LIBRARY OF CONGRESS. Chap. Copyright No. Shelf_.X.^_-. UNITED STATES OF AMERICA. THE MISSOURI SUPERVISOR, GUIDE IN THE USE ADOPTED TEXT-BOOKS, J. P. THURMAN, Superintendent Rich Hill Public Schools, FRANK DEERWESTER, Assistant in Department of Pedagogy, Warrensburg State Normal. m - 1 1898 RICH HILL, MO.V,U./,S. A., „. „ WARREN BROTHERS, FU:!^4fefig^go9l -* 1898. ^X^^ N^cVfjM "^^^ ( -) 1 Copyright, 1898, By J. P. THUKMAN, AND FRANK DEERWESTER. LblS5S ■TS PREFACE. The authors of this book are not at war with existing educational conditions and ideals. Being Missourians by birth, educated largely in Missouri schools, and having been for years teachers of Missouri youth, they have faith in her educational system and hope for her future. It is a grand work that is going on in this state under the name of education. Within the narrow circle of their influence the authors have been contributing their mite toward the great end. Now they seek to widen this circle, modestly daring to hope that their humble efforts may not be in vain. Originality in the sense of startling novelty is not claimed for this book. It does not pretend to reveal the royal road to knowledge. The authors do not believe this is the best book on the subject of pedagogics that has ever been written. On the other hand they do believe that Experience, in her varied intercourse with them, has taught them some lessons which may be presented to others in a less expensive way. With 3,000 inexperienced teachers entering the pro- fession each year, with nearly 4,000 more having less than three years' experience in teaching, and with the new and improved series of text-books now going into use, there ought to be room for such a book at this time. 6 THE MISSOURI SUPERVISOR. The recommendations of this work are not believed to be radical. Conservatism in plan and method has been the aim. Nothing impossible or chimerical has been advocated. The aim is to direct the thoughtful, aspiring teacher, whether experienced or inexperienced, by safe paths, and yet possibly new ones, to higher ground — to direct not by an explicit "take thou," but by thought-pro- voking suggestions. These, so far as they may be of value, the artist will absorb and embody in his teaching. The artisan, the rote-teacher, will not be injured by them. The authors have sometimes been at a loss to know just how far to go in their recommendations. Writing for so mixed an audience is no easy task. In the main the plan has been to address themselves in a suggestive way to the majority of their prospective readers. The great teaching-body of Missouri has been the audience which imagination has convoked. No attempt has been made to show what can be done where all the engines and energies of a mighty city school system are turned in any given direction. On the other hand, it is confidently hoped that the work herein presented, as to matter and method, is such as will be an inspiration to many thou- sands in Missouri's noble army of teachers. The Authors. CONTENTS. PART I. CHAPTER I. PAGE Course of Study for District School 9 CHAPTER n. Daily Program for District School 29 CHAPTER HI. Some Points of School Management 42 PART II. CHAPTER I. Reading, Literature, Spelling 70 CHAPTER H. Arithmetic 116 CHAPTER HI. Language and Grammar 163 CHAPTER IV. Geography in CONTENTS. CHAPTER V. History and Civil Government 216 CHAPTER VI. Physiology 235 CHAPTER VH. Vertical Writing 237 Appendix 24S THE MISSOURI SUPERVISOR. PART FIRST. CHAPTER I. COURSE OF STUDY. INTRODUCTION. The course of study which follows is not theoretical, nearly every part of it having been worked out, directly or indirectly, under the observation of its authors. Notwith- standing the dissimilarities of rural, village, and town schools, it is believed that this course of study is suitable for each. It may be said, however, that if any class of the three has, ' more than the others, been in the authors' minds, it has been the first — the rural school. To under- stand the foregoing remarks requires an appreciation of the authors' idea of the purpose of such a course for any kind of school. A course of study, they believe, is intended primarily to set forth the contemporaneous sections of those great lo THE MISSOURI SUPERVISOR. lines of human thought which are deemed worthy of the attention of persons in pursuit of knowledge. The primary question is not so much where the line shall be drawn be- tween the successive years as it is what work in language, science, numbers, etc., shall be pursued contemporaneously. This is the question of vital importance. The authors' answer to this question is the course of study. Incident- ally they have answered the former question, too, realizing, however, that "school year" is only a relative term — meaning anywhere from six to ten months. The work as outlined contemplates at least seven months. Eight will result in better work, and nine, of course, will be still more satisfactory. In some schools the work suggested for a year may be accomplished easily and more may be desired. If so, there are two courses open: one is taking up supple- mentary work of a related kind, the other is advancing into the work of the next year. Where schools can not do the work suggested, the opposite courses are open — omit- ting parts of least importance or ending the year at such a point as marks the well-completed work. It may be seen, therefore, that the course of study is to be used as a spirit- level to keep the structure plumb more than as a tape-line to ascertain the height. Character of work is deemed of greater significance than amount of work — a symmetrical advancement along all lines superior to an abnormal devel- opment along a single line. This unsymmetrical, "lop-sided," sort of development is so prevalent in rural schools that the authors sincerely hope that this work may, at least, do something toward bringing matters to rights once more. Where a pupil or a THE MISSOURI SUPERVISOR. ii school has advanced in this abnormal and unhealthy way, the evil can not be cured in a day. To attempt to do so would be unwise. Gradually must the pupil or the school be "evened up," by checking here and pushing there, de- voting little effort to one line, much effort to the other. 12 THE MISSOURI SUPERVISOR. > > a O "3 o 13 o o "re 5 n O "3 o Eg o 0._; O Si OS > o . o h ■Ji CI OJ 5 a . ■5.S -' "^ so, s: a < K O O "is o "a O a o ^ ^ ^ H 00 oiw2 dp; ^ S V i S w E-x 2 S « 3 ^ «5^^ n.V I- P.a| a z < 2! si < 6 -5 "3 O -J s s 5 «J c a^ - * U -j; S = dj cc s * 55 So ••^ C ft i O 3 «Ut/5 P-i is a • < y ■r. - S a c ^2 Is "^ s s 5 ■0 oo gj 2 "j" "• ^ 5 2?-2 .£••2 5 "iJ d ^ a- ^ o JJ 00 ""' HJ OJ 03 i_ t>^ _u (^ o t; " - d.dl s ■poti !? «o5d cfl: P P- 7? o j? !-• CO ■si 3 •X ft C5 O lI ^ _ CI dJ T' rt o . fe Oi 'J3 p. d aj . ■J5 e. .-a o d (LI . u d V ■ C — t-'d "S . X P. i-'d te ■S .£■> ftp.-- -i 1 M d d >■ l-H d > 6 d ^^-c 3 p o re 3 o 5 CI U o s = > s i-T i ^2S ^ ^2-a& Mil 2^ 5^^ •^>. 5^: 00 >% THE MISSOURI SUPERVISOR. 13 B.— BY SUBJECTS, READING. FIRST YEAR. COURSE I: Complete thoroughly Franklin Primer and First Reader. Note: — Course I. is a minimum. It is suggested for schools having a term of average length, no chart, and no Werner Primer. In addition to completing the work one or two classics can be read with pleasure and profit by the class. COURSE II: Miss Striker's Chart for six weeks or two months. Franklin Primer and First Reader completed. Note: For schools having the chart. COURSE III: - Werner Primer, followed by a rapid reading of Frank- lin Primer. Complete thoroughly Franklin First Reader. SECOND YEAR. Franklin Third Reader completed. Supplemental work: Any two classics recommended for this grade. See Appendix. 14 THE MISSOURI SUPERVISOR. THIRD YEAR. Franklin Third Reader Completed. Supplementary work : Any two classics recommended for this grade. See Appendix. FOURTH YEAR. Franklin Fourth Reader, Part First (pp. 1-104.) Supplemental work: Any two classics recommended for this grade. See Appendix. FIFTH YEAR. Franklin Fourth Reader, Part Second (pp. 204-328.) Supplementary work : Any two classics recommended for this grade. See Appendix. SIXTH YEAR. Franklin Fifth Reader to page 201. Supplementary work: Any two classics recommended for this grade. See Appendix. SEVENTH YEAR. Franklin Fifth Reader, pp. 201-430. Supplementary work: Any two classics recommended for thlt grade. See Appendix. THE MISSOURI SUPERVISOR. 15 LITERATURE IN THE LOWER GRADES. 1. Two classics are to be read critically as supple- mentary reading in each grade. 2. If this plan be acted upon, it will be seen that at the end --f the common school course, sixteen classics will have been added to the student's store of knowledge — in the same time the readers are usually completed. 3. Reading is fragmentary; classics are usually com plete, giving additional interest. 4. Graded literature insures constant growth and S}'mmetrical development. 5. The sixteen classics contemplated embody the best thoughts of all mankind of the past and pres- ent. 6. The geography, history, home-life, religions, super- stitions, philosophy, the struggles, hopes, and aspi- rations of mankind are contained in these classics. 7. The millions of boys and girls on the farm, in the village, factory, mine — everywhere — have a 7-ight to something better, and more complete, than what they have received in the past. Any country, village or ward school can do this supplementary work laid out in this course. 8. The object of all reading, either regular or supple- mentary, should be to lead up to literature in its highest forms. g. Our adopted readers have on an average sixty- three lessons for each grade, leaving ample time i6 THE MISSOURI SUPERVISOR. for at least one period each week to be set aside for supplementary reading. lo. The time spent will increase the interest in the regular classes in reading. SPELLING. SEVER' S PROGRESSIVE SPELLER. Note: Prof. Sever kindly furnished the graded course and the suggestions following: Second year, pages 1-30. Third year, pages 30-60. (Finishing Part I.) Fourth year, pages 60-90. Fiftli year, pages 90-120. Sixth year, pages 120-150. Seventh year, pages 150-165. (With review.) OBSERVATIONS AND SUGGESTIONS: 1. Spelling is arranged in accordance with certain principles involved. 2. The words are grouped under general rules and in general classes. 3. The law of association is most helpful in spelling. The words are therefore grouped according to their similarity or dissimilarity, agreement or dis- agreement, association with thoughts they repre- sent, and the forms they have. 4. The law of association requires that the meaning and application of words should be taught with their spelling. THE MISSOURI SUPERVISOR. 17 5. The grouping is around subjects, as Geography, Medicine. 6. The words are arranged under rules. 7. The necessity for correct use of words involves the necessity of correct spelling. 8. The word-forms appeal to theieye; correct forms should be presented. g. Diacritical marks are valuable only when their use is known. They must be used with such fre- quency as to render familiarity certain. 10. Word-building from root-words is freely intro- duced as a form of association. 11. The teacher must have enthusiasm for the work. 12. Work should not be all written nor all oral, but should be combined to suit surrounding conditions. 13. The teacher should make word-lists of all incor- rectly spelled words in written spelling. These lists should be reviewed in special lessons. ARITHMETIC. FIRST YEAR. Numbers from one to ten. For detailed statement of the work, with suggestions concerning materials and meth- ods for this and following grades, see Methods of Arithme- tic in this book. SECOND YEAR. I. Study numbers from ten to twenty. x8 THE MISSOURI SUPERVISOR. 2. Writing of numbers to 999. 3. Roman notation to one hundred. THIRD YEAR. FIUST HALF: 1. Reading and writing numbers to 9,999. 2. Multiplication and division to lo's. 3. Study of individual numbers from 20 to 30, (further if time permits.) SECOND HALF: 1. Milne's Elements to p. 118. 2. Supplementary work as needed. 3. White's Oral Arithmetic to p. 22. Note. White's book is recommended as one in every way worthy to accompany our adopted text in written Arith- metic. It is believed that no pupil should recite "arithme- tic" more than once a day. Nevertheless there should be a great deal of oral Arithmetic. White's book represents a minimum accompaniment for a course like Milne's. As to method, it is suggested that White's book be used co- ordinately with Milne's books as follows: 1. As a preparatory review, before taking up a topic that is not entirely new — as addition (Milne's Ele- ments p. 89), for which some of the exercises in White (pp. 8-1 1) would be an excellent preparation. 2. As a drill and review in connection with, or follow- ing the work in Milne. There may be an occasional "day off" from the written work for an oral drill. 3. As a preparation for the written work, where the topic is a new one. Milne introduces each new topic with a series of inductive exercises. White's book will furnish valuable material supplementary to these. For example: pp. 55-62 (White) should be given in connection with pp. 138-140 (Milne's Elements), and then the pupil will be prepared for the written work THE MISSOURI SUPERVISOR. 19 on p.p. 141-144 of Milne. It is understood, therefore, that the various topics in the Oral Arithmetic are to be studied in connection with the same topics in Milne's books. FOURTH YEAR. 1. Milne's Elements, pp. 1 18-188. 2. White's Oral, pp. 23-27, 35-48, 55-68, 73-98 (omit- ting any parts or problems that are too difficult for the class) FIFTH YEAR. FIRST HALF: 1. Milne's Elements, pp. 188-231. 2. White's Oral, pp. 103-123. SECOND HALF: 1. Milne's Standard, pp. i-go. 2. White's Oral, pp. 28-34, 49"54» ^9> ^^^ ^^'^y other omitted parts up to this point. SIXTH YEAR. 1. Standard Arithmetic, pp. go-231. 2. White's Oral, omitted work between pp. 70 and 123, with occasional re\-iews of other parts withi;* same limits. 3. Supplementary oral work, if needed. SEVENTH YEAR. 1. Standard Arithmetic, pp. ?oi-282. 2. White's Oral, pp. 123-143. 3. Other supplementary work, if needed. EIGHTH YEAR, r. Standard Arithmetic, pp. 282-438. 2. White's Oral, pp. 143-176. 20 THE MISSOURI SUPERVISOR. LANGUAGE. FIRST YEAR. I. Nature of the JVork. The language work of this year must, of necessity, be largely oral and incidental, and may be taken up in connection with each of the other lines of primary work. The work should be in the form of conversation lessons upon appropriate topics. These exercises increase the child's power of expres- sion, stimulate mental growth, and establish good habits of speech. Using the good with sympathetic help leads to the omission of the bad. Naturalness of expression should be the aim. To secure this requires an interesting topic, a sympathetic interest on the part of the teacher and guide, and sympathetic criticism when criticism is necessary. II. Materials, drawn from the parallel lines of work, thus securing that natural correlation which should perme- ate all instruction. The materials come from: 1. The reading lessons, which the child reproduces, or about which he talks, and which he copies as soon as he learns to write. 2. Nature lessons, on trees, plants, flowers, fruits, leaves, insects, domestic animals, rain, snow, ice, etc., in which both observation and expression are encouraged. 3. "Geography" lessons in which he acquires and uses terms relating to place, direction, color and form. 4. Child literature, appropriate stories read or told THE MISSOURI SUPERVISOR. 21 by the teacher and re-told by the pupil. 5. Memory gems, suitable in sentiment and difficulty to this stage of development. III. AiT>i, This year's work is intended to secure to the child the following: 1. Meaning and use of many new words. 2. More fluent and accurate use of his present vocab- ulary. 3. Discriminative use of simple terms likely to be misused; such as I, me, he, him, her, she, we, us, a, an, this, that, these, those, is, are, was, were, see, saw. 4. Connected thought and connected expression of thought in good form — descriptive and narrative. 5. A growing familiarity with the mechanical ele- ments — capitals and marks of punctuation — when copying is begun. 6. Correction of some inaccuracies in pronunciation and use of words. SECOND YEAR. This year should include the following lines of work: 1. Description, oral and written, of plants, animals, and manufactured objects present, and from mem- ory, using connected discourse. 2. Correct use of common words likely to be misused impressed by repeated use — governed by needs of pupils. 3. Some attention to the construction, not dissection, of simple sentences. 4. Oral and written reproduction of reading lessons. S3 THE MISSOURI SUPERVISOR. Stories, etc., especial attention given to narration. 5. Dictation exercises of suitable character. 6. Simple descriptive and narrative compositions. 7. Close attention to the mechanics of composition. 8. Memory gems. 9. Simple letter-writing. THIRD YEAR. I. Text-Book Work — DeGarmo's Combined Book, Part I. II. Supplementary Work: 1. All the lines of work pursued in second year^ each adapted to the increasing intelligence and expanding powers of the pupil. 2. Elaboration of the sentence — using more involved forms. 3. Supplying ellipses. 4. Completing paragraphs and weaving contexts about selected sentences. FOURTH YEAR. I. Text Book—De Garmo's, Part II. II. Supplementary: 1. Continue the work of the previous year. 2. See Methods in Language lor fourth year, in this book. FIFTH YEAR. I. Text ^(^r'Z-— DeGarmo's Part III., or Parts III. and iV. (In a graded school with a high school department in which it is possible to use Patrick's second book, it may be desirable to spend but one year on Parts III. THE MISSOURI SUPERVISOR. 23 and IV. The rural schools are denied these high school texts and may with profit spend a full year upon Part III.) II. Supplementary Work: 1. Continuation of such forms from preceding years as are suited to the pupils, and each teacher must determine this matter for his own school. 2. Composition work, completing stories, making up stories, as suggested in Methods for fifth grade — elsewhere in this book — are appropriate here. SIXTH YEAR. I. Text ^^^/^— DeGarmo's, Part IV. and review, or Pat- rick's Lessons, to page 92. (See fifth year.) II. Supplementary work in composition writing, making abstracts and paraphrases,and such lines of previously suggested work as need further consideration. SEVENTH YEAR. I. Text Book — Patrick's Lessons to page 92, or (if already studied to this point) complete the book, (reviewing from page 80 at beginning of the year. II. Supple7nentary work in composition and in grammar. EIGHTH YEAR. I. Text Book — Patrick's Lessons completed from page 80, (or Patrick's Higher English), with suitable supple- mentary work in composition and grammar. 24 THE MISSOURI SUPERVISOH. GEOGRAPHY. FIRST YEAR. Observations of land, water, temperature, soil, plants, animals, men, occupations, sun, clouds, winds, etc. Learning of a few of the terms applicable to posi- tion, distance, direction, size, form and color. Reading of geographical stories, by teacher. 2. I. SECOND YEAR. Continuation of observation lessons of preceding year. 2. Suitable readings, making con^parisons with home regions. THIRD YEAR. 1. Further observations, leading to a clear concep' tion of fundamental geographic ideas, such as hill, stream, etc. 2. Idea of mapping according to scale, together with simple mapping of school-room, school-yard, town or district, county, and state. 3. Supplementary reading, with application to geo- graphic ideas. FOURTH YEAR. FIRST HALF: Rand-McNally's Elementary, text to p. 50. SECOND HALF: Same text, pp. 40-7S. THE MISSOURI SUPERVISOR. 35 Supplementary work for both halves: 1. Weather observations. 2. Study of industries. 3. Modes of transportation. 4. Products of field, garden, mine, forest, factory. 5. Imaginary journeys. 6. Reading. FIFTH YEAR. FIRST HALF: Elementary book, pp. 78-113. SECOND HALF: Same book to p. 152. Supplementary reading throughout. SIXTH YEAR. Rand-McNally's Complete Geography to p, 86. Supplementary reading. SEVENTH YEAR. Rand-McNally's Complete Geography, pp. 86-168. Supplementary reading. U. S. HISTORY. SIXTH YEAR, FIRST HALF: Morris's Elementary History, parts I., II., and III. SECOND HALF: Complete the book. 26 THE MISSOURI SUPERVISOR. SEVENTH YEAR. FIRST HALF: Shinn's History of the American People, to Part IV., p. 121. SECOND HALF: To Part VI., p. 233. EIGHTH YEAR. FIRST HALF: Shinn's History of the American People, Part VI., to P- 317- SECOND HALF: Parts VII., and VIII. CIVIL GOVERNMENT AND HISTORY OF MISSOURI. Text Book: — Rader and Thummel's Civil Government and History of Missouri. FIRST PLAN:— SEVENTH YEAR. History of Missouri, pp. 147-40S. EIGHTH YEAR. Civil Government of U. S., and of Missouri, pp. 1-147. SECOND PLAN:— SEVENTH YEAR. Civil Government of U. S., and of -Missouri. THE MISSOURI SUPERVISOR, a? . EIGHTH YEAR. History of Missouri. THIRD PLAN:— SIXTH YEAR. History of Missouri. SEVENTH YEAR. Civil Government of Missouri. EIGHTH YEAR. Civil Government of the United States. PHYSIOLOGY. I. Oral lessons, occasionally, throughout the course, begin- ning in first grade with naming, some of the obvious parts of the body, head, hand, foot, eye, ear, etc., and gradually extending to parts less obvious, as heart, lungs, brain, stomach, etc. There should be lessons on food, its use, and how to eat it. Also on the hygiene of teeth, skin, eating, drinking, breathing, circulation, rest, exercise, and sleep. Some of the effects of stimulants and narcotics may be noticed. II. Baldwin's Essentials, eighth grade, one year's work. VERTICAL WRITING. Adopted Books: — Natural System of Vertical Writing First Year, Book I. 28 THE MISSOURI SUPERVISOR. Second Year, Book II. Third Year, Book III. Fourth Year, Book IV. Fifth Year, Book, V. Sixth Year, Book VI. Seventh Year, Book VI., and Business Forms. DAILY PROGRAM FOR DISTRICT SCHOOLS. 29 CHAPTER II. DAILY PROGRAM FOR DISTRICT SCHOOLS. ADVANTAGES OF SYSTEM. Life without a program is aimless. Great enterprises cannot be successfully conducted without a fixed program. The time-table of a railroad is its program. All trains arrive and depart on time, and every passenger /-111 1 • • r 1 •*- Pi'ogram soon finds that he, too, must be on time, if he Brings Success. wishes to catch the train. A certain distance must be covered within a definite period, and if a train gets behind time, it must so remain, or endanger the lives of its passengers by running at a speed that is considered unsafe, — for it is manifest that the com- pany, in arranging its schedule, adopted the fastest time consistent with safety. This unvarying program pro- motes promptness. The employes arrive upon time to take charge of their various duties. The section men know when the train will arrive, and loosen no spikes, and remove no rails till it has passed; then in safety they time their labor to the on-coming of the next train. The traveling public examine the program and promptly present themselves at the station in ample time, 30 THE MISSOURI SUPERVISOR. for they have found by past experience that it will be carried out to the minute, whether they are ready or not. The thousands of employes time their actions to the pro- gram, and the hundreds of thousands of patrons accept its decree as final, and never call in question its fulfillment. One moment's reflection will show the far-reaching effects of its abandonment. Think of waiting for a train, some- where up the track, the arrival of which is only conjectural. It sometimes gets in on time; sometimes, behind time; sometimes, ahead of time. It sometimes runs slow; some- times, fast, — sometimes at a dangerous speed. The many are inconvenienced, tortured and damaged, simply because there is no fixed program. A great railway system has much to do in a limited time. Each employe must do his part within the prescribed limit. In no other way could it be called a "system." Without this uniformit}', it would be declared inadequate, and wholly unsuited to the pur- poses of its existence. The business man who has system in the management of his affairs is almost always successful. He is prompt in opening his office, or building, in waiting upon his cus- tomers, in his collections, and in meeting his obligations. His promptness begets promptness in all who have dealings with him. The farmer who has a time for everything will soon have all persons who are in any way connected with his business adjusting their actions to his program. System, increased work, and larger profits, are the necessary results of his program. The laws of health, from a physiological standpoint, DAILY PROGRAM FOR DISTRICT SCHOOLS. 31 require that a daily program should be kept, and strictly followed. Rising at a regular time, eating systematically, exercising regularly, bathing regularly, sleeping regularly give health, strength and buoyancy of spirit and mind. Timing one's action to the work in hand is following a program, no matter in what avenue of life. Persons who do this are systematic, and no one is systematic who does not do so. Why in all successful enterprises, is a program adopted by persons having charge of them? The answer comes, "It pays." If this is the correct answer, then there is no place where it will pay so well as in a school. In any school the true teacher never does all he sees that needs to be done. His field of activity is limitless. He has six short hours each day in which to supervise, per- sonally, his school. He is to promote the . , .... , -, A. Program greatest development possible m each pupil. Aids Teacher and Pupil. His success is not measured by the soul-ex- pansion of one, of five, but of all. The close of the day must witness a mental development of all. His success is measured by the difference of intellectual and moral power of his pupils at 9 a. m. and 4 p. m. He sees so much to be done that he would become discouraged, were he not a hero for humanity. He sees the situation, and heroically does all he can, in the most effective way at his command. He realizes that he cannot do so much alone as when assisted by his pupils. Accord- ingly, he assigns work for the students to do in a given time, the amount being what they can be reasonably expected to do in the time. Pupils of similar attainments and similar capabilities are put to work upon labor of like 32 THE xMISSOURI SUPERVISOR. kind and amount. The teacher is the sympathetic fore man, who lays o1it the work, and sees that all hands are busy. He sees that he can accomplish more work by planning, laying out work, and seeing that every one under his direction does his duty, than to try to do the work and let his assistants sit idly by. At stated intervals, the time when a given piece of work is supposed to have been accomplished, the foreman examines to see if it has been fully done by each in a workmanlike manner. If he finds that some can not do their work, he shows them how, and makes their failure the ground of their future success in similar cases. When the pupil has completed the work assigned, he has a right to have his next work assigned, and to begin upon it. A program would of necessity be a good one, which would give just enough time between the recitation periods to prepare the lessons. The recitation period should be just long enough to allow the teacher to test the pupil's knowledge of the subject, to explain any work that can not be done by the class, or can not be done without a waste of time; to give such outside information as bears directly upon the lesson; to enrich, to expand, or to intensify it, and to point the way in the following lesson, when the papils need direction. Such a program presup- poses that the teacher has enough judgment to know what a certain class can do in a given time, in a given subject. If classes are overburdened, they cannot be prepared, when their time to recite arrives. Their knowledge of the lesson will be meager, and their recitation slow and spirit- less upon the part they happen to know, and a much DAILY PROGRAM FOR DISTRICT SCHOOLS. 33 longer time will be required for the imperfect recitation, thus encroaching upon the recitation period of the next class, with a corresponding shortening of the , . , r 1 1 11, .A Program Study period for the class that has' just Leads to System. recited. Getting behind time causes rushes, hurry, confusion, and a dangerous recklessness as in the case of the belated train. The program for the whole day is behind time, the equilibrium of the school is destroyed; system, so far as that day is concerned, is absent. On the other hand, just enough time is used for the study period, and everything moves systematically according to the time-table. Industry and great work mark the session. The term is made up of days; successful days continued make successful schools. Enthusiastic teachers frequently consume too much time in the recitation. In their enthusiasm, they forget the work that is before them, and, to that extent, fall short of being good teachers. No teacher ever . . A Program heard a slow recitation when the lessons were Leads to Thorough!] ess. thoroughly prepared; no teacher ever heard a quick recitation where lessons were poorly prepared. Being on time acts upon students as the railway time- table does upon the emploj'es, causing them to be ready and to do the work prescribed in the alloted time. The knowledge that the teacher will not "run over-time" pro- motes regularity, industry, and desirable habits of study and action in the pupil. A program also presupposes that a teacher knows the object of the recitation. . „ ■' A Program Such a teacher will at once, when the class correct °Habits 11 11 r 1 1 °f Study. IS in position, test the knowledge of the class — 34 THE MISSOURI SUPERVISOR. not deliver a lecture to show how much he knows about the lesson. The recitation is for the pupil', not for the teacher. The teacher should not lead the pupil to his answer. The pupil, in the best way under the circumstances, should be permitted to recite freely and fully, or represent to the teacher what he has assimilated and made a part of him- self. When the various members have given sufficient evi- dence that they have mastered the lesson and have assimi- lated it, the teacher should then correct any erroneous ideas the class may have, and make clear any facts that are left obscure, and give any suitable relative matter to emphasize the points brought out, or to supplement, or to enrich the contents. When this is done, the next work should be as- signed with any necessary suggestions in regard to its prep- aration, or special work to be done in connection with it. Incidents remotely connected with the lesson are out of order, as a rule, and indicate a lack of preparation of the lessons upon the part of the teacher. When these details have been completed, the recitation is finished, and should cease. As suggested in another chapter, it is, occasionally, necessary to vary the program for a single day. There may be some subject requiring additional time for explana- tion, or elaboration. Upon such occasions the Rarely \^ried. extra time should be taken, but the rule should be, "Follow your program," breaking it should be very rare. Subjects like the Greatest Common Divisor, Longitude and Time, etc., cannot be explained in the time ordinarily given to the recitation. In such cases we would have to run over time. These cases should DAILY PROGRAM FOR DISTRICT SCHOOLS. 