Cornell University Library LA 13.S55 The history and science of education ... 3 1924 013 018 126 B Cornell University M Library The original of tliis book is in tine Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924013018126 THE HISTORY AND SCIENCE EDUCATION FOR INSTITUTES, NORMAL SCHOOLS, READING CIRCLES AND THE PRIVATE SELF-INSTRUCTION OF TEACHERS BY WILLIAM J. SHOUP, M.S. AUTHOR OF GRADED DIDACTICS; EASY WORDS FOR LITTLE LEARNERS AND HOW TO USE them; shoup's graded speller, etc. NEW YORK •:• CINCINNATI ■:• CHICAGO AMERICAN BOOK COMPANY Copyright, iSgi, by AMERICAN BOOK COMPANY. Press of J. J. Little & Co, Astor Place, New York CONTENTS. PART I. CHAPTER PAGE Prefatory 5 I. Empiricism and Beyond, g II. The Development of the Mental and the Moral Faculties, 15 III. The Objective Period of Life — The Kindergarten, 22 IV. How the Kindergarten System may be made Service- able TO the Ordinary School, 32 V. Object Lessons especially adapted to the Latter Part of the "Objective Period" of the Child's School Life, .... . . 40 VI. Object Lessons Continued and Amplified, . . 49 VII. Recapitulation and Elucidation of the Perceptive AND the CoNCEPTIVE FACULTIES, WITH A BRIEF GEN- ERAL Statement of our Mental Phenomena, . . 57 VIII. Importance of Certain of the Conceptive Faculties, with Methods of cultivating and utilizing them, 68 IX. The Third Stage of Intellectual Development, . 78 X. The Fourth Stage of Intellectual Development. Inductive Reasoning and its Application to Teach- ing, 86 XI. The Rational Combination of the Inductive and the Deductive Methods in Teaching, . . .94 XII. The Moral Faculties and their Cultivation, . 106 XIII. The Moral Faculties and their Cultivation — Con- tinued, ........ . 115 PART II. I. A Glance at the Antediluvian World, the Import- ance OF Writing as an Educational Factor, with A Sketch of Chaldean, Babylonian, and Assyrian Education, . . .... 123 (3) CHAPTER PAGE II. Education, Systems of Instruction, etc., in Ancient Egypt, India, AND China 133 III. The Education and Schools of Ancient Greece, . 145 IV. Education and Schools of Ancient Rome, . . . 156 V. The Evolution of the New Old World, . . .165 VI. The Educational Forces in Europe during the Me- diaeval Ages, ... .... 177 VII. The Italian Renascence and the Revival of Learn- ing, . . 190 VIII. The English Renascence and the Educational Prog- ress of Europe in the Sixteenth Century, . 200 IX. Educational Reformers, ... . 210 X. Educational Reformers — Continued, .... 220 XI. The More Recent Educational Avi^akentng in Foreign Lands, 234 XII. American Education during the Colonial Period, . 247 XIII. The Fostering Hand of the General Government in Education, 264 XIV. The Development of the American System of Com- mon Schools, .... ... 274 XV. The Present American System of Common Schools, . 290 Index, 305 THE HISTORY AND SCIENCE OF EDUCATION. THE EVOLUTION OF MIND AND THE CONSEQUENT SCIENCE OF EDUCATION APPLIED TO THE ART OF TEACHING. PREFATORY. Let no one suppose that the higher departments of fhe teacher's profession are attained without some effort, or that honorable distinction is the result of chance. There is no royal road to preferment here, any more than in other departments of professional life. Here, as elsewhere, ' ' The heights by great men reached and kept, Were not attained by sudden flight; But they, while their companions slept. Were toiling upward in the night." If you expect to rise above the rank of a non-professional teacher and become an educator in the higher and better sense of the term, you must make yourself familiar with the laws that govern the development of the human mind ; and you must learn to adapt your teaching to those laws. Having made this advance, you should learn to regard (5) 6 HISTORY AND SCIENCE OF EDUCATION. your calling as a profession rather than a trade, and should expect, too, the more desirable positions and the better salaries. Let no one persuade you that to gain such honorable position in the higher departments of educational work at the present time is any trivial matter. There are those who will tell you that there is no science in teaching, and that for you to study the " philosophy of teaching " is to waste your time. How can these people know, having themselves confessedly never " wasted any time " in the study ? There are those who will tell you that the salaries paid are inadequate to compensate you for any such outlay of time and labor. The salaries paid where non-profes- sional work will pass unchallenged are as high as are paid for a similar grade of work in other callings, and to expect skilled workmen's wages for unskilled workmen's labor is scarcely honest. The additional compensation is usually fully commensurate with the additional preparation re- quired for the higher grades of work. They will tell you next that teaching is a thankless task. If you are willing to continue on from year to year, going through the same old routine and doing mechanically the work laid out for you by others, do you really think you would be entitled to any superabundant amount of gratitude ? Those who find teaching a thankless task are usually those unworthy of thanks. To the teacher, indeed, there is always genuine gratitude from those whose opin- ions she most highly prizes. It is difficult to see how any one can derive much real