaiice, joyful. The words laid, paid, said, staid {stayed \'^\)XQiQXXQ(S), daily, raiment (from arrayment), gaiety, and gaily are exceptions to this rule. Rule IX. — The Terminations -?^i' AND -ise: The termina- tion -izc, when it has the force of to make, to give, or to practice, is generally preferable to -ise; in other cases -ise is the usual termination; as, rationalize, brutalize, philosophize, 80 PEDAGOGICvS OF ORTHOGRAPHY. § 7 phiralizc, canonise, civilise, legalise, organise, apologise ; but, 1-ise, disguise, enterprise, surprise, supervise, advise. The student will notice that -ise is usually a part of a Latin root, while -ise is from -iso, an ending of Greek denominative verbs — verbs derived from adjectives or nouns, and denoting sometimes a state, but more frequently the exercise of agency or activity. According to analogy, English denominatives of this kind should be spelled with -ise ; as Americanise, lionise, centralise. Nearly all words in -ise are mixed derivatives. Rule X. — Compounds: Compounds usually preserve the spelling of their simple components ; as, uphill, peacemaker, racetrack, innkeeper. One letter is dropped or a hyphen is used if three letters of the same kind come together; as, ill- loo king, cJiaffincJi, Ross] lire or Ross-shire. Some permanent compounds drop an I irowi full, all, and fill; as, always, handful, fulfil, withal, careful, sinful. To avoid having three s's come together, we have misspell, missend, misspend, etc. 65. Correlations of Spelling-. — There is no subject more widely correlated with other subjects than orthography. vSince it includes every word in the English language, it may be correlated with every subject in the treatment of which English is employed. The extreme advocates of correlation urge " Robinson Crusoe " as a textbook from which may be evolved all other school studies — the physical and mathe- matical sciences, history, philosophy, ethics, logic, economics, engineering, etc. But why is not the spelling book better suited for the purpose than the work of Defoe ? The subject that one must know in order to understand all that a given word implies, rises easily and naturally from the considera- tion of the word itself ; while the way is long and tortuous from the situations in "Robinson Crusoe" to the sciences supposed to be implied by them. Nothing could be more obvious than the transition from the spelling of a term to its §7 PEDAGOGICvS OF ORTHOGRAPHY. 81 meaning and use, and to the sciences in which these are exempHfied. But without doubt the student will see how iitterly absurd such a scheme of ccjrrelation would be, and how slight and vague the results from attempting to unite all subjects into a coherent whole consisting of related parts. " Spelling for the sake of .spelling" should include nothing more than orthography, pronunciation, syllabication, and form ; and the study (jf words for practical use should take into consideration only such terms as are within easy reach of the pupil's intelligence, and are of probable future utilit3\ In brief, no subject should be so correlated with others as to destroy or weaken the unity of effect that should be sought in all rational teaching. In teaching history, for example, when we call in the aid of geography, it should be only for the purpose of illuminating and emphasizing the subject of history. If geography is to be learned, let us study geog- raphy; if history, let history engage our undivided attention. Correlation work should be incidental and illustrative — merely a means to a more important end. "Too many irons in the fire at the same time " is as bad for the educa- tor as for the blacksmith. The best results in teaching are realized when pupils are engaged through a given period with not more than three or four subjects. This is deemed a wise policy to pursue with the students in our colleges ; much more .so is it W'ith the immature minds of children in our common schools. But the contrary practice prevails. How" often do we meet pupils of the common and the high schools, having under their arms great bimdles of books, all of which they are attempting to study simultaneously. This absurdity is encouraged by the belief on the part of parents that the number of books carried by their children is a meas- ure of their progress. The pride of parents in their children, in the schools, and in the teachers, increases with the number of books brought home. The writer's advice to teachers would be: Do not attempt too many tilings at once ; do tliorouglily ichat yon attempt ; avoid confusion and unnecessary correlating; subordinate to your main purpose all outside considerations. 82 PEDAGOGICS OF ORTHOGRAPHY. § 7 It requires in the teacher a higher degree of skill to instruct children in a few subjects than to aiiinsc them with many — to master one subject than to get a smattering of a vari- ety. But there are education, training, and discipline in the one; in the other, only mental dissipation, and undoing for genuine study. METHODS IN ORTHOGRAPHY. APPROVED DEVICES AND ^YORD LISTS. 66. Classi float ion of Orthographical Worlc. — As has already been stated, the object in the study of words is two- fold; (1) the attainment of proficiency in mere spelling, together with correct pronunciation, syllabication, and familiarity with compound forms; (:2) the acquircn':ent of a knowledge of the meaning and use of words, including tlieir composition and derivation. The first of these objects was the only one that received serious attention until within the last twenty or thirty years. Even pronunciation, syllabication, and form were regarded as tmimportant compared with oral spelling. Written spell- ing was practiced but little, the ear alone being regarded as the only organ required in learning words. But since the eye, the muscles concerned in utterance, and those employed in writing have become agents necessary to the work, many new devices have been tried and found useful. The purpose in what follows is to indicate some of the best of these in sufficient detail to make them clear to the beginner in the work of teaching. 67. Lists of Words. — It will be necessary to give, in illu.strating each device, a few words that are suitable for that purpose; but the student must not assume that these are in any case sufficient for the actual work of the classroom. He should extend them according to the needs of his classes. He will find that these lists will grow under his hands, and §7 PEDAGOGICS OF ORTHOGRAPHY. 83 that from time to time they should be revised and amended. ■ New methods, too, necessitate new lists, different in some respect from every other. Much labor may be saved, even if some effectiveness is lost, by using in class a textbook in spelling, and many of these are so excellent that not much can be said against substituting them for collections made from them by the teacher. Indeed, these books will, in general, be found better than selections by the teacher, since not many teachers can be entrusted with a work requiring such nice judgment and exact appreciation of the needs of his pupils. In the suggested exercises that follow, no attempt will be made to separate those intended for discipline in spelling from such as are valuable for other reasons. In fact, it will be foimd that many of the words that are required in an ordinary vocabulary are of difficult spelling; and it is espe- cially important that the orthography of this latter class should be made perfectly familiar to the pupil. 68. Short Woi-ds That Are Often Misspelled.— There are many words of this kind that are indispensable in a vocabulary. They are doubly useful, therefore, and every teacher of spelling should have a collection as complete as possible. They should be in exercises in pronunciation, in oral and written spelling, and for actual use in sentences. A few of them are here given. enough could often those does whose again which always should there done once they any many what their where been hear whose much these were why busy here sure since else of off to two C9. Lessons in Abbreviations. — One of the first things that should be taught in connection with orthography is how to spell, write, and punctuate abbreviations. In addition to this, the pupil should learn to u.se them in speech and wri- ting, and to distinguish between those that are admissible 8J PEDAGOGICS OF ORTHOGRAPHY. and those that are not. important : The following; are some of the most don't they'll aren't hasn't couldn't thro' etc. doesn't he'll wasn't hadn't wouldn't Mr. mayn't I'll she'll didn't won't e'er Mrs. we'd we'll isn't weren't haven't ne'er Geo. they'd After the pnpil has reached a certain stage of progress in arithmetic and geography, there should be systematic prac- tice in the abbreviations used in those subjects. This is something that is rarely done, and yet it is a matter of much importance. The abbreviations of denominate numbers should be written at dictation, for until this work is under- taken in school, uniformity will never be attained. In geography, every pupil should know how to write the gen- erally accepted abbreviation for the name of each state, and for each large city whose name is abbreviated. Advanced pupils should be made familiar with such other abbrevia- tions as are in very common use; as, /. i\, C.O.D., Dr., Cr., ct al., A. Al., LL. D., ibid., A. B., Ph. D., M. D., Hon., etc. '70. Words Liiable to Be Mispronoimcetl. — Regular exercises in words of this kind should be practiced in every school where spelling is taught; yet this is almost entirely neglected. Even teachers show by their pronunciation that they themselves would be benefited by such exercises. Not many persons, perhaps, could be found able to pronounce correctly at sight the following words: extirpate obligatory squalor vagaries arbutus legislature misconstrue bronchitis parachute docible potpourri communism psalmody granary anchovy rationale bouquet mauve acoustics gallows equation repertory coquetry acacia municipal deficit isolate isothermal porpoise tortoise cortege complaisance combative alias admirable The teacher should procure lists graduated in difficulty, and use them for practice until they have been thoroughly mastered. If he is observant, he will be constantly finding new words to add to his lists, among which should be many § 7 PEDAGOGICS OF ORTHOGRAPHY. 85 of local peculiarity in pronunciation. This is an exercise that will be very beneficial, not only to the pupils, but to the teacher. He will get from it much added precision in his own speech. It need scarcely be added here that these lists will be equally useful for spelling and for other exercises. 7 1 . Study of Pliouics. — There are two principal methods of acquiring a correct and finished articulation. The first of these is by the imitation of good models, and the second by a systematic study and practice of phonics. There are, however, practical difficulties in the employment of either method. If all models, all persons whom we hear pronounce the words of our language, gave exactly the right sounds of the letters, articulated the syllables clearly and distinctly, and placed the accent just where it belongs, the first method would be an ideal one. For we are by nature imitative. Children in a home where English is always elegantly spoken, readily acquire the same manner of speech, some- what modified, unfortunately, by what they hear from their playmates outside. A perfect environment for the cultiva- tion of finished speech cannot be found in this or any other civilization. People that have been carefully educated and trained cannot, or, at least, do not, avoid colloquialisms, localisms, crudities of every kind, even slang, in their speech. And, when it is remembered that each person is in some degree a teacher of many persons, even though undesignedly, the extreme difficulty for people in general to acquire finished speech will be obvious. The principal obstacle in the way of learning correct speech from study and practice in phonics is that very few teachers are thoroughly acquainted with this subject. Of late years, however, much progress has been made, from the necessity that teachers have felt of knowing the Phonic method of teaching children to read. Even this small amount of discipline shows itself afterward in a more accurate pronunciation and articulation when children .speak and read. But it is only from an extended practice of phonics that the best results come. The writer has frequently observed the 86 PEDAGOGICS OF ORTHOGRAPHY. § 7 precise utterances of persons that are expert in shorthand wri- ting — phonography. With them the sounds^ and not the letters that make up words, engage constant attention. They must know the correct sound and articulation of words before any attempt is made to write them ; and the practice of trying their organs of speech upon words is indispensable. In this way an instinct for correct pronunciation is formed, just as is the case with spelling; and this establishes itself as an imperative upon their utterance. It would seem to follow, then, that a systematic and per- sistent practice in phonics would prove to be a good invest- ment in training our children ; but, as is true of nearly every other subject, if it is to be made profitable in a high degree, the teacher must know it thoroughly, both in theory and in practice. If he will procure a good manual on phonics, — of such there are many, — and will persist in phonic spelling until he is thoroughly master of the subject — until it has made its influence felt upon his own speech — he may then expect to make it profitable in his classroom work. If the writer were asked to advise a teacher concerning this pre- paratory work, his advice would be, study phonography — shorthand writing by sound — until you can write it cor- rectly and rapidly; and to do this, you do not need a teacher. You will then be able to teach phonics to your pupils in a way that will modify their speech for the better. 73. The Use of Suffixes in Teaching. — Scarcely any teacher of orthography fails to give instruction in the mean- ing and use of prefixes in forming derivatives. These are nearly all from Latin or Greek, and each usually has an exact meaning. This, however, is not so of suffixes in gen- eral. They are mostly of Anglo-Saxon origin, and, with a derivative, their effect upon the meaning is often difficult of statement in words. Hence, suffixes are generally neglected in our language work. So important are they, however, that the writer gives here the most important of them, with their meanings as nearly as possible, together with some suggestions as to the best method of using them. § 7 PEDAGOGICS OF ORTHOGRAPHY. 87 73. Alphabetical Arraiigenient of tlie Prlnciiial Suffixes. — The numbers preceding the suffixes refer to their meaning- as given in Art. 74. SUFFIXES. 1 ac 16 en 12 ion 2 or 4 age 3 ence 20 ish 22 ory 1 al 3 ency 19 ism 21 ous 2 an 2 ent 2 ist 18 ress 3 ance 2 er 2 ite 28 ric 3 ancy 26 ery 3 ity 24 s 2 ant 24 es 21 ive 2 san 1 ar 18 ess 18 ix 8 ship 1 ary 24 est 16 ize 23 some 2 ast 24 eth 7 kin 25 ster 5 ate 17 ful 15 less 1 tial 6 ble 16 fy 7 ling 3 ty 7 cle 8 head 11 ly 3 ude 3 cy 8 hood 12 ment 7 ule 28 dom 2 ian 8 ness 12 ure 27 ed 1 ic 1 nic 13 ward 2 ee 1 ile 7 ock 22 wise 2 eer 9 ing 10 oid 14 y 74. Meaninj? of Suffixes. — There are some exceptions to the force of suffixes as given below. It will be necessary, therefore, that judgment be used in interpreting their sense in derivatives. 