35 be the exceptions, just as a train is compelled, occa- sionally, to be behind time. Even in the cases cited above, it is better, when it can be divided, to give only so much of the subject as can be completed in one recitation. The one thing to bfe borne constantly in mind by the teacher is the day's work as a whole, and work in such a way as to make the success of the day most- complete, rather than the single recitation. As before mentioned, successful davs are the units by which success- ful terms or years are measured. \ It should be kept in mind that a program suitable tO all the peculiar conditions of the school is necessary. The teacher in charge is the person to decide this point. Al- most every district would require a program slightly differ- ent from the one adjoining. Even in the same school, the program would vary slightly from year to year. The teacher, the first few days of school, should adjust his program to the school, not his school to his program. When this program is The Program adjusted to the peculiar needs of the district, should be •' ^ Adjusted to there is no reason why it should not, but every *^^ school, pedagogical reason why it should be followed. Some of the benefits to a teacher personally are: 1. System in his school work, in his professional studies, and in his other activities tor personal and profes- sional advancement. ^ 2. Increase of power as a teacher, arising from necessary preparation for each recitation. The familiarity with the contents of the texts, and with suitable supple- mentary matter, gives power that can not be supplied 36 THE MISSOURI SUPERVISOR. by an acquaintance with other texts. The true teacher, by skillfully directing the pupils, enables them to take from the lessons their meaning, and creates in them the consciousness of power. Text books are their What a . , . f . , , Program does guidcs, and contam the mtormation to be glean- for a Teacher. ed by them. Supplementary work is necessary, but it should not take the place of the text. Limited time for recitation demands extended preparation. Extended preparation brings professional power. From the student's standpoint, some of the benefits to be derived are: 1. He receives justice. There is no justice in giving to one class time that rightly belongs to another. Usually, in such cases, the time is taken from the many for the few who are in the upper grades. "The great- What a , 1 ,1 1 1 1 1 1 Program does est good to the greatest number, should be the for the Pupils. watchword Oi every earnest teacher. With eighty-two per cent of pupils in the first four grades, justice requires that those above this point should not be permitted to have time that belongs to those below it, simply because the teacher does not happen to like the lower grade work, and wants to take a review in higher subjects. The best teachers are those who are successful in the lower, as well as, in the upper grades. 2. The students become accustomed to system, and use it in whatever they do. ,, The habit of doing all things with system is soon formed, and is, in itself, invaluable. 3. Sell-control is strengthened. Students learn to give up individual preferences for the opinions of others. 4. Ihey receive a greater return from the schools. DAILY PROGRAM FOR DISTRICT SCHOOLS. 37 They study- more, assimilate more, learn self-reliance and to do a definite work in a given time. In many ways they are made stronger by adjusting their actions to the program. PROGRAM FOR DISTRICT SCHOOL. s a v 3 -a d C 1 f 3 "O 2 2 c c u u a 4; ° 2 ■a 13 Fourth Group, Fourth and Fifth Grades or both Combined. Fifth Group, Sixth & Seventh Grades or both Combined. ft 2 6 S o5 w 9:00- 9:10 10 OPENING EXERCISES. 9:10- 9:20 9 -20- 9:30 9:30- 9:45 9:45 10:05 10:05-10:30 10 10 15 20 25 Num Arithmetic Arithmetic Arithmetic Arithmetic 10:30-10:40 10 RECESS. 10:40-10:50 10 150- 11:00 10 10 10 10 10 15 15 His. or Civ. Gov. of Mo. Reading.. Reading.. Geograpiiy 11:20-11:30 11:30 11:45 11:45-12:00 Elm. Geog. (Civ. Gov. < or Shi'n's Com. Geog. (U. S. His. 1:00- 1:05 05 10 10 10 10 10 '5 20 OPENING EXERCISES. 1:05- 1:15 1:15- 1:25 1:25- 1:35 1:35- 1:45 1:45- 1:55 1:55- 2:10 2:10- 2:30 Reading.. Reading .... Reading .... Reading .... ...... •-— ^ mg Physiology Writ iug Writ mg 2:30- 2:40 10 RECESS. 2:40- 2:45 2:45- 2:50 2:50- 3:00 3:00- 3:15 ^•.i5- 3:30 3:30- 3:45 3:45- 4:00 05 05 10 15 15 15 Lang-age Lang'age Lang'age .. Lang'age.... ( Patrick's (Gramm'r Spell .;!;".l'.'..Spell Pat.Gr'm'r Speil '"g ing iiig 38 THE MISSOURI SUPERVISOR. COMMENTS UPON THE DISTRICT PROGRAM. The program above provides for the teaching of all common school books adopted by the Missouri Text. Book Commission. Should a school not use all the books, it will be an easy matter to divide the time among The Program i • i • ,i for Adopted Other subjects, leavmg the program practically Books. as suggested. All schools should be worked up till they can give this common school course provided by our laws. No teacher, however, should attempt to adjust the entire program to his school unless the con- ditions will warrant the adjustment. His judgment must be his guide in deciding what are these conditions. The Commission thought the adopted books were suitable for the pupils of the grades mentioned. A full examination, and one year's use has verified this conclusion. An inspection of this program shows that it will bring system and save time, and grade the school sufficiently close; yet, not so rigidly as to put children into an educational This Program . , . , , , . . , Grades a straight-jacket, by crowding into the same School. classes children of widely different powers and advancement. The object of classification is to facilitate work by grouping together pupils of similar attainments and advancement, thus, making one recitation serve all equally. The program provides for eight years of school, divided into six groups. It is seen that the students in the first three readers form distinct grades, while the pupils of the fourth and fifth grades are united in the Fourth Reader and accompanying subjects; the sixth and seventh grades are also united in the Fifth Reader and other corresponding DAILY PROGRAM FOR DISTRICT SCHOOLS. 39 work. The eighth has advanced to such an extent that separate classes are required. This seems a proper amount, and a rational division of labor, for pupils at their various stages of development. The consensus of the best educational thought confirms this opinion. To grade a school successfully, the teacher in charge 7nust know what is the work embraced in each grade, and the pupils, also, should know it. The program should be placed artistically upon the board, or printed upon manilla card-board, and placed upon the wall where it can be seen. A clock should be provided. Then the student soon adjusts his study to the time allowed. He also sees in what year of his school course he is, and in what branches, if any, he is behind. He is encouraged to strive to "even up" his work, and also to endeavor to complete his grade during the term. It is not recommended that a student be held in a grade, simply because he is behind in one or two branches. He should be encouraged to keep his work symmetric, and should learn to know when his advancement is har- monious. The student at one glance sees what is the work of the hour, of the day, of the term, of his school life, in the common school. It will be observed that twenty-six recitations have been provided for. The number has been made large in order to meet the necessities of any school. Should there not be so many required it is easier to form Meets the Requirements fewer classcs than to find time for more. The of any School. authors are aware that programs suggested by institute instructors, courses of study, and works upon 40 THE MISSOURI SUPERVISOR. school management rarely ever contain more than twenty- two recitations. After consulting a large number of strong district teachers in various parts of the state, they are forced to say that the great majority contain more than this number. Whenever classes can be united to good advantage it should be done. The teacher is the only person competent to decide what ones should be combined. When this is done, the time gained can easily be given to other classes most advantageously. The day's work may be said to be divided into four important groups: i. Arithmetic before recess. 2. His- tory and Geography from recess till noon. 3. Reading from noon till recess in the afternoon. 4. Lan- The Day's Work guage and Grammar from afternoon recess till Grouped. the closing of the day's session. The excep- tions to this classification are Writing, Spelling, and Primary Reading. By grouping together the various classes in the same subject, a longer time is given to the concentration of the minds of the whole school upon that particular subject. The time element can no more be eliminated from mental than from mater*ial growth. During these periods, if a student is not studying his own lesson, he hears another recite on the same subject. This continued concentration produces healthy growth. If classes on other subjects were introduced, this continuity would be destroyed, and the attention diverted. It will be observed that at least an hour is given to the preparation of almost every lesson before recitation. There can be no reasonable excuse for a pupil's not having his lesson ready. In addition to the time given by the DAILY PROGRAM FOR DISTi^rCT SCHOOLS. 41 program, the first and second grade pupils should study at least thirty minutes, and all others, not less than one hour at home. As an evidence that this has 1 J L "^^^ '^*™^ been done, a certam amount otwork should be Giveu to Preparation. required to be handed in. Home study is •worth one-third of the whole day at school. The teacher who does not have it done is losing, to a large ex- tent, the support of the parents. When they work at home the parents almost of necessity know of the charac- ter of the work being done at school, and feel an interest in all the work the child does. They render material aid to the pupil on the individual plan. The dull pupil has good lessons, and the bright one has time for investiga- tion and research. The whole community come to the conclusion that "That teacher knows his business. The children bring their books home and study every night." The foregoing program can with slight modifications, be adjusted to any Missouri school. It may not possess all the merits, but is believed to be worthy of the consid- eration of experienced teachers, and to serve as a tempo- rary guide to the inexperienced. It embodies the recommendations of the Committee on Course of Study for Missouri Schools for i8g6, the suggestions of a large number of district teachers, and the experience of the authors, modified to meet the requirements of the adopted text books. ii THE MISSOURI oujTctvviovjK.. CHAPTER III. SOME POINTS ON SCHOOL MANAGEMENT, EDUCATION AND EDUCATIONAL AGENCIES. The people of the United States expend annually in support of their schools something like a hundred million dollars. The sum permanently invested in buildings, grounds, and equipments, is several times as Cost of large. All of this money, together with the Education. vast sum given incidentally to our schools, is expended for what? A single word answers, Education. And regarded as an investment merely — forgetting the humanitarian significance of the movement — \\.pays. For, whatever the shortcomings of educators and the deficiencies of our educational system, the millions invested in educa- tion are more productive of good than those other millions expended for coast defense or armed cruisers, and much more so than the billion and a half dollars wasted annually in tobacco and liquor. Our own state sets apart nearly seven millions from her yearly income for the education of her children, and whether the burdens of taxation rest lightly or heavily upon our citizens, the moneys paid for school purposes rarely provoke complaint. SOME POINTS ON SCHOOL MANAGEMENT. 43 These facts are construed as an indication that educa- tion is in some measure, at least, accomplishing an acceptable purpose. But what is that purpose? Is it to fit the coming man or woman to "fight The the battle of life"? If this means fitting Purpose of Education. him to enter the race for "the almighty dollar," by concentrating all his purposes and all his strength upon this one end, narrowing his mental and spiritual horizon within the circumference of a silver circle, one and one half inches in diameter, the answer is a decided negative. But if the question means the getting of a living by productive labor, the answer is "Yes and much more." Education ought not to unfit one for earn- ing an honest living, either by making him impractical and unable to deal intelligently with the problems of life or by giving him distorted conceptions of his own dignity or that of profitable labor. It is a low conception of educa- tion, however, that looks only to the material side. Every normally constituted human being ought to be capable of earning an honest living, but he should be able to do more. He should be able to live rightly — to live as becomes a being endowed with the possibilities of good and evil, a being who stands at the apex of creation with the whole universe at his feet. "Not for livelihood but for life" is the expressive formula of education as enunciated by one of her ablest exponents. "Complete living," says Spencer, "is the purpose of education." Such ideals as these are worthy of, and demand the consideration of every true teacher. No sciieme of education can ignore the individuality 44 THE MISSOURI SUPERVISOR. of the pupil himself, an ever-present factor which may facilitate or neutralize the normal efficiency of the great educational forces, Home, School, Church, Agencies"''' Society, and the Press. The influence that these agencies wield varies as the individuals vary. It cannot be foretold with certainty. In the main, we have reason to expect certain results, but frequently our expectations are upset by genuine suprises. The indi- viduality of the learner sometimes asserts itself in peculiar, yet emphatic ways. The same sun melts wax and hardens clay. It is not within our province to attempt a statement of the relative importance of the various agencies named above. We are directly and immediately concerned with the work of the School. Its educational influ- The School . . as an ence operates in a variety of ways, some direct. Agency. Others indirect. Indirectly a school can edu- cate by its very presence in a community. . A university on a Stanford estate, a modern ward school in a crowded city, or an "up-to-date" school in a rural community can edu- cate their respective neighborhoods. There may be "ignorance in the shadow of Harvard," but there would be more ignorance were there no Harvard. A school educates many whose names are not on its rolls. It may be able to imbue not only its pupils but an entire commu- nity with a healthy educational spirit. It is positively invigorating to inhale the educational atmosphere of some schools and some communities, and as killing to breathe that of others. Pupils, teachers, patrons, visitors are alike stimulated. Sometimes this influence, whether good SOME POINTS ON SCHOOL MANAGEMENT. 45 or evil, emanates primarily from some citizen, who may or may not be a member of the board, but generally it de- pends, if it be a good influence, for its inception, at least, upon the teacher. And this brings us to the consideration of the principal factor in the success of ever}' school. This influence of the teacher in moulding educational sentiment in the school and for the school is of the first importance and should be regarded by the teacher as a legitimate responsibility. The needs and con- ditions of the community and the capabilities Educ-itionai .' ^ Sentiment. of the teacher must determine what shall be done, but the resourceful teacher will do something to arouse such a sentiment. It may be the organization of a rending circle among the young people of the community, or among the older pupils, or of a liter- ary or dramatic club under proper restrictions. It may be through the school library, through interesting general exercises in the school, or through other ways that the tactful teacher will devise. The fact remains that in many, very man}' communities, both rural and urban, this sentiment is almost entirely lacking. It is to be hoped that every such community will soon produce or im- port a leader with the grace and grit to save it from itself. The teacher ought to be the educational leader of the community, whether that community be as populous as a Greater New York or no more so than the most sparsely settled rural district. He should rank in educa- tional matters as high as the physician, lawyer, and minister do in their spheres. In minor cases we may see fit to dispense with the services of all, but in the serious 46 THE MISSOURI SUPERVISOR. ones we go to those who profess to know. We seek out the specialist. The teacher should be a The Teacher ^^/" ,. , specialist in his sphere. He should be oen ilducational ^ ^ ^^^ ^''- whose advice upon the difficulty of locating a school site, the construction of a school building, the pur- chase of school supplies, the ventilation of a room, the selection of a good book, the care of an injured child, the avenue to a boy's affections, the choice of an occupation, or any one of a score of similar matters, would be safe and valuable. When a community finds such a leader, it will be loth to let him go. Sometimes ignorance or prejudice m?y try to drive him out, but rarely will it succeed. Such qualities as those enumerated above, together with those directly related to the work of instruction, will call for a remuneration of more than twenty-five dollars a month, for six or seven months of the year. But is it a manifes- tation of over-confidence to say that such teachers will not long be kept at such wages? Is there not sufficient liberality, aye, is there not sufficient business-sense, among Missouri's tax-payers to lead to a fair reward for such services? It is pleasant to dream of a time when in many a Missouri community there may be found a man or woman who will long have been recognized as the educa- tional leader and guide — loved and respected by all, amply qualified in all that pertains to the work of education and amply remunerated to banish all fears of want immediate or remote. And must it be forever only a dream? Much has been written upon the qualifications of the teacher, and legislators, actuated by a desire to protect helpless childhood, have legalized attempts to ascertain SOME POINTS ON SCHOOL MANAGEMENT. 47 whether would-be teachers possess a certain standard of qualifications. The perennial discussions of "the certification of teachers" at educational meetings, state and national, and the biennial efforts of our own General Assembly to amend existing laws, show that the law makers have not arrived at an entirely satisfactory method of determining even a minimum of qualifications. Furthermore it is everywhere conceded that no test save that of actual ex- perience is altogether satisfactory. There are Qualifications. some very desirable qualities which no exami- nation can reveal, some elements of a teacher's equipment that must be sought through other means. Here lies one of the strong arguments for the supervision of schools. With much ingenuity and nicety of detail the "Qual- ifications of the Teacher" have been outlined by a number of writers. We purpose neither rivalry nor plagiarism. Yet we do desire to set forth a few of the teacher's qualifi- cations- — partly to emphasize, partly to supplement. The first qualification that is usually demanded by examiners, patrons, and school officials is scholarship. It is extremely doubtful whether the prevalent notions corresponding to this term are at all times clearl}' defined and at all times correct. But suffice it to say that the term ought to stand for much more than it now does — far umore than our current system of examinations can possibly reveal. It is unquestionably true that the standard ought to be much higher than it now scholarship, is. Less than a year ago two would-be "first-grade" teachers were unable to state in an institute 48 THE MISSOURI SUPERVISOR. the name of the ruling sovereign of Great Britain, a dozen n ore could not tell the temperature at which water freezes, and thirty-three out of a total of eighty-two failed to name three American poets and three poems of each. It is possible that a person may be an excellent teacher and lack a knowledge of these things, but the probability is that these deficiencies are matched by others equally glaring. It is not assumed that the teacher's knowledge should be encyclopedic, but to the question, are the per- sons just mentioned qualified to teach Missouri's boys and girls? There is but one answer — an emphatic. No. A radical and sudden change of standards is, of course, inadvisable, but one sufficiently marked to he noticeable is necessary. The interests of our schools demand it, ard surely the time is not far removed when public sentiment will join in the demand. "A four years' high school course for all grade teachers" may startle us now, but the time is com'ng v\hen this will be demanded, and those who are progressive will begin to prepare for it now. With so many good higfi schools, academies, colleges, state normals, and universities ' accessible, there are but few who will to do so who can not equip themselves with a broad general culture. Reform ought to come in three places — among teachers themselves in a professional spirit that will compel higher scholarship; among lu ensing officers in a determined effort to supply existing deficiencies; among patrons and the general public in a demand that their school rooms be barred against incompetency. A second qualification is a clear conception of the SOME POINTS ON SCHOOL MANAGEMENT. 49 objects and nature of education. It is feared that 100 m my teachers go about their work with very indefinite notions of what can and ought to be accom- plished in the school-room. Oh Education! conception ol Education. Education! How many crimes are committed in thy name! Sometimes, well-meaning and conscien- tious teachers lack this right conception of their work. Too frequently, however, the important work of teaching is carried on by those who are supremely indifferent to all the higher ideals of their trade and whose definition of education, if truthfully written, would be, "The popular institution which seems perfectly willing to employ me at a good salary with the privilege of doing just as little as possible in return." Is it not time that teachers were asking. What is Education? What is it for? How is it to be accomplished? Am I tit for the work? What is my duty to my pupils? Closely associated with the foregoing, is a third qual- ification, love for the work. Novice, if you do not love children and cannot interest yourself in them, keep out of the profession. Teacher, do you dislike your work, do you "hate the whole business," do ^ove for ' -' the Work. you find the work a task, are you teaching "for revenue only"? If so, resign at once. Get out of the profession. "The place whereon thou standest is holy ground." The true teacher so loves his work that there is a constant temptation to overstep the limits of time, a constant desire to do more than has yet been done, a con- stant striving after better things in matter and method, a constant longing for the strength and wisdom necessary so THE MISSOURI SUPERVISOR. to faithful work. If these things be in him and abound he will be neither barren nor unfruitful. There should be not only a love for the work, but also a love for work. He who has an insuperable aversion to all kinds of hard labor will never satisfy us as a teacher. The laz}' teacher — God pity his pupils. Very few people — and children are not exceptions — have respect for a lazy person. On the other hand, we innately respect him who can work and is willing to work. The lazy teacher "is too lazy to do anything else;" he is too lazy to get to school ahead of time; too lazy to take an occasional romp with the children; too lazy to be on his feet frequently; too lazy to sacrifice his own personal ease to help a slow or unfor- tunate pupil; too lazy to plan and prepare his work; too lazy to teach except "by the book;" too lazy to draw his salary — never. The teacher should be pre-eminently a person of "good habits," including in that phrase much more than the popular interpretation demands. Our ideal of the teacher is a high one — but better to err with ^°°'?, virtue than to shine with the lack of it. High Habits. o ideals rarely discourage; low ones frequently destroy. Therefore, beyond the commonplace virtues of truthfulness, honesty, temperance, and purity, we de- mand of our teacher such other habitual virtues as prompt- ness, perseverance, neatness, politeness, modesty, patience, order, and self-control. These habits should not be of the spasmodic type. They should constitute the warp and woof of his being. Other elements in the teacher's equipment might be SOME POINTS ON SCHOOL MANAGEMENT. 51 named, but their enumeration would be foreign to our pur- pose. We pass to the consideration of the teacher's work. The teacher's part in arousing and maintaining a liealthy educational sentiment in the community has been considered. The more commonly recognized lines of his activity are instruction and discipline. Both require a high order of ability and both are not Teacher's Work. necessarily within the power of every teacher. Of course, everybody can instruct — after a fashion, as he can govern — alter a fashion. But the ideal instructor and the ideal disciplinarian combined in one person live mostly in theory. The former is he who can guide success- fully to self-instruction; the latter, he who can guide suc- cessfully to self control. It is a faulty conception that regards instruction as a mere in-pouring of facts. It is rather, as its etymology suggests, an in-building; but it should be that sort of in-building that goes on within a tree, or an animal body, in which the crude material is built into living tissue and becomes a vital part of a living organism. The teacher should strive to make his instruc- tion equally vital. Facts, so far as their impartation is a factor in instruction, ought to be the crude food-elements which, by such mental processes as the teacher shall direct, are to be assimilated and incorporated into the mental organism. The result of such an acquisition will be a symmetrical development, a growth of all the powers of mind. Discipline ought to do for the emotional and volitional natures what instruction, as outlined above, does for the intellectual nature of the child. Precepts, rules, maxims, 52 THE MISSOURI SUPERVISOR. should be acted, lived, by the child, from motives of his own and from choices ol his own. Herbart is undoubtedly correct in assuming that, in education, the most important element — the whole of it, he would say — is morality. Judged from this standard what a woeful affair we make of education! How little we are doing, or, at least, how little we are doing well, toward the development of a self-direct- ing morality, which is the only true morality. Let us hear the conclusion of the whole matter. That teacher fails in his duty, who has not trained his pupil to self-instruc- tion and self-government. THE FIRST DAY OF SCHOOL. The novice in teaching, unless he be of those who rush in where "angels fear to tread," looks forward with trepi- dation of spirit to "the first day of school." And well he may, for in many respects it is the most important of the term. In the hope that something may be said to help the teacher over the difficulties of this, the hardest of all days, this section is written. Primarily it and the one fol- lowing are written with the rural teacher in mind, but it is hoped that these sections are worthy of the attention of all teachers. The first day's labors, like those of any other day, can be lightened by preliminary preparation and foresight. No day's labors, much less those of the first, should be begun without a plan. This should include a clear f , . 1 , , , • • Preparation conception of what is to be done and how it is for Battle. hoped to do it. Both of these points can be determined only after the teacher has studied the condi- SOME POINTS ON SCHOOL MANAGEMENT. 53 tions under which he will have to labor — size of school, previous classification, educational sentiment of commun- ity, educational needs of community, social and financial conditions of community, school equipment — building, grounds, apparatus, furniture —and, in the light of these conditions, has estimated the educational possibilities of the community. To determine these matters satisfactorily will require a study of the records left by the former teacher, and, if possible, a conference with him, a friendly talk with the board, and, if necessary, with some of the patrons and pupils, and a visit to the school building. A teacher well known to the writers went to her school-room on the morning of the first day, and found the seats loose from the floor and piled in one end of the room. Such a state of affairs will never lighten the first day's labors. The school-room should be clean, and the teacher may have to see to the cleaning. A school record, a bell^ crayon, and drinking vessels should be at hand. Before or during the first day, each teacher must solve the question of classification so far, at least, as it concerns his school. In this matter there is much room for diversity of judgment and for serious error. There are two extremes — the one, the individual, 5'^''?-- "go-as-you-piease" plan, once almost univers- ally prevalent in rural schools; thp other, the "iron-clad"' gradation of many city schools. Most rural and village schools have grown out of the former, and happily, they cannot attain the latter. How much classification is best has not been fully determined. On a few points, how- ever, there seems to be agreement. It is conceded, for 54 THE MISSOURI SUPERVISOR. example, that there is both economy of time and a posi- tive gain in recitation benefits in a certain degree of clas- sification. On the other hand, there is a harmful loss in throwing together in the recitation pupils of widely differ- ent powers. The ideal would be classes of moderate size with frequent promotions, the intervals not exceeding three months. This is fully possible only in large city schools, and but few of them have seen fit to try the plan in its fullness. In rural schools, there can be not even an approach to it until we abandon our present school unit — the district. When this extravagantly expensive and pedagogically unwise plan shall have been abolished, we can hope for that degree of classification that will be pro- ductive of great good. The Committee of Twelve pointed out that eighty-two per cent of all public school pupils are in the first four years' work, and the suggestion of this Committee is the consolidation of the pupils above this grade into Central Schools. If the six or seven schools found in many congressional townships in our State were controlled by a common board, four of them could easily care for all pupils in the first four years, a fifth centrally located could, with two teachers, provide better instruc- tion and at least one year more of it than our present sys- tem can possibly furnish. It is doubtful whether in many townships, there would be any increase of cost whatever. And if there were a slight increase of cost, the character of the instruction would be so much improved that the in- crease of taxation would be willingly borne. But many years may pass before we secure this re- adjustment of our school affairs. Until the change shall SOME POINTS ON SCHOOL MANAGEMENT. 