pleasure from the thanks of those whom he knows in his secret heart he has not instructed in the most enlightened way. Make yourself worthy the gratitude of those for whom you labor, and you will surely receive it in most generous measure ; and PREFA TOR y. 7 you will then enjoy it, too, in a way you never could have done when, as an honest man or woman, you felt that you did not deserve it. Teaching is not a thankless task, though the falsehood has been repeated so often that many have actually been led to believe it, notwithstand- ing the abundant evidence to the contrary on every hand. " But," your Job's comforter will urge, " teachers be- come narrow-minded and are regarded as of little value in a social way." Undoubtedly too many do grow narrow- minded and lose caste in the community. There is but one way to avoid this, and that is to make yourself broad- minded. The second part of this objection is, however, like the last one considered, much more traditional than real. There is no natural prejudice against the teacher's calling, and on this side of the ocean teachers have always enjoyed high social rank. In exceptional cases it has been because the individual was unworthy of association with the better class of people, and not because his occupation or profession was deemed degrading by the broad common sense of the community. In Great Britain, however, until within the present generation, the case was somewhat dif- ferent ; but here, too, the prejudice seems to have been caused by the nature of the men who occupied the teacher's desks. Since the government has taken more direct con- trol of the schools and provided them with teachers worthy of the name, this prejudice has rapidly waned, and ere long the teachers of England will enjoy the high social rank the dignity of their profession justly entitles them to claim. It is recorded that the ancient Romans, wishing to cast an indignity upon one of their most distinguished citizens, elected him to an office corresponding to that of our road supervisor or path-master. But he filled the office so well, and improved the public highways to such an extent that he raised the office to one of high dignity, and made it 8 HISTORY AND SCIENCE OF EDUCATION. coveted and sought after by those aspiring to honorable distinction. So let our teachers bring credit upon their office by- improving the work of the schools, and we shall hear no more about the teacher's office being less honorable than that of the other learned professions. Occasionally some Anglo-maniac, aping the English airs of a quarter of a century ago, still attempts to assert his own superiority by reiterating the obsolete assertions of his trans-Atlantic models, that our professional teachers are in- ferior, intellectually, to men in the " learned professions. " In answer to one of these, the author showed in a magazine article, recently, that the educational standard among our professional teachers is much higher than that of any other profession — the ratio of college-trained men and women among them being more than twice as great as that in any other calling; while it was also shown that the stand- ard among those who are commonly classed as non-profes- sional is much higher than that required for entrance into the lower ranks among either doctors, lawyers, or minis- ters. Will you not do your part in making our calling still more honorable in the estimation of the public— iJj' making it so in fact 1 HISTORY AND SCIENCE OF EDUCATION. PART I. CHAPTER I. EMPIRICISM AND BEYOND. Empiricism — During the world's earlier stages of civilization — before the science of chemistry was known, and while anatomy, physiology, and hygiene were yet very imperfectly understood — the effects of various herbs and drugs in killing or in curing, as the case might seem to be, were carefully recorded. It is probable that many of the " cures " were due to other causes than the drugs administered; while the deaths or relapses may have often been due to causes other than the apparent ones. But imperfect as the system was, much of it has stood the test of more modern scientific experi- ment, and is retained by the most enlightened physicians. The doctors of those times knew little of the nature of disease or of medicines, but people afflicted with certain diseases seemed to be helped in the majority of cases by given remedies, and they, therefore, prescribed these to others similarly afflicted. Such a system of practice — practice based on the results of observation rather than on scientific investigation of principles — is styled empiricism; the person who employs it is said to be an empiric; and his methods are said to be empiric or empirical. (9) lO HISTORY AND SCIENCE OF EDUCATION. The value of any such system must obvious' depend on the extent of the observations on which it i lased, and the care with which they are made. In an event, it is certainly a much more rational system than the reverse one — of merely assuming a certain course, to be correct, and then continuing to practise it in spite of disastrous results. However contemptuously certain classes of writers may speak of our "practical men," it is certain that without empiricism the machinery of every-day life would soon get sadly out of gear, and much of it would come to a dead stand. It has been stated, and not