1. Pertaining to; having ; as, maniac, material, momentary, stellar, partial, syllabic. 2. He tliat is, does, makes, or belotigs to ; as, Cuban, complainant, scholiast, engineer, assignee, Israelite, artist, grammarian, partisan. 3. The state of being or doing; as, reliance, privacy, servitude, oddity, reference, belligerence, relevancy. 4. State, or charge ; as, brokerage, nonage, pupilage, storage. 5. To make, when it forms a verb; as, scintillate, aerate, predicate. 6. Able, or capable, of being or doing ; as, lovable, legible, stable. 7. Little, or young ; as, particle, duckling, manikin, lambkin, hummock, granule. 8. Condition, or state of ; as, childhood. Godhead. 9. Continuiiig ; as, striking, walking. 88 PEDAGOGICS OF ORTHOGRAPHY. § 7 10. Resembling ; as, spheroid, anthropoid, typhoid. 11. Z/Xv, in an adjective; z« « ;//rt;/;/^r, in an adverb ; as, womanly, scholarly, slowly, musically, rapidly, only. 12. Cotidituni, or act of ; as, lodgment, movement, tenure, fusion, closure. 13. Toward; as, forward, westward, windward. 14. Abounding in ; as, rainy, dewy, smoky, sandy. 15. Withoitt ; as, moneyless, dreamless, hopeless. 16. To make ; as, blacken, beautify, legalize. 17. Full of ; as, beautiful, hopeful, gleeful. 18. T/ie fetninine of ; as, tigress, lioness, poetess, executrix. 19. Having reference to a creed, or faith ; as, egotism, altruism, deism. 20. So)neiuhat, or pertaining to; as, greenish, sweetish, Danish. 21. Having the quality of ; as, evasive, dolorous, glorious, envious. 22. IVay, or in the manner of ; as, otherwise, edgewise, likewise, endwise. 23. Full of ; as, gladsome, lonesome, burdensome, toilsome, irksome. 24. With nouns, s and es denote the plural ; with adjectives and adverbs, er and est denote degrees ; with verbs, s, est, and eth denote the actor. 25. TJic person, or thing, that ; as, teamster, punster, roadster, trickster, malster. In spinster, stcr is a feminine ending. The only other Anglo-Saxon feminine ending remaining in English is en in vi.xen. 26. The art of; as, witchery, cautery, cookery, archer}', gunnery. 27. Did, in a verb ; completed action, in a participle. 28. Territory of, or office ; as, dukedom, martyrdom, bishopric. 15, Exercises Witli Suffixes. — Many interesting and profitable exercises are possible with suffixes, but of course they belong in advanced vv^ork in orthography. In these exercises, while spelling is, as always, important, it is the meaning of the root and of the suffix, together with the special application of the word in actual use, that must engage the attention. For, it must be remembered that, while the meaning denoted in the etymology of a word always contributes to a better understanding of its present sense, the two are often widely different. Thus, ambition means literally a going around, from avibi and itiis. In Rome, 2,000 years ago, an office seeker went around amoj^g his voting friends. Today the word denotes merely an aspiring after something supposed to be higher and better § 7 PEDAGOGICvS OF ORTHOGRAPHY. 8!) than that ah'eady attained. The word admire formerly meant to %vo)idcr at, and in this sense it was used by vShake- speare and Milton; now it has no such meaning. No hint of immortality lingers in cemetery; but, to the ancient Greek, Koiiirjri]piov, koimeterion, was a sleeping room, dear and diminutive, in which the weary slept, and rested, and ivaked. The following will serve to indicate some of the many exercises with suffixes: 1. Form by suffi.xes various derivatives from each of the following words, and illustrate their use in sentences: good, return, sly, hope, man, etc. . 3. With each of the following suffixes, form five derivatives, and illustrate them in sentences: -en, -oid, -udc, etc. ;j. In the following derivatives, {a) mention the primitive part and the suffix ; {b) give the literal and the present meaning, and account for their difference in sense; (<;") illustrate in a sentence the 'present meaning of each ; {d) write a brief composition in which shall occur the following: nameless, planetary, globule, revolving, stellar, etc. 4. Mention the derivatives with suffixes in the following, and give their meaning: (Here follows a quotation, either prose or poetry.) 5. By means ()f suffixes, convert the following into diminutives: book, braiieh, goose, grain, hill, etc. 76. Psycliological Use of Rules. — Among the last exercises in learning to spell, pupils may be required to state or to write rules in exact language — a constructive work that makes too severe a demand upon the minds of mere children. It is an accepted principle in pedagogy that facts should precede inductions; examples, rules; processes, principles and generalizations; the concrete, the abstract; the .simple, the complex. To formulate a rule and cause it to be mem- orized, and then to proceed in applying it to particular cases, is a reversal of this order. The teacher's aim, therefore, should be to develop from many examples a general method of procedure — a rule. Whether this rule is merely noted, cursorily stated, or expressed briefly and precisely in writing, should depend upon the intelligence of the pupils. But, while it is not wise to require children to apply rules arbitrarily imposed by the teacher, work in spelling should 90 PEDAGOGICS OF ORTHOGRAPHY. § 7 not be conducted at random. It is much better to deal with words that are classified. These classes may be determined by the rules that g-overn their spelling, by the roots they contain, by prefixes and suffixes as modifying the meaning of roots, by similarity in sound or meaning-, or by any other common characteristic. 77. Exercises With tlie Rules of Spelling?. — The statement has already been made that young children should not be required to commit rules of spelling to memory or to apply them. The teacher may, however, devise many valu- able exercises with rules, and yet avoid such requirements. The following will indicate how this may be done. He may write upon the board or dictate: 1. Many words ending in e drop this letter before a suffix beginning with a vowel ; as, love — loving, lovable, lover, etc. Find ten words of which this is true, and write their derivatives. 2. Write derivatives from the same (or other) ten words, having the suffixes begin with consonants. 3. Some words ending in ce and ge retain the c before a suffix ; as, peace— peaceable; strange — strangeness, strangely. Prepare a list of five words showing this, and write their derivatives. 4. Many words ending in a consonant double the consonant before a suffix beginning with a vowel; as, rtm— runner, running. Find twenty such words, and write their derivations. 5. Monosyllables ending in a single consonant, preceded by a single vowel, double the consonant before a suffix beginning with a vowel ; as, strut— strutted, strutting. Write, with their suffixes, ten words showing this. In this way pupils may be made familiar with the operation of all the important rules of spelling, without being required to memorize them. 78. Exercises With Compoiina Words. — It is impor- tant that pupils should give careful attention to compound words, and should be familiar with the forms in which these are usually written, whether they are hyphened, solid, or separate. They should learn, too, that a process of change is always in operation, and that the approved forms of today will many of them be different in ten or twenty years. They § 7 PEDAGOGICS OF ORTHOGRAPHY. 91 should understand the direction of the drift in this matter, and know that a condition of permanency is reached only when the compound has assumed the solid form. They should know that a solid compound may fall apart if it be but rarely used. Thus, at first we doubtless had licgf lord and licgc man; later, they took the hyphen; then they became solid, and now we should write them separately. Such things as are gradually introduced, become very gen- eral, and then are displaced by something else, often have, with respect to their names, a history like this. The teacher can place upon the blackboard something like the following, have the pupils copy it, and do the required work in accordance with the schemes indicated below. 1. Write as many compounds as you can, and give tlieir approved forms ; Compounds. Approved Forms. Compounds. .Approved Forms. love self-love hat \ hat-box self \ \ box 3. Write the approved forms of the following pairs of words: slcain — boat, eye — lash, wheel — barrow, side — light, mi lie — man, silk — weed, etc. 3. Prepare a list of twenty compounds in which a hyphen should be used ; and a list of twenty solid compounds. 4. Write in correct form ten compounds whose second element is book, and ten whose first element is fire. 5. Write and use in sentences ten solid compounds, and ten hyphened compounds. *T9. Etymological Exercises Involving Spelling. — Nearly all spelling books contain many of these exerci.ses, usually intended for advanced pupils. Some of our edu- cators oppose having pupils do work of this kind, but their reasons for the opposition are, many other authorities think, not very convincing. As has been said, orthography is gen- erally recognized as one of the divisions of grammar, and there seems to be no good objection against combining exer- cises in etymology with tho.se of spelling, provided always that they are not beyond the intelligence of the pupils. 02 PEDAGOGICvS OF ORTHOGRAPHY. § 7 Certain is it that much can be done in this way to relieve the monotony of routine spelling. The teacher will find in some of our latest spelling books innumerable exercises of this kind. These should be noted by the teacher, and suitable lists and working directions prepared. The following exercises will serve to illustrate what is intended: 1. By means of suffixes change the following nouns into adjectives: critic, odor. myste7-y, center, home, practice, wind, sphere, story, egotism, etc. 2. Write other nouns containing the ^ame roots as appear in the following : sphere, siniplcness, pore, justness, truth, vanity, precision, friendship, pallor, requisition, etc. Illustrate in sentences the differ- ent ways in which each pair of nouns is used. 3. Find five nouns {a) that take .f in the plural ; {b) that take es ; (r) that change/ into 7/^ J- ; {d) that change/^ into 7V'.f ; (r) that change y into ies ; etc. 4. Write and give the meaning (or use in sentences) of derivatives containing the following Latin roots: rupt,fer, cept, viit, le7>, gress, dud, din, did, pugn, etc. 5. Write and define (or use) derivatives from the following Greek roots: poly, pod, phi I, phon, thesis, onyin, nod, graph, nion, etc. 80. Synonyms and Antojiynis. — It would be difficult to devise exercises more entitled to a place in the classroom than those with words of the same, and words of opposite, signification. The teacher is aware, of course, that it is not easy to find two terms of exactly the same meaning, which may, therefore, always be u.sed interchangeably; and it is upon this fact that the peculiar richness of our language and its fitness for training the judgment of the pupil depend. A great variety of exercises, each with a slightly different object in view, may be prepared by the teacher. This matter has been treated at considerable length in Pedagogics of Grammar, but it is deemed best to make in this place some additional suggestions. 1. Discriminate the following words and illustrate their uses: frail, delicate, sickly, unhealthy, diseased, fragile, sick, ill, failing, tatsouttd, wasted, worn, emaciated, etc. 2. Arrange the following verbs as exactly as possible in pairs hav- ing opposite meanings: claim, affirm, assert, maintain, assure, assert, allege, gainsay, contradict, dispute, deny, waive, retract, disprove. § 7 PEDAGOGICvS OF ORTHOGRAPHY. <)3 8. Place these words in the order of their strength, beginning with the weakest: ^l^id, contented, pleased, rejoiced, elated, jubilant, rapturous, triumphant, joyful, happy. 4. Find the nearest opposites for the following words : symmetry, harmofty, diversity, prosperity, analysis, urbanity, rejection, cen- sure, bravery, refinement. 5. In the order of their intensity of meaning, write ten adjectives descriptive of the emotion occasioned by failure. Illustrate their use in sentences. It is scarcely necessary for the writer to say that work like the foregoing may be of many degrees of difficulty, and suited, therefore, to children in various school grades. But this adaptation must be made by the teacher, for no one could prepare a textbook for general use. This is perhaps the reason why we have so little language work of this kind in our schools. 81. Words Denoting- Collections. — Our language con- tains many words, each denoting a collection, but they cannot be used interchangeably. Thus, we may say a bevy of girls, but not a bciy of ivo?ncn or boys ; a covey of par- tridges, but not of geese ; a band of robbers, a drove of horses, a Jioek of birds, etc. In learning our language one of the chief difficulties experienced by a foreigner lies in the neces- sity for discriminating words of this kind ; and what is true in the case of foreigners is true also in that of our own children. Both are equally beginners, and what must be done for the one should be done for the other. In our schools, no special training in these matters seems to be regarded as important. Whatever there is of it is accidental, and it is just this purposeless work, this absence of prevision, that detracts so much from the value of a teacher's work. Let it be determined in advance what is important to be learned and why, and let relative or comparative values be fixed as nearly as possible, and then let each matter be incor- porated as a distinct part of a general scheme of work. This is something that cannot safely be trusted even to the best memory. No teacher should expect that necessary things will be suggested to the teacher at the right time and place. 94 PEDAGOGICS OF ORTHOGRAPHY. § 7 They may or they may not occur to him when they should; hence, the value of note books. These books, collectively, should speedily constitute a source from which may be drawn the material, the devices, and the methods of procedure that are indispensable in organizing the work of a coming term. The teacher will be surprised to learn that there are in common use more than two hundred words of the kind referred to above — words denoting collections. The follow- ing suggested exercises will be found useful in practice : t. Prepare a list of words that denote collections, and make the list as nearly complete as possible. 2. Write twenty of the words in (1) that are in commonest use, and modify each by a prepositional phrase ; as, a pool of maftufacttirers, a gala.xy of beauties. 3. Find the collective nouns that may be modified by each of the following phrases: of robbers, of bees, of cattle, of dishes, of minerals, of plants, etc. 4. Write the following collective nouns, each with one or more appropriate modifying phrases: presbytery, synod, council, cotigress, squad, squadro7i, series, colony, den, legation, knot, succession, syndi- cate, universe, school, wilderness, battery, catalogue, etc. 5. Find from a dictionary the derivation and the literal meaning of the following collective nouns: synod, canopy, gala.xy, presbytery, horde, universe, collection, aggregation, succession, constellation, niultititde, catalogue, complement, etc. 82. Words Expressing Diffei*ent Aspects of tlie Same Idea. — All our writers on synonyms arrange words in accordance with some leading ideas. These ideas may have relation to physical qualities as perceived by the senses, or to metaphysical qualities as conceived by the mind. Most words having metaphysical or ideal applications were origi- nally employed in a physical sense, and it is a knowledge of this sensible use that gives vividness to words when they are transferred to ideal uses. Thus, a linguist sees a needle in ac2itc, ahorse in cavalier, a ladder m scale, clunbinginascoid, a flock in pecuniary, or gregarious; and st in stajid, station, steady, stake, status, substantive, etc. tells him the story of erectness and fixity ; hence, the importance to the student of finding the root or original physical sense of words, especially § 7 PEDAGOGICS OF ORTHOGRAPHY. 