55 come, teachers must labor as best they can under existing conditions. And what is the teacher to do? First, we reply, there must be a recognition — a fuller recognition than most teachers now seem to have — of the importance of educational symmetry. Under the mistaken idea that all of life is wrapped up within some one "practical" study, pupils are allowed, aye, even encouraged by both teachers and parents to "specialize" on that particular subject. Generally, though not always, that subject is Arithmetic. In any case, the teacher should realize and endeavor to get pupil and parent to realize that the student who has "ciphered through the Arithmetic" without any knowledge of Geography or the ability to write correctly an English sentence is educationally "unbalanced." This does not mean that on the very day on which the pupil is "ciphering" on page 147 of Blank's Arithmetic he must be parsing the sentences on page 351 of Dash's Grammar. But it does mean that there is a more or less clearly pre- scribed amount of work in the study of his mother-tongue that ought to accompany equally clearly prescribed amounts of work in otiier lines, and the pupil ought to advance along these several lines proportionatel}'. Harm will come, of course, if this system be made too rigid, but in nearly every rural school there are pupils whose work in Mathematics is from one to five years ahead of their work in Language, and the}'^ need "righting up." The aim of the course of study published elsewhere in this book is to set forth what is thought to be equivalent sec- tions of work. It should be used frequently as a sort of spirit-level to test the levelness of the pupil's educational THE MISSOURI SUPERVISOR. Structure. Recognizing that the school course extends over some eight years and includes five or more general types of work with some "extras;" then, a strict gradation would call for more than forty recitations each day, a number entirely too great for the length of the school day. This number must, therefore, be reduced. The reduction be- gins with such subjects as penmanship for which the skillful teacher needs but one time period, even though there are different grades represented. In no subject will it be necessary to maintain the theoretical eight classes. The exact number to be maintained in each subject must be determined by the condition of the school. In the .suggestive daily program which is given elsewhere, the aim is to show how the condensations may be effected. In the light of the best information at his disposal the teacher prepares a program for the first day. He may be able to approximate closely to what will be his permanent pro- gram; the nearer, the better. At the same time, unless there is good reason for it, he should introduce no startling innovations. At no time should he purposely cast reflec- tions upon the work or methods of his predecessor. Where innovations are introduced they should be explained, so that all can comprehend. The work of the first day should begin on time. Pupils will seat themselves, and, except for manifest reasons, this seating ought not to be changed for the present. If possible, and-it is nearly always so, a familiar song may be sung. Its influence will last through that day and many subsequent days. The teacher will show his skill by getting everybody to work at once. This can be ac- SOME POINTS ON SCHOOL MANAGEMENT. 57 complished by assigning preliminary lessons to all the reading classes. Chart pupils may be given a "picture book" for entertainment and possibly to cultivate friendly relations toward the teacher. Those beyond the fifth reader will probably study History and may have a lesson assigned them. The others, if there be others, may be assigned work in some other branches. Everybody is now employed. The teacher, as rapidly as possible, makes the rounds of the room, confers with each pupil,^ inquires kindly concerning his studies and gets his name on a previously prepared slip. The inquiries made will reveal much concerning the classes needed and the places of beginning work. The teacher can now write upon the board the assignments of lessons for classes in Arithmetic and Geography. (The most of this should be review work.) The reading classes may now be called in order, beginning with the primary. The recitations should be brief, but each pupil should participate. At the close, assign work for the next recitation and state when it will be expected. In this way go through the program of the day. "Push things." Keep everybody busy. Organize every needed class if possible. Have every exercise brief but significant. Watch the classification and the work to determine the needs of individuals and of classes. Intro- duce tactics as needed — as classes are called and dismissed and in dismissing and calling school. Let everything be done decently and in order. At the close of the day's work announcements should be made concerning the next day's work, time of beginning school and the like. A few simple rules may be announced, if the teacher thinks best.. S8 THE MISSOURI SUPERVISOR. Some teachers, apparently, can dispense with all rules. Many others have failed in the attempt. If rules are adopted, they should be general, few, simple, and justifi- able even to a child. They should be presented as the needs of the school and not the arbitrary fiats of the teacher. School government, whether by rule or without rule, should instill self-respect and encourage self-control. It is not likely that there will have been any serious breaches of propriety during the day. Should there be, they must be dealt with on their merits. Should a dispo- sition to "whisper" manifest itself, the teacher will politely ask that the act be not repeated, because of its disturbing others. Should it be repeated, the offender should be reminded of the former request. Very rarely will it be difficult to get through the day without trouble. At the close, or earlier if the teacher thinks it best, his policy in regard to the matter, may be announced. In some way, however, every school ought to recognize the fact that whispering is an evil and forbid it. When all the business of the day is over, sing a rousing song, and dismiss in order. Before returning on the morrow, the teacher should review the first day's work thoughtfully, profit by all its experiences, and plan his work for the second day. ANOTHER DAY AT SCHOOL. Important as is the "first day," the whole term can not be judged by it. Neither can it be taken as a pattern by which all other days are to be cut. There are certain phases of school work that do not develop until after the SOME POINTS ON SCHOOL MANAGEMENT. 59 permanent organization is effected. Were we to look in upon a dozen "good" schools we should find that each has its individuality — no two are exactly alike. It is under- stood, therefore, that a school may be successful and not be modeled after a successful neighbor. Neither do we claim that to be pronounced "good" must it be patterned after the one herein described. We aim in these following par- agraphs merely to picture a school that was counted successful, and, according to our view, one that merited that judgment. In this school the teacher was at his post of duty a full half-hour before nine o'clock. He saw that the room was properly warmed. He placed any needed work upon the board. He was there to speak a pleasant good morning to the pupils as they entered. Earjy ° ^ "^ '^ •' Arrival, His mere presence served to exercise a whole- some influence over the assembling pupils. There was no shouting, no scuffling, or running over desks. There was animated conversation, however, in which teacher and pupils joined, and in which the courtesies of life were duly ob- served. Five minutes before nine the bell was rung, pupils who were indoors passed quietly to their seats; those upon the play-ground formed in lines before the door and on signal marched into the school-room. The building being a modern one, has a cloak-room, through which the lines passed and in which the wraps were left, each in its ap- pointed place. Had there been no suitable cloak-room, the wraps might have been gathered by monitors on the in- side. At nine o'clock the teacher's bell proclaimed that school had begun. The few absentees, some of whom came 6o THE MISSOURI SUPERVISOR. in later, were quickly noted without a formal roll-call. As a rule, however, there was little tardiness and absence, both of which are inimical to successful work. No school can be counted successful in which there is much of either. From the first day the teacher of this school Tardiness ^ ■, ■ • • r and had striven to create a sentiment in favor of Absence. regularity and punctuality. By beginning in the long, pleasant days of autumn, it was easy to set the sentiment going with such an impetus that even the short days were not able to overcome it. There was no scolding, but by appealing to the nobler feelings of child- hood, and above all, by making the work so interesting that every day and especially the beginning of everyday was counted a thing too valuable to lose, the main point was gained. Wide-awake, enthusiastic pupils were set to work upon the laggards. Parents were visited. All these and many other things were done, and can be done again by every teacher, toward breaking up that lamentable irregularity and lack of punctuality so prevalent in many schools. There are worse things than tardiness and absence, it is true, but few schools have to contend with them. The teacher who succeeds by rational methods in overcoming these twin evils, will find that many others will disappear in their train. It is possible to use silly or barbarous methods to overcome them. Such, of course, are to be avoided. That which will come nearest to being a "sure cure" is interest, and this should be the teacher's first recourse. Following the roll-call were opening exercises. These were varied from day to day. One morning they would con- SOME POINTS ON SCHOOL MANAGEMENT. 6% sist of interesting chemical or j)hysical experiments. (Many such have been described in the Youth's Companion.) The next day there would be a opening ' ■' ■' Exercises. few short recitations by different pupils, and quite frequently there were songs sacred and secular, (but not sillv), in which all joined. Occasionally the news of the day was presented in a "paper" edited by the language classes. Sometimes an interesting story or chapter from an interesting book, the Bible included since there were no objections, was read. "Queer queries," concerning the common things of the world about them elicited interest and enthusiasm. Science lessons on such topics as "How coal is made," "Where rubber comes from," "What the moon is like," etc., were given. An interesting biography, now and then, was included. Memory gems were recited occasionally. "Whittier's Day," "Washington's Birth- day," and the like had literary and historical value. Health lessons, good morals, and gentle manners appeared. A program committee assisted the teacher and helped to increase the interest. The influence of these opening ex- ercises toward preventing tardiness and absence and increasing the interest of both pupils and patrons, aside from their culture value, was great. After the opening exercises were over, the teacher gave such general explanations as were needed, and the school settled down quietly to its legitimate work — study and recitation. A program, printed by the teacher, upon manilla card-board, was con- working by ^ ' Schedule. stantly before the school for the guidance of both teacher and pupil. If the teacher is in touch with 62 THE MISSOURI SUPERVISOR. his pupils, he can soon determine whether they are rightly- dividing their time. It will not require many days to de- termine this. Then if it be ascertained that the pupil is neglecting his Language work for his' Arithmetic,his Geog- raphy for his History, or any or all for an interesting book, a change can be effected. In our school the time and attention of the teacher were almost entirely occupied with recitations. True, the least inclination toward evil was sure to find the all-seeing eye of the teacher turned full upon it, but in spite of that the teacher taught with all his might. There were no- interruptions, requests, or questions from those who were not reciting. The books, pencils, knives, etc., Schooi-ioora were providea m advance, and each pupil Conditions. Studied his own lesson. Each decided for him- self the propriety of any movement from his seat, knowing full well that the abuse of any privilege meant an abso- lute forfeiture thereof. Feet and books were moved quietly, because each had been made to feel that unneces- sary disturbances were absolute thefts of time. There are but few pupils so obstinate that they will persist in causing disturbance after the matter is properly presented by a teacher for whom they have respect. When a general spirit of listlessness seemed to be developing, all work was put side for two minutes while a song was sung or a calis- thenic drill given with several of the windows open. Pure air is an efficient ally of law and order. Many an insur- rection has been suppressed by this agency alone. In the passage to and from recitations, to the black-board, and about the room the same principles governed. All work in SOME POINTS ON SCHOOL MANAGEMENT. 63 which a number participated was directed by signal. Rise, Pass, Seats, Turn, Erase, and the like, were frequently heard and promptly obeyed. The recitations showed preparation on the part of the teacher and pupil. Each member was interested and any lagging was instantly detected. The recitation was more than a "quiz." It was a place of positive teaching. Something new was constantly evolving. The relations of teacher and pupils were free from constraint, yet respect- ful and genteel. There was no scolding. Work was ready because pupils knew that no work escaped preparation. It was only a question of now or later. The attitudes of teacher and pupils, in the recita- The ^ '^ ' Recitation. tion or out, were never unseemly. Tones were low, yet distinct, and the language employed was as good as its users could make it. Questions were asked and di- rections given but once. Hands were raised to indicate a willingness to answer. Pupils were encouraged to ask appropriate questions, and the uplifted hand indicated such a desire. Pupils were not called upon in any definite order. No one knew when his time was coming, except when he became inattentive. Bright pupils did not monopolize the time. Every mind in the class was kept on the alert from beginning to end. With this teacher every recitation was a part of a general scheme. As such it served to further a certain general aim. But in addition to this general object, each lesson had its own specific purpose or purposes. It might serve to test the pupil's preparation of work assigned; to give a drill in thoughtful expression; to ascertain the further needs of the pupil; to 64 THE MISSOURI SUPERVISOR. provide needed help by question, suggestion, reference, or statement from the teacher and by the variety Purposes. of ideas and modes of expression among pupils; or to impress ideas by the various forms of review that the recitation furnishes. Sometimes several of these ends were sought through the various phases of the recitation or even through a single aspect of the lesson. But such a thing as a purposeless recitation or even a recitation without a definitely recognized pur- pose was unknown in that school. To secure these ends requires effort — forethought and determination. The teacher is the principal factor in the success of the recitation, although the pupil also has a part. The teacher's part begins in his preparation for the assignment of the lesson. The term "preparation" is used advisedly. Lesson assignment ought to mean some- thing more than a mere, "Take the next." The nature of the lesson itself, the capabilities of the pupils, the amount of time at their disposal, the relations of this lesson to past and future lessons, the amount and kind Assigning of help necessary, all should be in the teacher's Lessons. ^ •> ' thought in making the assignment, and to get them there requires effort. After the teacher has deter- mined what the assignment shall be, he should make it with such unmistakable clearness that no pupil can mis- take the amount or nature of his work. The time neces- sary for such an assignment, even for writing it upon the board, occasionally, will be well invested. This definite- ness rarely precludes an assignment in such form as to accommodate the varying capacities of the pupils. If the SOME POINTS ON SCHOOL MAMAGEMENT. 65 lesson be assigned topically, yet skillfully, the weakest and the strongest alike can employ the full time allotment. When the lesson is once assigned, it is, in a measure, handed over to the pupil. Knowing what is expected of him and knowing it will be required of him, he sets about his work. Whatever preliminary preparation .^a^- 3 is necessary, he makes. If he be an ideal stu- of the ( lycsson, dent, he enters into the work with a vim. His entire thought is given to the contest at hand. With con- fidence in himself and in the teacher's judgment in the assignment, he expects, he desires nothing but complete success. The artifical and external incentives which must be applied to others are not needed for him. His motive power comes from within. He has learned that he has power and how to use it in genuine effort. In short, he has acquired the power of self-direction — he can study and wills to study. Before the hour for the recitation artives, the teacher finds time to take up the lesson in. detail and plan its presentation. He determines the method — whether interrogative, topical, or lecture — the sequence of topics and the amount of time each shall receive, the supplementary matter to be introduced, the illustrations necessary, the management of each class so that each pupil shall get the greatest possible benefit. He refreshes his knowledge of the lesson so that it stands out clearly before his consciousness with its relations distinct. Fresh from this preparatory review, the teacher meets his pupils and imparts to them his own fervor of thought. There can be nothing cold or lifeless in such a recitation. 66 THE MISSOURI SUPERVIbOli. Sympathy of interest prevails. Sincerely and earnestly does the teacher strive to make this recitation the means of putting into the soul of the pupil something that was not there before. For such a recitation, a beautiful room, slate blackboards, library, apparatus are but accessories. There are but two vital and indispensable elements in that organic unity — these are teacher and pupil. Given a Garfield and a Hopkins and the recitation is a foregone suc- cess, even with a log for a recitation-seat and the forest for a school-room. Under ordinary circumstances, however, it must be admitted, Mark Hopkins will have a much easier time with his Garfield, than he would likely have as teacher of a class in the ordinary grammar or high school. In other words, it is less difftcult to stir the soul of one Garfield to a white heat, than to arouse a perceptible warmth within the class of forty. So varied are the tastes and capabilities of the forty that despite the teacher's enthusiasm and mas- terly comprehension of the subject, some there will be who will fail to catch his spirit, and hence the need of good judgment relative to the more mechanical elements of the recitation. There may be such mismanagement that even the fullest familiaritv with the lesson and the most glowing enthusiasm will not avail. The teacher must not keep his eye so continuously fixed upon the stars as to fail to take an occasional look for possible obstructions to his feet. In the ideal recitation the confidence of the pupil is not abused by a manifest failure. Neither is he purposely kept in the dark concerning the purpose of the re citation, as the manner of some is, until a final "grand stand play" SOME POINTS ON SCHOOL MANAGEMENT. 67 can be made. The ideal recitation is not developed on the plan of the modern novel with a resplendent climax at the end of a protracted mystery. It is not expected that the pupil will foresee the end as the teacher sees it, neither ought the pupil to be expected to relish a shock of enlight- enment at each initiation into some new truth. Another characteristic of this ideal recitation is concentrated thought on the part of the pupils. With the end, so far as they perceive it, as a goal, they employ their energies in hard, steady, consecutive thinking. The teacher's method is such as to direct them into channels of contin- uous thought, and the pupils have sufficient power to keep themselves there. In too many recitations, neither teacher nor pupil seems to have the power of persevering. They move by jumps which are as likely to be backward or side- ward as forward. Questioning is the usual avenue by which the teacher enters the pupil's circle of thought. The primary purpose of questioning — that of eliciting information — is lost in class questioning, and other ends take its place. „. . , . ... Purpose ihe primary purpose of class questioning is of Questioning. not always the same. At one time it may be to test the pupil's recollection of certain facts or his preparation of certain work. At another it may be to ascertain the correctness of the pupil's ideas or his degree of comprehension of a given subject. Again it may be to direct and develop thought, thus leading him into paths which his feet would not otherwise tread. These objects increase in dignity and importance in the order named, and although it may not be claimed that the 68 THE MISSOURI SUPERVISOR. last is the most general aim of class questioning, it may be said that no other equals it in value. , Nevertheless, it is true that much class questioning never rises beyond the dignity of a mere memory test. Fellow-teacher, what is the object of your questioning? Is it insti-itciivc, educative? Does it guide and stimulate thought? There are times, of course, when the desire is to ascertain what the pupil knows and how correctly he knows it, but too few are the teachers who know of the higher value of questioning. The form of questions must be governed, in part, by their purpose. If the aim be to direct and develop thinking, certain forms are at once excluded. There will be neither guidance nor development in questions that are ambiguous or indefinite, or those that overwhelm the pupil, in those that require an answer of merely j'^i' or no, or put a pre- mium on guessing. Questions should be concise, varied, and suitable to the advancement of the pupils. The answer should be concise, yet complete, in full statements, usually, and pertinent to the question. These qualities our teacher endeavored to embody in his class-work. In the meantime his spirit is felt throughout the school. He governs by encouraging right and preventing wrong — by appealing to the pupil, in the best ways possible, to choose to do the right, prevent- ing, by creating an atmosphere unfavorable to wrong-doing and one not in sympathy with it. Success in school gov- ernment depends largely upon the ability to repress the evil and develop the good until the latter obtains undis- puted sway in the life of the individual. The evil is repressed by allowing neither time nor opportunity for its SOME POINTS ON SCHOOL MANAGEMENT. 69 development. Pupils who are kept constantly busy under the watchful, sympathetic eye of an honorable and capable teacher and who feel constant appeals made to a noble principle within, will soon yield to the good. Rare will be the exceptions. If the teacher has the tact to force his pupils to assume the responsibility for their own choices of conduct, they will generally choose right. Good disciplinarians are seldom made by precept. But imperfect ones may be helped by suggestions. The following rules for the teacher will be suggestive, at least, if thoughtfully considered: 1. Be capable in teaching. 2. Be honorable in action. 3. Have ideas of right and stand by them. 4. Be strong, not vacillating, 5. Begin to govern in time. 6. Keep pupils busy. 7. See everything that happens — before it happens. 8. Appeal to the best that is in every pupil and compel him to realize the character of his acts. 9. Be not afraid to talk with a pupil alone. 10. Let the offender suffer the natural consequences of his wrong-doing, as far as possible. In concluding this chapter on School Management, the authors desire to emphasize the fact that it is onl}'' a chapter that they have attempted. A "philosophy" of the subject is beyond their aspirations. To set this forth some helpful suggestions has been their Chapter. desire, the height of their ambition. TO THE MISSOURI SUPERVISOR. PART SECOND. CHAPTER I. READING. INTRODUCTION. Reading ranks first in importance in any course of study. Without it no other subject could be pursued. No other subject influences human conduct so much. Religions and forms of government are changed by it; Reading iu a Course of the achievements of the past are laid at our study. feet through its influence; illustrious deeds of departed heroes are held up for our admiration; the philosophy of the ancients is compared with that of the present; through it, we receive the choicest thoughts of the greatest intellects of all ages. Through it, we are enabled to converse with Homer and Aristotle; with Virgil and Caesar; with Caedmon and Bseda; with Chaucer and Spenser; with Bacon and Shakespeare; with More and READING. 71 Milton; with Whittier, Bryant, Longfellow — any poet, historian, or philosopher of any age. Reading is the key that unlocks the storehouse con- taining all knowledge. What, then, can be said cf its importance? Who should be able to reap its benefits? How well should it be understood? When should it be commenced? What are its dififi- importance of Reading. culties? "There is no other subject so important" is the universal answer. Every intelligent creature with a soul to expand should receive its benefits. Without it, mental growth would almost cease; the energies of a people would be confined to narrow limits; gossip, scandal, and ignorance would take the place of discussion, social intercourse, and intelligence. It should be so well understood b}^ all that the thought and feelings of the author as represented upon the page should be instantly presented to the reader's mind with- out waste of mental energy in removing difficul- ties. The eye of the reader should possess Thoroughness -^ ^ in Readiug. such skill that the instant it catches the word the idea should appear in his mind, and he should scarcely be conscious that the word is there- — he is conscious of the soul of the word, the idea, but not of the word itself. Reading should be so mastered that the reader feels a keen interest in the article read; feels that he is listening to the narrative by the author in person; he should l1 of the beneficent results sometimes claimed for it. It is pos- sible to "go to seed on mathematics." This not Too much . , , . , of a Good mfrequently happens and not alone to those Thing. country boys, who in their desire for "practical" arithmetic refuse to study almost everything else. What- ARITHMETIC. 117 ever may be the final decision of the educational experts as to the prominence of the mathematical element in a model course of stud}', it will not be questioned that in many of the rural schools of our state this factor is receiv- ing undue attention. What shall it profit a boy if he gain the ability to solve every problem in the classic "third part" and lose the lessons of History, Literature and Science? Or what shall he give in exchange for the ability to speak or write correctly an English sentence? It is not that he should love Arithmetic less but that he should love other things more? Before taking up the matter of method in its applica- tion to the various divisions of the subject of Arithmetic, certain general principles, which will be kept constantly in mind by the writers, and should be as constantly regard- ed by the teacher, are set forth. GENERAL PRINCIPLES OF ARITHMETICAL TEACHING. I. First Teaching should be Concrete: — The child's first ideas of numbers are obtained through objects and can be obtained in no other way. True he may learn the language of numbers without the objective basis, but that language will be content — less concrete ' ° ° Work. until by the use of objects he puts a meaning into these empty forms. Better far is it to follow nature's way, which is to teach through contact with things. Gradually, however, the pupil must pass from the concrete things to the abstract relations. From one apple, one book, etc., he must rise to the abstraction one and similarly with two, three, etc., with the ten or the hundred. liS THE MISSOURI SUPERVISOR. with period, multiple, denominator, ratio, and, in fact, \yith the whole circle of arithmetical terms. He begins with crawling on all fours, but he must learn to walk. 2. P7-ocesscs Should Precede Rules: — This is but an extension of the preceding principle. If the idea for which a term stands should precede the term itself, is but logical to say that the idea of a process should precede its description in the form of a rule. Painfully vivid in many a memory are the recollections of rules that "must be learned" before eyen the simplest problem was given. It is a valuable exercise to write one's own rules from one's knowledge of how a certain pro- cess is carried on. 3. Principles Outweigh Rules: — The pupil who has realized the force of dividing the terms of a fraction by the same divisor will not halt long at reduction of fractions to Icwest terms. After he has mastered the cube, he will be troub'ed little with bins, wood-piles, wagon-beds, and stone walls. Possessed of the fundamentals of percentage, , . its applications are easy. Memorized rules are the husks of Arithmetic. He has wandered far from the home of good teaching who would fill his pupils with such food. 4. Arithmetic Should be Made to Fit into the Home-life and the School-life of Pupils : — This means that the bins and feed-lots and stores, and the lessons in history and Geog- raphy, Literature and Science should be allowed to contrib- ute material for arithmetical work. Pupils will not only solve such i:)roblems willingly but will delight in devising problems from the same sources. 5. Learning by Doing is the True Way: — Squeers's ARITHMETIC. 119 sending Nicholas to "do" horse after "learning" horse was pedagogical as well as economical. The boy who has curried a horse knows a horse as he could never know from books alone. "Horse" seems to get into his nervous and mental mechanism in a most enduring and satisfactory way. So it is with the bin or yard one measures, with the weights or measures he handles, with the figures he con- structs, with the checks or notes that he writes. The products of his own powers are more real to him than those about which he reads or hears or even those which he merely sees. That number work which is coupled with some constructive activity possesses most vitality and interest and effectiveness. 