without reason, that there is no surer test of the relative degree of civilization of a country than the amount of soap it consumes; but how many of the millions who employ this cleansing agent most abundantly possess any definite knowledge either of the chemical composition of the soap itself or of the real science of its agency in removing soil and grease .? Three fourths of us, probably, are as ignorant of these things as are " the great unwashed." More than this, it must be acknowledged that the most expert chemists are not always models of personal cleanliness. Neither can it be -disputed that much of the world's most practical work in mechanics, engineering, invention, etc., is done by men who do not possess, in the scientific sense, a knowledge of the principles they employ. Many of our most accurate surveyors could not demonstrate a single one of the formula they use if their life depended on the effort, and few telegraph operators, comparatively speak- ing, are scientific electricians. Beyond. — Thus far, your work in Didactics has doubt- less been largely of an empirical nature — /. e., your con- clusions have been drawn from experience rather than from investigations of the nature of the human mind and EMPIRICISM AND BEYOND. ii the laws of ','i6fental development. Recognizing the fact that the great ^ ?jority of our teachers must for many years to come be^uf&wn from the graduates of the common dis- trict schools, with little' special training for their work, it is usually the aim bf works on education to present for the inexperienced teacher's use such devices and methods, and such adaptation of studies to the age of the pupils, as have been found most practicable under ordinary circumstances. Though these may^ all be really based on scientific prin- ciples, and may have been abundantly tested by the experi- ence of the most trustworthy teachers, it has been deemed prudent to defer the philosophy of education until the student-teacher's age and experience should render such investigations more easy and profitable. It is believed that the inexperienced will, by following such practical direc- tions, teach a much better school than would he who sets out in a way of his own, without chart or compass to guide him, and learns only through experience's proverbially dear school. The carpenter's apprentice may get along very well in many departments of his work by following the directions of the master-builder, and the edifice when completed may be both as beautiful and substantial as though each ham- mer and chisel had been wielded by a master hand ; but had the untrained builder attempted to do the work un- aided by the architect's directions, it would have proved a most unshapely building when completed; if, indeed, the loose-jointed structure had not toppled over and buried him beneath its rubbish as the reward of his folly. Besides this, he would have wasted much time and material in the " cut-and-try " methods he was forced to adopt in his labor. But there will come a time when this same workman, if he is attentive to the directions given him, will have gained such skill in the use of tools, and such knowledge of the 12 HISTORY AND SCIENCE OF EDUCATION. Structure of buildings, that he will weary of doing mere ap- prentice work, and will aspire to become a master-builder or architect himself. With his present practical knowledge and skill, the gulf will not be an impassable one, and by a comparatively small amount of earnest study he may pass from being the mere follower of the directions of others to be himself a director. Do you say it would have been much better had this would-be builder studied carefully the ^science of architec- ture before laying hand to the hammer or the saw — that he would then have known why each mortise was to be made in each particular beam, and why material of a given kind is most suitable for the foundation, of another kind for the superstructure, and of a still different kind for the roof ? No doubt such knowledge would have been valuable, and had not the material been selected for him, or at least had he not been given instruction by the master-mechanic as to what kinds to employ for each particular stage of the work, it would not only have been highly presumptuous, but posi- tively criminal in him to begin as he did. But being in- formed what kind of material to use, he set to work without stopping to analyze its properties. He assumes, as he has a right to do, that the knowledge of the master-builder is reasonably reliable, follows his directions, and at once be- gins acquiring skill in the use of tools, and knowledge of the structure of buildings. During the time he is thus en- gaged, he is learning, too, in the most practical way pos- sible, the various properties of the material on which he labors, and is acquiring a fund of information that will be of infinitely more value to him when he becomes a master- builder himself, than if it had been learned only theoret- ically. Then, too, the building had to be reared in a given time and a sufficient number of skilled workmen could not be EMPIRICISM AND BEYOND. 