95 of such as have strayed entirely away from that meaning. Indeed, without knowing- the etymology of words, it is impossible to use them with perfect discrimination. The pupil, in order to acquire this knowledge, must have access to a standard dictionary, and inust know how to use it; and, therefore, the exercises suggested below can be undertaken with profit only by advanced pupils. 1. Find, and illustrate the use of, ten verbs implying motion down- '■a'tird; also, ten implying vioiion upward. 2. Write all the words you can that implj' increase in physical volume; in physical area ; in physical length. Select from your lists those words that have ideal ai^plication, and illustrate their use. 3. Find ten verbs implying use of the sense of sight. Explain and illustrate their difference in meaning. 4. Referring to (3), give all the related nouns, adjectives, and par- ticiples. Thus, verb, view; uoim, view, vision; tuljeetivo, visible, viewable; particii>lo, viewing. 5. Make lists of the verljs, the nouns, and the adjectives employed with reference to motion from a place; with reference to motion toward a place. Explain their difference in meaning. 83. Words Belonging to a Given Environment. — A valuable and much used exercise with words consists in requiring the pupil to write correctly lists of words belong- ing to particular situations. Thus, the field, the garden, the kitchen, the parlor, the farm, the city, the ship, and the railroad each has a great many objects, actions, qualities, processes, and products that belong there. vSome of the terms denoting these things are of difficult orthography, and all are useful in an ordinary vocabulary. It should be remarked that exercises of this kind deal mostly with nouns, and are therefore suitable for the work of young children. In giving a notion of the meaning of nouns, children may be required to indicate any, or all, of the following: 1. Its physical qualities; including shape, size, material, color, smell, etc. 2. Its origin. Did it grow, or was it made by man ? Etc. 3. Its use or function. This last is perhaps the most important basis of classification, and the one most commonly 96 PEDAGOGICS OF ORTHOGRAPHY. § 7 employed. Of course, many exercises of this kind with other parts of speech are possible. Some of these are : 1. Write the names of animals that are useful to man, and state in what respect they are useful. 3. Mention some common wild flowers ; also, some grown for orna- ment. 3. Give the names of useful plants and trees ; also, the names of the fruits and vegetables, domestic and foi-eign, that you would expect to see in a large market in New York City. 4. Write (a) the names that are difficult to spell of parts of the human body; (/^) the words that denote what the mind can do. 5. Give the names {a) of ten _/is/i; (/') of ten trades or professions; (c) of ten tools; (li) of ten terms used in miisie; (e) of ten birds; {/) of ten inetats; {g) of ten precious stones; (//) of ten games; (z) of ten terms used in geography. 84. Spelling- From. Pictures. — Closely related to the exercises indicated above is that of spelling- from pictures. In both cases the reality is absent, and the pupil is required to find a substitute for it — in the first, a mental picture, and in the second, a physical representation. The mental picture cannot be reproduced for reference by the teacher and the class in criticizing the pupil's work, while the physical picture is more convenient for this purpose than even the reality. In this fact lies the opportunity of introducing verbs, adjectives, adverbs, and other parts of speech besides nouns. Pictures suggest and represent things and their qualities; they suggest actions in various degrees, and rela- tions that require prepositions and conjunctions. With the picture before him, the pupil may be asked to explain in what he found a suggestion of particular words in "his list. It should be added here that with young children no better subject for a composition can be found than that furnished by a good picture. From the requirement that a pupil shall tell merely what he sees in the picture, this exercise may rise in difficulty into an account of the differences and like- nesses of qualities in the objects depicted, the actions sug-- gested and their purpose, the manners and degrees of the action, the cause, purpose, and result of the conjunction of olijccts and actions in the picture; and with all these may § 7 PEDAGOGICS OF ORTHOGRAPHY. 97 enter relations of time and place. In short, the pupils mi write, as if from their own experience, a composition cover- ing the things shown by the picture or suggested by it. Many teachers require their pupils to indicate by a picture of their own making, at the top of the paper, with or without marginal pictures, the main points or incidents related in the composition. Thus, if a pupil is writing about the polar bear, some very striking pictures may be made showing the animal in his habitat and in characteristic action. It is urged as a reason for this practice that the inventive power of the mind is increased by means of the picture — a claim about the truth of which there can be no doubt. Even the mature reader gets a very much more realistic and vivid impression from an illustrated book than from the text alone. How much our interest in the " Pickwick Papers" would be lessened if the pictures of the inimitable philosopher were missing. 85. Exercises Witli Prepositions. — To be able to choose m every case the appropriate preposition, is by no means a simple matter, and it should be persistently and carefully taught. The subject, however, receives but little attention, generally none at all, in our schools. Although no question ot pronunciation or spelling is involved, the very vital rela- tion of the preposition in our vocabulary gives this part of speech peculiar interest and importance in language teach- ing. No excuse need be offered, therefore, for introducing the subject at this point. The c[uestion as to what preposition should be used with a particular word is determined in general by one or more of tnree circumstances. 1. By tJic prefix of the uKird; as, advert to, inscribe upon, etc. Here the first prefix means to and the second on or upon. Hence, the English prepositions are determined by the mean- ing of the Latin prefixes. 2. By the meaning of t/ie word ; as, patient in or amid misfortunes; reason of ox against a principle or theory, j^>r an action ; disappointed at a failure, in love, of what was expected. 98 PEDAGOGICS OF ORTHOGRAPHY. § 7 3. By common 7isagc; as, confide to one's care, in one's word or honor ; two persons may have confidences zuith each other, or there may be confidences among several persons ; preserve in alcohol, xvith care, for my son, by vigilance, from danger, against future need. In the exercises necessary for the proper development of this subject, the teacher may : (1) Supply the pupils with words each of which takes one certain preposition, and he may require them to indicate the preposition and illustrate its use. (2) Supply certain prepositions, and the pupils may use each in sentences with other suitable words. (3) Supply sentences with blanks indicating missing prepo- sitions, and require the pupils to fill the blanks. (4) Require the pupils to use a specified word with several diiferent prepositions, illustrating each in sentences. It must not be forgotten that this is a work intended not so much for discipline as for practical use ; hence, the exer- cises should be confined to the probable future vocabulaiies of the pupils. No time should be expended upon combina- tions that are rarely met or used. 86. Form and Matter of IJetters. — If there is a subject with which orthography is more closely correlated in practice than it is with any other, that subject is letter writing. One of the most frequent and important applications of the knowl- edge gained from a study of orthography is to correspondence. Nearly everything connected with this subject has relation to orthography. Of our latest textbooks on spelling, almost all contain exercises in letter writing. vSome of the expedients employed are for the teacher. (1) To supply brief letters showing the approved forms, positions, punctuation, etc. of the various parts. These are to be copied by the pupils with the object of making the mechanical construction and arrangement of letter elements familiar to them. (2) To dictate to the pupils brief letters, and require them to be written correctl}'. § 7 PEDAGOGICvS OF ORTHOGRAPHY. 99 (o) To furnish in outline the data of letters, and have the pupils write them in full. (4) To require pupils to write various kinds of letters to imaginary correspondents. In this work, spelling- is to be attended to closely, but even more important are pronunciation, capitalization, division of words at the end of lines, parag-raphing, and general correct- ness of form. 87. Pedagogical Objections to Correlative Work Ijike the Foregoing-. — The writer is aware, of course, that in many quarters there is much opposition to the inclusion in orthography of anything more than spelling, pronunciation, and syllabication. A late spelling book contains the follow- ing in its preface : "Grammars, rhetorics, geographies, histories, and even systematic works on composition, are useful — and so are spelling books. But it does not follow that they should all be combined in one. It is possible to drive a nail with a chisel ; but nails can be driven better and quicker [more quickly] with a hammei\ So a textbook is better for a special use by being specially adapted to that use. "These facts will account for the absence from this work of many puzzling exercises in the construction of sentences, and in fitting words to parts of ready-made sentences, as well as for the lack of lessons and examinations in geographj', grammar, and history, with which some of the modern spelling books abound. It is believed to be better at times to concentrate the attention of the student upon spelling; and, accord- ingly, that all matter tending to distract his attention from the special work of learning to spell should be excluded from the spelling book." 88. Remarks I"i)on Tliese Objections. — It may be remarked that the author of the foregoing criticism on the correlation of spelling is head master of a normal school where provision is made for the systematic study, in its proper place, of everything required to prepare students thoroughly for aij intelligent comprehension and discharge of the duties that await them. But this is not the usual case in the schools where spelling is taught. In most schools, the student will in all probability never hear in the classroom anything on the subject of letter writing, unless the teacher 100 PEDAGOGICv^ OF ORTHOGRAPHY. § 7 introduces it in correlation with something else. When he studies geography, he will give no attention to the spelling and pronunciation of geographical terms. Of punctuation, too, he is likely to hear nothing. Indeed, nearly every teacher is, from his own experience, aware of the truth of these statements. The writers on hygiene tell us that a variety of physical food is necessary to health, and that the assimilation and appropriation of its useful elements are better and easier if these eleinents are varied in character. We all know how weary one becomes of a diet consisting exclusively of oat- meal, eggs, or meat. Something like this is true of the mind. If a pupil is compelled to concentrate his attention exclusively i:pon one subject, he makes less rapid progress in it than if his time is judiciously divided among several subjects. Even a philosopher finds rest and relief from his abstruse specialty by resorting at times to the newspaper or the novel. Knowing that certain indispensable things are not dis- tinctly provided for in the course of study that he follows, the thoughtful teacher will consider how, and in connection with what subject, he can supply the omission. He is convinced that eveiy person should know how to write a creditable letter, and that ignorance in this will be the occasion of much futvire embarrassment and even pecuniary loss. He sees to it, therefore, that at the right time and place the want of prevision on the part of those that arranged the course of study shall cause his pupils the least possible disadvantage. He realizes that he is " confronted not by a theory but by a condition. " Yet, whatever work of this kind may be necessary, the teacher must never lose sight of the main subject in hand. Its unity must remain and be exemplified in his work. 89. Correlation of Spelling With General Informa- tion. — There are many matters of general information that are often overlooked in elementary education — and this is all the education received by 95 per cent, of American § 7 PEDAGOGICS OF ORTHOGRAPHY. 101 children. These matters are not merely ornamental — they are extremely useful and important. The man or woman that knows nothing of the great men, inventions, discoveries, epochs, battles, and creeds of the world is badly handicapped as a member of society, and he can learn about them only incidentally. No school will teach him anything worth speaking of about these matters. We must rely upon our teachers to supply data that are indispensable to a wide mental horizon — to large views of men and things,, the world and its contents. Many of our spelling books suggest lines of w^ork of this kind — work that meets in the best possible way the cravings of the mind to know, of the imagination to create, and of the fancy in its aerial play. This is not a diversion of time from a more important subject ; it is a legitimate and necessary attempt to provide for a real want of the mind. Some of these exercises are indicated in briefest outline below, but besides these there are many others of equal importance. 1. Learn to spell the following names of authoi-s ; find out what you can about each: Dickens, Thackeray, Macaulay, etc. 2. Who were the following named persons; when did each live; for what was each celebrated ? Croesus, Theseus, Hercules, Lycurgus, Aristides, Demosthenes, etc. 8. Who wrote the following ? Tell something of each work : "Pick- wick Papers," "The Caxtons," " Romola," etc. 4. Find out and write correctly the names of the " Seven Sages of Greece." Tell something about each of them. What were the " Seven Wonders of the World ?" 5. What cities are known as follows ? " The Hub," " The Crescent City," "The City of Churches," "The City of Magnificent Distances," "The Electric City," etc. 6. Write the names of each of the United States, and give, as far as you can, their popular names. 7. Write twenty geographical names of South America that you consider of difficult spelling or pronunciation. 