6. Habits of Order, Neatness, and Accuracy Result from Proper Mathematical Training: — Youth is the plastic period of life. Every repeated act tends to becomes ha- bitual — as true of the bad as of the good. "Sow acts and you reap habits." Carelessness, slovenliness,- inaccuracy- order, neatness, accuracy — which shall it be? The harvest must be as the sowing. This group of undesirable habits, characteristic of so many of our advanced students, can be traced at least as far back as the elementary school. True, the origin may be in the home, but the teachers (and none more so than the teachers of mathematics) are responsible for the permanency of those habits. If a boy cannot be led to see a difference between good form and chaos and to show by his work that he does see it, he will, when he reaches manhood, rarely drive a straight corn-row, mow the weeds xhe along his hedge-ways, house his self-binder, or HaWt. j. 120 THE MISSOURI SUPERVISOR. write a letter that any one save an expert can decipher. Let his occupation in life be what it may, the results of early mistraining will cling to him, to his hurt. 7. The Purposes of Arithjnetical Study are Various: — (i) Arithmetic has a practical value to which reference has been made. A knowledge of Arithmetic is necessary to the successful management of a household, a farm, a store, a shop, or an office; and a mastery of the general principles of Arithmetic sufficient for the solution of such problems as are likely to arise in any of these places, should be given to every normal boy and girl. (2) Arith- metic has a disciplinary value, not only in the formation of habits but also in the development of mental power — "the power to put two and two together." (3) Arithmetic has a preparatory value. It is the basis, under our present arrangement of courses, for all subsequent work in math- matics and much work in the natural sciences. The necessity for clear concepts and right habits of thought is, therefore, apparent. PRIMARY NUMBER WORK. Reference to the Course of Study, (p. 17), wilb'show that the first year's number work is with numbers from one to ten. It includes the following: I. Meaning of each of these ten numbers and First Year's {he Written and oral expression for each; the Wcrk. ^ ' latter in three forms — verbal, Arabic and Roman. 2. All additions of integers of which the sums are below II. 3. All subtractions of integers in which the minuend is less than 11. ARITHMETIC. 121 4. All iriultiplications of integral factors in which the products are less than 11. 5. Division of each number below 11 by all integers not larger than itself. 6. Some work with the half, third, fourth, fifth and multiples of these fractions. 7. Denominate units whose equivalents can be ex- pressed in numbers less than 11. 8. The signs +> — > X, -^, and =■=. g. Concrete problems almost without number, to im- press and apply the foregoing. The materials needed for doing this work well are as follows: 1. A box of wooden tooth-picks — for Materials for splmts — and a few rubber bands. primary Number Work. 2. A pint cup, quart cup, gill, gallon, and bushel measures. 3. A pair of scales. 4. Foot-rules and yard-sticks. 5. One-cent, five-cent, and dime pieces. 6. A large quantity of shelled corn, some acorns, beans, buttons, etc. 7. Apples and potatoes, for fractions. S. Hewett's Manual of Primary Arithmetic. g. A numeral frame. 10. A set of number cubes. The tooth-picks will cost five cents, the bands two; the measures can be borrowed; the scales can be manu- ' factured by an ingenious boy; the rules and yard-sticks can be secured free from advertisers; the coins can be saved 122 THE MISSOURI SUPERVISOR. from last pay-day; the pupils will contr-' -ite each an ear of corn or an occasional apple or potato; Cost. the Manual is listed at 27 cents, the numeral frame can be obtained for 90 cents, and the cubes cost 50 cents per hundred. Thus the entire expense is small, and even one or both of the last two articles men- tioned may be omitted, though at a certain loss. For teaching the various combinations and separations of numbers there is nothing to equal the cubes; for dry measure nothing surpasses shelled corn, and for frac- tional divisions the apple is unrivaled. For rapid work in addition and subtraction the numeral frame is excellent. It is hoped that no teacher will under estimate Importance of Objective the importance of these objective aids. Chil- Vv'ork. ■' dren can be taught to "count" without them, and so can a parrot with equal mental gain. By all means should the various operations of this year's number work be largely concrete. As a guide for the teacher, our State Text-Book Com- mission recommends Ilevvett's Primary Arithmetic. The work of the first year is therein well presented, and every teacher of primary Arithmetic needs the book. Manual" ^^^ ^^^^ 7^ pages of this manual should be covered during the first nine months of school life; but inasmuch as the pupils cannot read, the book is for the teacher only. These recommendations must not be construed as an unqualified endorsement of the work. There are very few works on the subject of methods (or any other) that the thoughtful teacher will endorse throughout. In fact the more thouiihtful and self-reliant a ARITHMETIC. 123 teacher is the less likely is he to follow any book without question. No author of a treatise on methods expects or desires more of his book than that it should be suggestive to progressive teachers. It is in this light that Hewett's book should be considered. Certain changes are suggested in the belief that they supply deficiencies or remedy defects. The changes proposed are the following: 1. Teaching of each new fraction by dividing a unit — a thing Hewett expressly forbids. But notwithstanding the weight of his authority, we are constrained 1 r • ■ 1, /- Changes to assert that tractions are "broken units first Recom- mended. and "relative units" afterward. Without instruction the child will no more answer the question, "One is what part of two?" than he would, "One is what power of two?" Our suggestion is that a unit — an apple — be cut into two like parts and the "one-half" and "two halves" taught; that two units be cut into halves and the fact discovered that one-half of the two together make a one; that a half of four ones is the same as two, etc. Pro- ceed similarly with the thirds — one, two and three — with the fourths, and fifths. Other fractions may be deferred until the next year. 2. Early in the work, e. g. , in connection with six, teach the sign (x) and its meaning, tabulate the multiplica- tions already studied, and add to these tables new products as learned. At the end of the year the blackboard should contain the following summary: 124 THE MISSOURI SUPERVISOR. 1x1=1 lx2==2 1x3=3 1x4=4 1x5=5 2x1=2 2x2=4 2x3=6 2x4=8 2x5=10 3x1=3 3x2=6 3x3=9 etc.. 4x2 = 8 10x1=10 5x2=10 3. The sign (-^), "divided by," in such expressions 8-^2=4, should be interpreted as meaning "how many 2's in 8?" should be introduced toward the end of the year, and may be used in the construction of tables like these: 1-^1=1 2-f-2=l 3h-3 = 1 4-^4=l 5^5 = 1 2-f-l=2 4--2=2 6--3=2 8--4=2 10-^5=2 etc.. etc., 9-3=3 10-^l=10 10-^2 = 5 The pupils may also be taught to measure even where there are remainders, as 8 equals 2 threes with 2 remaining, 9 equals 2 fours with i remaining, etc. 4. The Roman notation for these ten numbers should be taught near the end of the year. 5. The zero (0) should follow the introduction of the minus sign for use in such expressions as 5 — 5=0, 3 — 3 = 0, etc. 6. As the several numbers are studied, their use in the various denominate scales should be set forth. Thus in the study of "two," the child is taught that two pints are the same as one quart. The "pint" is presented to him concretely, and he measures the pint cup into the quart. So in connection with the three he learns 3 feet equal i yard; with the four that 4 gills equal i pint and 4 ARITHMETIC. 125 pecks equal i bushel; that 5 cents equal i "nickel;" 7 days equal i week; 8 quarts equal one peck; 10 cents equal i dime and 10 dimes equal 1 dollar. After considerable ma- terial of this kind has been gathered, the pupil, for "busy work," may fill out some such schedule as this: ( ) gills = I pint. ( ) pints = i quart. ( ) pints = quart. or ( ) quarts = i peck. ( ) quarts = gallon. ( ) pecks = i bushel. The second year's work, in the main, is similar to the first. The pupil deals with larger integers and smaller parts, but his increase in mathematical stature permits it. The numbers to 20 are studied, the year's work be- . , . r , - , Second gmnmg with a review 01 the nrst ten numbers. Years Work. In this review it is desirable to introduce some new features, and this affords an opportunity for the study of the sixths, sevenths, eighths, ninths and tenths of the unit and of the corresponding integers. Should a short school year force the ninth month's work toward the mid- dle of the second year, there should still be a review when "ten" is reached. With the numbers above ten, the cor- responding fractional parts should be presented. Counting by 2's, 3's, 4's, etc., and the extension of the multiplication and division tables and the inexact divisions are important matters. Some new denominate units and scales are to be added, as follows: 12 inches equal i foot. 12 months equal i year. 16 ounces equal i pound. 126 THE MISSOURI SUPERVISOR. There should be much concrete work with "these new and the old units, using both multiples and parts. Halves, thirds, fourths, sixths, eighths and tenths should receive much attention. Lengths, heights, widths, distances should be measured in appropriate units, and, wherever possible, should be converted from one to the other. Prac- tice drawing lines one foot, one-half foot, one-fourth foot long, or putting dots certain distances apart, then measure to test accuracy of work. Estimate lengths of To Train , . , . i i i i i the objects by movmg the hand along them, eyes Judgment. closed. Estimate heights of pupils, ceilings and other objects. Select the longer or shorter of two lines, the larger of two similar and nearly equal surfaces, the heavier of two objects, etc. Construct squares upon given lines, then measure. From a miscellaneous assort- ment of sticks or lines select all beyond, less than, or equal to a certain stick or line. Select the six-inch line, the ten-inch stick, etc. Cut (from paper) or draw six- inch, two-inch, three-inch squares. Practice cutting lines and rectangles into halves, thirds and fourths. Estimate contents and weights. Estimate the number of dots, grains, etc., in an irregular group. Test the accuracy of every estimate by exact measurement, weight or count. The value of these exercises is great. Speer's Arithmetic, Part I., is full of just such work. In the work with denominate numbers, the aim should be to have each unit clearly defined in the learner's mind. "Yard," "pound," "pint," etc., should mean something definite to him. After passing ten and getting a fair start toward twen- ARITHMETIC. "7 ty, the pupils will delight in running ahead of the wagon, and many a time the teacher, who is busy with some number will be approached with, "I know what the next number is." It requires only ordinary From lo to 20. ^ - J and to 99. • ability to grasp the principle involved and to make up the new numbers ahead of the class-work. The development of the new numbers is an easy task. Like- wise, when 20 is reached, a few minutes will suffice to start the pupil equipped with splints on his way toward 30. After seeing that two "tens" and one are 21 and that 22 and 23 are similiarly made up, he will himself write and name the others. So, also, when he has passed 30, he will go on to 40 and to 50, 60, 80, gg. (See Hewett, pp. 124-132, for suggestions.) One method of presenting the hundred, 10 tens, is shown on pp. 132-3 (Hewett.) Having seen one "hun- dred" in the large bundle and comprehended its writing, the pupil will have no difficulty with two "hundreds," three, four, and so on to nii.e. Then going back to 100, show and write 101, 102, , no, iii, 112, , 120, 121, , 130, 131, , 140, , 150, etc. With this start, nothing more than an occasional question or suggestion will be necessary to enable the pupil to write the numbers to ggg as "busy work." As an aid to the understanding of the numbering of reading lessons the Roman notation to one hundred may be taught without a systematic attempt to master the principles. During the first half of the third year (i8th to 22nd month) the reading and wriiing of numbers to four places. 128 THE MISSOURI SUPERVISOR. gggg, will give employment for seat work. This can be done without the splints. There should also Year— be as mucli addition and subtraction by 2's, '^'s. First half. g's, as time will permit. This will serve as a basis for the multiplication and division tables, which should be carried to 10 tens and preferably to 12 twelves. The study of individual numbers from 20 to 30, and of such useful numbers as 36, 48, and 60, may be continued after the plans of the preceding years. Pupils now have strength to undertake more difficult types of fractional, work and such work as finding ^-, |^, |^, 4, ^, of 13, 17, 23, etc., is possible. The schools of Kansas City show magnificent results with even younger pupils and more difficult work. WRITTEN ARITHMETIC MILNE'S FIRST BOOK. By the middle of the third year the pupil will be able to use the elementary text. The matter of the first 77 pages will have been canvassed so thoroughly that the work may begin with page 78. The alert ?|*i'"^'s . „ teacher will have drawn from these 77 pages many valuable exercises and suggestions. Now, the pupil passes from "number work"to"arithmetic." Pen- cil and tablet are much more in demand. Numbers entirely too large for oral manipulation are to be operated with; numbers so great that he has at best only a vague and general notion of them. New methods come in also, and these must be mastered. Thus the learner has really reached a new epoch in his educational career. No difficulty will be experienced in extending the ■ ARITHMETIC. 129 principles of numeration and notation to numbers of more than four places. In those schools in which the pupils have not been taught as the preceding pages . Notation have sugsfested, it may be necessary to establish and ^° Numeration. these principles concretely. If so, let the splint bundles be produced and the basis laid for a comprehen- sion of our system of notation, and the ordinary child will not comprehend it satisfactorily unless it is presented con- cretely. But splints and objective aids should be used only as long as they aid. Used too long they weaken, but let them be kept on hand to be used in case of emergen- cies. Gauge the pupil's power, and then exercise it just so far as to develop it by requiring its best efforts. Keep him engaged with small numbers until he is ready for large ones. Here, as elsewhere, Milne's book is rich in exercises. Use them with discrimination. Use such as suit the case in hand, and as many as are necessary to accomplish the desired purpose well. If more are necessary, draw upon some other text, but select judiciously. Avoid the wasting of the pupil's energy upon ambiguous or obscure problems. It may not be amiss to say a few words on the subject of expression. The cardinal virtues of mathematical expression, are clearness, conciseness, accuracy and good form. Ambiguity, wordiness, inaccuracy and carelessness in both oral and written expression Kxpressiou. are to be avoided. Every word or character used should have an unmistakable meaning and a specific purpose, and every unnecessary element should be omitted. Attention to these points will secure a discriminative use J30 THE MISSOURI SUPERVISOR. of the "and" where necessary and its complete omission in the reading of whole numbers, where its use is unnecessary, will provide the hyphen in such expressions as "forty-six," and "ten-thousandths," will require that "is" and "are" be properly used and that the cipher be called naught or zero, but never "aught." These are merely suggestive and are typical of those "little things" by which scholarship is identified. When the "operations" of Arithmetic are taken up, in addition to the qualities already mentioned, rapidity be- comes a desirable aim. Ultimately the fundamental operations within the range of simple numbers Tiie should become almost automatic. Such com- Aiin. binations as g-\-6, 15—9, gx6, 54-^9, etc., should require no more thought than is required to recog- nize the word "cat" when seen. The recognition of the power of the combination of either the letters or the figures should be quicker than thought. Strive for rapidity of work. Encourage pupils to work rapidly. Compel them to do so. Time the pupil, then encourage him to do the work in less time. Stimulate in him a desire to surpass his former records. Endeavor to carry into the Arithmetic class some of the spirit of bicycling and foot-ball. Throughout the study of Arithmetic it will be neces- sary to solve problems dealing with abstract numbers only, but the preference should be given to those involving con- crete relations. The mechanical element will be the same in the two, but the first is only mechanical. The latter involves thought. Thus the mechanical work is the same whether the problem reads "Multiply 26 by 40," or "Find ARITHMETIC. 131 the cost of 40 acres of land at $26 an acre," but the former is almost devoid of mental discipline, and hence 1 r 11 Til Concrete the preference expressed above. In the solu- Problems and Analysis. tion of these concrete problems there will be an explanatory analysis, but care must be taken that this analysis does not become a meaningless or mechanical form. "Mere words" are to be avoided. The exercises in articles 67, 73, 81, 96, 118, 150, etc., are typical of our author's method of introducing new topics. This line of work is one of the most valuable and suggestive features of Milne's books and illus- trates what is commonly called "inductive ^fP'l'd'^'^i'^^ •^ Method. teaching." Invariably based upon what the pupil is reasonabl}^ expected to know, these exercises are so well chosen that they lead the learner step by step, "from the known to the unknown," from his former acquisitions to a new definition, principle or process. The contrast between such a method and that of plunging at once into definitions and rules is truly great. The teacher will cer- tainly not fail to utilize these exceedingly valuable prelim- inary suggestions in introducing new topics. If this method is not a familiar one, it will pay to investigate and use it. The amount of drill work like that given on page 104 (Milne) must be governed by the needs of the pupils. To drill on what pupils have mastered is to waste valuable time and energy. But there is not much danger that pupils will know these elementary combinations too well. Through class-drills, busy-work, and 2^"'!: the like, the deficiencies of earlier training are 132 THE MISSOURI SUPERVISOR. to be supplied. This applies to addition, subtraction and multiplication with equal force. Before the pupil is allowed to begin serious work with the pencil, the work with .simple numbers should have reached the automatic stage. There is in mathematical work a process analagous to that of stopping to spell out words in reading. The two are alike despicable. The teacher will observe how articles 89-92 prepare the way for article 93. The "first process" of page 11 1 should be repeated with other numbers until comprehended, then the pupil is ready for the "second process," MuUipii- which is only a shorter form from which the cation. -' unnecessary elements have been omitted. A comparison will show the essential unity of the two as well as the advantages of the second. In general it may be said that "short cuts" should follow general solutions. The relations of the two should be shown by solving a problem, first by the general method, then by the short form, and then comparing the two. An apparent exception — and it is only apparent — to this principle appears in division. Nearly all books pre- sent "short" before "long" division. If the two were methods intended for the same problems, the Division— . , i , , ■, Long and poiuts Urged by some that the long method Short. logically precedes the short would be well taken. But inasmuch as long division is used for one class of problems i:and short division for another, the order of the two is to be determined not upon some fancied relation of the terms long and short but upon the real relations of the two classes of numbers. ARITHMETIC. 133 The pupil who has comprehended the "carrying" in simple addition can use short division with any divisor for which he knows the corresponding multiplication table. It is not with short division that pupils have trouble, but nine out of every ten teachers will tell of the terrors of long division. The remedy is not to be sought in reversing the order of the two, but in a more logical presentation of the more difficult of the two. If the following steps be taken in order, it is believed that much a Remedy, of the difficulty attending this subject will vanish: 1. Solution of two or three problems properly be- longing to the short division class, writing the work out in full (i. e. — by long division.) 2. Solution of many problems with 10, 11, 12, etc., as divisors, gradually increasing to larger ones. 3. Divisions with divisors less than 100 until the principles and methods are mastered, before trying the larger divisors. Without one word about "abstract" and "concrete" numbers it will be possible to secure a recognition of both in the work of multiplication and division. Insist upon analy- ses that viean somepiing and the recognition can be secured. "If one orange costs 2C, 36 oranges cost 36 times 2c," never "2 times 36 which is 72c" as too many teachers permit it to be said. "If one orange costs 2c, 72c will buy as many oranges as 2c are contained times in 72c, which r ■ rr-ii r -ii r ^ Concrete and IS 30 times. 1 heretore 72c will pay for 36 Abstract Numbers. oranges at 2c each." Again, "If 72c is the cost of 36 oranges, each orange cost ^ of 72c, which is 2c." 134 THE MISSOURI SUPERVISOR. All of the work implied in this paragraph is possible with third grade pupils, because accomplishment isi^the best proof of possibility. Article 128 would make an excellent assignment for "to-morrow's lesson." Let a fcvv of the lists be placed upon the board just before recitation time, then after com- parison and corrections, the tests of article 129 can be deduced. The pupil should be drilled until he can readily name all the factors of numbers below 150, and can quickly apply the tests of divisibility to any number. Thus when he sees 120 he ought to be able to think 10 X i2=r(2 X5) X (2X2X3) The fractional idea will not be new to the pupil when he reaches page 145. With his previous training he will have no difficulty with pp. 145-g, and after these experiences, he will have no trouble with "numerator," "denominator," "mixed number," etc. So far as the pupil has Fractions. dealt with fractjons prior to this time, it has been in finding parts of integers, e. g. — in find- ing ^, |, f, of 6 cubes, 7 cubes, etc. Now he begins work in changing, combining and separating fractions. The fraction becomes of itself a concrete number, — five- eighths mean five units of a certain kind (eighths), and seven eighths mean.seven of the same kind. Eighths is here the "fractional unit," and while new eighth it selfsignifies the division of the unit into equal parts, a new unit is formed by this division and this new unit may be increased in number or divided into smaller units. It will some- times help the pupil to solve such problems as the foliow- insf'. ARITHMETIC. 135 7 eighths 7 eighths 7 eighths 3 eighths 4 eighths 3 5 eighths — — — 3 eighths 21 eighths 15 eighths ■^ of 8 eighths=2 eighths; 8 eighths-^2 eighths=4. The pupil will need much oral work with fractions. Every type of reduction and each of the "fundamental oper- ations" must be impressed through a multiplicity of varied exercises. White's book and other texts can be drawn upon for material. There is need for much "mental" or "oral" Arithmetic. The bane of much of the work of to- day is the lead pencil. Encourage the pupil to use his mind much, his pencil little. Of these oral problems simple analyses should be given. When the problem is solved with pencil it may be desirable to change the method of solution, but in any case the explanation should accord with the solution employed. Opinions differ somewhat concerning the treatment of the subject of least common denominator. Our author must receive credit for his courage in divorcing least com- mon multiple from least common denominator. It is true that pupils ought to be able to discern ^^^^t common ■^ '^ ° Denominator. by a sort of intuition the L. C. D. when the series of denominators involves only small numbers, and to this end there should be much drill with a great variety of fractions. But there will be many instances when "inspection" will not determine the desired denominator. What then? Two courses are open. One 136 THE MISSOURI SUPERVISOR. is to teach that the L. C. D. is always the L. C. M. of the denominators and proceed to show a comprehensible method of finding this L. C. M. The other is to teach a process which no child will comprehend,, and this our author does in both his books. Is not the former course preferable? L. C. M. is a subject permitting beautiful treatment in Arithmetic, and the principles and methods should be the same in Algebra. Why not present this method when needed? Resolve the numbers into their prime factors, and take the product of such factors as are necessary to produce a multiple of each of the numbers. The arrangement of work in the solution of problems is important, but it must not be understood that there is but one good way of doing things. For example, the work in articles 167 and 170 may be differently ex- •'Form." pressed and yet be in good form. But let good form of some kind be insisted upon a/ways. Make much of the sign of equality, but insist that it be not allowed to prevaricate. Observe the accompanying state- ment as a magnificent example of "how not to do it:" <(Qv2 J6_l_l 1_7 There lurks in this form of statement a most insidious foe to good thinking. Its slimy trail can be traced through the entire mathematical work of many a pupil and many a school. Watch for it. The "three cases" of multiplication and of division lose their terrors if each is presented inductively and receives sufficient time. Have recourse to the concrete to show the ARITHMETIC. 137 effect of multiplications and divisions. If , . , rr 1 • Multiplication nothing better oners draw or cut squares into and Division of Fractions. parts of proper size. Do the thing, then ex- press it with symbols. For example, divide a square into i6ths; take ^ two times, three times, etc., and then ex- press the result as follows: 2xA=tVJ 3xf^=T9^; 4xA=M. etc. Show that the fraction is multiplied by multiplying the numerator. Show also that in the problems above i^g^=f, .J-|=:|, etc., and hence that dividing the denominator also multiplies the fraction. When the pupil realizes that \y.\, {\ times 4) can mean only "| of 4," that ^Xf means \ of 1^, etc., these "cases" of multiplication become very easy. Division of fraction by the integer can be presented with the divided square also. Separating 12 sixteenths into two, three, four, or six equal groups gives the data for suei]t.ei?cgr§ssions as ^1^2=^6^^; \^^^i=z^^, etc. If it be noted that dividing by 2 is finding \, by 3 is finding ^, etc., these problems may be expressed thus: i|-4=i of i|=i^, or ^g-. Thus two methods of division are reached. Division of integer by fraction should first be expressed thus: 4-f=¥-f=6 and |-^|=^-^^=|=1|. After these are thoroughly mastered show the ''short cuts" as follows: 4-i-J=-2-=6 and \-^\=^^^=^• 138 THE MISSOURI SUPERVISOR. Complex fractions should be read and interpreted as divisions. As such their solution is easy. Arts. 191-6 are highly important as a preparation for the future. Pupils must be able to determine the rela- tion of one integer to another at sight. Thus: 8=^ of 11, 8 acres =^ of 1 1 acres, and 8 twelfths =^ of 1 1 who!eT^ twelfths. Drill thoroughly upon the parts of the dollar and use these parts in problems (oral). In Art. 196 avoid the author's unpardonable sin of saying "-|r=32o, 1^64," a thing which is as impossible as 1=2. No amount of explanation can justify such statements. Say "-§■ of the number=320, -i- of the number^:=64," and the like. The baneful effects of these misleading forms are known to every thoughtful teacher who has tried to teach percentage. Decimal fractions should be begun with the writing of such fractions as -^, ^^, ^\-o, A' irU' tAx,' ^^^ with a review of the Arabic notation, particularly its tenfold ratio of increase or decrease through successive Decimal orders. If, in such a number as 8888 the value Fractions. ' of the second "8" from the left is one- tenth that of the first, of the third one-tenth that of the second, and so on, it needs no great mental effort to extend the principle to orders to the right of units. The necessity of the decimal point to fix the place of units will be apparent. Pupils will recall their former use of the point (pp. 85-6) and .will confirm the new principle by observing that in such a number as ^3.65 the "6" expresses tenths and the "5" hundredths of a dollar, or unit. The identity of the common and decimal fractions should be empha- ARITHMETIC. 139 sized through each of the fundarilental operations, and the pupil led to see the economy of the decimal system. Show that it is a saving to write .4X-i7=-'o68 rather than ^^X - yyQ=^6&_; that ;. 4-|-. I7=.57 requires much less' work than the addition of the corresponding common fractions, and so on. There should be rriuch 'drill on the identity of such fractions as .3 and -^^, .03 and yo'o' ^^^ The names and values of the first five or six decimal places should be so thoroughly learned that recognizing three or four or two decimal places, should cause the pupil to think instan- taneously thousandths, ten-thousandths, hundredths, etc., as the case may be. Drill until pupils can read and write decimals rapidly and accurately. The effect of removing the decimal point to the right or left should be taught. Pupils should be taught to recover from the prevalent mis- use of the "and" in the reading of numbers and taught its value in the joining of two kinds of numbers. The decimal termination "ths" should be used properly. The conversion of decimals to common fractions and of common fractions to decimals should be mastered, both as to process and explanation Drill carefully on the mat- ter of article 215. The correct pointing of decimal prod- ucts and quotients is important. To this end use articles 221 and 227 and supplement with similar exercises. The pupil must be led to see the rules for himself. "Accounts and Bills" can be made more real by using the names of home merchants and making the items of familiar articles at current prices. • If the suggestions of this course have been followed, the pupils of the second grade know many of the denomi- 140 THE MISSOURI SUPERVISOR. nate units. The inch, foot and yard; the ounce and pound; the pint, quart, peck, bushel and gal- Denominate Ion; all these are known, and, therefore, the Numbers. ' 7 j 7 teacher, at this point, will need only to classify and supplement. The child's knowledge of these units should be made real. Let him be made familiar with them, so that he will know the inch or foot when he sees it; the pound when he lifts it, etc. To do this he must have actual work with the units in both accurate and ap- proximate measurement.. All this, supposedly, has been done in the "number work." In the reduction and applications of denominate num- bers, our author is not his usual careful self. "Business methods" ought not to be slip-shod. Let us look at the problem in article 260. (first solution.) 1yd. =3 ft. 7 yds. =7x3 ft. =21 ft. 21ft.+l ft. =22 ft. 1ft. =12 in. 22 ft. =22x12 in. =264 in. 264 in. +4 in. =268 in. ARITHMETIC. 141 (second solution.) 