13 procured. The few who could be had were needed either in laying out the work for the unskilled artisans, and directing them in the use of tools, or their labor was de- manded in the higher grades of work, which only skillful hands can do at all. Just so it is in the work of teaching. In the ideal state, all our teachers should not only be trained in the branches they are to teach, but they should also have a systematic knowledge of the nature and functions of the human mind and soul — i. e., they should be trained in mental and moral philosophy. But it must yet be many years before this ideal state of things can exist; and, like true philosophers, we must take things as we find them, and make the most of them. As Wendell Phillips observes, " Common sense plays the game with the cards it has. It does not ask an impossible chess- board, but takes the one before it and plays the game." Most of our teaching must, of necessity, be done by apprentices, but " there is always plenty of room higher up," and it is presumed that you are now qualified to go a step beyond mere empiricism and investigate the laws of mental and moral development, and the consequent studies and methods of instruction best adapted to the various stages of the child's unfolding mind. It is not proposed to give here any thing like a sys- tematic course in psychology or mental philosophy. It is only proposed to present as much of the nature of the mind and its faculties as may be necessary to a rational idea of the underlying principles of common-school edu- cation. ANALYSIS OF CHAPTER I. Empiricism illustrated by ancient medical practice. The weakness and the vahie of medical empiricism shown. The usefulness of empiri- cism in every-day life — mechanics, engineers, telegraphers, even in- 14 HISTORY AND SCIENCE OF EDUCATION. ventors may do excellent practical work without a scientific knowledge of the principles involved. The student-teachers now better prepared for more scientific work. The teacher's progress illustrated by that of the carpenter's apprentice, who becomes a master-builder. How the empirical knowledge gained in his apprenticeship may further his later scientific researches. Why and how apprentice work may be used without injury to the building. Why it was necessary to employ apprentice work. Why teachers should study mental and moral philosophy. Since it is impossible, at present, to procure any large number of teachers thus qualified, common sense dictates that we do the best we can with the material we have. The present work is by no means a treatise on psychology — it merely gives, in a very brief and simple form, the primary laws of mental and moral development, and their practical application to school work. SUPPLEMENTARY QUESTIONS. Other causes being equal, in whose hands would you rather trust your life in the case of dangerous sickness — the empiricist, or the scientifi- cally trained physician ? Why ? Admitting the fact that a man may be a successful farmer without any scientific knowledge of the chemical composition of soil, fertilizers, etc., can you still state any good reasons why it is desirable that we have scientific agriculturists ? Admitting the fact that excellent work may be done by teachers who know nothing of the theory of education, would you regard this as a sufficient excuse for not studying the theory as well as the practice of teaching ? Can you show that the teacher of an independent rural school has more pressing need of an understanding of the underlying principles of education than has the teacher of any given grade in a city school? Is the fact that you have taught for some time by empirical methods a reason for, or against, your now studying the scientific principles underlying mental evolution ? Why, or why not ? CHAPTER II. THE DEVELOPMENT OF THE MENTAL AND THE ' MORAL FACULTIES. It has been said, " There is nothing great on earth but man, and there is nothing great in man but mind." If by " mind " is meant not only man's intellectual faculties, but his moral faculties as well, this statement will doubtless hold ; and since education consists mainly in the develop- ing and the training of these god-like faculties, it must be apparent that there is no secular calling or profession higher than the teacher's. " Cultivation of the Senses." — But the mind is reached, in childhood and youth, mainly through the senses, and as the senses are acted upon through physical organs, it must be apparent that the training of the mind is influenced to a very great degree by the pupil's physical organization — that is, by influences largely beyond the teacher's reach or control. The organs of the senses are the tools or implements by which the mind is supplied,' or by which it supplies itself with food and clothing, so to speak ; and it is all-essential that these tools be in proper condition for use. Theoretically, therefore, a system of education should begin with the cultivation of the organs through which the senses act, as the skillful mechanic grinds and whets or files and polishes his tools. But, practically, the tempering of the mind's tools is a matter far beyond the teacher's reach. He can not give the weak and watery-eyed clear vision, any more than he can make the deaf hear. The (15) l6 HISTORY AND SCIENCE OF EDUCATION. causes which affect these are much too deep-seated in the system to be visibly affected by any amount of "training" which the teacher can give. It may take several genera- tions of the most careful observance of sanitary laws to re- produce