8. When and by whom were the following inventions made ? Cot- ton-gin, telegraph, kinetoscope, steamboat, gunpowder, printing, mainner's compass, telescope, etc. 9. Write the names of ten characters in Greek mythology. Tell something of each. Also, ten of Roman and ten of Scandinavian mythology. 102 PEDAGOGICS OF ORTHOGRAPHY. §7 10. Give the names of ten of the world's greatest military leaders, and tell something interesting about each. How much besides the spelling and pronunciation of the names involved above should be required will depend upon the circumstances in each case, and, of these, no one can better judge than the teacher. That much of this kind of work should have a place in the classroom seems to the writer indisputable. 90. Test Words for Spelling;. — Most works in orthog- raphy contain lists of words for test spelling. In these lists will nearly always be found terms that are never employed even in learned conversation. vStich words have no other claim to attention than that their spelling is difficult; but, since we have an abundance of useful words of irregular spelling, it is well to use as many of them as possible. For examinations in spelling, however, difficult words, without regard to their usefulness, are nearly always chosen. The following will indicate in general the writer's notion of the kind of words selected as tests for teachers that are required to undergo examinations in orthography. The teacher can extend it as his needs require. Of course, only advanced pupils should practice such words. Similar col- lections graded to suit should be prepared for each year of a pitpil's school life. whippoorwill cemetery alpaca cochineal caterpillar calendar paroxysm separate operate opportunity suppurate crystallize flageolet parricide bronchial sedative psychology catastrophe hyacinth pyrotechnic raspberry pentateuch hydraulics pennyroyal patriarch decalogue corollary syllogism Pharisaic caisson philanthropy altruism accouter acerbity saccharine foliaceous calking gauger giaour philippic phylactery philology etymology antonym pseudonym shillalah barytone alinement anachronism plagiarism garlicky redeemable dentifrice plaguy sergeant chalybeate vicinage pimpernel immaculate pleurisy PEDAGOGICS OF ORTHOGRAPHY. 103 taciturn rarefy necessary abatable hysterics asphyxiate daffodil cabalistic dactylic czarevitch apologize mustache bandanna whinneying dagueri-eotype scintillate anonymous quinsy mignonette caviling flagitious facetious acquiescence catalepsy casuistry centennial annually elixir cauterize damageable aberration chirurgeon caricature erysipelas basilisk mahogany macerate dilemma pistachif) maintenance sibylline appendicitis apostasy cymbals symbols sedentary monotony supersede procedure precedent accelerate hybridizing proceeding deceiving believing ichneumon persimmon banana lachrymose pharyngeal emissary shampooing calcareous emollient kerosene em^iyrean empiricist attrition gazetteer poignancy lascivious chrysalis diapason synthesis antipathy delirious isosceles nominative pyramidal hypotenuse melodeon labyrinth parliament sovereign esophagus bronchitis aqueduct contiguity colonel soliloquy gelatin boudoir piecemeal barbecue chameleon truncheon incensed cephalic reconnoiter reconnaissance sycophancy judgment syllabication bourgeois fricassee demoniacal cerulean trysting jaundice landau jinrikisha obscenity amphitheater anagram piquancy diaphragm macaroni incai'cerate cicatrice sinecure auspicious seditious irascible implacable diphtheria rutabaga rhythm indelible stratagem anathema malfeasance chimerical ribaldry meerschaum lieutenant peritonitis ephemeral transient jeopardize incomparable symbolize syzygy surplice symmetry allopathy hydropathy homeopathy caoutchouc chibouk brochure anthracite capacitate desiccation pneumatics mnemonics refragable synagogue gossamer britannia tumefaction buccaneer metallurgy desuetude innocuous chiropodist knicknack susceptible synecdoche nonpareil diaphanous omniscient macaroon ligneous catarrh diarrhea asthma pneumonia sciatica rhetoric sycophant iUi PEDAGOGICS OF ORTHOGRAPHY ^7 capillaries auricle Eustachian hymeneal rebellion incredible hickory cynosure sassafras sycamore patella jessamine fuchsia alyssum amaryllis iguana succotash quintessence emanation transcendent garrulous cadaverous kaleidoscope criticism tantalize titillate appellant subjjoena propeller boatswain azalea asparagus ageratum sieve anemone acacia callisthenics acrobatics centipede cyclopedia accordion cauliflower aureola aeronaut ventriloquist deference taciturnity gayety luncheon acquiescent glycerin ipecacuanha annatto rhomboid finical chancellor belladonna bergamot broccoli bouvardia ealadium columbine plaguing cannibal obsequies auscultation chalcedony sardonyx sarcophagus acoustics satellites laryngeal comparable insidious lettuce lineament excellence achievement bereavement bouquet tmesis metonymy simile metaphor allegory honeysuckle chrysanthemum chinkapin purslane jjheasant portulaca licorice A SERIES OF QUESTIONS AND EXAMPLES Relating to the vSubjkcts Treated of in this Volume. It will be noticed that the various Question Papers that follow have been given the same section numbers as the Instruction Papers to which they refer. No attempt should be made to answer any of the questions or to solve any of the examples until the Instruction Paper, having the same section number as the Question Paper in which the questions or examples occur, has been carefully studied. PEDAGOGICS OF ARITHMETIC. (PART 1.) (1) Explain what is meant by automatism in arithmetic, and describe the inost eifective means of attaining it. (2) Give two examples of arithmetical drill exercises that have no obvious purpose, and two others, each of which has a very definite object. State the object of each of the latter pair. (3) Give a general account of the concrete appliances that should be used in the first work in arithmetic. (4-) Give in your own words the substance of the para- graph on the grammar of arithmetical language. Give Dr. Bain's general principle, and illustrate it by an example. (5) Describe and illustrate the exercise called "Telling Stories in Arithmetic." In what respects does the child receive profit from these stories ? (G) Write the formulas given in Art. 21, and make an easy example in fractions illustrating each. (7) Explain some of the advantages to be gained by the use of type formulas. (8) Make an example illustrating each transposed form of the equation ;// = cd—ab^ as explained in Art. 33. §1 2 PEDAGOGICS OF ARITHMETIC. § 1 (9) Describe the various drills that are useful in teaching addition. (10) Make a drawing of the "General Scheme" of drill work in subtraction, and show the blackboard form that you woulxl use when 8 is the subtrahend. (11) Show the form for blackboard drill in teaching multiplication by 9, with carrying. (12) Show by a drawing the "General Scheme" for divi- sion drill. (13) Give in your own language the substance of what is contained in Art. 37 on the perception of number. Explain its application to pedagogics. (14) Explain the common method and the scientific method of teaching notation. (15) Describe fully and illustrate the use of and \n read- ing numbers. Give cases that would be ambiguous without the help of the distinction in question. (16) Give a concise sketch of the earliest work in frac- tions, as outlined in Art. 50. (17) Subtract of from 7^ in the manner explained in Art. 53 (13), and write in full the explanation of each step. (18) Describe the best method of subtracting 4| from 9|. (19) What should children be required to say in multiply- ing orally ^ by T ? 5f by 8 ? 7f by 5 ? (20) Show, by dividing such a figure as a circle, square, or line, that f of f is \. (21) Write ten examples suitable for " t'?*?/'/*'/ ]]\)?-k'' in connection with the study of "The Number 5" (Art. G7). (22) In connection with the study of "The Number 0" (Art. 68), prepare ten good questions for use under the head of "The Applied Number." § 1 PEDAGOGICS OF ARITHMETIC. 3 {2o) Write for "The Number 7 " suitable work under the head, "The Subdivided Unit." (24) Write the matter for measuring with 3 and with 4 in connection with the study of " The Number 9." (25) Write in full, suitable matter for the woi-k included under all the heads in connection with the study of " The Number 7." In doing so, follow the plan given in the Instruction Paper. (2G) If a drill form like the accompany- ing were placed on a blackboard for oral work, what analysis of each should be | of required of the piipils ? Write the analysis in full. 8 = ? (27) Give the best analysis that you can for the following example: If f of a number is 12, what is | of the number ? (2.S) By means of a diagram find the sum of i and i. (20) vSht)w by a diagram the several successive steps in the analysis of the following example: If | of a certain num- ber is 15, what is 4 of the number ? Make your diagram as neatly as possible. (30) Show very neatly five good blackboard forms for drill work in fractions, and write out in full the proper oral statement that you would require the pupils to give for each drill. These drills should be of your own devising. PEDAGOGICS OF ARITHMETIC. (PART 2.) (1) As in Art. 3, use the following example and show what form the minuend will take in order to explain the carrying necessary in the following example : From 10,011,010 take -4,875,927. (2) Use the example 8,012,805-5,871,698, and write a full explanation of the method of subtracting by addition. (3) Explain and illustrate the method of subtracting the sum of several numbers from one number by the method of adding. (4) Write ten multipliers of special form similar to those given in Art. 11, and explain what is special in each. (5) By the method explained in Art. 13 perform the following operations, and show the diagram for each : {a) 05X37; {h) 123x450; (r) 3, 004x532; {d) 4,507x23; (^•) 824X3,502. r [ci) 2,405. \b) 50,08§. Ans. .j (r) 1,030,048. j \d) 105,041. t 0') 2,935,088. (0) By the method explained in Art. 14 find the value of the following: (^?) 3,214x998; {b) 59, (i48 X 9,997 ; (r) 3,420X1,000; {ci) 8,697x992; ^c) 9,999x10,004. { {a) 3,207,572. I \li) 590,301,056. Ans. -! [c) 3,44(5,556. \d) 8,627,424. . {c) 100,029,996. 2 PEDAGOGICS OF ARITHMETIC. § 2 (T) Perform each of the following divisions by the best method: («) 736,284-=- 98; (^) 3,692,847^ 007; (^ 43,2(;4,795 ^1,002; {d) 386,400,101-1-9,992; {c) 730,401, 061 h- 10,008. I (.0 7,ol3if. {l^) 9 7- Ans. -I (0 43, 178^^2 • I {d) 38,670|Mi I 0) 72,981t-VVoV (8) Solve the following by the method explained in Art. 22'. {a) 842,376 -^ 123; {b) 5,964,872 h- 7S9; {c) 1,230,256 -r- 204; (fl') 987,024,673 -^ 27,042. \ [a] 6,848iV%. A^, ! (^') ^560/i- '^"'- ■] (.) 6,030iff. [{d) 36,499ifi.i|. (9) Give with illustrations the principles relating to the divisibility of numbers by 2, 3, 4, 5, 6, 8, 9. (10) Explain how you would ascertain without referring to the table whether 937 and 1,747 are prime numbers. Give for each number the list of divisors that you would try. (11) Show the operation of separating 59,400 into its prime factors. (12) By the abbreviated method explained in Art. 35, find the G, C. D. of the following: {a) of 11,407 and 22,631 ; {b) of 13,221 and 27,685; {c) of 16,147, 208,947, and 329,929. r (a) 61. Ans. j (/;) 113. I (0 241. (13) Find the value of the following, and arrange your work as suggested in Art. 39: {a) f +f + }§ + 11+ H; (/,) 44-|-8f + 7H + 13t + 16f. AnsM-) ^tV I {b) 50ifi. § 3 PEDAGOGICvS OF ARITHMETIC. 3 (14) As directed in Art. 41, perform the followino^ opera- tions, clearly indicating or explaining each step : (a) :)2| X (Jl|- ; (/;) 1231X4(351; {c) 41i->|X(;34. {(a) 2,023if Ans. ; (/;) 57,509|. [{c) 31,429if. (15) Explain fully, and illustrate the precedence of signs. (IG) Make as clear as possible the reason for inverting the divisor in dividing one fraction by another. (IT) To what single discount is each of the following series equivalent: (a) 30^, 40^, 20^, and 10^ ? (/;) 30^, 20^, 10^, and bi ? (r) GO^ 60^, and 40^ ? | {a) 09.76^. Ans. \ \h) 52.12^. L(6-) 90.4^. (18) By means of the formiila, / = , find in what time, at G^, 1800 will yield *110.40 interest. Ans. 2 yr. 3 mo. 18 da. (19) Find the exact interest at m of $4, GOO from Jan. 20, 1900, to July 30, 1900. Ans. 1108.32. (20) By the sixty-day method find the interest of *8,300 at G^ for 238 days. Ans. 1329.23. (21) What is the difference between the true discount and the bank discount of an obligation for $75,000 discounted 45 days before its legal maturity at 6^ ? Ans. $4.19. (22) By the method of equal factors find the cube root of 226, correct to five decimal places. Ans. G. 09119. (23) By using the formulas in Art. 97, {a) find (^ when V = 1,000; (/;) find Fwhen C = 12. Ans -^ ^''> ^^•^•'• ■ \ (/;) 29.18. (24) By the methods explained in Art. 100, find five sets of numbers that may exactly represent the three sides of a right-angled triangle, and prove that they are correct. (25) By nsing the formula given in Art. 101, find the sum of all the odd numbers less than 100. Ans. 2, 500. PEDAGOGICS OF GRAMMAR. (PART 1.) (1) In what two respects can a person be benefited by the study of English grammar ? (2) .What is meant by inflected as applied to language ? (3) What are the four usual divisions of grammar ? (4) Why should the first of the four divisions be excluded from textbooks on English grammar ? (5) Why should the subject of Punctuation be treated in a work on English grammar ? (G) What objections are there to the use of the exclama- tion point ? (7) Write {a) an exclamatory-declarative sentence; {b) an exclamatory-interrogative sentence; (r) an exclamatory- imperative sentence. (8) Explain the meaning of syntax. (9) What is meant by the statement that tJic sentence is the unit of thought ? (10) On the left of a vertical line write five modified subjects, and on the right five suitable modified predicates. (11) Explain in what way you would teach pupils to dis- tinguish subjects from predicates. (12) Give a rule for the choice of words in expressing your thought. §3 3 PEDAGOGICS OF GRAMMAR. § 3 (13) Explain exactly what is meant by the word modifi- cation as it is used in grammar. (14) Distinguish between qualify and liuiit. (15) Analyze by mapping and by diagram : " Maud Muller on a summer's day Raked the meadow sweet with hay." " The evil that men do lives after them; The good is oft interred with their bones." (IG) Explain what is meant by general modification as applied to words in a sentence. In what respect does it differ from grammatical jnodificatioii / Illustrate. (17) Classify sentences with respect to form, and with respect to use. Give illustrations. (18) Tell, in your own language, what is meant by the extension and the comprehension of common terms. (l!)) Analyze by diagram, but do not dismember, the following sentence : " He was like some one lying in twilighted, formless pre- existence, andstretching out his hands lovingly towards many- colored, many-sounding life. " (20) Contract the following into simple sentences: "He had a very noble old age, and grew daily better known to people that lived in the cities of the plain." "A time comes for all men when the helm is taken out of their hands." ' ' The children were playing in the churchyard where the grass was green. " (21) Rewrite the following so that it shall contain no independent elements: "Self-reverence, self-knowledge, self-control, These three alone lead life to sovereign power. " (22) Explain in what respect the study of grammar has practical value. § 3 PEDAGOGICS OF GRAMMAR. 