7 (yd.) 1 ft. 4 in. 3 ft. 21 ft. 1 ft. 22 (ft.) 12 in. 264 in. 4 in. 268 in. To the first and the preferable solution there can be but one possible objection — its length. The second endeavors to obviate this objection by an artificial device (the paren- theses to indicate the numbers which become abstract mul- tipliers). The explanations to the two solutions are alike, word for word, and are identical with the author's. The work is better than his. When we reach reduction to higher denominations It ought to be remembered that the divisors are concrete, the quotients abstract. In the measurements of surfaces and solids, our author fails to apply what he de- 1 • • 1 r- r, 1 A 1 Rectatignlar velops m articles 268 and 273. A rectangular surfaces and Volumes. figure one inch long and one inch wide is a square inch. A rectangle 6. in. long and one in. wide con- tains 6 X I sq. in. A rectangle 6 in. long and 2 in. wide con- tains 2 times 6 sq. in. Hence for practical work we may write only: 2x6 sq. in. = 12 sq. in., supplying the rest orally. For problem one, article 271, we would write: 142 THE MISSOURI SUPERVISOR. 22x5^ sq. ft. =121 sq. ft.; or 5|X22 sq. ft. = 121 sq. ft. Similarly, for article 276, we would write,8 X 5^X 3-| cu. ft. =147 cu. ft.: or we may use the form below: 3| cu. ft. 28 cu. ft. 5V 147 cu. ft. Both of these fit the author's explanation. In the measurement of both surfaces and solids, pupils will de- light in making and solving original problems from actual measurements. Let them measure real floors, walls, ceilings, yards, boxes, bins, cellars, wood-piles, wagons, cribs, hay-mows, etc., make and solve their own problems, and exchange with other pupils. ADVANCED ARITHMETIC^MILNE'S SECOND BOOK. Milne's "Standard" Arithmetic will be introduced about the fortieth month. In the first 200 pages there is little that is new except the problems. These deal with larger numbers and are to that extent more dif- ^iJ°^'f j„ ficult, but the principles remain the same. "Standard." ' ^ ^ This is the time for mastery of principles and mechanical processes. The pupil who has studied the "Elements" carefully will have little trouble now aside from an occasional "hard knot" that has been allowed THE MISSOURI SUPERVISOR. 143 to get ill among the "review exercises." Those who have not studied the earlier work may be deficient in both knowl- edge of the principles and skill in their application. To such, the introductory oral exercises, the explanations, and the principles will be new, and the teacher must use them here as he does the corresponding material in the "Elements" for younger pupils. It will be necessary, therefore, in taking up each new topic — whether simple addition, factoring, multiplication of decimals, or any other topic — to ascertain just what each pupil knows of both principles and processes and to begin with the known in pre- senting the unknown. This applies to pupils wlio have stud- ied the "Elements" as well as to those who have not. The first 200 pages of the "Standard" ought to give the pupil a mathematical polish, so to speak. Inaccuracies in operation, crudeness of expression, both oral and written, looseness and disjointedness of thought, bungling methods, slowness in work — all should disappear, leaving the corresponding virtues in their stead. Cultivate rapidity in the mechanic- al processes, but never at the cost of neatness. Encour- age "mental" work and "short cuts." Draw on White's book and the "Elements" for oral exercises. Many prob- lems formerly requiring pencil can now be solyed without it. Practice the addition of two or three columns (White, p. 49), and the "short cuts" in multiplication and division (White, pp. 51-4; Milne, pp. 161-2). Place upon the board an addition problem of twenty numbers of twenty figures each. Challenge the whole class or school to add correctly. Change a few figures and renew the challenge with a time limit of so many minutes. Challenge the 144 THE MISSOURI SUPERVISOR. school to ascertain the continued products of the numbers from one to twenty-six. There should be much rapid work with common frac- tions — changing to lower terms, to mixed numbers, to decimals, naming the least common denominator — and with decimals, both pure and mixed in convert- Some . . T-. -11 1 • Important ing to common fractions. Drill also in express- Matters. ing various fractions in hundreths. Thus: .625 =62|, .3475=341' -333 3-=- 33^-. -J^-jo. The problems on pp. 128-g should receive careful attention as preparatory for work in percentage. The aliquot and other much- used parts of the hundred should receive special attention. The problems on p. 163 are valuable and should be sup- plemented by similar ones on the buying and selling of live stock, the market reports in some daily paper furnish- ing ample material. The work with fractional denominate numbers is largely new, but the principles are not. Such numbers should be treated as nearly as possible as integral numbers would be treated in the same problem. Empha- size the comparisons on p. 185. Teach the "business year" and decimals thereof. The value of the bushel in pounds and in inches should be studied Practical ^ud applied to wagons, cars, cribs and Problems. ^ '^^ o ' ' bins. The "Mo." column, p. 423, will furnish the equivalents in pounds. It must be remembered, how- ever, that corn "in the ear" requires 70 lbs. of weight or about 3850 cu. in. of contents to constitute a bushel, and that 56 lbs. of shelled corn and 32 of oats constitute the bushel in Missouri. , ARITHMETIC. 14S For reasons satisfactory to himself, presumably, the author has stowed the metric system safely away in a quiet corner where many a pupil and many a teacher will have ample reason for overlooking it. The supe- riority of the metric system over our present f^g^^^'^"'^ systemless system is so great, its value in scien- tific work so apparent, that it is time for teachers to believe and to teach that it will be but a few years until all civil- ized nations will be using it. The men and women of twenty years hence will be buying and selling by the metric system. The teachers of to-day ought to be teach- ing it. No teacher of Arithmetic who passes this subject by unnoticed is doing his whole duty. In presenting the metric system to a class, let the basal nature of the meter be emphasized. Get some pupil to manufacture a meter-stick. Divide one side into deci- meters and paihl tlie alternate divisions. Divide another side into centimeters and paint alternate sections. Require pupils to make similar sticks and to use them in making numerous measurements. Use the results of the measure- ments in practical problems relating to lengths, distances, etc. Emphasize the Km., M., dm., and cm., and the con- version from one to each of the others. Drill upon the prefixes and their meanings and upon the conversion of common to metric units and the reverse, both accurately and approximately. After the length measures are mas- tered, apply them to surfaces and solids and drill as be- fore. Go slowly and work thoroughly. For capacity measures, construct a wooden or tin measure one decimeter in each dimension. This is the cubic decimeter or liter. 146 THE MISSOURI SUPERVISOR. Require the pupil to estimate contents in the appropriate metric unit and to test by measurement. When weight units are taken up do the same with them. Manufacture metric substitutes for the ordinary scale weights and use the new in weighing. Actual contact and use are neces- sary to the actualization of this knowledge. The subject of longitude and time is so much dreaded that the teacher's part in an actual problem in a lesson is indicated in the following questions and directions. The lesson may be suggestive, but of course no teacher will copy it verbatim. Pupils' answers are omitted. Point toward the sun. Toward where it will be at noon. Will it move from one place to another? Why does it seem to move? Is it visible at all times? Why not? What is the shape of the earth? What A Lesson iu . . Longitude Will represent it.'^ Lome to the globe and show and Time, why the sun is not alwaj's visible. What do we call the time when the sun first appears? Show why it seems to rise? How often does it rise? Why? Locate our home on the globe. Represent sunrise at our home. Locate Denver. Can 3'our friends in Denver see sunrise when we do? Why not? Locate Wash- ington City. Can the President see the sun when it is sunrise here? Why? In which direction is Washing- ton from us? Locate some other place east of us. Can the people there see the sun at our sunrise? In which direction is Denver? Name another place west. Can its people see the sun at our sunrise? Name some place east of Washington. Where does the sun appear to them when the sun is just rising at Washington? ARITHMETIC. 147 "Why? Then what is true of the eastern of any two places? And if the sun seems higher, what is true of the time? Then what is true of the time of the western of two places? Name some places that have earlier time than we. Later. Earlier time than New York has. Later. San Francisco. When it is noon here, what is true of the time at Philadelphia? At Honolulu? At sunrise here, what are people probably doing in London? In Tokio? What time is it now? What is the time at Denver? How much earlier? Well, let us try to determine. How long from sunrise to sunrise? And during that time what has our town done? What has been the shape of its path? How many degrees are in that circle? How many hours are required to travel it? How many to travel half of it? How far do we travel eacK hour.f* In which direction do we travel? W^here will we be one hour from now? And who will be here in the path where we are now? Find some place about 15° west of us. Then how much does Denver time differ from ours? Suppose it were 30° west? 45°? 90°? 35°? 66° east? 72° east? 71°? 5°? i°? ■J-°? (This is how many ' ?) i'? |'? Then a difference of 15° marks what difference in time? A difference of 15' of longitude? A difference of 15" of longitude? etc., etc. Then if you could compare your watch with that of a per- son 15° east of us what would you find? 15° west? 30° west? If you were to travel 30° eastward what would be necessary? 45° westward? 5° eastward? 15' eastward? (Explain that there would be no change necessary to keep with the R. R. or "standard" time until the meridian of Wheeling, Buffalo, etc., is reached and that the time 148 THE MISSOURI SUPERVISOR. for the 90th and the 75th meridians, etc., is made to an- swer for territory presumably about 7^ degrees on either side.) Note: — There is but one other important matter to present, (aside from the problems) and that belongs to Geography, rather than to Arithmetic, yet it will likely have to be taught here. This is computing the difference of longitude between two places. This can be presented by such questions as the following: Name some place east of us. How far? Another. How far is it.' Which is the farther? How much? How far apart are they? (Same for two other places east. Two west. For one east and another west. Same for places east and west of Greenwich.) To understand the measurements of plane figures one needs only to master the rectangle. All others are to be measured by it. Therefore review from the "Elements" and drill upon the form of analysis with all sorts Plane of practical problems — fields, lots, walls, ceil- ings, floors, windows, carpets, walks, etc., from the pupil's own ineasurements. If that absurd idea of "feet xie,et gives square feet," is in the pupil's mind, get it out at any cost. Fight it out on this line if it takes all winter. This point gained, advance as follows: 1. The parallelogram: "A parallelogram 10 ft. wide and 46 feet long contains the same area as a rectangle of the same dimensions, hence the area equals 10X46 sq. ft., or 460 sq. ft. Prove the equivalency of the rectangle and other parallelograms by cutting paper forms.) 2. The triangle: "The area of a triangle is one-half that of a rectangle of the same base and altitude, (prove this by cutting paper), hence a triangle whose base is 30 ft. and altitude 12 ft. contains ^ of 12 X30sq. ft. =6x30 sq. ft., or 180 sq. ft. ARITHMETIC. 149 3. The trapezoid: "The area of a trapezoid is equal to that of a rectangle of the same width and whose length is equal to the average length of the two sides. Prove as above. Hence, if the two sides are 15 and 11 ft, the average , ,. 15 ft. +11 ft. , . , . , length is =13 It., and the area of the trape- zoid equal 10X13 sq. ft., or 130 sq. ft. 4. The circle: Present a circle and note circumfer- ence, diameter and radius. Measure various circles and determine relation of circumference and diameter. Thus 22-4- 7^:3^ = 3. 14+. Note the constancy of this ratio and its nearness to 3. 1416. Solve the problems in articles 258-9. The area of the circle may be determined from at least three relations: a. To the triangle (see article 259); A = Cx — . b. To the rectangle (see Kennedy's Mathematical Blocks); A = — xR. c. To the square; A = D2x.7S54. Of the three, the last is the simplest and the one pre- ferred. To present it, require a 6-inch circle to be placed upon a 6-inch square and estimate comparative areas. The estimate will generally be about | or .75. Give exact pro- portion, .7854. In other words, state that the area of every circle is .7854 of the corresponding square. This requires no more "faith" than the 3. 141598 or 3. 1416. Let the fol- lowing serve as a model solution: Find area of a circle 10 feet in diameter. A lo-foot square contains loxio sq. ft. = 100 sq. ft. A lo-foot circle contains .7854 of 100 sq. ft. = 78.54 sq. ft. 156 THE, MISSOURI SUPERVISOR. 5. Plastering, papering and paving which are only applications of the rectangle with a few added technical points explained in the notes. 6. Regular solids, which are based upon the Solids. rectangular volume, e. g. : A solid I ft. long, I ft. wide and i ft. high con- tains I cu. ft. A solid I ft. long, J ft. wide and 4 ft. high contains 4X1 cu. ft. =4 cu. ft. A solid I ft. long, 6 ft. wide and 4 ft. high contains 6x4 cu. ft. = 24 cu. ft. A solid 18 ft. long, 6 ft. wide and 4 ft. high- contains 18x24 cu. ft. =432 cu. ft. These may be condensed into 18x6x4 cu. ft. —432 cu. ft. If the height, width and contents are given and the length is required, the written expression may appear 5... ' thus: , ^ 6x4 cu. ft. =24 cu. ft. 432 cu. ft.-^24 cu. ft. =18. The cylinder combines the circle and volume, e. g. : If the diameter of a circular cistern is 6 ft., the basal area = . 7854X36 sq. ft. =28.2744 sq. ft. If the cistern is i ft. deep the contents are 28.2744 cu. ft. If the cistern is 8 ft. deep the contents are 8x28.2744 cu. ft., or 226.1952 cu. ft. Percentage can be robbed of half its terrors by the right presentation of the topics preceding it. Both common and decimals fractions are preparatory to percentage. ARITHMETIC. 151 It is a case of proceeding from the general to the special. From the general treatment of Percentage, common fractions, the pupil passes to the con- sideration of fractional parts of the denominations, tenths, hundredths, thousandths, &c. , and when percentage is reached the work is further narrowed to decimals of the denomination hundredths. In percentage there are three problems of which the following are typical: 1. What is 7 per cent of 800? 2. s6 is 7 percent of what number? ?fl;''^^ „ J / r "Cases." 3. 56 is what per cent of 800? Each of these has its counterpart in both common and decimal fractions. In the former they read thus: 1. What is ^2o °^ ^°°^ 2. 56 is y-J-Q of what number? 3. 56 is what part of Soo? In decimals they reappear as follows: 1. What is .07 of 800? 2. 56 is .07 of what number? 3. 56 is what decimal of 800? By the time the pupil has had a satisfactory drill in finding -^^ and .07 of 800 he ought not to be troubled over "7 percent of 800." And if he be able to determine the number of which 56 is yq-qj or -oj, he ought not to hesitate with the problem when it reads "7 per cen,t. " The conti- nuity of problem 3, through these three phases of arith- metical work is equally apparent. These problems, there- fore, suggest the propriety of dwelling long upon these particular types of problems in both common and decimal fractions and of emphasizing the identity of the percentage 1.53 THE MISSOURI SUPERVISOR. problems with those of fractions. The drill will fit the pupil to perceive the identity. Having grasped this idea, he is ready for its application to concrete problems, and there is no reason why the foundations for profit and loss, com- mission, brokerage, insurance, and the like, should not be laid. In other words, while being drilled upon the mechani- cal phase of finding 2-1- per cent ot $1200 let him ascertain the sum gained at 2^ per cent upon a house costing $1200, or his pay if he received 2| per cent of the proceeds for selling the house for another, or the cost of insurance at 2^ per cent of the value. No pupil need hesitate a moment at any of these, and having solved them, when he reaches the formal consideration of profit and loss, commission and insurance, the difficulties will have been anticipated. Pupils must be fortified against the too prevalent idea that percentage has to do with money only and that 10 per cent means "10 cents on the dollar" necessarily and uni- versally. To accomplish this the teacher should give many problems in which the "base" bears such names as acres, days, bushels, miles, cattle, gallons, etc. Preliminary to the work in percentage the pupil should receive a thorough drill in the rapid converting of the most frequently encountered percentage forms into their fraction- al equivalents. Thus i2|^ per cent=^; 6^ per cent=^ig^; 10 per cent=-jij, etc., and when he encounters these num- bers in problems, let him be encouraged to select the best possible method of solution. For instance, should he be required to find 33^ per cent of 182^, he certainly ought to proceed at once to use ^ as the equivalent of 33^ per cent. Another current weakness can be obviated by writing ARITHMETIC. 153 in figures such exercises as these: One-fourth of one per cent; 25 times one per cent; one-half of one per cent; one half of 100 per cent; one-fourth hundredth; 25 hundredths, etc. Very little should be said about "cases" and formulae. Many a pupil works as mechanically as a "nickle-in-a-slot- machine" and very much after the same order. Just as soon as he can make a guess as to the "case," the wheels begin to whir. It may not be neces- and Formulae. sary to shun absolutely the very word "case," the "BxR = P," etc-, but it is asserted upon the basis of repeated experiences that pupils may master the subject of percentage without hearing or using these terms at all, and it is asserted with equal positiveness that much of the life- destroying work in percentage is due to mechanical jug- gling with "cases" and formulae. The following solution is reproduced from a popular work on Arithmetic as another illustration of "how not to do it." 10 per cent. =^300. I per cent. =3^ of ^300 = ^30. 100 per cent. =100 X ^30 = $3, 000. Inasmuch as "10 per cent" means .10 or ^, we are confronted with the startling statement that the abstract number with a value of -^^ is equal in value to a concrete number with a value of 300 ones. It is not permissible to explain that these equations mean something different. Equations ought to mean what they say. On the same ground we would object to letting "100 per cent equal the cost," "■§■ equal the value," and similar expressions. An 154 THE MISSOURI SUPERVISOR. error analogous to these was pointed out in the discus- sion of common fractions. It is refreshing to turn now to the excellent solutions to be found in the "Standard," pp. 238-241, 243 and 249. The meaning and the "general method" of interest are acquired in the "Elements," but the "six per cent" and other methods are to be presented now. The former should be taught well,- as -should a few of the Interest. "short rules. " The pupil should not be over- whelmed with "methods," but let him learn to compute, readily and accurately by short and simple "methods," interest at our prevalent rates, 6 and 8 per cent. Having acquired several methods, he should strive to determine the one most suitable to the problem he has before him. There is no one universally "best method" for interest. To develop the power of determining the best method, let various methods be employed upon the same problem and the best chosen. Do the same with other problems and compare, endeavoring to determine where each method fits best. Important distinctions can be illustrated by computing upon ^600, at 6 per cent for four years: 1. The simple interest; 2. The annual interest; 3. The compound interest — paj'^able annually. 4. The compound interest — payable semi-annually. A comparison of results and the methods by which they were reached will be profitable. Having to account for the difference of results will lead the pupil to search out the essential likeness and unlikeness of the four prob- ARITHMETIC. 155 lems. An air of reality can be given to the work in all of 'these types of problems as well as n those of partial pay- ments and discount by giving the problems in the forms of notes. If the teacher will secure fifty blank forms and fill out as many notes, negotiable, non-negotiable, demand, joint and several, simple interest, annual and compound, etc., etc., his pupils arevery likely to comprehend, not only these several kinds of- notes but the very meaning and nature of interest itself. These notes can be preserved and used year after year. In addition to these, the pupil himself should have training in filling out and endorsing notes in the various recognized forms. The interest calculations can be combined profita- bly with a review of former work. -Let one boy buy of another a tract of land, a crop of wheat or a drove of hogs at current prices and in payment give an interest-bearing note upon which he makes partial payments. Then let them agree upon a date of settlement and determine the sum due. Or let the purchaser go to a third boy, a banker, and borrow the needed amount of money according to the principles of bank discount, which subject, by the way, may nicely precede and pave the way for true discount. In these and similar ways, written Arithmetic will be made "practical." and comprehensible. The same helpful turn can be given to "stocks and bonds," by organiz- ing a company, securing a charter, issuing cer- stocks, tificates of stock for various numbers of shares, declaring dividends, making assessments, "watering stock," selling stock, etc. Much of the difficulty in the way of comprehending 156 THE MISSOURI SUPERVISOR. bond transactions is due to a lack of comprehension of the language employed. "Make haste slowly" is a wise motto here. The pupil should be initiated gradually into the difficulties of the subject. There should be a thorough drill upon the meaning of "U. S. 4's," "Mich. 5's," "5 per cent stock," "bought at 90," "at 112^" or "at 25 per cent below par," "8 per cent on the investment," "10 per cent dividend," etc. With . these points compre- hended through illustration and drill, this subject will lose most of its terrors. In connection with exchange all waj's of paying dis- tant creditors may be discussed. On the day preceding the taking up of exchange let the class be asked to tell on the following day of all the ways in which they Exchange. could pay for a bill of goods purchased from New York. A comparison of the purchase of a bank draft with that of a postoffice or express money order will be profitable. Let it be announced to-day that to- morrow John will again go to his class-mate, the banker, and purchase the draft which the latter will be expected to write. The class will be ready to criticise the methods. In exchange, as in all other applications of percentage, it is very important to be able to recognize the "base." Em- phasize the fact that in simple interest, bank discount, stock certificates, bonds or exchange, this "base" in the face of the note, bond, draft, etc., and that all percentages are computed thereon. The only exception is in the case of true discount, in which the "base" is to be ascertain- ed. Let it be remembered also that commission is computed upon the sum of money that passes from buyer to seller. ARITHMETIC. 157 Compound proportion follows the mastery of simple proportion. No topic in Arithmetic has served as an intellectual opiate more freqtiently than this. It can be presented in such a way as to lead to a valuable type of reasoning, and again it may be — and Proportion. too frequently is — presented so as to lead to nothing but a blind groping for answers. Simple propor- tion as well as work in fractions must give the pupil the ability to recognize instantaneously that as 2 yd. are to 4 yd., so is the cost of 3 yd. to that of 4 yd. That if 5 men do a certain piece of work in 6 days, 5 men in 8 days will do more, or 3 men in 6 days will do less, etc., etc. The principle that ratio can exist between like num- bers only can be utilized by arranging the data like this: (See problem 14, p. 322.) yd.l. yd. b. yd. d. 352 2| 11 ? 2| If The statement, solution and explanation appear be- men da. hr. 54 28 10 112 25 81 low. 54 28 10 2| If 112 1 25 I 8^ }- : : 352 yd. 1. : (x) yd. 1. 2| I li J 352x1X^x25x33 5 3 jL^A-419jl 158 THE MISSOURI SUPERVISOR. Explanation: The required term, the fourth, is to be "yd. long," hence 352 "yd. long," is the third term. Since 54 men dig a trench 352 yd. long, 112 men will dig a longer trench, and the result (so far as dependent upon the number of men) is larger than the third term, therefore the second is larger than the first, and the first couplet is 54:112. Since a trench 352 yd. long is dug in 28 da., a shorter trench will be dug in 25 da., the fourth term is less than the third, the second is therefore less than the first, and the couplet is written 28:25. Since a trench 352 yd. long is dug when the workmen work 10 hours a day, when they work 8-^ hr. a day, the trench will be shorter, the fourth term is less than the third, etc. Since the workmen dig a trench 352 yd. long and 2^ yd. broad, if they dig one 2|- yd. broad it must be shorter, therefore the fourth term is less than the third, and the second must be * * etc. And so with the next couplet. If the problem is treated in a manner something like that indicated above, the ordinary pupil w//jV understand it. The study of involution should familiarize the pupil with the terms, power,exponent, square and cube, with the square of all the numbers to 12, (25 if possible), with Involution. the cubes of all numbers to 10 (or 12), with the expression of squares and cubes "in terms of their tens and units," and with the relation between the number of figures in any number and the number of figures in its square and cube. With these points master- ed he is ready to begin the study of evolution. For the ARITHMETIC. 159 usual methods of finding square and cube roots, two so-called "explanations" are offered by Roots of ^ -' Numbers. authors— the one by means of squares, figures and cubical blocks ("geometrical"), the other by an analy- sis of the square of any number of two or more figures into its three, and of the cube, into its four constituent parts. The latter "explanation" explains, the former does not, it only illustrates a particular class of concrete problems. To say that we "double the root already found," "because we have to add on two sides of the square" or that we "take three times the square of the root already found," "because we have to add on three sides of the cube" is to talk non- sense with all except a few problems. The "geometrical explanation" may be a satisfactory illustration of these few cases, but as an explanation of square or cube root it is a most deceptive failure. The explanation for problem 2, p. 329, and the explanation at the bottom of p. 337 are universal in their application and really explain, which facts commend them. If it be said against them that they are algebraic, we may reply that they ought not to be too algebraic for a pupil completing the subject of Arithmetic, or if so, that inasmuch as they offer the only logical expla- nation of the work, the pupil ought then to solve by the rule and attempt no explanation at all. To call the "geometrical explanation" an explanation, is to practice deception. In cube root particularly, give a logical explanation, solve blindly by rule, or let the whole subject go over until the pupil reaches it in algebra, and the last is the most rational course of all. There is a men- tal discipline in the mastery of cube root prior to the study i6o THE MISSOURI SUPERVISOR. of algebra, but the discipline arises largely from the extra exertion required to master a subject that is out of its logical place. In Average of Payments and Average of Accounts, like Partnership, the fundamental principle is that of equivalency, and if all are to be studied, the rational thing to do is to study them in succession. The principle of equivalency appears in Partnership like this: "If A invests $800 for 9 months, his investment is the same as $7,200 for 1 month, for 9 X $800 = $7,200. " In Average of Payments and Average of Accounts it arises like this: ''By paying $300, 4 months before (or after) it is due, A gains (or loses) the use of $300 for 4 months, which is equal to the use of $1,200 for i month, for 4X$3oo = $i,2oo." This is certainly a better treata^ent than that on pp. 369- 372 (Standard). Time is what is sought and, therefore, the comparis n should be made upon that basis. Problem i, p. 36S, would be solved as follows: $ 400 for mo. =0x$400, or $ 00 for 1 mo. $ 300 for 2 mo. =2 X $300, or $ 600 for 1 mo. $ 400 for 4 mo. =4 X $400, or $1600 for 1 mo. $1100 $2200 $2200 -^$ 1100 = 2. Therefore, the average term of credit is 2 months. The Savings Bank Accounts, p. 374, are worthy of study in view of the fact that it is only a question of time when our government will follow the example of Great ARITHMETIC. i6i Britian, Austria, Prussia, France, Italy, and other nations in the establishment of Postal Saving Banks. By direct attention to this subject in our schools, we are making sentiment in favor of its adoption and preparing for its use when it is adopted. The foregoing pages of this chapter contain only oc- casional references to White's Oral Arithmetic. This must not be construed as an intended slight to that valuable book. In the Course of Study, Chapter I of this volume, provision is made for articulating the oral with the written Arithmetic. In suggesting this plan, two thoughts have been considered. The first is that oral Arithmetic is too important and too valuable to white's oral ^ Arithmetic. be omitted from the school course. The sec- ond is that two recitations a day in Arithmetic require an amount of time for that subject entirely disproportionate to its relative importance. The result is a plan whereby the oral and written phases of the subject appear contem- poraneously, without neglecting or making a hobby of either. The following suggestions were made by Professor White to a body of Missouri teachers: 1. Read the note to teachers, pp. 3 and 4. 2. Let the pupils do the work, and give them time to do it. 3. The inductive (or development) work is the soul of the book and should be done inductively, i. e., in the point by point method. Let the class answer the first question in a development exercise — be sure that all can answer it. Then give the second, and let it be answered in the same way; and so on, till the exercise is i62 THE MISSOURI SUPERVISOR. completed. This, in almost every case, will secure the apprehension and comprehension of the principle involved — which, of course is the thing aimed at. 4. If at any stage in the development process a con- siderable number of pupils fail to answer one of the sequent questions, let the teacher give other questions like the one in the book, but, perhaps, simpler. The design is that the pupil's mind be led gradually and naturally from what it knows to what it does not know. 5. Emphasize the beginnings of ratio, pp. 30-34. 