healthy and acute organs of sight, hearing, touch, taste, or smell. Care of the Organs of Sense. — It behooves the teacher, however, to guard with the greatest care such tools as nature has furnished the little ones for the cultiva- tion of their minds. As the carpenter watches his appren- tice to see that he does not dull or ruin his saws and planes and other tools by cutting into half-hidden nails or grit, so the faithful teacher will watch that her apprentices do not ruin their infinitely more valuable tools of the mind by careless using. This is especially true of the eyes — the organs of the highest of the senses. While she can not cure weak eyes, she may, by proper vigilance and the influence which her position affords her, prevent their further injury, and here the old saying that " an ounce of prevention is worth a pound of cure " has peculiar application. The judicious tempering of the light in a school-room for a single term may do more toward acute vision in a commu- nity than seven generations of the strictest observance of sanitary conditions in the wa}' of curing the mischief when it has once been done. It is the true province of the teacher, therefore, to train the mind in ihe proper using of such tools as nature, or per- verted nature, has provided it. Physical education, the tempering of the mind's imple- ments, is the foundation of education. Ay, it is even more than this— it is the sub-stratum of rock, or clay, or mud, or shifting sand, on which the structure stands or falls, but it is usually laid long before the teacher has any thing to do with the pupil. DEVELOPMENT OF THE FACULTIES. ij The Faculties of the Mind Before discussing the various faculties of the mind in detail, the following general facts regarding intellectual and moral development should be first considered : The human mind, though in many respects a most com- plex organism, is one indivisible substance, having various states and modes of action; these states and modes of action are called Faculties. The various faculties fol- low certain laws of evolution ; they may be developed by being properly trained on appropriate themes, or they may be dwarfed and stunted by being exercised on inap- propriate subjects, or by being overstrained. In addition to this, they may admit of improper or abnormal develop- ment. The mind communicates with the external world through five channels — Touch, Taste, Smell, Hearing, and Sight. The faculties are first exercised on material objects and the phenomena of the external world through the senses ; these material aids, therefore, greatly promote the activity of all the faculties of the mind. Though the same faculties exist in most minds, their natural force differs widely in different individuals, and the same processes that will develop them in one child may be inadequate in another ; still, there are certain general prin- ciples that apply to the great mass of unfolding minds. There are certain of the faculties, such as attention, that require some effort of the will to bring them into action — these are called voluntary faculties. And since the child is naturally of a social nature, and since pleasure is one of his chief incentives to action, he is usually best trained in company with others of his own age, and by whatever means the most pleasure may be commingled with the effort of attention. Kind nature has also provided a cer- tain amount of refining pleasure in the healthful exercise of the faculties ; and the love of the beautiful and of the 2 1 8 HISTORY A NX) SCIENCE OP EDUCATION. wonderful are also actuating principles in the child-mind ; their gratification is, therefore, to be considered of great importance in all rational systems of instruction. Modes of instruction which violate these principles are apt to give rise to harsh and cruel modes of discipline, and to turn the hearts of the little ones away from that which would other- wise have proved their chief delight. The repetition of the same or similar acts gives rise to habit. The habits of attention and concentration of the mind to any subject are the key-stones of education. It is not to be expected, however, that the habit of concen- trating the faculties upon a single point,/i??- any considerable length of time, can be fully attained by children ; their love of change and novelty precludes this. Let the primary teacher ever bear this fact in mind. Some of the faculties naturally repose or lie compara- tively dormant until a later period of life. The attempt to develop these faculties before their natural time is doubtless one of the chief causes of children's distaste for school. The faculties are never so vigorous as when they are exercised voluntarily, and they are never thus exercised on unnatural subjects or before their natural time. The natural teacher is, therefore, the one that studies to place before the pupils such mental aliment as they, at that par- ticular stage of their intellectual development, most crave. Children have a natural craving for knowledge, as well as for occupation, and they need only to be directed to the proper mental nourishment in order to educate themselves to a very large degree. The vigor of any one of the faculties, and the desire for its further development, increase as it has been judiciously exercised. The sooner a faculty is called into healthful action, the greater, ordinarily, will be its vigor ; but the teacher must be sure that the action is healthful. He can DEVELOPMENT OF THE FACULTIES. 