3 (23) What subdivision of grammar is it that treats spe- cially of sentences combined in paragraphs and other con- nected composition ? (24) What are restrictive clauses, and what are coordinate clauses ? Illustrate each. (25) By means of diagrams show the difference in respect to form of the following sentences : "The house, which my father owned, was burned yester- day." "The dog that bit the boy was killed by a policeman." (26) Explain imder what circumstances ambiguity is likely to result from the use of pronouns. Illustrate. (27) Prepare a scheme to be put upon a blackboard for a lesson in the synthesis of sentential elements. Explain how it should be used. (28) Explain the difficulty in defining subject and predicate. (29) What is meant by pleonasm ? Give two oi'iginal examples, and two that are quoted. (30). Write five complex sentences, using in each a dif- ferent connective. (31) Explain what is meant hy false syntax. Give five examples. (32) State the exact difference between a simple sentence and a compound sentence. Illustrate each. (33) Write {a) a compound declarative sentence; {b) r compound interrogative sentence ; (r) a compound imperative sentence. (34) Write a simple sentence having subject, predicate verb, and object, compound. (35) Give, in your own words, the substance of the para- graph on the "Order of Sentential Elements." (30) Supply connectives, if necessary, and arrange the following elements with a view to the best effect. Give reasons for your arrangement. 4 PEDAGOGICS OF GRAMMAR. § 3 Her sails rent by storms A ship entered Chesapeake Bay- Once upon a time IVIore than 250 years ago With a cargo of slaves On a beautiful June morning. (37) Distinguish clearly between syntax and etymology. (38) What disadvantage arises from treating etymology and syntax separately ? (39) State some objections to etymological parsing. (40) Explain fully the distinction between sex and gender, and illustrate by sentences in which both words are correctly used. (41) Criticize the following definition: "A noun is the name of any person, place, or thing that can be known or mentioned, or that can be conceived by the mind." Write such a definition as you would approve. (42) Explain two of the devices used in what is called "sentence building," and tell how you would employ. them in teaching grammar. (43) Explain a good working method of systematically enlarging a pupil's vocabulary. (44) If a child uses for the first time an objectionable word, should he be warned to avoid the word, or would it be better to ignore the matter ? Why ? (45) Should or should not young pupils learn grammat- ical definitions ? Why ? (4G) What important objection can be urged against most systems of grainmatical diagrams ? (47) Find ten substitutes for nice as commonly used, and write expressions in which each appears as a modifier. (48) Describe an exercise intended to enlarge the pupil's vocabulary. PEDAGOGICS OF GRAMMAR. (PART 2.) (1) Explain and illustrate what is meant by relation in grammar. (2) Define the pronoun, mention the principal classes, and give examples of each class. (3) In how many senses may the following sentence be understood ? " Mr. A told Mr. B that he ought to engage a man to take care of his horses." Write them all so that they cannot be misunderstood. Rewrite the sentence in the best manner, so that it shall mean that the horses belong to Mr. A and that Mr. B is to engage the hostler. (4) Explain the meaning of A The A The son of a the the a - poor widow. (5) What is meant when we say that an adjective viodifies the i/ieaning of a noun, as in the expression small hoy ? (0) Without using prefixes, write ten pairs of adjective antonyms. (7) Prepare a suitable blackboard drill, in some such form as is shown in Art. 43, to teach the difference between don't and doesn't, and in the drill use all the suitable pronouns. §4 2 PEDAGOGICS OF GRAMMAR. § 4 (8) Find five adjectives, each of which shall be a mean between extremes, and give the extremes. (9) Prepare a blackboard drill the object of which is to teach pupils to use the irregular verb lie (to recline) correctly. (10) Write five sentences in which verbs usually active are employed as neuter verbs. (11) Write five sentences in which the verb is used both as active and as neuter, indicating each use by modifiers. (12) Explain the term active as used with reference to verbs, and illustrate. (13) Write the inflection of the first personal pronoun. (14) Distinguish between the comparative and the super- lative degree. (15) What must a declarative sentence contain in order that the verb shall be regarded as transitive ? an imperative sentence ? Illustrate. (16) Explain why it is impossible fully to define the verb. (17) Write the principal parts of see, drink, ring, come, eat, be, run, sing, zvrite, find. (18) Give ten of the adverbs most frequently used with adjectives to indicate degrees of comparison other than those called regular. (19) What are the principal means of adding new words to our language ? (20) Why are the irregular verbs more forcible than the regular verbs ? (21) By means of a diagram analyze the following sentence : "Yet I doubt not through the ages one increasing purpose runs, And the thoughts of men are widened by the process of the suns." (22) Show a tabular classification of the pronoun. § 4 PEDAGOGICS OF GRAMMAR. 3 (23) By means of prefixes write five pairs of antonyms. (24:) Explain what is meant by approximation and liiini- nation in arriving at tlie exact meaning of words. Illustrate. (25) Beginning with the weakest, prefix the following words to the adjective sick^ in the order of their degree of meaning: very, quite, exceedingly, positively, uiiiisually, extremely^ extraordinarily, deeidedly. (2G) Explain and illustrate what is meant by asserted and I5y assui/ied predication. Mention the forms of the verb in which the predication is of the latter kind. (27) State the idea most conspicuously expressed by each of the several modes. Illustrate. (28) Write five sentences, each containing a verb that is really in the subjunctive mode. (20) " Would, indeed, we had been. In lieu of many mortal flies, a race Of giants, living each a thousand years. That we might see our own work out, and watch The sandy footprint harden into stone." [a) Tell the mode and the tense of each verb in the fore- going. {b) Give the syntax — that is, explain the function— of race; oi years ; oi out ; oi indeed. (c) Classify the sentence with respect to form; with respect to 2ise. (d) What is the subject of ivonld ? of harden ? (30) In what way may a modal adverb be distinguished from an ordinary adverb .? Write five sentences, each con- taining a modal adverb. (31) Write a synopsis of the verb come in the indicative mode, first person, singiilar. (;)2) Give two rules for the use of sJiall and will, and write illustrative sentences. 4 PEDAGOGICS OF GRAMMAR. § 4 (33) In what sense were shall and xvill originally nsed, and what changes have they undergone ? (34) Write five sentences, using in each both should and ZOOllld. (35) Explain the meaning of each of the following: {a) " If you should come, I would return with you." (/;) " If you would come, I should return with you." {c) "I will go, and nobody shall prevent me." {d) " I shall go, and nobody will prevent me." (3G) Which of the following is correct ? Give reasons for your answer. " If the time should ever come, etc." " If the time would ever come, etc." (37) Write sentences, using the following, first as adverbs and then as prepositions: off, by, near, above, over. (38) Write two sentences containing verbs in the infini- tive, the infinitive having a subject and an object. (39) Correct the following sentences, and give the reasons for your corrections: {a) " We certainly expected to have called." {b) "I would be very glad to have seen him." (ical f (5) In history, what is meant by chronological sequence ? Write about 100 words describing- a fishing- trip, and observe chronological sequence in your description. ((») What is meant by the order of cause and effect ? Out- line a supposed case in which this order is observed. (7) Explain briefly why it is so difficult to write an inter- esting and intellig-ible historical textbook. (8) State why some school studies are liked by children and some are not. (9) Explain why it is easier to teach arithmetic success- fully than it is history. (10) What are the principal advantages to be derived from a thorough knowledge of the history of one's own country ? 2 PEDAGOGICS OF HISTORY. § 6 (11) In what respects is a student more benefited by a familiarity with general history than he is by knowing the history of his own country ? (12) vState, briefly, the qualifications necessary in a teacher of history. (lo) Explain what effect the perfecting of submarine navigation would be likely to have upon naval warfare in the future. (14) Mention five works, not school textbooks, that you would advise a teacher of history to read, and state what benefit would be derived from each. (15) Give the titles of five familiar poems, not mentioned in the Instruction Paper, that a teacher of history could advantageously use with his class. (IG) Explain the advantages derivable by students of his- tory from reading historical novels. (17) Mention the titles of five valuable historical novels. (18) What is meant by the " Story of Scheherezade " ? (10) Explain what is meant by the "historic sense." Mention three of its principal phases. (20) What advantage may be derived from the use of myths in teaching history ? At about what age of the pupil are myths and fairy tales valuable ? (21) How is biography used in teaching history in Ger- many ? (22) State the usual objections against memorizing- a his- tory lesson in the exact words of the author. (23) Prepare a list of ten questions suitable for use as "historical recreations" in United States history. (24) Describe, in outline, the Biographical method as it is employed in Germany. § (5 PEDAGOGICS OF HISTORY. 3 (^5) Under what circumstances is the Catechetical method to be condemned ? (26) Describe in your own language the Laboratory method. (37) Give an outline of the entire German course in history. (28) What are the chief obstacles to be overcome in using the Lecture method, and how may they be overcome ? (20) What do you inidcrstand by the "ethical sense" in history ? Illustrate. (30) How would you proceed to awaken and develop the ct Ideal sense ? (31) State two psychological facts that necessitate fre- quent reviews. (32) Cite two historical illustrations of the principle that luijust treatment of the weak and defenseless results, sooner or later, in the discomfiture of the stronger. (33) vState the underlying principles that should control the method of a teacher in conducting a history lesson with a class of young pupils. (34) Referring to (33), what are the methods of securing the ends desired ? (35) Give, in your own language, the reasons for begin- ning with the Biographical method earlier than is done in Germany. (36) Describe in outline the Comparative method. (37) Of the various methods described in the Instruction Paper, which, in your judgment, is the best ? Give your reasons. (38) Explain and illustrate the application of the division of labor in teaching. (30) What are some of the objections urged against the division of labor in teachino: ? 4 PEDAGOGICS OF HISTORY. § 6 (40) What is meant by the term correlation when applied to branches studied in schools ? (41) Explain, briefly, the correlation of history with phys- ical geography. (42) What subjects, besides those mentioned in the Instruction Paper, are correlated with history ? State in what respect. (43) Why may not all the subjects in a curriculum be so correlated as to be taught at the same time ? (44) What objections are there against using the story of " Robinson Crusoe " as a correlation center ? (45) Explain in what respects the subjects of sociology, civics, and ethics may be correlated with history. Which is the most important correlation ? PEDAGOGICS OF ORTHOGRAPHY. (1) How is orthography related in classifieation to grammar ? (2) State in detail what subjects are included under orthography. (3) Explain what is meant by "a perfect alphabet." (4) How is a nation's progress in civilization affected by the character of lang'uage ? Illustrate. (5) Write the approved singular and plural forms of the names of the vowels. (6) Give the plural of the following: A, &, q, [], X. Express in words the meaning of the plurals you have written. (7) Write ten words, of which five illustrate an easy, and five a difficult, coalescence of sounds. (8) What are the chief advantages to be derived from a knowledge of correct syllabication ? (9) Prepare a list consisting of twenty words of difficult syllabication, and, by hyphens, divide them properly. (10) Write directions such as a young teacher should need in conducting an oral spelling lesson. Let these include {a) the teacher's directions to the pupils, and (b) the rules of procedure that he himself should observe. (11) Prepare a list of {a) ten solid compound words; {b) ten approved hyphenated compounds. § 7 % PEDAGOGICS OF ORTHOGRAPHY. § 7 (13) Through what three stages of union do two words pass in forming finally a solid compound ? Hlustrate. (13) What change of accent is usually made during the transition of two separate words to the form of a solid com- pound ? Give two illustrations. (14) Each of the following is ambiguous: ^^ black horse ti'oops," "■wild ivestern melodies,'' "• Poems Here at Home,'" "■ Freneh and English dictionaries.'" Write them so as to show with precision their various possible meanings. (15) Write five practical suggestions relating to com- poimd words. (16) Explain and illustrate the meaning of syndud, abbre- viation, and contraction. (17) Explain briefly the tw^o different impressions that may be made upon the mind by a word. Illustrate by ineans of a landscape. (18) Mention two distinct objects that should influence a teacher in selecting lists of words for work in orthography. (19) Under what conditions is it better for the teacher himself to prepare lists of words for the orthographical work of his own pupils ? (20) Designate the three principal uses that words serve. Which is the easiest to master and which the most difficult ? Give reasons for your answers. (21) Give and illustrate three of the most useful rules for spelling. (22) Indicate by diacritical marks the sounds of the vowels, and illustrate each soimd by a word that contains it. (23) Give in outline a plan of proceeding in an ordinary spelling lesson. (24) Indicate what should be required of a pupil in spell- ing orally the word refractory. § 7 PEDAGOGICvS OF ORTHOGRAPHY. 