6. Call attention to "Special Cases," pp. 49-54; 86- 87; and in the various review exercises throughout. 7. Call attention to the unique presentation of com- position and factoring, beginning on p. 55. 8. See the easy method of explaining the division of one decimal by another: problems 16, p. 90; 14 and 15, p. m. LANGUAGE AND GRAMMAR. 163 CHAPTER III. LANGUAGE AND GRAMMAR. GENERAL PRINCIPLES AND SUGGESTIONS. Language, more than any other subject of the school course, is a part of the warp and woof of a child's being. He may have little use for history, civics, numbers or geography, but if he live in a community with his fellow- men, he will use language. Daily, almost hourly, he will communicate with others. This constant use, beginning with the plastic period of infancy and extending to the close of life, serves to sink the roots of Language and ' Habit. habit deep down into the fibers of being. . Thus habit becomes, in reality, "second nature" to him. This formation of habits begins with the child's first, attempts at speech, and, therefore, he takes with him on the first day of his school life the effects of at least three or four years of daily repetition of the commonest language forms. Fortunate is the teacher if this novice in school affairs hails from a home where good language is the rule. But such homes are exceptional, sad to say. In the majority of cases the pupil will bear in body and mind the marks of three years or more of daily use of incorrect and inelegant i64 THE MISSOURI SUPERVISOR. modes of expression, and the scars will be all the more deep and enduring because of the very plasticity of child- hood. Since every year of further use will serve to deep- en and broaden these marks, it behooves the teacher to make their continuance as brief as possible. Let the work of uprooting begin at once. This is one instance in which the tares and wheat are not to be allowed to grow together unto the harvest. Uproot, trample out the tares now growing, and look to it that as few as possible be allowed to creep in through subsequent sowings. Notwithstanding the fact that the average person speaks a thousand words for each one that he writes, it remains true that with many teachers "language teaching"' is associated exclusively with written work. But let it not be forgotten that language may be oral as well Oral and . i -i i r Written as written, and that while the two forms are Language. related and inter-dependent, proficiency in one does not necessarily imply proficiency in the other. The one-sided view referred to above has resulted in a dual defect in many a language course. These "sins of omis- sion" are as follows: first, a partial neglect of the oral phase of thought expression in all grades; second, the consequent omission of all language culture below the third grade, or the time of beginning text-book work. Both are serious omissions. The general purposes of language are "to get and to give" — acquisition and ex- pression — and let it not be forgotten that much of the "giving" must be oral. Therefore, let us have a cultiva- tion of the power to clothe thought in oral dress, with ease, with vigor, and with fitness. The continuity of LANGUAGE AND GRAMMAR. 165 these two phases of language work through the grades from the first up, as well as the relative degree of attention they should receive has been crudely illustrated in the ac- ■^ Eighth Grade. First Grade. companying schedule. This diagram is intended to con- vey the idea tliat there is to be no cessation in either kind of work, but the predominant oral phase of the primary grades is largely displaced by the growing written ele- ment. Language involves two elements — meaning and ex- pression—and the latter exists for the sake of the former. The thought side is the important one and the one worthy of emphasis. There may be a mechanical juggling with content-less words, but it has Thought and no place in legitimate language work. The Expression, first requisite, therefore, is something to ex- press — ideas. The possession of the idea should lead to the desire to express it, and this, in turn, to the realization 166 THE MISSOURI SUPERVISOR. of a need of language. In this we have the -logical; series underlying language work. Give, the, pupil something to say and a sufficient motive for saying, it, and ke will usually, though not necessarily, find the means. The conclusion from the foregoing propositions is that the teacher should first help his pupils to acquire thought • — pure, clear and useful thought. Its sources are many — objects, events, persons, books, pictures, etc. That his thought may possess clearness and distinctness, the pupil must learn to observe carefully, to listen attentively, to read reflectively. The thought, when acquired, must be expressed. This expression should be correct and fluent and, at the same time, characterized by simplicity and naturalness. Some there may be whose natural state seemingly is characterized by inaccuracy or halting or bombast. If so, such should be born again into the king- dom of better things. A "second nature" should be ac- quired, and old things should pass away. Expression should be "natural," but the good in expression should be the natural. One of the prominent traits of childhood is the tendency to imitate. This tendency is no less strong in linguistic than in other domains. Prompted by an innate impulse, the child imitates what he Imitation. hears as well as what he sees. Good models, therefore, are important. Many of the models from which the pupil's linguistic possessions are ac- quired are the current expressions of the home. If the home is one of rehnement and culture, the models will possess the same qualities. The teacher can hope much, wish LANGUAGE AND GRAMMAR. 167 much, but he can do little toward improving these home influences. The models set in the school-room, however, are largely within his control. Let them be the best pos- sible. The language of the teacher should be free from slang, vulgarism and obvious inaccuracies, and so far as it is defective, the teacher's aim should be to make it better by study, reflection and practice. But the language of pupils is imitated by other pupils, hence the preventive value of an earnest endeavor to improve the general linguistic tone of the school-room. Correctness and ele- gance of expression are caught quite as much as taught. On the other hand, it must be admitted that inaccuracy and inelegance are as contagious as any other evil which the school-room helps to disseminate. And sometimes a single vigorous-minded pupil can inoculate an entire school with the microbes of slang. There is another class of models — those of literature. Too frequently do teachers overlook the influence of the pupil's reading upon his modes of expression. The young reader who lives in a world in which thoughts are invaria- bly clothed in elegant word-habiliments will catch the spirit of his environments and think and talk in elegant language. The linguistic atmosphere, like the moral, leaves its mark upon those who live in it. Consciously and unconsciously may one obtain from what he reads a training in the correct and vigorous use of language. As has been implied already, much of the teacher's work must be corrective. There will be numerous errors in the language of the pupils in the recitation, on the play-ground, in written work. Many of them will be the i68 THE MISSOURI SUPERVISOR. habitually incorrect forms imported from the home. Not only must they be corrected, and this in a manner that will not discourage or antagonize, but the pupil must be set on guard to prevent the repetition of the mistakes. He must understand that incorrect forms will not be ac- cepted. The teacher who succeeds in informing his pupils of the most frequent errors in their speech and of the corresponding correct forms, who inspires those pu- pils with so strong a desire to shun the wrong as to keep them continually on the alert to prevent a repetition, has given his charges a fair start toward victory. Only by the combined efforts of teacher and pupil can the crudities of early childhood's speech and the inaccuracies to which children of all ages are prone be eliminated. Only by constant, patient, zealous effort will the haven Criticism by c r ■ 11 •!/->••• 1 1 Teacher and of fair speech be attained. Criticism by teach- Pupil. er and classmates will be in order, but what is desired above all things else is criticism by the pupil him- self. A reflective "self-consciousness" must be awakened. The pupil must be led up to the point of desiring to speak and write correctly. If the school-room errors in the use of English should be noted and classified by the teacher, they will be found to fall into a very few classes. Mispronunciations, confusion of participles with tense-forms, of nominative with objective forms of the pronouns, and of singular with plural verb-forms, use of double negatives and colloquial- isms — these nearly exhaust the list. Therefore, a well-directed and continuous campaign against these expressions should be conducted. Work LANGUAGE AND GRAMMAR. i6g should be carefully planned to involve the correct forms corresponding to these inaccuracies. When a , • , ... Ill Overcoming mistake is made, see that it is replaced by a Evil with ^ ■' Good. correct form. If the pupil knows the correct form, require him to produce and use it, otherwise it must be supplied by another pupil or by the teacher. At any rate, the pupil must use the correct form, otherwise the time spent in criticism is wasted. The principles apply with equal force to written and oral expression. Written work must be examined and the errors marked. Nothing conduces more to habitual slov- enliness and disorder than the impression that written work is never examined and that a folded paper, with anything or nothing within will answer all requirements. Teachers are responsible for what they accept as much as for what they give. Better far is it to have less writing, have it ex- amined, criticized and corrected, than to have much written in a careless, indifferent way. As far as possible, the pupil should be his own critic — a question from the teacher, an interrogation point or some other suggestive symbol serv- ing to direct the pupil's attention to the weak point. Fre- quently, composition work may be placed upon the black- board and the class become critics. Criticism, in all cases, should be directed to those points which the pupil may reasonably be expected to regard in his usage. After the criticisms are all in — whether of flagrant ... , . . . r 1 1 • 1 Criticism violation of simple rules or of the higher mat- and Improvement. ters of good style — the pupil should be expected to re write, profiting by the suggestions received. The re- writing should be regarded as a privilege rather than a I70 THE MISSOURI SUPERVISOR. penalty. This view may be secured, if the teacher be tact- ful in presenting the matter to his class. Language work should be food, not "medicine" to the pupil. ^ After a second writing and a second criticism, the com- position may be transferred to a "composition book" and preserved. If the date of writing be attached to each, the pupil will, in later years, derive both pleasure and profit from an occasional inspection of the steps by which he climbed. These composition books may be purchased for a few cents or manufactured from suitably-ruled paper. Occasionall)' a composition may be written on a topic used some months before, without re-reading the earlier exer- cise until after the latter is completed. For indicating mistakes and suggesting improvements, a simple system of symbols is desirable. Variations of the following have been used by many teachers, placing the symbol in the margin, and underscoring the error if desired: C — mistake in the use of capital. P — mistake in punctuating. S — mistake in spelling. G — mistake in grammar. Wd — wrong word. ( ) — re-write. (Enclosing the part.) Wr — careless writing. Par — new paragraph. ? — inquire about this. A simpler form has been recommended, consisting of an oblique line (blue), through an error in spelling, punctua- tion, or use of capital, a line under a misused word, and parentheses about anything that needs reconstruction. LANGMGE AND GRAMMAR. 171 Sometimes old€r pupils may be trusted to criticise the work -of a lower grade. This will be good for the examiner and fof'the teacher, but the teacher should not fail to in- spect at least a part of the work. A COURSE IN LANGUAGE. Language work is many sided. It embraces training both direct and indirect. It includes much work of the text-books, but much additional work not found therein. In the following pages the aim will be two- fold — to suggest means of getting the most a Language "o 00 Course. good from our adopted texts and to indicate lines of supp'ementary work. Without attempting to sep- arate the 'two, we append hereto an outline of what is thought to be a fairly comprehensive course in language. I.- Uotistant use of language, oral and written, lead- ing tO'fluency and ease of expression. This begins with the beginning of speech and ends with life itself. It is given io the teacher to direct the current of thought and expression through several years of the early life of his pupils and this opportunity should result in the acquisition of a fluent and easy use of a rich and well-selected vocab- ulary. 1. Friefid/y criticism from teacher and classmates, leading to the eradication of error. This also, is a feature of the entire course, beginning with the simplest grammatical forms and leading up to the more abstruse elements of rhetorical finish. 3. Cd^/j'/^cr sentences, gems, parts of reading lessons and the like, from which much of the mechanics of com- 172 THE MISSOURI SUPERVISOR. position will be acquired. This work begins with the ability to write and may be continued with profit even to the fifth or sixth grade. Correct copying necessitates close observation, and thus another benefit is obtained. 4. Memorizing choice selections of literature. An- drew D. White has said that he is profoundly thankful to those early teachers who led him to store his memory with the beautiful gems of literature. Many a less noted per- son has ground for the same gratitude. Aside from the memory culture is that higher gain, the enrichment of the mind with the finest things in literature. From near the beginning to the very close of the language course there should be this storing in memory of suitable selections. A selection to be suitable should express a complete thought-unit, should reflect some universal experience and should be such as will grow on the learner as he grows older. Thus to memorize "Lo, The Poor Indian" without the setting is to miss the "beauty of the whole." "Paul Revere" contains nothing that is universal, nothing especially worthy of memorizing. Compare with "Abou ben Adhem" or "Something Undone" and the absence of the universal elements will be noticeable. 5. The mechanics of composition — punctuation, capi- talizing, paragraphing, abbreviations — begini^ing-with the copying work and extending through all the written work of the pupil until these points no longer need attention — i. e. , until their correct application becomes habitual. There is so little of this whole matter that it can be intro- duced gradually and yet effectively, so that the pupil ac- quires a mastery of the mechanical side of composition LANGUAGE AND GRAMMAR. 173 without a formal study thereof. The pupil ought to attend to much of this mechanical work in the same automatic way in which he dots his i's and crosses his t's — and habits are formed by repetition. 6. Description of objects, pictures, persons and places, proceeding from the very simple to that which is highly complex. Description may be either oral or writ- ten. The former may be begun before the child has learned to write. As soon as friendly relations are estab- lished between him and his teacher, he can be induced to "tell about" familiar things. Soon he can be led to ob- scrve and then to tell. Whether the lesson be one in read- ing or numbers or nature-study, it is also a lesson in language. There will be constant opportunity for oral description. Nor ought this phase of the work to cease when the pupil learns to write and acquires the power of written description. An occasional exercise in oral description is not amiss for older pupils. But after the pupil learns to write, there should be much of the written description. It may be of a simple- object like a top, or a complicated mechanism like a locomotive, an air-pump or a sewing machine, of the teacher's desk or Westminster Abbey, of a microscopic view or a mountain, of a picture from the wall, magazine or text-book, of well-known per- sons, or of places familiar to the writer. With such a wide range of materials as a basis and with the principle that "every lesson is to be a language lesson" as a guide, it is clear that this descriptive work may be continued through all grades of school work. 7. Narration of events present and past. The 174 THE MISSOURI SUPERVISOR. foundation for this line of work is telling what things are doing. From telling that "James is coming," it is an easy transition to a series like "James is coming;" "he is standing;" "he is opening his book;" "he is reading:" "he, is closing his book;" "he is sitting down." From the telling of a thing wliilc it is occurring, there is no difficulty in passing to the telling as if it were past. And from the single event past the child can be led to tell of the series past. And here open up the illimitable fields of the past so far as the pupil's knowledge can penetrate. What he has done, what his friends, animal and human, have done, what others, noted and obscure, have done — all these may be narrated in a style varying from the simplest to the most ornate. Consequently this phase of language work is suitable for all grades beginning quite early in the first. 8. Dictatio)2, suitable for any grade after the pupil has learned to write. The principal uses to which this kind of exercise can be put are the correction of work al- ready prepared or the taking of new work to be corrected later. Dictation can be made a valuable aid in the me- chanical phases of composition. g. ; Reproduction, oral and written and adapted to any grade. Th3 child should be trained to gather thought from a single reading or hearing, and to reproduce it in connected, form. But let it be remembered that the thought of a selection may be reproduced quite fully with- out repeating the original words. This form of language work can be used nicely in connection with the Reading and History both regular and supplementary. There ought LANGUAGE AND GRAMMAR. ^ 175 to be no difficulty in finding material for this kind of work. Reproduction, however, must not be allowed to usurp the place of originalthought. Each has its place in language work, but the very ease with vvhich selections can be read and reproduced may influence both teacher and pupils to look with undue favor upon the reproductive work. 10. Supplying ellipses in sentences. These sentences are to be written upon the blackboard and blanks left in- dicating the place where the omitted word or phrase is to be supplied. Such exercises are of value in leading to a discrimination between correct and incorrect forms, be- tween words similar in sound but unlike in meaning, and between words almost synonymous. These lines of work are illustrated below. In the first group the pupil is directed to supply the proper forms of see; in the second to use to, too and two correctly; in the third to insert enough or sufficient as may be proper. I President Cleveland. Have you him? John two presidents, etc. whom did you speak? Which— — shall I bring you? Shall Charles come ? etc. Although he never had money, yet it was evident that he had — -^to meet all reasonable demands, etc. 11. /^-F^crz'/;?^^^ r6';;/<'.\7.f about isolated sentences. This will prove profitable anywhere between the third and sixth grades. Select a sentence from the middle of a well- writ- ten paragraph and let the pupils supply a setting, or write the first sentence of a paragraph and require the pupils to complete it. 12. Coinpleting Unfinished Stories. Read to the pupils 176 THE MISSOURI SUPERVISOR. a portion of some new story. Have it discussed if need be, and reproduced to show that it is fully in mind. Then allow pupils to complete the story according to the individ- ual likings. Often there will be profit in allowing other pupils to criticise these endings. Old copies of the "Youth's Companion," ''St. Nicholas," and the like will be helpful here, and stories can be found for almost every grade. 13. Making up s/ories from pictures or from sugges- tions. The value of pictures in this connection is great. Such pictures as were found m Miss Hyde's primary book and such as appear in almost every issue of the better class of juvenile magazines will be of immense value. Suggest- ive directions may call forth imaginative productions. For example: "Write a story of a little boy seven years old and his little five year old sister who started out to see the circus." Or: "Tell the story of a little fish that disobeyed its mother and played about a fly. " Or, for older ones: "Write an account of a man who has been living on a lonely island for fifty years and now returns to the United States." 14. Writing letters, business forms, advertisements, telegrams, notes, receipts, news items for local papers, etc. This will be "practical" and interesting work. A weekly "paper" may be issued, with some of the older pu- pils as editors. The paper may be made a resume of the news of the week as written up by the pupils, the best be- ing selected for "publication." Skillfully managed, this device may be made productive of much good. Every editor will testify to the need of such work. LANGUAGE AND GRAMMAR. 177 15. Paraphrasing and atnplifying selected passages. For these purposes suitable selections may be made from the reading matter of pupils or teacher. Sometimes the two lines of work may be combined, but not usually will it be desirable to unite them For paraphrasing, poetry is par- ticularly suitable. Such poems as Evangeline, Snow- Bound, Deserted Village, Enoch Arden, and many shorter ones may be utilized occasionally for this purpose. The amplification may be of a descriptive sentence, a proverb, or any expressive quotation. Paraphrasing is closely re- lated to -'reproduction," and, therefore, is available for nearly all grades. Amplification ought not to be at- tempted until pupils have developed considerable power of thought. 16. Using the dictionary. The "dictionary habit" is one of great value to any student. Many studants never learn how to use the dictionary, and many more never form the habit of doing so. Every school-room wherein are pupils above the primary grades should be supplied with one of the standard dictionaries, and every pupil above the primary grades should own a small dictionary. Spelling, pronunciation, etymology, meaning and use of words are to be found in the dictionary. From it also may be drawn material for the study of synonyms and paronymns. 17. Composition-writing. This is an important type of language work. The descriptions and narratives re- ferred to above , are included under the broad term "com- position." But there is another phase of the composition process, the more formal and frequently more dreaded one. 178 THE MISSOURI SUPERVISOR. which usually bears the exclusive title "composition." The common dislike for the composition exercise is generally due to the air of formality in which the whole subject is enveloped. When the pupil is assigned a subject that is neither entirely above nor entirely below his plane, and one about which he knows or can know something, he will lack that unwholesome dread of the work. Much of the antipathy to composition-writing is of the same nature as the dread of letter-writing so common among adults, due largely to the mere fact of be- ing apart from the accustomed round of experience. What is usual. and habitual is easy. It is the line of least resistance. The conclusion from these premises is evi- dent. Make it usual and habitual to express thought both orally and in writing and neither will be dreaded. The earlier compositions will consist of few and dis- jointed sentences. But practice in writing and the study of selections with "quality rather than quantity" as a motto, will gradually develop the power of connected discourse. Without "making a hobby of language," a pupil who passes through such a course as we have out- lined ought to attain a fair degree of proficiency in the use of English. A recent writer, Prof. J. B. Wisely, has pre- sented the following as his ideal, yet fears that^it is set too high, a fear that ought to be groundless: '■'■I tvish my pu- pils, as a result af their composition work, to be able to take a subject, think the thought of it carefully and accurately, organize that thought about a purpose, and express it ac- curately and appropriately in a paper of printable English, neat inform, properly punctuated, capitalized, paragraphed LANGUAGE AND GRAMMAR. 179 and tvith no misspelled words.'" Every teacher of children ought to be able to say, "my sentiments too." Early m their composition-writing pupils ought to discern that certain thoughts hang more closely together than others do. Thus in writing about the horse we may tell "how he looks" and "what he does," and thus the child will be led to appreciate the purpose and method of paragraphing. At first this divisi-on into paragraphs may be secured by a few broad questions; as for example, What is a wagon? What is the shape of the wheels? What are the kinds of wagons? What are wagons used for? Later on the pupil alone or with the aid of the teacher works out an outline, such as the following: i I. Parts and their uses. Wagons - 2. Kinds and their uses. ( 3. How and where made. [ I. Qualities. *Coal .<■ 2. Uses. ( 3. Where and how obtained. Steel [ I. Qualities. I 2. Uses. I 3. Kinds. [ 4. How made. [ I. Appearance — size, shape, color, covering. ryy p 1 ! 2. Principal parts — description and uses. ' 3. Habits. [ 4. Uses. *The form of these outlines was suggested by Prince's "Courses and Methods." iSo THE MISSOURI SUPERVISOR. l' I. Appearance — size, shape, color. The Tea | 2. Principal parts — root, stem, leaves, etc. Plant "I 3. Where found. l^. Use — preparation for. Lincoln -\ [ I. Birth — time, place, parentage. 2. Home and early influences. 3. Boyhood and youth. 4. Education. 5. Public career. 6. Domestic life. 7. Death — when, how. [ S. Character. ' I. Location. 2. Size. 3- Divisions. 4- Principal streets. St. Louis - 5- Points of interest. 6. Chief industries. 7- Educational advantages ■v" -8. Municipal organization. I 9- History. A Trip to Jefferson City ^ 1. Time and place of starting. 2. Route taken. 3. The intervening country. 4. Objects and incidents of the way. C I. When reached. I 2. How received. 5. Destination -j 3. 4- [5- 6. Length of stay. 7. Return. General impressions. Later impressions. Places visited. LANGUAGE AND GRAMMAR. i8l C I. First building — when, where, why. j 2. Construction —how, cost. Railroads J 3. Extent. { 4. Organization. j 5. Benefits. [6. Ownership. Benefits of Railroads. 4- 5- 6 17- To those who furnish labor and materials To employes — number, wages. f 1. Grain. To produc'rs of -•, 3. |4- To new countries. To travelers. To publishers. To governments. Live stock. Manufactured goods Minerals. Lumber. fi. Frequency — tendency of the times. j 2. Cruelty to horses — examples. Cruelty to | 3. ; Cruelty to dogs. Animals. -[ 4. Cruelty to birds. I 5. Cruelty to other animals. I 6. Effects on the person. [ 7. Best means of prevention. These outlines are merely typical. Instead of "Wagons" the teacher may substitute Watches, Printing- presses, Sewing-machines, Pumps, Steam-engines, Cars, Boats, Plows, Houses, Stoves, Books, etc. For "Coal" he may put Salt, Iron, Gold, Water, Wool, Marble, Asbestos or Petroleum. "Steel" belongs among manu- factured articles along with Wine, ;^Rubber, Ice, Glass, Lumber, Flour, Sugar and Thread. The "Camel" may i82 THE MISSOURI SUPERVISOR. be displaced by the Horse, Ox, Sheep, Dog, Elephant, Cat, Pigeon, Whale, Hog, Seal, and the like.- With the "Tea Plant" might be grouped the Coffee, Banana, Lemon, Apple, Grape, Corn, Wheat, Hemp, etc. Lincoln is but one from a long list of names eminent in the world's history and from this "honor roll" many other names may be chosen: Grant, Stonewall Jackson, La Fay- ette, Whittier, Irving, Major Andre, Pochahohtas, Flor- ence Nightingale, Edison, Webster, Gladstone, Greely, Franklin. For St Louis and Jefferson City may be writ- ten the name of an}' town in Missouri or elsewhere. Somewhat like "Railroads" ma}' be discussed Banks, the Telegraph, etc. Many topics cannot be outlined accord- ing to a model but each must be considered independ ently. 1 8. Analysis of selections from standard literature — not hair-splitting grammatical dissection, but an attempt to determine the thought of the author, his purpose in ex- pressing it, and the method by which h,e attempts to ac- complish his purpose. This will necessitate some sort of outline of the selection. Afterward, this outline may be used again as a basis for a composition. ig. Tt'chnical grammar, for the sake of its training in analysis, its help in determining correctiforms, and its explanation of the correctness or incorrectness of any ex- pression. 20. Figures of speech and the simple qualities of style, which will be worth more to the pupil than would unlim- ited "word dissection." LANGUAGE AND GRAMMAR. 183 DE GARMO'S BOOK. It is believed that by the beginning of the third year the pupil will be able to take up and and use De Garmo's book. Part I can be mastered easily in one year if the pu- pil has had any language-training during the DeGarmo fwo years preceding. Should this preliminary work have been neglected, it will be best to de- fer the use of the text-book for a time. The pupil needs a limited amount of drill in the use of oral and written language forms before beginning the formal text-book work. The nature of this preliminary work has been in- dicated in the preceding pages, but a brief recapitulation is given below: I. Much use of language under the sympathetic guidance of a teacher who realizes the importance of habit and the ease with which it is acquired. This language is to be the expression oi thought — the enthusiastic thought of minds alive with interest in their fellows and in the world about. There will be facts to communicate, discov- eries to reveal, descriptions to give, and stories to narrate. Under the guidance of the capable teacher the child ac- quires habits of easy and correct expression of thought. 2. Copying from written or printed forms A Resume. and from dictation, according to ability of pupils. 3. Writing simple sentences which have been pre- viously expressed orally. 4. Reproduction, oral and written, of reading lessons or stories which pupils may have read or heard. iS4 THE MISSOURI SUPERVIbOR. 