19 not, therefore, have too thorough knowledge of the laws of mental evolution, nor can he be too vigilant in studying the development of his scholars' minds. The cultivation of the reasoning faculties must not be too long delayed, but it is ruinous to attempt to force these before their natural time, as is so often done in our common- schools. The faculties, in their evolution, act and re-act, more or less, upon one another. Thus, the moral faculties are stimulated by the development of the intellectual facul- ties, and vice versa. These should, therefore, be cultivated simultaneously. For the purpose of cultivation, the faculties may be arranged in certain groups, but the cultivation of one of these is apt to develop others more or less. Our subjects, as well as our methods, of instruction must, of course, be varied to suit the different classes or groups of faculties under training. The human mind, even in early infancy, is far from being a sheet of blank paper on which impressions are written by the hands of the various senses. There is a living soul back of all this that reads and classifies all these impres- sions. .ANALYSIS OF CHAPTER II. The mind of man is the noblest work of the Creator ; to train it is a lofty calling. The mind is reached through the senses — the senses are the tools of the mind. Theoretically, then, education should begin with cultivating the eye, ear, etc. Practically, this lies beyond the teacher's sphere. The teacher should, however, carefully guard from injury the sight, etc., of her pupils. The teacher's province is to train the mind in the use of the senses. General facts of mental and moral development. The mind an invisible entity — its faculties. Development of the faculties by training — Stunting — Abnormal development. 20 HISTORY AND SCIENCE OF EDUCATION. Five channels of communication with the external world— the mind first developed through these. General principles that apply to unfolding minds. The voluntary faculties. The use to be made of companionship, of the pleasure of mental effort, of the love of the beautiful and of the wonderful. Habit — Attention and Concentration — Young children can not con- centrate their minds on a subject, except for a very brief time. Some of the faculties partly dormant until a more mature age. Importance of developing the faculties in their due order, and of exercising them upon appropriate subjects. The natural love of knowledge. The vigor of the faculties increases with proper exercise. They should be called into healthful action as early as may be — hence the importance of teachers knowing the laws of mental development. The faculties, in their development, stimulate one another. The moral and the mental should be cultivated simultaneously. The faculties may be arranged in groups — the subjects of the methods of instruction will vary according to the group under training. The infant mind is not a sheet of blank paper for the senses to write impressions on. SUPPLEMENTARY QUESTIONS. What are some of the ways in which pupils may injure their sight ? What means should teachers take to prevent this ? Are any of the other organs of the senses liable to be injured in con- nection with school duties? If so, what, and how? Is it right to hold the pupil to account for the imperfect learning of lessons when there is reason to believe that his failure is due to natural inability ? What is your opinion of the teacher who ridicules his pupils under such circumstances ? What do you think of the propriety of such things as "dunce blocks" and " dunce caps " in school ? Are the faculties apt to be symmetrically developed in self-educated men ? Why, or why not ? Give some noted examples. Are the large classes in our graded schools well calculated to meet the various shades of natural ability in pupils ? What statements in this chapter apply to this question ? It is stated in this chapter that the love of the beautiful and the won- DEVELOPMENT OF THE i^ACULTIES. 21 derful are actuating principles in the cliild-mind, and tiieir gratification is, therefore, to be considered as of great importance in all rational sys- tems of instruction. In what ways can the teacher apply these in the ordinary school ? HoHr long may you reasonably expect to hold the attention of the six-year-olds to any given point ? When their attention begins to waver, what should you do ? If you find it impossible to hold your pupils' attention at all to any subject you may be trying to present to them, what should you con- clude ? CHAPTER III. THE OBJECTIVE PERIOD OF LIFE— THE KINDER- GARTEN. Childhood : The Objective Period The various stages of man's life have been differently classified by dif- ferent writers of high authority. Pythagoras gave but four, while others give five, six, seven, etc., and Solon in- sists on ten such periods or divisions in our career from the cradle to the grave. But whatever artificial sub-divisions philosophers may make, and however difficult it may be to draw exact lines of demarkation, two great periods are as strongly marked as are those of spring and summer — ^viz.: manhood or wo- manhood and the period which precedes it. While it is