3 (25) Explain why pupils should not be required to write the same words many times for punishment or for other purposes. (20) What is the "Flash method" in teaching- spelling? Mention one objection against this method with one reason for the objection. (27) Mention the four principal methods of making chil- dren acquainted with the meaning of words. (28) Construct sentences that will show by the method of particular instance — by context — the most usual meanings of the following words: division^ mutual^ deception^ rapidly^ honesty. (20) Explain how English spelling is correlated with every other subject that is taught in our language. (30) Explain and illustrate the formation and meaning of English diminutives. (31) By means of diacritical marks indicate the pronunci- ation and syllabication of the following words: Aristidcs, obligatory, pharyngeal, maniacal, financial. (32) Use the following words with suitable prepositional phrase modifiers, denoting that to which each term is usually applied : band, horde, eonneil, congress, troop, squad, detail, brace, gang, cloud. (33) Find the nearest opposites, without prefixes, of the following woids: indolent, agile, courteous, publicity, liberal, candid, dormant, truthful, stupid, humility. (34) Give the names, difficult to spell, {a) of ten animals; {b) of ten plants; {c) of ten minerals. (35) Give words descriptive of the qualities of an apple, as follows: qualities perceived {a) by the sense of sight; {b) hy the sense of taste; {c) by the sense oi feeling. (30) Of words suitable for a spelling exercise, write {a) ten denoting animal products; (/;) ten denoting vege- table products. 4 PEDAGOGICS OF ORTHOGRAPHY. § 7 (37) Write the abstract nouns that contain the same root elements as the following: sphere, Jinaniinoiis, timorous, loquacious, porous, fierce, heroic, cowardly, perverse, opaque. (38) Prepare a list of the verbs that would likely be required in describing {a) a picnic; {b) a day at school. If any are transitive, write the probable object of each. (39) Describe an important use of pictures in language teaching. (40) Annex to each of the following adjectives a phrase modifier, beginning each with a suitable preposition: redo- lent, delighted, ■ friendly, neigliborly, fastidious, capricious, renoivned, actuated, suitable, uncertain. (41) Explain tipon what three circumstances depends the question as to what preposition shall be used with particular words. Illustrate. (42) Find adjectives or verbs after w^hich each of the fol- lowing prepositions may be used: concerning, betivcen, among, after, against, toivard, in, into, respecting, regarding. (43) Write the names of ten American authors with whose -v^ritings a cultivated citizen should be familiar, (44) Write correctly twenty geographical names whose spelling you regard as difficult and important. (45) Prepare a list of fifty words commonly mispro- nounced, but not found in the Instruction Paper. INDEX. Note.— All items in this index refer first to the section (see Preface) and then to the page of the section. Thus, "Prosody 3 13" means that prosody will be found on page 13 of section 3. A. A reminiscence A year's work Abbreviated division, General method of Abbreviations, Abuse and use of " and contractions " in denominate numbers " in metric system " Lessons in " Mixed " Pluralizing " The meaning of.. " The period with " used in science . . Abode of life. The earth as the.. Absolute possessive pronouns.. . Abstract nouns Abuse of the idea of place " " utilitarianism Accents, Primary and secondary Acquiring a vocabulary Action and state " Cause and consequence of historic " Predicated or assumed . . Active and neuter. Verbs that are both " intransitive verbs " transitive verbs Adding and subtracting frac- tions by inspection . . . " by groups " horizontally " two or more columns at once Addition and subtraction in one operation St-c. Pa.irt' 5 12G 1 09 2 23 r 33 7 31 2 69 2 70 7 83 7 34 7 3G 7 33 7 35 7 3(3 5 3.5 ■4 (i 3 7() 5 29 7 41 7 28 3 63 4 38 6 42 4 43 4 7.5 4 3.5 4 35 o 45 2 5 o 5 o 6 o 3 Addition, Drill work for " of denominative num- bers , " of long columns " Proofs of Adjective, Derivation and office of the " Inflection of the " pronouns " " Demonstra- tive " " Distributive " " Interroga- tive " " Possessive.. Table of the Adjectives and adverbs as re- lated to verbs " Brown's classifica- tion of Cardinal Classification of Common Comparison of Compound Criticism of Brown's classes of Meiklejohn's classi- fication of Numeral Ordinal Participial Pronominal Proper Qiialitative Quantitative Remarks on table of Serial Sec. 1 28 64 1 2(J 10 17 6 15 15 15 15 16 14 14 15 14 13 13 14 14 17 24 INDEX. Src. Pjire. Advanced work, Methods in ~ 1 " '■ with formulas.. 1 ~G Advantages with duodecimal scale 1 45 Adverb, Conjunctive 4 It " Interrogative 4 70 Modal 1 r; " Position of the 4 7'8 " Simple 4 T6 Table of the 4 79 The 4 73 Adverbial elements in conjunc- tions 4 sr " objectives 4 78 Adverbially, Prepositions used.. 4 81 Adverbs classified with respect to meaning 4 78 " classified with respect to u.se 4 70 Adversative conjunctions 4 80 Aliquot parts, Division by 2 15 " " Extension by 2 14 " " Method of, in in- terest 3 82 " " Multiplication by 2 13 Alphabet, A perfect 7' Alphabetical arrangement of suffixes 7 87 Alphabets 7 2 Alternative conjunctions 4 80 Ambiguity 3 41 " from vise of pronouns 4 7 " Use hyphen to avoid 7 30 American Philological Associa- tion 7 10 Amount of work less important than method 1 70 An early requirement in geog- raphy 5 08 Analysis by diagrams 3 28 " Models of 3 29 " of sentences 3 27 " Remarks on method of 3 35 " Review of details in . . . 3 32 "And," Use of, in numeration. . . 1 44 Anecdote of Hogarth 1 5 Angles, Measuring and con- structing 5 75 Anglo-Saxon prefixes ■... 4 25 Angular measurement 5 73 Annual interest 2 87 Antonyms 4 23 " by prefixes 4 20 Apparatus, Legitimate use of, for illustration 1 15 Apparent motion of svin 5 93 Appliances, Concrete . , 1 11 Sec. Page. Application of abbreviated divi- sion to G. CD. 2 41 " " drills to practical work 1 30 Applications of percentage 2 77 Applied number. The 1 73 Approximation 2 30 Arabic notation 1 38 Argument 3 Arithmetic, Advanced 1 4 " Elementary- 1 4 " Intermediate 1 4 " Pedagogics of 1 2 " Primary 1 3 " Schemes for earliest work in 1 5 Arithmetical language, (Gram- mar of 1 17 " progression 2 115 " stories 1 22 " 1 53 study, Divisionsof 1 3 Art and .science, Distinction be- tween 1 3 " of questioning. The 5 123 Article in " Forum" on spelling 7 51 " " "Forum " on spelling. Criticism of 7 54 " " "Forum " on spelling. Remarks on 7 53 Articles 4 15 Assistance, Illicit, by the teacher IS Assumed action 4 43 Attention, Importance of 5 47 " Voluntary 1 4 Authority of dictionaries. 7 31 Auxiliary verbs 4 66 Average requirements in educa- tion, Approximation of 5 18 B. Sec. Page. Bank discount 2 93 Barbauld, Mrs 5 41 Bases of notation 1 44 Basis of science. Ultimate 5 36 Beethoven 5 41 Bicycle notes 5 85 " Surveying with 5 83 " The, in geography 5 81 trip. Map of 5 88 Bilineal writing 6 4 Biographical method 41 " " a s a d V o- cated by Herbart 50 " reading 5 14 Blackboard, Drill schemes for. . . 1 28 " in teaching 1 10 INDEX. XI Sec. Page. Books of reference 5 i;W " " '■ in country districts. . . . ]() " " travel and adventure . . 5 133 " '' " geography.. 5 134 Botanical help.s -5 63 "Bread-and-Butter " Sciences, The 5 15 Brevity, T'orce gained by 3 55 Brooks', Dr., method of cube root 2 108 Brown, Dr. Goold 4 15 Building, Sentence 3 48 Business multiplication 2 10 C. Sec. Page. Camera in geography. The 5 56 Canada, Interest laws of 2 94 Canceling in fractional work 2 51 " simplified 2 52 Capital-and-boundary in geog- raphy 5 110 Capitals and punctuation 3 14 Cardinal numerals 4 15 Care in use of relatives 3 44 Carrying 1 30 Case, Definition of 3 81 Cases 3 81 " Ntimber of 4 2 Catechetical method 6 2" Cause and consequence 6 42 " effect 2 97 " " " in teaching ge- ography 5 122 Causes on which the value of geography depends 5 20 Certain prepositions, Misiise of. . 4 84 " words, Use of preposi- tions with 4 8:3 Changmg rates of interest 2 85 Children, Distaste for history in 6 Chinese language. The 7 3 Circle 2 110 " Use of, in drills 1 29 Classes of interjections 4 89 " nouns 3 74 " " pronouns 4 5 Classification of adjectives, A new 4 10 " " adjectives. Brown's 4 13 " " adjectives, ]\Ieiklejohn's 4 11 ." " adverbs with respect to use 4 76 " " orthographical work 7 82 Sec. Page. Classification of participles 4 .56 " ■' processes iti d e nominate numbers .... 2 60 " " questions 5 124 " " questions. Re- marks on 5 125 " " sensations 5 43 " " sentences, Connectives in 3 57 " " sentences. Summary of 3 56 " " sentences with respect to form 3 20 " " sentences with respect to use 3 18 " " studies. Com- pleteness of. . 5 12 " " studies. Gen- eral '5 10 " " verbs 4 32 " " " Remarks on 4 40 Classroom drawn to scale 5 79 Clay modeling 5 100 Clubs, Historical 6 35 Coalescence of sounds 7 8 Cobbett's grammar quoted 4 31 Collecting devices for teaching orthography 7 .53 Collection of examples with "Shall "and "Will" 4 72 Collections in natural science ... 5 60 " Miscellaneous 5 05 " of false syntax 3 62 " Words denoting 7 93 Collective nouns 3 76 Column spelling 7 46 Columns, Addition of 1 29 Comenius, A maxim of 7 40 " Maxim of 5 41 " Committee of Fifteen " 5 24 05 "Committee of Fifteen," Re- marks on report of 6 67 Common adjectives 4 13 " tisage 3 52 " use, Words in 7 58 Comparative and superlative. Forms of the 4 28 " degrees of adjec- tives ; 4 21 " importance of sen- tential elements 3 69 " method, The 6 52 Xll INDEX. Comparative methods, Remarks on Comparison of adjectives " " rules for partial payments " Other expressions of Comparisons, Pictured Compass, The mariner's Complement, Predicate Complete living Complex sentence " sentences. Synthesis of Composite numbers, Study of... Composition, Historical, consists of " S en t e n ce s com- bined in Compound adjectives " interest " predicate " pronouns " sentence sentences,Mapping of " subject " " in predicate.. " words,Evolution of... " " Exercises with " " Inconsistent forms of " " Remarks on... CompoundinK' of words " " " Perplex- ing na- ture of " words, Rules for Compounds, Creek and Latin... " Hyphened Solid Comprehension Concepts from pictures " in elementary science. Conclusion Concrete appliances Conditions affect e d u c ational values " expressed by sym- bols " of success in history, The " " success in teach- ing fractions Congress, Geographical Conjunction, The Conjunctions, Ad V e rbi al ele- ments in.- " Adversative " Alternative Sec, Page. 4 22 5 102 5 75 3 33 .5 16 3 24 3 54 1 8.5 3 12 4 14 2 88 3 23 4 7 3 23 3 ai 3 22 3 2;i 7 27 7 90 7 27 7 30 ' 20 r. 20 7 22 7 31 7 20 7 20 4 10 5 57 5 40 6 72 1 11 1 21 G 58 1 49 5 90 4 85 4 87 4 80 4 86 Sec. Page. Conjunctions, Copulative 4 80 " Correlative 4 87 •' Corresponsive 4 87 Illative 4 87 " Subordinating 4 87 Table of 4 88 The coordina- ting 4 86 Conjunctive adverbs 4 77 Connections 4 85 Connective elements 3 33 Consideration of spelling. Gen- eral 7 37 Constructions, Special 3 .58 Contractions 7 35 " and abbrevia- tions 7 31 Cooperative method, The 6 .55 Coordinate clauses, Ambiguity from 3 41 Correlation, M ean i n g of the term 6 65 " of h i s t o r y w i t h ethics 6 71 " "history with geography 6 09 " "history with political science 6 70 " " history with soci- ology 6 70 " " s p el 11 ng w i t h general in for- mation 7 lot) Correlations of history 6 04 " " spelling 7 80 Correlative conjunctions 4 87 " work, Objections to 7 99 " " Remarks o n objections to 7 99 Corresponsive conjunctions 4 87 Cotton 5 64 Country districts. Hooks of refer- ence in 6 16 Critical stage, A 5 51 Criticism, Ethical 6 43 " of Brown's classes of adjectives 4 14 " " definition of adjec- tives 4 20 " " historical action. . . 6 43 Crusoe, Robinson 7 80 Cube root 2 100 " " Dr. Brooks' method of 2 108 Cyclometer 5 83 " Surveying with bicy- cle and 5 83 Xlll D. Sec. Page. Daily work, A 4 42 Dates, Difference between 2 05 IDecimal base of notation 1 44 " " " Objections to... 1 45 " method of percentage. . 2 72 Decimals, Division of 2 25 "Decimation" 1 29 Declension 4 2 Defecttve verbs 4 35 Defining by opposites 7 74 " " synonyms 7 74 " words in connection with spelling 7 75 Definition, Failure of 3 4 " of case 3 81 " " English grammar 3 3 " "geography 5 27 " "grammar 3 2 " " language 3 1 " "orthography 7 1 " " subjunctive mode 4 47 " " tense 4 58 " " the adjective 4 11 " " " preposition.... 4 79 " " " pronoun 4 4 " " verb 4 30 Definitions of adjectives com- pared 4 20 " " the noun 3 72 Degree, Comparative 4 21 Positive 4 19 " Superlative 4 21 Degrees of adjectives . 4 17 " " predication by parti- ciples 4 57 Demand for cause and conse- quence of action 42 " " time of historic ac- tion G 42 " " truth of narrative C 41 Demrtistrative adjective pro- nouns 4 15 Denominate numbers 2 .58 " Abbrevia- tions of.. 2 1)9 " " Addition of 2 04 " " Classifica- tion of process- es in 2 00 " " Division of 2 08 " " Multipli- cation of 2 07 " " Nature of factors Sec. Page. Denominate numbers, Order of subjects in 2 .59 " " Subtrac- tion of.. 2 04 Derivation and office of the ad- jective 4 10 Description 1 " of topographic sur- vey maps 5 107 Detail in anal)-sis. Review of 3 32 Determination, "Shall" and "Will " denoting 4 08 Development of historic sense.. 45 Devices and word lists 7 82 " for teaching orthogra- phy. The collecting of 7 03 Diacritical marks 7 .50 Diagrams, Analysjs by 3 28 " of multiplication 2 9 Dialogue, Another specimen of Socratic 5 130 Dickens, Charles ' 2 Dictionaries, Authority of 7 31 Dictionary, Standard 7 10 Didactic questions 5 125 Different aspects of same idea, Words denoting 7 94 Difficult to teach history 8 Difficulties 5 07 Difficulty in syllabication 7 13 Discipline and utility 7 01 Discount, Bank 2 93 " True 2 93 Discounts, Serial 2 70 Discrimination among facts, Necessary 5 111 Discussion of rules 7 25 Distaste for history by chil- dren Distinction between art and science 1 2 " between mapping and analysis 3 27 Distributive adjective pronouns 4 15 Divisibility of numbers 2 33 Division by aliquot parts 2 15 drill. Development of. . 1 33 " " General scheme of 1 35 " " scheme in detail 1 35 " French method of 2 4 " 2 23 " of interjections into classes 4 89 " " labor in teaching ... C 02 Proofs of 2 28 " Short methods in 2 15 See. Division slightly greater than 10, 100, etc.. 3 " " less than 10, 100, etc 2 " Special cases of 2 Divisions of arithmetical studj-.. 1 ". "geography 5 Divisor, Inverting the 2 Drill and repetition. Necessity for 7 " for addition 1 " " division 1 " " multiplication 1 " " subtraction 1 " " " General scheme of 1 " with irregular verbs 4 " without a purpose 1 " work 1 Drills applied to practical e.v- amples 1 " Fundamental 1 " in fractions. Useful 1 " Purpose of 1 Duodecimal base, Advantages of 1 E. Sec: Earliest sensations, The 5 " sense preceptions 5 " work in arithmetic 1 Early requirement. An 5 Earth as a whole, The 5 " " the abode of life 5 Echo the sense, Interjections 4 Eclectic method. The G Education, Specialization in 5 " The new 5 Educational fact modifies theorj^ 5 " progress. Manner of 3 " value of outdoor life 5 " values 5 Effect of writing the same word many times 7 Element of place in geography.. 5 " " success. Teacher's personality an 7 Elementary arithmetic I Elements, Connective 3 " Independent 3 " Omitted 4 " Order of sentential.. . 3 " Synthesis of senten- tial 3 Emerson, Ralph Waldo Ends of specimen lesson. Method of securing 6 English grammar, Definition of 3 " s}'nonj-ms, Works on. . . 7 INDEX. Pii^e. Sec. Pajre Enlarging pupils' vocabularies. . 3 06 19 Environment of bicycle trip " Words belonging 5 89 17 to a given 7 95 IS Equalization of factors 2 3 106 3 Error as example 60 23 Established usage 7 23 54 Estimate of place in geograph- ical value. Dr. Harris's 5 21 65 Ethical criticism 6 43 28 Etymological exercises involv- 33 ing spelling 7 95 32 3 80 30 3 67 " and syntax. Com- 31 bined treatment of 3 69 41 " and synta.x, Treat- 10 3 3 68 !) " Meaning of 07 Euclid's rule 2 114 3G Every lesson a language lesson 1 71 2S Evolution 2 9 98 05 " by factoring 102 28 " Equal factor method 45 of " Geometrical ilhistra- 2 103 Pa.i,^^. tion of 2 102 48 " Methods of teaching. . 