5. Sympathetic correction of errors in all these forms of work. When the text-book is taken up, it should be used with that same good sense which characterizes the intelli- gent teacher at all times. Text-books are the working tools of school life. No true teacher lashes himself hand and foot to any mast. The teacher may be an artist or an artisan, but if he attempts to follow any author unreservedly the title of artist must be denied him. In De Garmo's book are many excellent exercises. But the artist teacher will find places and ways of departing from the ways of the book. In some instances it will be to omit, in others to supplement. At all times let it be realized by Following teacher and pupil that text-book pages are not the Book. f f r fs a measure of success or failure. Improvement in the use of the mother-tongue is the criterion of progress. This it is that the teacher's eye should be seeking to discern. The exercises of our text-book will prove helpful to this end, especially when used in the light of the author's valu- able hints as to the purpose and method of the several lessons. Supplementary work similar to that of lessons IX, XVI, XXIII, XLVII, XLVIII, may be provided in abundance, "^sop," "Robinson Crusoe," and other books of stories may be drawn upon for work similar to lessons XX, XLVI, LXXX. These exercises may be handled in such a perfunctory way as to render them valueless. On the other hand they may be so conducted as to be of very great value. Let the incidents be stated in answer to the teacher's questions. For example (lesson LXXX): What was one thing Robinson Crusoe lacked? What did LANGUAGE AND GRAMMAR. 185 he make instead? What did he do each morning? After his return what did he do? What did he shoot one day? How did he feel? What did he see? How did he then feel? Etc., etc. After going through the exercise in this way, the teacher may ask questions or give directions that will require several statements, as "How did Robinson spend his time?" Or, "Tell about Robinson and the kids," etc. In this oral work good language must be re- quired. After the thought has been mastered and ex- pressed orally, it should be expressed in writing. This can be done out of class, but must be submitted for criticism. For the right presentation of the work required by De Garmo's book certain things are necessary. Of these, two are specified: a knowledge of mythology, literature, and history, and a trained imagination. Unless , , . , , . .,, , , Requirements one possesses these, his teaching will be barren from the Teacher. indeed. It will be a desert land through which he will conduct his "language" classes. The teacher who doesn't enter into the spirit of Robinson Crusoe, Ulysses and Lincoln, will make a flat failure of the language lessons relating to them. Exercises in description (see lesson L) may be multi- plied. In such work the thought of lesson XLIX should be applied. In this grade, the oral phase is quite prominent. The oral language of pupils must be closely watched by both teacher and pupils. This is not limited to the reci- tation of the language class. "Every lesson is a language lesson" to the extent of requiring the use of language and i86 THE MISSOURI SUPERVISOR. providing opportunity for impressing good forms of speech and uprooting bad ones. Reproductions of stories, simple descriptions, accounts of the reading lesson Oral Work. may be put into oral form and may be of great value. Sometimes this oral work may precede the written, sometimes may be used independently thereof. Beginning with this grade and increasing in difficulty with the development of his powers, the pupil may be trained to think sentences into appropriate settings. Thus such a sentence as "Once a year they returned to their former home," or "The postman handed me a box this morning" may furnish the basis for an interesting para- graph from each pupil. Here the individuality of the several pupils will appear. Give rein to the imagination in such work. Insist upon two things only — that the pupil do his own work and that it be his best. "Part II," the fourth year's work, may be supple- mented in much the same way as has been suggested for "Part I." The stories, both historical and legendary, may be supplemented by others of like or unlike "Part 11"— nature. "Boys (and girls) who have made Fourth Year. -^ V o y themselves famous" may be talked about and written about — thus introducing the pupil to an interesting phase of history. The comparison of adjec- tives, lesson X, may be pushed farther. A more thorough drill on the work of lesson XXVIII will be desirable. Exercises 72, 75 and 84 go well together, and the uses of shall and will need even further elucidation. Lesson XLVII may be extended indefinitely. The treasure houses of Greek, Roman and Indian history and mythology LANGUAGE AND GRAMMAR. 187 have been unlocked and their contents given to us in innumerable volumes. All these are accessible to teachers of the present day. Lesson LIV may be followed by a study of love and like, think, expect and guess, teach and learn, stop and stay, etc. In addition to the text-book requirements, there should be further work in oral and written discourse. Reproduction of stories and of reading lessons, incorporating isolated sentences into contexts, description of objects and actions are within the scope of fourth grade work. In his written work, let it be assured beyond doubt that the pupil has not only something, but a clear-cut and very definite something, to say. The pre- requisite for this is something definite in his thought. Require him to know the story definitely before tr^'ing written reproduction; to see objects and actions clearly before describing them. The fifth year's work comprises Part III (or Parts III and IV,) of DeGarmo's book. The first is but a continua- tion of the work of the year preceding, with a near induct- ive approach to the confines of technical „ -I-. TtT 1 -1, Fifth Year— (jrrammar. Fart iV approaches nearer still. Parts iii and IV. What a compliment it is to our author that a pupil is inducted into technical Grammar without realizing the fact! Under the old regime there was no uncertainty upon this point. The event was usually suggestive of a plunge bath or the filling of a tooth. DeGarmo's book, therefore, forms an excellent basis for Patrick's. If desired, Part iV may be disposed of briefly since the same topics come up in the later book. But the author's sug- gestions and method are so helpful that the time neces- iS8 THE MISSOURI SUPERVISOR. sary for a more careful treatment of the twenty-eight lessons of this section of DeGarmo's work can be spent here with profit. The work of this part will not be difficult for one who has had what precedes in DeGarmo's book. Supplementary work will be necessary in connection with Part III and desirable for Part IV, if that division is extended thtoughout the sixtli year. Work similar to lessons IX, XXI and XXXI, may be added. Time may permit and the teacher will doubtless desire to add to the "Fables and Fairy Stories," to the selections from the "Life of Lincoln," the "Adventures of Ulysses," "Stories from Rip Van Winkle," and the science studies in Chap- ters III and V of Part III and throughout Part IV. LESSONS IN GRAMMAR. It is believed that a pupil properly trained in the use of his mother tongue — and this does not imply an undue amount of attention to the subject or the neglect of anything else— will be ready for lessons in Grammar at the beginning of the sixth year. This is sufficiently early to satisfy the most ardent advocate of A New Book— technical grammar. On the other hand, the Patrick's. "language enthusiasts," after seeing the pupil safely through such a course as we have outlined, includ- ing both DeGarmo's admirable text and much supplement- ary work ought to be willing to relinquish him for a few minutes each day to the grammarians. In this way the pupil acquires both the art and the science — the former by practice at his most impressionable period, the lattei after LANGUAGE AND GRAMMAR. 189 his reason has had a sufficient development to enable him to comprehend a science. In choosing this mean between the extremes of "all grammar" and "no grammar," we are, doubtless placing ourselves on safe ground. It will be observed, however, that the ^'grammar" of Patrick's book is far from being an encyclopedic aggregation of defini- tions, diagrams, rules and exceptions. Nevertheless the main facts of English Grammar are clearlyDset forth and abundantly illustrated from the rich mines of English and American literature. These illustrate the points of technic- al Grammar- — they illustrate also the best products of the English mind. Whether created or quoted — illustrations should be something more than a mere formalism. Superintendent Patrick claims that the '■'■exercises are a marked feature" of his book. He may well be pleased with them. A pupil who thinks his way through both or even one of the Patrick books will know more of English than if he had the 300 pages of some of the more formida- ble texts "by heart." Two years should be given to Patrick's first book. This will afford ample time not only for doing well the work of the book, but also for a continuation of the work in composition. This composition work will resemble that of the preceding years, but will be of increased difficulty. It ought also to be free from many of the errors and crudi- ties of the former work. There ought to be a finished composition from the pupil twice a month to the end of his school course. In the main, the plan of the "Lessons in Grammar'' is obvious, as the author claims. On the other hand, igo THE MISSOURI SUPERVISOR. there seem fo be some slips that indicate a lack of logical coherence, e. g., on page lo, where there are fo°b^e^ Watched ^^^^^iscs upon "the Complement of a copulative verb," although the pupil does not learn what a copulative verb is uiitil he reaches page 40, and for the "complement of a copulative verb" he must wait until he arrives at page 43. This defect can be obviated by the omission of the objectionable exercises -on page 10. Again, the definitions and presentation of infinitives and par- ticiples on pages 49, 50, 87 and 88 of the "Lessons" are completely at variance with what we find on pages 22-25 o^ the "Higher English." This discrepancy cannot be ex- plained as the enlarged view of an advanced over an ele- mentary text. The differences are fundamental. If- the participle "has the properties of a verb and adjective or verb and noun" in the higher book, it ought to do so in the lower. The gerund, which in the elemelitary book, is a "participial infinitive," recovers completely and is a well-behaved participle in the higher— a reformation we are glad to, record. A similar unsatisfactory treatment of mode is noticeable. In the "Lessons" (page 52), "there are three modes— the indicative, imperative and the sub- junctive." On page 59 of the same book is a synopsis which may be cofistrued as implying six modes — the three just named, together with the "conditional, j^tential, and the obligatory"-^while on page 38 of "Higher English" we are told that "there are four modes— the indicative, the potential, the subjunctive and imperative." We might infer from this that there are "three modes" of classifying modes. Our suggestion is that our author be taken at his LANGUAGE AND GRAMMAR. 191 best. Neither he nor any other thoughtful teacher would have us present things as contradictory aS' these are, even though the contradictions are' mostly between the succes- sive books of a series. We may expect an elementary text to lack the fullness of a high school text, but a science does not contradict its teachings to children when it attempts to instruct adults. All things considered, we hesitate not to pronounce the view of the higher book on these contra- dicting points much the more satisfactory. Its treatment of the infinitive, the participle and mode is clear and log- ical. We commend it, therefore, for this reason, for the teacher' s guidance. By taking two full years for the completion of the ele- mentary book, ample time will be found for the introduc- tion of much supplementary work in connection with each topic taken up. The good teaching of almost every book requires this supplementary drill work. State law prohib- its the use of any other book as a text, but the earnest teacher will find in other texts much available material of great value and this may be used. "Exercises" should be multiplied until the successive topics are well mastered. The needs of the pupils must determine the amount of supplementary work. There may be a great deal of work based upon pages 61-64 ^^^ 74' ^^^ that of pages 166-192 may be extended almost indefinitely. A few words of caution will not be inappropriate here. First, if pupils have not had much drill in "language" work, endeavor to introduce a great deal of it in connection with the Grammar. Proceed very slowly with the Grammar, and be not easily discouraged. Next, see that the "exer- 192 THE MISSOURI SUPERVISOR. cises" represent the pupil's own work. Take care that the work is not done /or the pupil and that he does not inherit illustrative sentences from a preceding class. Constant watchfulness backed up by a wholesome sentiment is the surest preventive. Patrick's second book, the "Higher English"is largely a continuation and expansion of the "Lessons in Gram- mar." In many instances it is but little more than a review. In others the two are contradictor}', as has been shown. In the last third of the book, however, the author enters new territory and acquaints the pupil with figures of speech and style. Copious exercises are introduced to impress what has been presented. It would be well could every young person against whom the doors of the "High School" are closed, be permitted to have at least such a taste of the well of higher English as in offered in this book. Life's horizon would be greatly broadened, even with no further study. GEOGRAPHY. 193 CHAPTER IV. GEOGRAPHY. GENERAL DISCUSSION. Before the teacher is prepared to grapple with the how of Geography, he should have devoted considerable thought to its what and %uhy. In other words, the question of methods in Geography does not concern him until he has determined what constitutes Geography and why the subject is taught. Signifying etymologically "a description of the earth," Geography has been construed by some as an encyclopedic accumulation of facts about locations, heights, distances and the like, all resting upon a basis of maps and printed descriptions. To quote the expressive what is ^ ^ -ax- Geography? language of Prof. King, "Geography has too frequently been treated as though it was the science of the where, map-drawing its chief glory, and the memory of words its only means of acquisition." Casting aside this erroneous conception, we are confronted with a multitude of other views, each differing as its possessor's power of interpretation", his "apperceptive power," differs. To one "the earth" is merely the local neighborhood projected into the unknown. While to another it signifies a great 194 THE MISSOURI SUPERVISOR. world-organism energized by those forces that make history possible and help to make it what it is. The pupil begins with the "neighborhood" view; he should grow toward the broader. More and more clear it must become to him that there is a "soul of the world," a great inner unity of plan and purpose like that which pervades the human body and makes it more than hand and foot and eye — in short, makes it an organism. It is needless to add that this higher conception of the earth should be the conception of every one who undertakes to teach Geography. To conceive the subject as a series of map-descriptions is to miss its true purpose altogether. The danger of this broader view is that it will lead to an undue extension of the sphere of the Geography. It must not be allowed to encroach upon the domains of Geology, Physics and History. Each of these has its own sphere. Geography, in short, must not attempt to cover the whole circle of human knowledge. What then is Geography? As a working basis for teachers, there is probably no better definition than this of unknown authorship: "Geography is the science of the earth as an organism, affecting and affected by J^^ man's institutions." As such it touches without Answer. encroaching unduly upon the whole circle of natural and social sciences. It gathers facts from all these sources and relates them into a science^ — the science of the earth inhabited. Geography, when properly comprehended and prop- erly presented by the teacher, is highly valuable. Even when it was taught solel)- for the sake of information to be GEOGRAPHY. 195 gained, it was considered worthy of study. Now with our enlarged conception of what Geography is, comes an enlarged conception of the purposes of its presentation. Geography properly presented to the child-mind awakens its powers into activity, giving them increased vie:or from their activity and offerin^j excellent Purposes of ° J <^ Teaching. opportunity for their training. The imagination is aroused and developed. Judgment receives excellent exercise. The conceptive powers are expanded. Imagin- ation gives originality; judgment becomes "common sense;" conceptive power means breadth of mind. A study that results in a marked development of these powers certainly has a high culture value. And it should not be forgotten that the culture value of Geography far outweighs its information value. But is geographical study to impart no knowledge? Is the student to learn nothing? Most assuredly he is to learn something, to learn many, many things, but the most important is the use of his own men- tal powers. Current methods of geography teaching are not per- fect. Some of the defects are very pronounced. The fol- lowing are of frequent occurrence: 1. Making Geography too largely a mem- ory study. Defects. 2. Making locality too prominent. 3. Mistaking map study for Geography study. 4. Failing to actualize through the imagination what is gleaned from maps and descriptions. 5. Too little comparison. 196 THE MISSOURI SUPERVISOR. 6. Failing to discern and emphasize what is of im- portance. 7. Artistic map drawing. "Humanity, not locality," should be the aim of geo- graphical study. Instead of burdening memory with a mass of insignificant details concerning heights, distances, products, boundaries, etc., — matter that will soon be for- gotten except by a few — how much more rational to give the time to a few typical regions and use these as a basis of comparison for all others, discriminating between those that have significance in human progress and those that are merely facts. A mere fact, with nothing but its truth to commend it, has no place in a school geography. It may be true that a certain peak is 15,086 feet high but what of it? Would not human history have been the same had that peak been 15,087, or even 40,000 feet high? How large a percentage of our pupils can advance any reasons for Chicago's marvelous growth or have an ade- quate conception of the resources of "imperial Missouri"? Too much attention is given to maps as realities. How many, like the lamented Nye, are disappointed in not find- ing Indiana yellow? How many think of the Amazon as a broad black mark, Washington City as a star, and Yellow- stone Park as a rectangle in the corner of the map of Wyoming? Is not teaching defective when the means be- come and remain the end in the learner's thought? Map-drawing should be an important adjunct of the work in Geography. It is possible, however, to make it too prominent and to give it a trend that is not wise. When a very considerable portion of the time allotted to GEOGRAPHY, 197 Geography is absorbed by map-drawing, or when the map- drawing degenerates into "artistic" attempts to vie with map-printing in variety of coloring Artistic Map- and nicety of detail, it is another case of a good servant that has developed into a bad master. To com- pel helpless Missouri children to reproduce from memory the minute irregularities of a line purporting to be at best, only an approximate representation of the coast of Maine or the sinuosities of the Tombigbee river, is both morally and pedagogically sinful. It is not denied that the child should know that the Maine coast is much more irregular than that of Florida, that Europe has better harbor facili- ties than Africa or South America, or that the Tombigbee makes its way slowly and tortuously through the alluvial plains of Alabama, but these are quite other matters. What then are the legitimate uses of map-drawing? The answer is to be found in a study of its effects upon the student's mind. Properly directed, map-drawing gives a comprehensive grasp of relations, binding the isolated and fragmentary together into a whole. Legitimate ° ^ D Results. It develops the power to seize upon that which is salient and to give expression to it in symbolic form. Finally, map-drawing may be made to impress up- on the memory the things worth the while. To the teach- er himself it has additional value as a means of illustra- tion. Every teacher ought to be a "chalk-talker." How can map-drawing be made to subserve these useful ends? Not by the methods commonly employed. These benefits cannot be claimed for the prevalent type of map-drawing. A practical kind is the rapid, yet neat, off- igS THE MISSOURI SUPERVISOR. hand sketching for illustrative purposes — to show com- parative areas, routes of commerce, causes of climatic con- ditions, belts of production, general direction of slopes, strategic points in war, etc. The ability to put into an off-hand sketch the location, boundaries and slopes of the Mississippi basin, a summary of one's knowledge of South America, or the objective points of the French and Indian War reveals more than a half hour's written ex- 5:^ap ^. amination can do. The pupil who is trained Sketching. ^ ^ to do such work neatly and rapidly is deriving a practical value from his map-drawing. Much, there- fore, should be made of the off-hand sketch-map. Of the artistically-drawn map Redway has said: "It is certainly not an essential element in the education of the average pupil." There are other forms of m?L^-7naki7ig that have value. The "progressive map," one that grows day by day as the pupil progresses in the study of the political or physical features, productions or history of a continent The Progressive or couutry, is of interest and value. The map Map. may be made by the teacher at the board or by the pupils during or after the recitation, or by both teach- er and pupils. If the teacher will prepare a card-board outline, the correct outlines of maps for pupils may be pre- pared with very little labor, and yet a correct outline be secured for the pupil's work. To show physical features several methods are em- ployed — sand, paper-pulp and putty being used for raised maps, and color, shading or contour-lines for relief maps. The raised maps may be made of sand or paper at little GEOGRAPHY. 199 expense. The putty map will hardly justify its cost. The other two riiav be made useful in Physical •' Maps. connection with such physical maps as those in the books of the Rand-McNally series. In making the sand-map the following steps may be observed: 1. Sift a thin layer of sand over the board, mark out the outline with a pencil, take away the outside sand with a brush. 2. Sift over the great highland regions in proportion to height. 3. Pour sand through a little funnel to represent the mountains and watersheds. 4. Trace the rivers and lakes with the pencil point. For the pulp-map, crumple a poor quality of newspaper, put it into ajar and cover with boiling water. After a few da3's the fiber will have disintegrated and the pulp may be applied to an outline map traced upon a muslin cloth which has been tacked upon a board of convenient size. With no undue waste of time, pupils can prepare physical maps in colors or by shading. The latter plan is used in our adopted text. The representation by contour-lines is the most accurate of all in the hands of a skilled engraver with sufficient data before him (See Professor Marbut's inap of Missouri in the second book, Rand-McNally. ) A map of this kind is the most valuable of the physical maps, but it is too difficult for construction by pupils. One of the first duties of the teacher of Geography is to ascertain what basis of knowledge his pupils bring to the work. No normally constituted child can live in the world for six years without learning something of the e'e- 200 THE MISSOURI SUPERVISOR. ments of Geography — of land, water and atmosphere, and the forces acting upon and through them. Some children know much more about these things than others 'fi.^ „ do, but all children, whether from city or coun- try, know something. Rain and snow, frost and dew; heat and cold and their effects; succession of day and night and of the seasons; sun, moon and stars; wind, clouds, smoke; boiling and freezing of water; some plants — their care, growth and uses; some animals and minerals and their uses; means of communication and travel; occu- pations and manners of life; manufacture of certain articles; races of men, religion, government and education; city and country; some of the units of land and water surface — hill, stream, pond, creek, river; soil, sand, rock, clay, mud and gravel; descriptive terms like round, long, green, blue, up, under, hot, cold, hard, soft, smooth, rough, high, low, wet, dry, light, dark, large, small — these are some of the things about which even children of six will have ideas, more or less incorrect and indefinite, it is true, but yet sufficiently akin to the genuine to serve as a basis for geographical work. How interesting it should be to the child to begin his study of Geography with these partially familiar matters and have unfolded to him the mysteries of the unknown. And how dull and depressing, on the other hand, to attempt to initiate the pupil into this new field through the door-way of map-drawing. This is the period in which the child's observing powers are keenly active — his reason, as yet, practically dormant. Hence the subject-matter and the learner seem admirably fitted for each other. Geography is suited for observation and constructive work. GEOGRAPHY. 201 and the child mind is never more at home than when, engaged with these things. Eye, ear and hand are the agencies through which the throbbing energies of child- hood go forth. Wise teaching utilizes all of them. "Observation work" should have a prominent place in the presentation of Geography, especially in the primary grades. The child should be led not only to see what has hitherto escaped his observation, and might always do so, but also to interpret what he sees. Children can reason about these things much more than is commonly supposed. From the basis of the "known," the child is led gradually into the unknown with such an easy An objective transition that all the naturalness of the home life is preserved, and, unrealized by himself, he becomes a thoughtful interpreter of the natural phenomena that he has probably learned to love already. This is certainly a better plan than tearing the child away from Nature's works and setting him to interpreting a kind in which he can have little or no interest. The teacher himself, to do this work successfully, should be a loving and thoughtful student of nature, otherwise it will be a case of the blind leading the blind. Having ascertained just what the children know, the teacher sets about directing them into the unknown. He leads them to observe the greater heat of summer and associate it with the greater altitude of the sun and the longer days. He leads them* to know that winds are air in motion, resulting from a difference in temperature between two places. The tea-kettle and the laundry furnish the key to evaporation and condensation and thus to clouds, 202 THE MISSOURI SUPERVISOR. rain, hail and snow. From rain and snow it is not difficult to lead to soils, moisture, vegetation, springs and streams. The pitcher of cold water is an illustration of From the . i i r r i Known to the the formation of dew. i he land forms of the Unknown. neighborhood will likely include the plain, the hill and valley, and from these the important subjects of slopes is reached. The slope leads to a consideration of the stream in connection with which there will be opportu- nity to consider such terms as bank, mouth, current, bed, bar, tributary and, possibly, falls, island, peninsula, isthmus, cape, bay and gulf. The conception obtained by contact with these natural forms far surpasses in clearness and correctness any that can be obtained from definitions, descriptions or even pictures. While studying the rains and streams, it will be easy to consider the changes wrought by these agencies — the cutting, carrying and filling — changes that occur by every road-side and are repeated on a larger scale in every stream. From this point it is but a step to the consideration of soils — alluvial, native or drift — and the abundance of vegetation on each. Plant and animal life may be studied with interest and profit. Many new things can be learned about the most common plants and animals, if the teacher have the wit to direct and to impart wisely. Bishop Vincent has said: "A child of five ought to be able to recognize all the trees about his home by the differences in their leaves. "As a matter of fact, what percentage of adults can do this? The answer to this question shows how far short of our possibilities we are falling. And what is true of leaves is true of a hundred other lines of thoughtful observation. The truth is that GEOGRAPHY. 203 the education of the present is still too suggestive of that of the Dark Ages, when youth were educated for another world than that in which they were living. The statement of Bishop Vincent, which has been corroborated by the testimony of hundreds of others, reveals what a child of five can do. Can we be accused of setting our mark too high in askmg the teachers of our state to train our children in using close, accurate observation on those things that they meet almost every hour of their lives? THE COURSE IN GEOGRAPHY. FIRST YEAR. The observations of this year are necessarily simple in chaxacter, but they should gradually increase m com- plexit3^ Some of the things which pupils may be led to observe and to talk about are: 1. Weather — ram, snow, frost, dew, clouds, wind. 2. Sun — rising, movement, setting, shape, light, heat. 3. Land — hill, slope, top, roads. 4. Water — rain, creek, river, pond, wave, well, spring. 5. Temperature — hot or cold, of air, water, metals, — freezing, thawing, melting. 6. Fire — fuel, warmth, ashes, smoke. 7. Soils — black, red, clay, sand, gravel, loam, dust. 8. Plants — kinds, places, sizes, uses, colors, growth. 9. The apple — size, colors, parts, growth, uses- 204 THE MISSOURI SUPERVISOR. 10. Growth — of seeds planted, of crops, trees, animals, self — food. 11. The horse — size, colors, uses, food. 12. Men — color, occupations, food. II. Tirvis of various kinds, all necessary to correct con- ceptions, are to be learned as far as possible through the child's own activities: 1. Position — above, below, beside, in front, behind, corner, middle, between — by actual placing. 2. Distance — near, far — by actual comparison. 3. Direction — right, left, east, west, north, south. East and west can be learned as the direction of the sunrise and sunset; north as the direction facing, with the right hand to the east and the left hand to the west, and the south behind. Mark them upon the floor and drill in many ways. 4. Size — large, small, tall, low, broad, ,slim — by com- parison. 5. Form —round, square, three-cornered, pointed, oblong, straight, crooked, — by study of objects. 6. Color — black, white, brown, red, green, blue, yellow, orange, violet — by means of decomposed sunlight and natural objects as leaves, flowers, fruit, etc. Ill Reading stories to the children from such books as will interest them in good reading and in Geog- raphy as well. * SECOND YEAR. The observations of this year become still more seach- GEOGRAPHY. 