true in a certain sense that "men are but children of a larger growth," the added growth has brought with it many new and greatly altered conditions, both of body and mind. " When I was a child I spake as a child, I understood as a child, I thought as a child ; but when I became a man, I put away childish things," wrote the in- spired and most learned apostle ; and he but recorded the experience of the millions of every land and nation. Up to this great turning-point, the child has been largely de- pendent upon others— his parents and his teachers ; but henceforth he was designed to provide for himself or to assume charge and instruction of others. This first great epoch of human life — the age when we are in a measure dependent upon others for guidance and support— may be roughly divided into three periods, viz. : (22) THE OBJECTIVE PERIOD. 23 Childhood or infancy, boyhood or girlhood, and youth. The mental traits of these three periods are as different as are their physical characteristics, and each accordingly demands its own peculiar studies and methods of instruction. Childhood, or infancy, embraces that period of our life extending to about the seventh year. It is characterized by extraordinarily rapid growth and development of all the physical organs. This stage in the child's mental growth has been not in- aptly termed " The Objective Period." That is, the little one is now most largely dependent for its mental food on objects foreign to or outside of itself. Its mind is much more receptive than self-active, its manifestations of self- activity being chiefly in the way of efforts to retain and classify the myriads of impressions which come to it from without, through the soul's five open gateways — tasting, seeing, hearing, feeling, smelling. This is, therefore, the great preparatory period of intellectual development. Perceptive and Conceptive Faculties. — The faculties most prominent in this period of the child's career are those known as the perceptive faculties — that is, those fac- ulties which, in the main, have to do with the reception of impressions from without through the senses. It must also be borne in mind that, especially toward the close of this period, the mind begins to have more or less definite con- ceptions of things as the result of impressions received. It begins to think of the qualities or properties of things, aside from the things themselves, and we say that the con- ceptive FACULTIES are being developed. The memory is especially active, and impressions now made are apt to be the more lasting. This fact should be utilized by every primary teacher, though care must be taken, at the same time, not to abuse this opportunity by storing the soul's workshop with a lot of material which 24 HISTORY AND SCIENCE OF EDUCATION. it will not be called upon to use for years to come, and which will then be found so rusted by disuse as to be prac- tically worthless. The most natural educators of the little ones are now their mothers, and the author has small sympathy with those philosophers who would either rob the mother of this sacred office or excuse her from its duties. The Creator has implanted in her heart an instinct deep as the very fountains of her soul, which insures much closer sympathy from her in her offspring's wants than any others can have, no matter how carefully trained they may be in the laws of physical development and mental evolution. God pity the children who are reared without a mother's tender love and watchful care ; and God pity, too, the woman who assumes mother- hood lightly esteeming the care and instruction of her little ones ! There is a time, however, toward the close of this Objec- tive Period of the child's career — say, during the time he is from five to seven years of age — when the mother's care is often largely drawn to her more tender offspring, and when she needs the devoted primary teacher's aid. Instruction during this period must be in the most rudi- mentary parts of the scholastic branches, and in its earlier stages it were better, no doubt, that no instruction in the ordinary studies of the schools be given. This is pre- eminently the period for objective teaching, and as it is characterized by intense activity and a love for play on the part of the little learner, kindergarten methods are espe- cially adapted to it. A brief statement of this system is therefore here appended. A Brief Statement of Froebel's Kindergarten Sys- tem.* — The Kindergarten (Ger., children's garden) is a peculiar system of education, founded by Frederick Froebel * Adapted from the " Dictionary of Education and Instruction." THE KINDERGARTEN. 