2 98 40 " of compound words .. 7 27 5 " " textbooks 5 112 08 Exact interest 2 86 31 5 125 35 Examples, Collection of, with ss "Shall" and "Will" 4 72 57 " ■ of false syntax 3 61 13 " of subjunctive mood 4 49 4 " of subjunctivemood, 10 Remarks on 4 50 G " Types of 1 )Si 54 l'3xclamatory sentences should 1 3 3 ' 19 Exercise in synthesis. Another.. 49 09 " Synthetic, for increas- 28 ing vocabulary Exercises in fractions 3 1 47 .50 " "syllabication 7 14 4 " with compound words 7 90 33 " " prepositions 7 97 34 " " rules of spelling. . 7 90 30 '' 88 51 Existing conditions affect educa- 5 1 8 4G Experiment with objects 14 47 Experimental questions 5 124 Explanation of methods 7 74 49 f> 2 3 Expression s of c o m p a r i s o n , 75 Other 4 22 Sec. Page. Extension of meaning of "Top- ical" 6 32 " " terms 4 10 Extremes and means among words 4 23 F. Sec. Page. Factoring 2 38 Evolution by 2 102 G. C. D. by 2 39 Factors, divisors and multiples. . 2 38 " Equalization of 2 100 " Nature of, in denomi- nate numbers 2 70 Facts of science should be dis- criminated 5 111 False syntax, Collections of 3 62 " " Examples of 3 01 Fifteen, Committee of 5 24 " 05 First teacher, The child's 5 52 Flash method in spelling 7 72 Force gained by brevity 3 55 Form and matter of letters 7 98 " " punctuation of abbre- viations 7 31 " Sentences classified with respect to 3 20 Forms, Graphic geometrical 5 104 " of comparative and su- perlative 4 28 " " passive progressive. . 4 02 " " pleonasm 3 59 " " written thought 1 " Other transitive 4 37 Formulas, Advanced work with 1 20 " in interest 2 78 " " mensuration 2 110 " percentage 2 75 Type 1 25 Formulated rules 7 25 Formulating of operations 2 32 "Forum," Article on spelling in 7 51 " Criticism of article on spelhng in 7 .53 Four, The number 1 77 Fourth root 2 101 Fraction method in percentage. . 2 75 " work. Later 1 .53 Fractional unit 1 8 Fractions 2 45 . " Addition and subtrac- tion of, by inspection 2 45 " and integers taught to.gether 1 8 " Caricelmg 2 51 " Exercises in 1 7 Sec. Page. Fractions, Greatest common di- visor of 2 55 " Least common multi- ple of 2 57 " Outline of plan of 1 50 Roots of 2 101 " Special cases in addi- tion and subtraction of 2 47 " Teaching of 1 48 " Written forms in 2 40 French method of long division 2 4 Fulton, Invention by 1 21 Functions of the several modes. . 4 45 Fundamental drills 1 28 " meaningof "Shall" and "Will" 4 07 " outline of geog- raphv 5 30 Future participle, The 4- .58 " tenses. The 4 01 Futurity, "Shall" and "Will" denoting 4 70 G. Sec. Page Geikie, Sir Archibald 5 07 Gender of nouns 3 7'8 " " sex 3 82 (General considerations concern- ing spelling 7 37 divisions of geography 5 33 " information 5 48 " " Correlation of spell- ing with 7 100 " law of sequence 3 53 " method of abbreviated division 2 22 " modification 3 .39 " principle in teaching, AG 7 " scheme of subtraction drill 1 31 " statement concerning abbreviations 7 31 " treatment of lesson in orthography 7 07 Geographical matter 5 20 (ieography,"Capital-and- Bound- ary" 5 110 " Correlation of his- tory with 09 " Definition of 5 27 " Fundamental out- line of 5 .30 " Graphic 5 95 " in pictures 5 50 " Matter and method XVI INDEX. Sec. Geography, Physical science the essence of 5 37 Pliny's 5 2G Sailor 5 109 '• Some points in teach- ing 5 113 The bicycle in 5 81 " " term 5 26 " " wheelman as a teacher of . . . . 5 82 " without a textbook 5 08 Geometrical forms, Graphic 5 104 " illustration of evo- lution 2 102 German geographical congress 5 90 " school, A specimen les- son in a G 48 Getting rid of objectionable words 3 65 Gibbon, Edward 4 Goethe 5 39 Government by prepositions 4 81 " surve}' maps 5 107 Gradation in treating the noun , 3 70 Cirammar, Brown's 4 31 Cobbett's 4 31 " Definition of 3 2 " of arithmetic 1 17 " Term "active" as used in 4 40 " Terms used by wri- ters on 3 70 Grammatical rules 7 23 " study. Value of... 3 4 Graphics of fractions 1 03 Greatest common divisor by ab- breviated division 2 41 Greatest common divisor by fac- toring 2 39 Greatest common divisor of frac- tions 2 5.5 Greek and Latin compounds. .. . 7 31 '• pedagogue 1 1 5 .51 " prefixes 4 27 Groups, Adding by 2 5 Grube method 1 H. Sec. Piiffe. Halves and thirds. First lesson in 1 51 Harris, Dr. William T 5 10 " " " " 5 17 Harvard University 7 16 Hearer, " Shall " and "Will " de noting will of 4 09 " Heimatkunde " 5 91 St'c. Page. Helps, Botanical 5 02 Herbart, Biographical method as advocated by 6 .50 Heredity in s^Delling 7 40 Higher power, " Shall " and "Will " denoting will of 4 69 Historic action, Cause and con- s e q u e n c e «f 6 42 " " Criticism of.... U 43 " " Time of 42 Truth of 6 41 " sense. Development of 6 45 Historical and biographical reading 6 14 " clubs 6 35 " composition consists of... 3 " recreations G 25 " textbooks G 6 " use of poems and bal- lads 6 23 History, Children's dislike of.. . . G G " Correlations of G 64 " Correlations of, with ethics 6 71 " Correlations of, with geography G 69 " Correlations of, with political science G 70 " Correlations of, with sociology 70 difficult to teach 6 S " Many methods in 6 27 " Preparation for teach- ing 6 14 " Purpose of studying. . . 9 " Reasons for early be- ginning of G 51 " Relation of, to other subjects 61 " Time given to G 13 " Vastness of 61 Hogarth, Anecdote of 1 5 Homer's "Catalogue of the Ships" 5 25 " Hoosier .Schoolmaster," The. . . 7 38 Horizontal addition 2 5 How history is usually learned 17 recited 6 18 " teacher must regulate his reading 6 11 Huber 5 41 Human needs. Relation of science to 5 30 Hyphen, to avoid ambiguitv. . . . 7 .30 Use of 7 30 INDEX. XVI 1 I. Sn: Pas-,: Idea of place, Abuse of ."i 3 ) Illative conjunctions 4 hi" Illicit assistance by the teacher 7 18 Illustrations of fractions, G raphic 1 63 Illustrative lesson, Remarks on 6 49 Imperative mode, The 4 64 Impi)rtance of attention 5 47 " " percentage 2 71 " " sentential ele- ments. Com- parative 3 69 Important and the trivial. The. . 5 108 Improvement of method. The. . . 3 -.50 Impulse to criticize 6 43 Inconsistent forms of compound words 7 27 Increasing vocabulary. Syn- thetic exercise for 3 47 Indicative mode, The 4 44 Inference from historic action.. . 6 43 " Test of power of 6 44 Inferiority of Roman notation.. . 1 47 Infinitiveand participle. Similar- ity of 4 55 " Complement of 4 55 " mode. The 4 51 " Sign of 4 53 " " "to" as part of the 4 54 " Subject of 4 51 " Time denoted by 4 55 Inflection of adjectives 4 17 " " nouns 3 76 Information, General 5 48 Inspection, Addition and sub- traction of fractions by 2 45 Instructional questions 5 125 Interest 2 78 " Annual 2 87 " Compound 2 88 " Exact 2 86 " formulas 2 78 " in history increased by public libraries 6 36 " laws of Canada 2 94 " " " United States. ... 2 95 " Short methods in 2 92 Interjection not a part of speech 4 88 The 4 88 Interjections, Division of, into classes 4 89 " generally echo the sense 4 88 Intermediate arithmetic 1 4 Interrelations of subjects of study 6 64 Interrogative adjectivepronouns 4 15 " adverbs 4 76 Sec. Page. Intransitive verbs. Active 4 35 Invention by Fulton 7 21 Inverting the divisor 2 54 Irregular verbs 4 32 " " Drill with 4 41 " " Remarks on 4 31 J. Sec. Page. Journal, Library- 6 37 Iv. Sec. Page. Klemm, Dr C 48 Know subject. Teacher must 6 10 Knowledge of subjunctive mode 4 48 " " words. Nature of our 3 63 L,. ^' 128 1 70 6 .56 7 72 6 31 6 26 6 26 7 74 7 82 6 27 7 18 6 59 INDEX. SfC. Pii.iTi'. Methods of interest by aliquot parts " " percentage " " procedure " " teaching evolution.. " " " h i s t o r y , Other. . . . " Remarks on lecture . . . '^' Success of, determined by use " Summary of Metric System " " Abbreviations in Mill, John Stuart " " " Political econ- omy of Miscellaneous collections of specimens " operations and suggestions Mispronounced, Words liable to be Misuse of certain prepositions.. . Mixed abbreviations " numbers. Multiplying Modal adverbs Mode, Definition of subjunctive " Examples of subjtinctive " Imperative " Infinitive " Necessary knowledge of subjunctive " Potential " Subjunctive Model lesson, A Modeling materials Models of analysis Modes, Functions of the " Indicative " of verbs " " " Remarks on Modification, General " in grammar " of words Modified, Neuter verbs cannot be Modifiers " The noun w^ith " Modify," The word Monitor and Merrimac Much used. Any method monot- onous if Multiplication, Drills for " of denom in a te numbers " Proofs of ". Short methods in " Unwritten •z 8:i 2 ri 5 69 3 98 G 55 38 r 29 6 60 2 115 2 ro ■5 21 30 84 48 34 49 47 49 46 51 48 44 46 119 106 29 45 44 43 43 39 37 20 74 ;k 71 37 Sec. Page. ^Multiplication, Unwritten, by two figures 2 8 '• without partial products 2 9 Multiplier of special form 2 8 " slightly greater than 10, 100, etc 2 12 Multiplying by aliquot parts 2 13 Museum, The National 5 63 My thologj', Scandinavian 6 50 X. Sec. Page Nature of our knowledge of words 3 63 Need for care in the use of rela- tives 3 44 " " mark of exclamation. Slight 3 16 Neuter and active. Verbs that are 4 75 " verbs 4 38 " " cannot be modi- fied ■. ... 4 74 Newlv coined verbs are regu- lar." 4 33 Notation and numeration 1 38 Arabic 1 38 " Common method of 1 42 " Decimal base of 1 44 " Roman 1 46 " Scientific method of... 1 42 " Two methods of teach- ing 1 42 Noun, Definitions of 3 70 " Meaning of 3 70 " Other matters connected with the study of the. . . 3 72 Table of 4 1 The 3 70 " with inodifiers, The 3 71 Nouns, Abstract 3 76 " Cases of 3 81 " Classes of 3 74 " Collective 3 76 '• Gender of 3 78 " Inflection of 3 76 " Number of 3 78 " Person of 3 7'7 " Sin' generis 3 75 " Verbal 3 76 Number of cases 4 2 " " nouns 3 78 Numbers, Divisibility of 2 33 " Perception of 1 38 " Properties of 2 33 Numeral adjectives 4 14 Numerals, Cardinal 4 15 Ordinal 4 15 XX INDEX. O. Sec. Pafre. Objection to specialization in training 6 63 Objectionable words, Getting rid of 3 65 Objections to correlative work. . 7 99 " " decimal base 1 45 Objective, Adverbial 4 78 Objects, Experiment with 1 14 " How to use 1 2 Observation, Orderly 5 50 Observations, Making and re- cording 5 81 " on sun's apparent motion 5 93 " upon methods. .. . 6 59 Obstacles to a perfect alphabet 7 11 Obtaining words for spelling work, Means of 7 62 Office and denotation of the ad- jective 4 10 " of the adverb 4 73 Omissions from textbooks 3 8 Omitted elements 4 36 One, The number 1 72 Operations and suggestions. Mis- cellaneous 2 30 " The formulating of. . 2 32 Opinions, Diverse, concerning value 5 6 Opposites, Defining by 7 74 Oral and written spelling 7 45 Order of sentential elements ... . 3 51 " " subjects in denominate numbers 2 59 " " topics in fractions 1 54 Orders, Teaching of 1 43 Ordinal numerals 4 15 Original examples by pupils .... 1 61 Orthography, Definition of 7 1 " General treat- ment of lesson in 7 67 " learned from reading 7 59 " Methods in 7 82 Other expressions of comparison 4 22 " forms of pleonasm 3 59 " methods of teaching his- tory 6 55 " transitive forms 4 37 Our knowledge of words. Nature of 3 03 " needs with reference to words 7 43 Outdoor life, Educational value of 5 .54 Outline of geography. Funda- mental 5 36 P. Sec. Paragraph spelling 7 Parent is the child's first teacher 5 Parsing, Etymological 3 Part of speech. Interjection not a 4 " " the infinitive. Sign "to" as 4 Partial payments 2 " " Rules of, com- pared 2 Participial adjective 4 Participle and infinitive. Simi- larity of the 4 " The future 4 Participles, Classification of 4 " Degrees of predica- tion by 4 " Remarks on table of 4 Table of 4 The... 4 Passages, Writing beautiful or striking 7 Passive progressive tense forms 4 Past emphatic tense forms 4 Pedagogics defined 1 " of arithmetic 1 " number percep- tion 1 " The word 1 Pedagogue, A Greek 5 " Greek 1 Percentage 2 " Applications of 2 " Decimal method of 2 " Formula method of 2 " Fraction method of 2 " Importance of 2 Percentage, Three methods of.. 2 Perception 5 " of number 1 " Use of 5 Perceptions, The earliest sense.. 5 Perfect alphabet, A 7 " " Obstacles to.. 7 Period with abbreviations. The 7 Person mentioned, " Shall " and "Will" denoting will of 4 " of nouns 3 Personality of teacher an ele- ment of success 7 Pestalozzi 1 Philological Association, Amer- ican 7 Phonies, The study of 7 Phrases 4 PliN-sical science the essence of geography 5 Pictured comparisons 5 Pictures, Concepts from 5 Page. 46 52 80 88 54 73 71 71 44 38 46 49 6 11 35 50 5 10 85 80 37 102 57 INDEX. Sec. Page. Pictures, Geography in 5 55 " Preparation of 5 58 " Spelling from 7 915 " Value of, in acquiring a vocabulary 5 59 Place, The element of, in geog- raphy 5 78 Plan of classroom 5 79 " *" paper 1 6 " " primary work 1 71 " " teaching fractions 1 -19 " " treating the verb 4 29 Plane, Location on 5 77 Pleasure and pain. Theory of ... . (J 5 Pleonas:n 3 58 Other forms of 3 59 Pliny's Geography 5 3{i Pluralizing abbreviations 7 3G Plurals of symbols 7 G Plutarch, Parallels of 53 Poe, Edgar A., Praise words of . . 6 2 Poems and ballads. Historical use of (5 23 Points in teaching geography .. . 5 113 Position of the adverb 4 78 Positive degree of adjectives. .. . 4 19 Possessive adjective pronouns.. 4 15 " pronouns. Absolute. . 6 G Potential mode. The 4 40 Power of inference. Test of G 44 Precedence of signs 2 29 Predicate complement 3 33 " compound 3 23 " Subject and 3 26 The 3 32 Predicating and assuming action 4 43 Predication by participles. De- grees of 4 57 Prediction, " Shall " and " Will " denoting a 4 71 Prefi.ses, Anglo-Saxon 4 25 " by antonyms 4 19 Greek 4 27 Latin 4 2G Preliminar J- questions 5 124 " remarks on the verb 4 29 Preparation for teaching history G 14 " of lessons G 20 Preposition, Definition of the 4 79 " Sign "to" regarded as a 4 53 Table of the 4 83 Prepositions, Exercises with. .. . 7 97 " Government by. . . 4 81 " List of 4 83 " Misuse of 4 84 " Use of, with cer- tain words 4 83 Sec. Prepositions, used adverbially.. 4 Present emphatic tense forms. . . 4 " tenses, The 4 Primary and secondary accents 7 " and secondary educa- tion one scheme 5 " arithmetic 1 " teaching 1 " work in detail 1 Prime numbers. Table of 2 Test for 2 Principle in teaching, A general G Principles and materials in spell- ing, 7 " concerning signs 2 " of the lesson. Underly- ing G " . of Roman notation 1 Procedure, Method of 5 Processes in denominate num- bers 2 Progress, Manner of educational 3 Progressive passive. Forms of.'. . 4 Projection, Mercator's 5 Promise, "Shall" and "Will" denoting a 4 Pronominal adjectives 4 Pronoun, Classes of 4 " Definition of 4 " Demonstrative 4 Indefinite 4 " Interrogative 4 Personal 4 " Relative 4 Table of the 4 The 4 Pronouns, Absolute Possessive.. 4 " Adjective 4 " Ambiguity from useof 4 " Compound 4 Pronunciation, Variant 7 Proofs of addition 2 " " division 2 " "multiplication 2 " "subtraction 2 Proper adjective 4 " use of short methods 2 Properties of numbers 2 Proportion 2 " Transformations of.. 2 Prose and poetry quotations 6 Prosody S Protractor, The 5 Public libraries increase interest in history 6 Punctuation and capitals 3 " in classification of sentences 3 Page. 81 63 59 26 28 26 26 13 6 a3 96 96 12 13 74 36 14 XXll INDEX. St'c. Page. Punctuation, Wilson's 7 ~G Pupil's vocabularies, Enlarging 3 00 Pure n u ui ber, The 1 'i% Purpose of addition drill 1 28 " drills 1 28 " " history study G 9 " "specimen lesson, Method of secur- ing 49 " " subtraction drill 1 30 Psychological use of rules 7 89 " value of geogra- phy 5 22 Q. Sec. Page. "Qualify," The word 3 38 Qualitative adjectives 4 14 Question and answer recitation. The 6 19 Questioning, The art of 5 123 Questions, Classification of 5 124 " Didactic or instruc- tional 5 125 " Preliminary or ex- perimental 5 124 " Testing or examina- tion 5 125 Quotation from Brown's gram- mar 4 31 " " Cobbett's gram- mar 4 31 Quotations, Prose and poetry 12 R. Sec. Page. Rates in interest. Changing 2 85 Ratio of oral to written work ... 