205 ing and accurate. Those relating to soils, weather, plants, animals and occupations particularly, are susceptible of great extension. The pupil is becoming better and better acquainted with his home, the earth, and the reading of such a book as "The Seven Little Sisters" will give him vague notions of regions far, far awa}', which belong to the same earth as his, but the world is, as yet, a world without form and without boundaries. THIRD YEAR. This year's observation work should deal with such fundamental conceptions as hill, valley, plain, cape, penin- sula, stream, river, lake, island, etc., — in which the aim should be to lead to a comprehension of what is vital in each. The sand table will aid in impressing the results of observation. Trips to the blacksmith's shop, the post office, grocery store and the like can be of immense value in many ways. Practice reading and consulting the ther- mometer and making records of the weather. The third year ought to impress upon the pupil the idea of boundary — limited area — of desk, room, yard, farm district (or town), township, county and state — and the idea of representation — mapping. The first represen- tation, "picture," upon the child's slate may be of his book or box, an object smaller than his slate. An attempt to represent his desk results in a difficulty — the size is too great — and a solution-- reducing the scale. In some schools systematic drawing presents the reduced scale earlier than this, but generally it is the ^fj^j^ Geography teacher who has the obstacle to sur- 2o6 THE MISSOURI SUPERVISOR. mount. A distorted drawing with one dimension dis-pro- portionately reduced will develop the idea of proportion. Then measuring the desk, e. g., one foot by three feet, represent it one inch by three inches, one half-foot by three half-feet, one two-inches by three twos, etc. The school-room, the yard, etc., can be reduced in the same way. Tell the pupil that maps are nearlv always hung with the north uppermost. Let him hang some of his maps and note the other directions. Teach that in nearly all maps the top is north. Apply this. In maps of room, yard and district, locate the most important object —stove and desk, school-house and well, school-house, roads, streams and some residences. In the township, county and state maps avoid details and start with the pupil's home. He has heard the county and state names. Help him to clear up his vague notions somewhat. Do not try to teach too much. It may not be out of place to note that our state is one of many making up a great country, the United States, which is, in turn, a part of a great body called North America. But anything more than this is unnecessary here. The pupil can now read for himself. Suitable books for the several grades are listed in the appendix. FOURTH YEAR. The pupil now prepares to study Geography on a broader scale. He is now to rely upon others for his infor- mation. He receives a text-book as a store-house from which much of this material can be drawn. If the work outlined for the preceding years has been done, the GEOGRAPHY. 207 pupil is ready for the first lesson of the Elementary text — upon the surface and shape of the earth. Should the teacher find that the fourth year pupils have not received any preliminary instruction, he should be very careful to introduce much supplementary work, of the kinds indi- cated, as he advances. An earth bounded by the covers of a text-book is too small for an intelligent pupil or a suc- cessful teacher. We shall proceed on the supposition that the work suggested has been done or will be done. The following suggestions are made in regard to the use of the adopted text: Use it as a reading-book, i. e. , read it and then pre- pare to tell in original form what has been read. Supple- ment lesson I, by telling of Columbus and Magellan, by referring to the appearance of ships approaching or reced- ing (see figures in lesson 7), and by introducing the globe to illustrate the form of the earth and of the horizon. (A croquet ball, or an orange and knitting needle will answer almost as well as an expensive globe.) Gather materials from the fields for lesson 3. In lesson 5, teach that vapor of water and carbon dioxide are also in the air, and em- phasize their importance. Write a composition upon the uses of air. Be sure that lessons 6 to 1 1 are learned out of doors. Many a pupil has suggestions, learned "entirely surrounded," etc., etc., and waited for years before comprehending. For such as isthmus, delta, etc , find the nearest possible illustration in the vicinity and use the molding-board, imagination and pictures. See that these fundamentals are comprehended. Ask why water flows and rain falls. Do not fail to illus- 2o8 THE MISSOURI SUPERVISOR. trate the points of lessons 12 and 13. Pupils will surely know the cardinal points. If so, add the semi-cardinals in lesson 14. In lesson 15, teach also eastern and western, land and water hemispheres from the globe. Supplement lessons 24 and 25. This is a good place to study some of the industries. Approach the idea of government from the rules of the school-room. In lesson 26, pause to map the room, yard and district, if not already done. A small black ball with a chalk dot upon it will show the value of meridians and parallels in locating. The divisions of the continents should be grasped as solids, not mere surfaces. FIFTH YEAR. The year may begin with a brief review. For lessons 29 to 34 use the globe with maps upon its surface. Such lessons as 33 and 34 and preceding ones like 8, 16, 18, etc., will be helped by pictures from books and magazines. Dwell long on lesson 36. Train the pupils to interpret maps, both physical and political. Work much with open text-books. Locate your home on the maps of pages 66 and 73 and other places relatively. Point toward them. In connection with lessons 39, 40, and many others, there may be interesting composition work. Write upon the history of a breakfast, the building and uses of a railroad, the raising of cotton, etc. Along with lesson 45 study Missouri from the supplement, question much upon sur- face — elevation, slopes and soil — with books open. Com- pare the new at all times with what is already known. Study the pictures and bring in otheis. In studying pro- ductions of England, Germany and the like, have pupils to bring articles from those countries. GEOGRAPHY. 209 SIXTH YEAR. With the sixth year the pupil begins the advanced book of the adopted series. In plan, the book is similar to the Elementary — a general presentation of geographic facts, followed by a study of the several geographical divisions. Some have contended that the first fifty pages are too difficult for sixth grade pupils, and in consequence, have begun with the map-work about page 50. This plan argues a double misconception — first, of the importance of the descriptive element and second, of the author's plan. How one can read the preface of the work and , . . ,11 Plan of the run so counter to the spirit we can hardly con- Advanced Book. ceive. To follow the order indicated is like planting corn and doing the breaking afterward in order to avoid driving over the plowed ground with a planter. The kc}' to the whole volume lies in these first fifty pages. The manner of treating them will reveal whether the teacher is an artist or a day-laborer. For a proper presentation of these pages the teacher must have mastered them, both as to subject-matter and method. The following suggestions are offered in connection with some of the lessons of this year: 1. Emphasize "due north"and south in the lesson on direction. Too many think that San Francisco is south- west of the north pole. 2. Be sure to use the globe in the work relative to longitude. 3. Use a card-board disc to separate the illuminated from the dark half of the earth's surface. Choose a dark afternoon and use a lamp in the lessons on day and night 2IO THE MISSOURI SUPERVISOR. pnd seasons. With an inclined axis, a lamp and the disc, it ought to be easy to show why nights vary in length and seasons change. 4. Illustrate the points of the lesson on the use of maps by turning to some of the maps of the volume. Read the "note to teachers," p. ig. 5. In the lesson on Atmosphere, the following illus- trations will help: A tube filled with 7aa/er in the absence of murcury; down, or paper streamers to show air cur- rents about the windows or near a fire; the air near the wall bp.ck of the stove is warmer than that nearer the stove; use a stone and a vessel of water to show comparative absorptive and radiating powers. 6. Combine the lessons on "Weather" and the "U. S. Weather Bureau" with accurate observations on the weather. Procure actual weather maps for study. 7. As such topics as earthquakes, iron, coal, petro- leum, salt, cotton, oysters, sponges, and the like are reached, they may be studied from other sources and used as a basis for language work. 8. Add to the work on the great "commercial cities." Study one thoroughly and, taking it as a type, compare others with it. g. Read of the Indians, their schools, etc. 10. In connection with p. 86, study the Missouri supplement, bringing out physical regions, soil, slopes, resources, railroads, etc. 11. Seek after reasons. "As long as the teacher's questions all begin with zvhat? or where? he is calling upon hie pupils for nothing but the exercise of memory, GEOGRAPHY. and thev are acquiring information. When he asks how? and why? his teaching becomes scientific, he is calling for an exercise of judgment and reason, and his pupils are acquiring wisdom and power." 12. The following outline is offered as a guide in the study of a grand division and, with some omissions, in the study of countries. Prof. King, who ranks as a prince among teachers of Geography, advocates the topical method of study for all grades, choosing simple topics for beginners. One of the chief advantages of the method is its stimulation to original thought and investigation. If not used to excess it is a great improvement upon the "question and answer" method of study and recitation. Below appears the suggestive OUTLINE. I. Position. 1. Hemispheres — northern, southern, eastern and western. 2. Latitude, longitude, zones. 3. Boundaries — land, water. II. Shape— outline map. III. Size — relative, absolute. IV. Surface. f Ranges. Mountain | Slopes. Systems. -j Direction. I Peaks — volcanoes. [ Heights. Mountain systems. Plateaus. Highlands \ Valleys. 2. Lowlands 3. Put on progressive map 01 • Interior. Flams. -,' ^ , Coastal. 212 THE MISSOURI SUPERVISOR. V. Drainage. I. Water-sheds. 2. River Systems 3. Lakes Source. Course. Length. ' Uses. Tributaries. Peculiarities- Salt or fresh. Inlets, outlets. Value. -comparisons. VI. 4. Putting on map. [ Names. I Location. Political J Capitals and chief cities. Divisions I Soil. I Drainage. [ Productions. ( Oceans. VII. Natural I Divisions I VIII. Climate Waters Land Kind / Seas. ( Straits, etc. [ Peninsulas. Capes. Islands. [ Isthmuses. [^Temperature. ! Winds. Moisture. Causes [ Healthfulness. Latitude. Altitude. Winds. Currents. I, Mountains. Slope. Moiscure. Nearness to sea. GEOGRAPHY. 213 IX. Produc- tions. X. Life J" Fertile and sterile regions. J ( Mineral. ] Kinds ■< Animal. [ ( Vegetable. '^ Vegetable. Animals. Races. Population. f Agriculture. Mining. Manufacture. Occupa tion. Human 236 THE MISSOURI SUPERVISOR. let them not be omitted. By means of specimen parts obtained from the butcher or the farmer at "butchering- time" the parts of the human bod}' can be better taught. Constant reference should be made to the pupil's own body and the parts located. A child ought to know whether his liver is in his abdomen or his left breast, and yet a pop- ular institute worker tells of the varied results obtained from the direction, "Put your hand over your liver," and he was talking to teachers. A few of the points to be emphasized are these: 1. The sanctity of a pure and healthy bodw 2. The dependence of happiness and usefulness upon a good bod}'. 3. General bodily hygiene. 4. Hygienic conditions — air, food, water, exercise, sleep. 5. Emergencies — what to do till the doctor arrives. 6. Effects of tobacco and alcohol. 7. Drawing as a means of expression and a test of comprehension. On the other hand, there are a few to be avoided. The following are examples: 1. "Book work," i. e. , memorizing what the book says in the exact manner it says it. 2. Attaching significance to the names of the various muscles and bones — particularly those of "learned length. " 3. Contradicting class teaching with actual living. VERTICAL WRITING. 237 CHAPTER VII, VERTICAL WRITING. A GREAT majorit}' of Missouri teachers have never (April, i8g8) taught vertical writing. The system has come to stay at least five years, and perhaps permanentlv. It is necessary therefore for all Missouri teachers 1 1 • r 1 1 J^iis to learn tlie merits of the system at the start, vertical System. and not wait till they "pick them up." A great majorit}' of the teachers who have tested it pronounce it a great improvement over the system formerly used. No teacher should pronounce the system good till he has tested it, nor pronounce it a failure until that fact is demonstrated. In considering the merits of any text-book the objects for which it is intended should be r r • iTiT • • • 1 Writing of first importance. Writing is meant to be a Practical Subject. read. Writing is a "practical" subject and should be given more attention by the country teachers, and by a great many in the villages and cities, than it receives. In hundreds of districts no attention is given to the subjects at all. Why? Much time is given to "practical" subjects. What is more "practical" than writing? W^e have almost daily use for writing, and use 238 THE MISSOURI SUPERVISOR. it many times as often as we do the very popular subject of Arithmetic. Every pupil has the right to demand that he be given the ability to write a letter with pen and ink within his first school year. Every teacher should feel that the present is the last year that the six-year-old is From the Student's gomg to attend school; that all the training for standpoint. the business affairs of life will be given in this year. Were this the case, would it not be our duty to confer this ability as early as possible? Then is it not our duty to do so anyway? The reply that it can not be done can not be accepted, for it is being done by hundreds of teachers. From the teacher's standpoint there is perhaps no subject by which he can do more legitimate advertising than through the writing. The written exercise, the spell- ing, the language lesson or a letter written on From' the Teacher's a slatc or tablet Sent home by the little boy or standpoint. girl for inspection, will do much toward strengthening the teacher in the estimation of the patrons. The written work of a school is a good test of the work being done. If a teacher can find time for any subject the writing lesson should not be omitted. SPECIAL SUGGESTIONS UPON TEACHING VERTICAL WRITING. 1. The teacher should be acquainted with every detail of the system in use. 2. The time assigned in the program to this subject should not be encroached upon by any other subject. 3. At the opening of the recitation, have the students VERTICAL WRITING. 239 appointed for that purpose distribute the material quickly and quietly. 4. Only three things are necessar}^ in writing: i. A correct conception of the letter or word; 2. Training of the muscles till this mental image can be projected upon the paper or board; 3. Practice till the correct form be- comes automatic. Before beginning have the class to examine the copy to be written. Call attention to any features that need special attention. Write any letter or word on the board that presents any special difficulty, the class observing the way the work is done. To impress the form of a word upon the mind, it is often a good plan to have pupils look from the book and imagine how it appears. Have the class trace it in space with you. Next have each write the letter or word on practice paper. Next have each to compare his work with the copy, and see where it differs. The teacher should also note where the students fail to execute the work properly. The object is to get a clear and correct concept of the form of a letter in the mind, and then to train the hand to project this mental image upon the paper. No student with an incorrect concept can write a correct form. The object of the repeated attempt is to train the muscles in executing the correct form — in establishing the correct muscular habit. When the student has put forth his best effort, and has reached something like the best results, allow him to put a definite amount in his copy book. Impress upon him that the copy book is to be used to put his specimens in, and should be a model of cleanliness, neatness and correctness. Teach the students that it is not Junu mucJi but how well 240 THE MISSOLRI SUPERVISOR. they do their work that gives them skill. The practice paper should be used at least each alternate day. In mixed schools, the teacher should pass from class to class, first fixing the mental images while the other classes are writing. All members of a class should work in concert. Some will want to go in advance of the others. Do not permit them to do so. 5. On the day the copy-book is used give a definite number of lines to be written, and see that each does no more. Train the students to continue to compare their writing with the correct form, the copy. The last line the student writes upon a page should be the best one. If it is not, the teacher can rest assured that the student has ceased to examine his copy. When the student approxi- mates the correct form, practice is necessary to establish the habit of correct writing, and as the habit of correct writing strengthens, correct writing becomes more and more automatic. 6. When the teacher sees that several are meeting the same difficulty, he should have the class stop their work, and show on the board what the error is and how to correct it. If only one or two are making it, he can show them individually. 7. To meet with complete success the student must have a desire to write correctly. Show that correct writ- ing comes from the correct mental "picture" of the letters, being traced out by the muscles. Show him that the mus- cular part is the result of habit. Do so in this v;ay: Have several students go to the board and write any line you may dictate. When they have done so, challenge each to VERTICAL WRITING. ^41 write it in a difierent "hand" immediately below. They can not do so — because they have formed a writing habit. Show them that it will take time to establish a correct writing habit, but when once formed it is as hard to break as the incorrect was. 8. Give attention to the general appearance of the writing books. See that the margins are of proper width, that too much ink is not used; that there are no ink spots on the paper; that the writing is uniform in size through- out any page. Call attention to the fact that the curves are very round and that a large number of the letters are modifications of the vertical straight line. g. Require all written work to be done neatly and according to the vertical system. Students will not like to do this at first, but it is best for them to make the change at once. If they continue to use the slant writing in writ- ten work and the vertical in the writing books, they are working against themselves. We learn writing for its use. We should learn it in the form that we use it. 10. The change will be distasteful to teachers and pupils at first. The teacher can do much towards making it popular by telling the students that it is new to them, and they will like it in a short time. In a large majority of cases this is true. Students like it better than the old system because it is easier. Teachers like it better because they get better results in shorter time. By permission of D. C. Heath & Co., the publishers, the following extracts have been taken from the "Teach- ers' Manual" that accompanies the adopted writing books. 242 THE MISSOURI^SUPERVISOR. They are from the authors of the "National System of Vertical Writing," Messrs. A. F. Newlands and R. K. Row, and represent the best thought upon the subject. SPECIAL FEATURES. The Natural System presents a much narrower page than most copy-books. In the plan of the books the needs of very young beginners have been first considered. It is realized that most writing, even by adults, is done upon very narrow note paper, and that it is Pa""^"^'^ when the beginner tries to carry the pen more than a few inches to the right of the median line of the .body that the mischievous twist of the body begins. Therefore the narrowest page consistent with the presentation of a connected sentence for copy is the best for the beginner. The Natural System uses only a base line, thus leaving a fair, clear, and attractive space for the pupil's work and presenting an absolutely hygienic page. An- other great mistake, akin to the use of space- No Guide . . . . Lines or rulmg IS the use of tracing copies. The reason Tracing Copies for their introduction was probably the same; namely, to compel, as far as possible, the young child to make the letter forms precisely the same as the copy. They sometimes accomplish this purpose, and the work is shown by teachers and others as an exhibition of marvel- ous skill. As a matter of fact it only shows how children can be led to work at such stupid and stupefying toil as guiding the point of the pen up and down, in and out, along a maze of lines usually so faintly printed as to be VERTICAL WRITING. 243 trying to the eyes. While engaged in this senseless, wasteful, harmful practice it is impossible for a child to really see the form of the letters, and the work in no way demands that he should observe them. Whereas, learn- ing to write requires that one should perceive clearly, not the whole essential form of the letter to be made, but also its relation to adjacent letters in the word. The authors of the Natural System of Vertical Writing have, in pursuance of their plans to confront the beginner with as few difficulties as possible, presented letter-forms as nearly like those of print as is . simplification consistent with ease in making the form with of Letter- Forms. a pen. The result is that any child who can read print can read the letters of this system at sight, and has to learn practically but one form of the letter. The Natural System conforms exactly to the hygienic principle, that as the first movements of the child are made by means .of the large muscles which are first devel- oped, and are therefore movements of a vague character and imperfectly controlled, whereas Large ^ J ' Copies. skillfully made movements of a minute sort depend on the small muscles which are latest differentiated and brought under control, it is in the highest degree wrong to set children to copying small letters made with hair lines. It is wholly unnatural for young children to make small forms, and undesirable that they should; they tire and become irritable if forced to do it. Observe their sewing and drawing as well as their unrestricted writing. Moreover, the correct form is much more easily and clearl}' perceived in large forms than in small ones, and the move- 244 THE MISSOURI SUPERVISOR. ment used is infinitely freer and more natural. All persons familiar with kindergarten practice know the revolution which is taking place in- it and the greatl}' increased size of the objects now used as well as the great increase in amplitude of the movements and the manipulations now required. So far from the ultimate size of letter being the proper one for a beginner, the child should be confronted with a very large copy, made with very emphatic and clearly distinguishable lines in which the letter form can be clearl}^ seen and studied, and the size of the letters should be gradually reduced as the pupil's control of his muscles increases. The importance of this principle can- not be overstated. Moreover, it is recognized that the size of the letter which the child will ultimately make will, and properly so, depend upon his own choice, and not upon an arbitrar}' standard of the copy-book. Every one knows that not all the school drill of the past has been able to establish a uniform size of letter or control the size of handwriting beyond the school period. In business and social life every person finally adopts and uses the size of letter which his taste, temperament, and con- venience dictate, and the great diversity in this matter no more excites comment or thought than do the different sizes of type used in books or in the headlines and news columns of our daily papers. In the Natural System the proportion between the height of the short letters on the one hand, and the stem, loop and capital letters on the other, is the very Proportion. simplest One that the mind can entertain, viz. : The height of the short letters is half that of the stem, loop and capital letters. VERTICAL WRITING. 245 In most copy-books the first drill is upon single letters or even upon a fragment of a letter, a process of course monotonous, and lacking interest to the child. The Natural System begins with letters group- Grouping, ed in words, and words of real interest to the children. This is in strict accordance with the modern method of teaching reading, and we think will be recog- nized as right. MATERIALS. It has been found that the most hj'gienic school desk is one having a slope of at least fifteen degrees, adjustable as to height and distance from the pupil. In vertical writing it is essential that all lines shall be 11 1-1 1 Desk, Strong, hence the pens must be 01 at least med- Pens and Pencils. ium breadth and firmness, and very smooth. Pen and ink should be used from the first. In schools where provision is not made for the use of pens and ink in the lowest grade a substitute will be found in a large, soft pencil. THE WRITING LESSON. It must be remembered that the child daes not try to reproduce directly on paper the cop}' before him. It is rather the mental image acquired by looking at the word or letter that his hand tries to represent on , j-^ . Training in the paper. Hence, an nnportant part 01 the Getting clear Concepts. writing lesson is to train the pupils in accurate perception of the forms and relations of the letters. This requires on the part of the pupil a careful, scrutinizing 246 THE MISSOURI SUPERVISOR. observation of each word of the copy so that the first general perception of the word as a whole is followed by a detailed analytic perception of the letters, their propor- tions, and relations, and then a re-grouping of these de- tailed concepts in a clear image of the whole word. For this reason when taking up a new copy, especially in the primary grades, it is best for the pupils to have separate sheets of practice paper. Let the pupils look at the copy for a short time, then close the copy-book and write it on their practice paper. They should then open the book, compare their reproduction with the copy, and this should be repeated until the pupils show that they have a fair concept of the form of the cop}. While it is desirable to cultivate a reasonable degree of freedom, especiall}' in the higher grades, there should be no careless work in the copy-books. If a pupil mani- fests a disposition to scribble, he should be Allow 110 . . . Careless limited to the practice paper until he shows Writing. that he is willing to do his best. Let the writ- ing of a copy in the book be a privilege, to be accorded in the first place as a sort of promotion from the initial lesson on the practice paper, and subject to forfeiture at any time subsequently, upon unmistakable evidence of indifference. No one need expect good results in writing who insists upon careful work onl}^ during the few minutes of the special writing lesson, and then permit carelessness in all other written work. In the public school Ordinary .... , . , , . . Class course all writing must be considered trainmg Writing. in writing, and more depends upon the wa}' the pupils are led to do their general work than upon VERTICAL WRITING. 247 special preparations for, or skill in conducting the special lesson. What has been said of the formative force of the pupil's general work is also true of the teacher's work. The teacher whose blackboard writing is uniformly neat and legible, will generall}' have a class of uni- . The Teacher's formly good writers, and one whose general General Writing. work is indifferent or poor will find these char- acteristics reflected in the work of his class. 24S THE MISSOURI SUPERVISOR. APPENDIX. REFERENCE BOOKS AND SUPPLEMENTARY READING. In the preparation of the following lists two general aims have been kept in view — to select books that would be especially helpful in the teaching of the Adopted Text- Books, and such as would impart a desirable type of culture including a taste for good literature. While the books are classified under "Language," -'History," etc., it must be remembered that a book that is suitable reading for the work in Geography can be made the basis for work in Language. In short, the several forms of mental culture are related and inter-dependent. The books named in these lists can be procured from several publishers whom we can recommend as reliable. In the accompanying lists the following abbreviations are employed: A — American Book Co., Chicago. Ap — D. Appleton & Co., New York. B — Boston School Supply Co., Boston. E — Educational Pub. Co., Boston. Es — Estes & Lauriat, Boston. G — Ginn & Co., Chicago. APPENDIX. 249 Ha — Harper Bros., New York. He — D. C. Heath & Co., Chicago. H & M— Houghton, Mifflui & Co., Chicago. L — Lee & Shepard, Boston. P — Public School Pub. Co., Bloomington, 111. S — Chas. Scribner's Sons, New York. > p X U -J) V - £ a <-^ 22 . U Hi CK 00 ° 2 u 2 ^ X n aj t S 4-. .2 £ K .0 n . 1^ 111 < X o o o M 2 S) s l-f V V pa - 2" ' 1-2. As al)Ove. 3. Each and All, L. 4. Aunt Martha's Corner Cup- board. 5. King's Geog. Readers, L. 6. All the Year Round. 7. World and Its People, S. 8. Stories of Industry. bi) H bo V < w o < o 1. Cats and Dogs, A. 2. Stories for Children, A. 3. Heart of Oak Series, H. 4. Five Cent Cla.ssics, E. See Reading and Litera- ture. 1-4. Same as first grade. 5. Fairy Stories and Fables, A. 6. Friends in Feathers and Fur, A. 7. Stories of Great Ameri- cans, A. 8. Stories of Industry, E. •0x0 5j <+-< - ' aj N III "- ci X tj X < s'a a o- §0 111 XX X >. Nearly all of foregoing: 2, 5, 8. As above. 12. Story of Troy, A. 9. Carpenter's Geography 13. Life of Ijncoln, E. Reading, H. 14. Pioneer Hist, Stories, P. 15. .Story of Troy, A. 16. Greek Heroes, G. a K il i/T T. a "5 . N 2 Same as Sixth. 11. Johonnot's Geography Reading, A. 12. Zig Zags, Es. Shaler's Fir.st Book of Geology, Ap. Methods and Aids in Geography, King, L. il ^ 3 8 .5 ^ •S a CO OJ >\ ««io aj S u: tr. ffi •c a S 8 ^>- X a a a n . dJ ■" X 1. Hawthorne's Grandlather's Chair,(three parts)H.&M. 2. Longfellow's Hiawatha, H. & M. £^ S2^ s S . xK 1. Evangeline, H. & M. 2. Addi.son's DeCoverlj' Papers, G. 3. Studies in I^ongfellow, Whittier, Holmes and Lowell, H. & M. 1. Lowell's Vision of .Sir Laun- fal and Other Pieces, H. & M. 2. .Snow Bound, He. 3. Scott's Lady of the Lake, G Masterpieces of American Liturature, H. & M. Masterpieces of British Literature. H. & M. FIFTH. k X a z K X hi X 'a" 1- a C 11 '^/^/^/^/^^^'%/%/^^/^/^9'^/%/^^/^/^^'%^'%/^ ^ Ask Your Dealer for S Regfister Advance PebMshaeg Compaoy, CHICAGO, ILLS. Missouri Depository with F, P, SEVER, HMrdHandl, Mo, note;:— Seud Missouri Orders to F. P. Sever.