1 CH Reading, Historical and bio- graphical 6 14 " Map 5 115 " Orthography learned from 7 59 " Teacher should regu- late 6 11 Reasons why history should be- gin early 51 Recitation, Map 5 118 " of history. The usual 18 " The question and an- swer 6 19 " The verbatim C 18 Recreations, Historical 6 25 Reduction ascending 2 63 " descending 2 61 " of radicals 2 102 Redundant verbs 4 35 Reference books in country dis- tricts 6 10 " Books of 5 132 Sec. Page. Reference to time by subjunc- tive mode 4 50 Reform, Spelling 7 9 Regular, Newly coined verbs are always 4 33 " verbs 4 32 Relation of adverbs and adjec- tives to verbs 4 73 " " history to other sub- jects 6 61 " " scisnce to human needs 5 30 " What is meant by 4 1 Relative, The, " what " 4 8 Relatives, Need for care in use of 3 44 Relics and mementoes 6 22 Remarks on classes of questions 5 125 " " classification of sen- tences 3 56 " " enlargement of vo- cabulary 3 66 " " illustrative lesson .. 6 49 " " method of analysis 3 35 " " modes 4 43 " " objections to correl- ative work 7 99 " " report of "Commit- tee of Fifteen" ... 6 07 " " table of adjectives. . 4 17 " " the irregular verb. . 4 34 " " " lecture method 6 40 " " verb. Prelimi- nary 4 29 " "Topical" 33 Reminiscence, A 5 126 Repetition, Necessity for drill and 7 05 Report of "Committee of Fif- teen" 5 24 Requirement, An early 5 68 Resistance, Least mental 3 55 Resolutions of Geographical Congress 5 96 Responsives 4 77 Restrictive clauses, -'\mbiguity from 3 41 Review of details in analysis .:. . 3 32 Reviews 6 24 " should be frequent 1 37 Rhetoric 3 12 Right-angled triangles 2 114 Robinson Crusoe 6 44 Roman notation 1 46 " " Inferiority of .. . 1 46 " " Principles of ... . 1 47 Root, Cube 2 100 Fourth 2 101 - " Square 2 100 INDEX. Si'c. Pifg'c. Roots of fractions 3 101 Rousseau, Quotation from 5 O'J Rule, Euclid's x! 114 " Merchant's i SO " Plato's -i 111 " Pythagoras' ~ 111 " United States i 89 Rules and definitions, Learning- - of 1 62 " for compounding words. . . 7 'Hi '• " spelling (■ 04 " " syllabication 7 15 " formulated T 25 " Grammatical ~ 23 " of spelling 7 77 " " " Exercises with 7 90 " principles, etc., Memoriz- ing 7 76 " Psychological use of 7 89 S. Sec. Page. Sailor geography 5 109 Salamis, Battle of C 47 Sand modeling 5 106 Saxon words 3 17 Scale, Plan of classroom drawn to 5 79 Scandinavian mythology 50 Scheme of division drill. General 1 35 " " " " in detail 1 35 " fraction work. Re- marks on 1 00 .Schemes of drill for blackboard 1 28 Science, Abbreviations used in. . 7 30 " Collections in natural . . 5 00 " distinguished from art 1 2 " Plan's place in 5 38 " Natural, in lower school grades 5 00 " Relation of, to human needs 5 30 Sciences, The " Bread-and-But- ter " 5 15 " The liberal and the lu- crative 5 15 •Scientific facts must be discrim- inated 5 111 Selecting books for spelling 7 49 Selection of words, Sources of.. 7 42 " " " Two objects determine 7 42 •Selections for mapping and anal- ysis 3 30 Semiuaria 6 40 Seminary method. The .50 Sensation 5 42 " and perception 5 40 Sensations classified 5 43 Sec. Page. Sensations, The earliest 5 48 Sense, Development of hislt)ric.. 6 45 " perceptions. The earliest 5 48 ■' training, Need for 5 41 Sentence, Analysis of 3 36 building 3 48 " Complex 3 24 "" Compound 3 23 " Simple 3 21 " Simple, with com- pound predicate 3 23 " Simple, with com- pound subject 3 22 " Simple, with com- pound subject and predicate 3 23 " spelling 7 40 The 3 17 Sentences classified with respect to form 3 20 " classified with respect to use 3 18 " Connectives in classi- fication of 3 57 " Exclamatory 3 19 " in composition 3 12 " Punctuation in classi- fication of 3 57 " Summary of classes of 3 .56 Sentential elements. Compara- tive importance of 3 09 " elements. Order of . . 3 51 .Sequence, General law of 3 53 Serial adjectives 4 24 " discoiints 2 70 Sex and gender 3 81 .Shakespeare 7 5 "Shair'and "Will" 4 67 " " " Collection of examples with 4 72 " " " denoting a prediction 4 71 " " " denoting a promise or threat 4 71 " " " denoting de- ter m ina- tion 4 08 " " " denoting fu- turity 4 70 " " " denoting person mentioned 4 09 " " " denoting will of hearer 4 69 XXIV INDEX. SfC. PdJl'C. Sec. "Shall" and "Will" d e n o t i n g will of higher power 4 " " " denoting will of speaker ... 4 " " " Fundamen- tal mean- ing of 4 Short methods in division 2 " " " interest 2 " " " multiplication 2 " " Proper use of 2 " words that are often mis- spelled 7 Sight or "Flash" method in spelling 7 Sign of the infinitive 4 " "to" as part of the infinitive 4 " " regardedaspreposition 4 Signs, Precedence of 2 Principles concerning 2 " Use of 1 " used in fundamental rules 2 Similarity of terms of the indica- tive mode 4 " " the participle and infinitive 4 Simple adverbs 4 Simultaneous addition and sub- traction 2 Singsong, How to avoid 1 Six-per-cent. method 2 " Six," The number 1 Sixty-day method of interest ... 2 Sketching map 5 Slight need for marks of ex- clamation 3 Societies, titles. Names of, abbre- viated 7 Socrates as a teacher 5 " The method of 5 Socratic dialogue, Another speci- men of 5 Sounds, Coalescence of 7 Speaker, "Shall" and "Will" denoting will of the 4 Special cases in addition and sub- traction of fractions ... 2 " constructions 3 " multipliers 2 Specialization in education 5 " " training, O b- jections to. . . 6 Specimen lesson in German school 6 Specimens, Serial 5 60 3(i 127 128 Speech, Interjection not a part of Speller's instinct. The Spelling, Article in " Forum " on " as taught years ago. .. . " Column " Concerning rules for . . " Correlation of, with general information " Correlations of " Exercises with rules of " from pictures " General considerations " Heredity in " Oral and written " Paragraph " Principles and mate- rials in " reform. " Use of a textbook in teaching " work. Means of obtain- mg words for Spencer, Mr. Herbert Sphere Square root Squares Stage, A critical Standard dictionary. State and action Stencil maps Stories, Arithmetical. Studies, General classification of Study and teaching, Method necessary in " of composite numbers. . . " " history. Children dis- like " " " Purpose of. . . " " phonics. The " " the noun. Matters con- nected with the " Value of grammatical Subdivided unit, The Subject and predicate " of the infinitive " Teachers must know. . . The Subjects of study. Interrelations of Subjunctive mode, Definition of " " Examples of " " has slight refer en ce to time Pasre. 88 38 51 37 100 80 90 96 37 40 45 46 62 16 . 70 112 100 12 51 10 38 101 102 22 53 10 14 85 6 9 85 72 4 74 26 51 10 32 64 47 50 INDEX. Sec. Pajfi'. Subjunctive mode, Knowledge teachers should have of 4 48 Subjunctive mode, The 4 46 Subordinatmg conjunctions 4 87 Subtracting, Two methods of... 2 2 Subtraction drill, General scheme of 1 31 " " Purpose of 1 30 Drills for 1 30 " of denominate numbers 2 04 " Proofs of 2 20 Success, Conditions of, in teach- ing history 58 '■ depends on use 7 19 " Teacher's personality an element of 7 50 Suffixes, Alphabetical arrange- ment of 7 87 "■ Exercises with 7 88 " in teaching, The use of 7 86 " Meaning of 7 87 Sui generis nouns 3 75 Summary of lessons 5 121 " on methods 60 Sun's apparent motion. Obser- vations on 5 93 Superlative and comparative. Forms of the 4 28 " degree of adjec- tives 4 21 Surface units 5 71 Survey maps. Government 5 107 Surveying with bicycle and cy- clometer 5 83 Syllabication 7 12 " Degrees of diffi- culty in 7 13 " Exercises in 7 14 " in spelling 7 16 " Rules for 7 15 Symbol of operation in multipli- cation 2 11 Symbols and their plurals 7 6 " Conditionsexpressedby 1 21 Synonjnns, Defining by 7 74 " Works on 7 74 Synopsis of all tenses 4 63 Syntax and etymology. Method of treating 3 68 " and etymology should be treated together.. 3 69 " Collections of, for cor- rection 3 62 " Etymology and 3 67 " Examples of false 3 61 " Meaning of term 3 10 Synthesis 3 46 Sec. Page. Synthesis, Exercise in 3 49 " Exeicise in, for m- creasing vocabu- lary 3 47 " of complex sentences 3 54 " "sentential ele- ments 3 46 System, The metric 2 115 T. Sec. Page. Table of the adjective 4 10 " " " " Remarks on 4 17 '• " " adverb 4 79 " " " conjunction 4 88 " " " noun 4 4 " " " participle 4 57 " " " preposition 4 85 " " " pronoun 4 10 " " " verb , 4 72 Tables of prime numbers 2 30 Tabular classification of sen- tences 3 56 " " Remarks on 3 .56 "Tale of Two Cities" 6 15 Taste for historical and bio- graphical reading (i 14 Teacher, Illicit assistance by the 7 18 " miist know his subject 6 10 " should have knowledge of subjunctive mode 4 4S " should regulate his reading. How 6 11 " Socrates as a 5 127 The child's first 5 52 " " wheelman as a 5 82 Teaching geography, Cause and effect in 5 122 " geography, Some points in 5 113 " history. Difficulty in. . . 6 8 " " Preparation for 11 " effractions 1 48 " " " Conditionsof success in 1 49 " orthography, The col- lecting of devices for 7 63 Teachers at Vienna, Views of... 5 97 Tense, Definition of 4 58 " forms. The passive pro- gressive 4 02 " of all modes, Summary of 4 03 The future 4 01 " past 4 01 Tenses, The present 4 59 Term "active" as used in gram- mar 4 40 XXVI INDEX. Sec. Page. Term "correlation," Meaning of the 65 " denoted by the infinitive. . 4 55 Terms, Meaning of 3 37 used by writers on gram- mar 3 70 Test for prime numbers 2 35 " of geographical value 5 31 " " power of inference 6 44 " words in spelling 7 102 Testing questions 5 125 Textbook, Geography without a 5 08 Textbooks 3 5 " and methods, Value of 3 7 " Evolution of 5 112 " for spelling. Selection of 7 49 " in teaching spelling, Use of 7 47 " Omissions from 3 8 " on history 6 " Preparing lessons from 6 20 The latest 3 5 " What, should contain 3 9 That, who, and which 3 42 The number "one" 1 72 Theory modified by fact 5 IG " of pleasure and pain 6 5 Things distinguished by differ- ences 5 40 Thought, Forms of written 1 "Three," The n\imber 1 75 Thurot, Quotation from 7 69 Time given to history 6 13 " or action. Demand for 6 42 " Subjunctive mode has slight reference to 4 50 To multiply bya number slightly greater than 10, 100, etc 2 12 " subtract by adding 2 3 Topical, Extension of meaning of 6 32 " method 6 31 " Remarks on 6 33 Topics, Order of, in fractions. ... 1 54 Topographical map, Description of 5 107 Training, Objections to special- ization in 6 63 Transformations in proportion.. 2 96 Transitive forms, Other 4 37 " When a verb is 4 .37 Travel and adventure. Books of 5 1-33 " " geography, Books of 5 134 Treatment of etymology and sj-n- tax. Method of.... 3 C7 " " lessons in orthog- raphy, General.. . 7 67 Treatment of thenoun, Gradation of 3 " " ' verb. Plan of.. . 4 Triangles, Right-angled 2 True discount 2 Truth, Demand for, m narrative 6 "Two," The number i Tyndall, John 5 " 6 Type formulas 1 Types of examples 1 U. Sec. Ultimate basis of science 5 Ul y sses 5 Underlying principles of the les- son 6 Unilineal writing 6 Unit, Fractional 1 " of thought. The 3 The subdivided 1 United States, Rule of partial payments in. . 2 " " topographical maps 5 Units, Linear 5 " Surface 5 Unity of primary and secondary education 5 University, Harvard 7 Unnecessary compounds. Avoid 7 Unwritten multiplication 2 " " by two figures 2 Usage, Common 3 " Established 7 Use, Adverbs classified with re- spect to 4 " and abuse of abbrevia- tions 7 " determines success.. 7 " of apparatus 1 " " a textbook in spelling 7 " " formulas in interest 2 " " hyphen 7 " "perceptions 5 " " pictures in teaching 5 " " poems and ballads. His- torical 6 " " prepositions with certain words 4 " "'pronouns. Ambiguity from 4 " " relatives, Care in the 3 " "rules. Psychological 7 ',' " signs 1 " " " in fundamental operations 2 Sec. Page. 70 29 114 93 41 73 37 56 25 23 Page. 36 22 48 6 8 17 74 89 XXVll Sec. Pag-c. Use of suffixes in teaching 7 8(i " " type formulas 1 25 " Sentences classified with respect to 3 18 Usefttl drill in fractions 1 (>•"> Utilitarianism, Abuse of 7 41 Utility and mental discipline 7 01 X. Sec. Page. Value, Educational 5 1 " " affected by existing conditions 5 8 " " Diversity of opinion concerning 5 G " in general 5 1 " is relative 5 2 Value of exactness and thor- oughness 3 40 " " geography, Dr. Har- ris's estimate of 5 21 " " geography, Psycho- logical 5 22 " " grammatical study... 3 4 '■ " textbooks and meth- ods 3 7 " Test of, in geography 5 31 Vastness of history til Verb, Definition of the 4 30 " Plan of treatment of the 4 29 " Preliminary remarks on the 4 20 Table of the 4 72 The 4 20 " when transitive 4 37 Verbal nouns 3 70 Verbs, Active and intransitive. . 4 3r) " " transitive 4 3.5 " as related to adjectives and adverbs 4 73 " Auxiliary 4 GO " Classification of 4 32 " Defective 4 35 " Drill with irregular 4 41 " Modes of 4 43 " " " Preliminary re- marks on 4 43 Neuter 4 38 " " cannot be modi- fied 4 74 " Newly coined, are alwaj'S regular 4 33 " Redundant 4 35 " Regular and irregular. . . 4 32 " Remarks on classification of 4 40 " " " irregular 4 34 Sec. Page. Verbs, Tenses of 4 58 " that are both active and neuter 4 75 Vienna, Views of teachers at. .. . 5 07 Vocabularies, Enlarging pupils' 3 GO " Remarks on en- larging 3 CO Vocabulary, Acquiring a 3 03 " Synthetic exercise for increasing. . . 3 47 V^ocabulary, Use of pictures in acquiring 5 .59 Voluntary attention 1 4 Von Humboldt 5 32 Von Ranke, Leopold G .55 "NV. .Sec. Page. Wall maps 5 117 What are abbreviations ? 7 33 " is meant by relation 4 1 " textbooks on grammar should contain 3 9 " The relative ' 4 8 " to omit from textbc^oks on grammar 3 8 "What words say " 7 70 Wheelman as a teacher, The 5 82 When a verb is transitive 4 37 White, Richard Grant 7 8 Whitney, William D 7 10 Who, which, and that 3 42 Whole, The earth as a 5 34 "Will "and "Shall" 4 07 " Will " and " Shall " denoting determination 4 OS "Will" and "Shall," Funda- mental meaning of 4 07 Will of the hearer, " Shall " and "Will" denoting 4 00 " of the person mentioned, "Shall" and "Will" de- noting 4 00 " of the speaker, "Shall" and " Will " denoting 4 08 Wilson, "Punctuation" by 7 20 Word "limit," The 3 38 " lists, Devices and 7 82 " "modify," The 3 37 " "qualify," The 3 38 Words belonging to a given en- vironment 7 95 " Compounding of 7 20 " Defining, in connection with spelling 7 73 " denoting collections 7 03 " " different as- pects of the same idea ... 7 04 XXVlll INDEX. Sec. Page Words, Extremes and means among 4 23 " for spelling. Select ion of r 42 " " " Sources of selection of r 42 " " " work, Means of obtain- ing 7 02 " Getting rid of objection- able 3 05 " in common use 7' 58 " spelling, Test of 7 102 " liable to be mispro- nounced 7 84 " Method of learning 3 04 " Modification of 7 20 " Nature of our knowledge of 3 03 " Pupils should copy 7 08 " " " pronounce 7 07 " " write,from dictation 7 OS Sec. Page. Words, Saxon 3 17 Work, A daily 4 42 Works on English synonyms. ... 7 74 Writers on grammar. Terms used by 3 70 Writing beautiful or striking passages 7 71 Bilineal 4 " Multilineal 4 _ " same word often, Effect of 7 09 " Unilineal 4 Written forms in fractions 2 40 " spelling 7 45 " thought. Forms of 1 X. Sec. Page. Xerxes' invasion of (Ireece 47 Y . Sec. Page, Years, Leap 2 113 " work 1 09 Z. Sec. Page. Ziller 50 m^ihwii CJ ^ 90 v^^ -- '^ \^ ^ .^■