25 designed to precede all other elementary trainingf, and to prepare the child for regular instruction by exercising all its powers, so as to render it self -active. While the reformers of education before his time, including Pestalozzi, whose assistant Froebel was, treated the youthful mind, more or less, as a passive recipient of truth, goodness, and beauty, it was his fundamental idea to set the child to do whatever it could be induced to do as a kind of amusement, exercising its observing faculties in connection with its playthings and games, and thus to create in it an interest in learning. He discovered, by means of half a century's attentive practice in teaching, in association with many other excellent educa- tors, that the faculties of many children are stunted in infancy and earliest youth by the want of appropriate mental food ; that every child may be developed (may develop itself) into a self-educator by appropriate amusements ; and that, in this manner, pleasure may be made the most efficient in- strument in the first stages of education. He, therefore, studied all the plays and games in use from the most an- cient times in order to find their special adaptation to men- tal and bodily growth, and thus formed a complete philo- sophical system of early intellectual culture. This culture was to begin in the earliest stages, with ball plays, accom- panied by snatches of song and rhyme ; later with a sphere, a cube, and a cylinder of wood, used for various amusing exercises, and calculated to enliven the attention and in- crease the self-activity of the child. The two little books for mothers, which contain his suggestions for this purpose, disclaim any merit of invention ; he considers them derived simply from a diligent observation of the methods of many excellent and successful mothers. But it was not from books alone that he intended mothers should learn how to train their children. They were to be educated, as young chil- dren, in a kindergarten, and afterward, before graduating 26 HISTORY AND SCIENCE OF EDUCATION. from the upper classes, to learn the art of infant education in a model kindergarten. It was in this way that he hoped to render, in the course of time, all mothers true educators of infancy, the centers of happy family circles, and the priest- esses of a higher humanity, so that they might be " in har- mony with themselves, with nature, and with God." But mere family education being liable to one-sidedness and exclusiveness, social education should begin early in order to complement the former. During a part of the day the child should be in company with many other children of the same age, he said, and should engage in such plays as supply, in a gradually ascending scale, proper food for the mental and bodily appetites and functions, while mak- ing the company of little ones as happy as possible. This can be done only under the guidance of a true teacher, who should be a woman, capable, by natural endowments and previous study, to take the place, in this respect, of the mother. The locality should be a hall in a garden, with flowers, shrubs, and trees, each child having his own flower- bed, so that he may learn how to raise plants and to enjoy nature. The playful occupations of the pupils comprise a great variety of plays in a given order, which, however, should not be absolutely fixed, but should afford a haalthy change, without inducing habits of imperfect attention and restlessness. None of these occupations were the invention of Froebel ; they had all been practised more or less before his time. But their combination into a harmonious whole, their adaptation for mental food in every direction, and their development in detail, must be set down as his creation; and the experience had with them in many hundreds of kinder- gartens is said to justify the wisdom of the system. There is s'till much controversy among the followers of Froebel themselves in regard to minor details ; and some improve- ment has been made upon his own first practical realization THE KINDERGARTEN. 27 of the idea, which, from insufficiency of means, could not be all that he desired; but the indefinite perfectibility of the system in practical details, according to its principles, insures its progressive success. The exercises of the kindergarten are alternately carried on in a sitting, and in a standing or walking position, for the sake of a salutary change, and are partly such as can, with- out special training, be guided by any good teacher ; namely, singing ; the reciting of child-like poetry, committed to memory by means of the teacher's frequent repetition; light gymnastics, marching exercises, and easy ball plays; acting the doings of men and animals; all these accompanied from time to time with song, or turned into objective lessons by frequent conversations on the things mentioned or repre- sented; also, amusing employment with playthings called gifts, of which there are several sets. The guidance of these occupations requires a practical training on the part of the teacher, and a theoretical study which can never be too thorough if the pupil's mental and moral development is to become what Froebel intended it to be. The teacher is not to teach them, but to lead his pupils by suggestions conveyed in questions or conversation, so that the child may become inventive. The teacher is to abstain from all learned lore — from using abstract expres- sions. Abstract notions are severely banished from the kindergarten; it is merely concrete things, which the child can learn through the senses, and can clothe in his own language, and can become familiar to him by his own men- tal assimilation. Neither is discipline to be maintained by authority, or by any mechanical means, but by the sugges- tions of the teacher, and by the pupils' own absorption in the interest of their occupations.* Thus children are, at an * This is tlie way the case is most commonly stated by the more radical adherents to the principles of Froebel ; but in practice it requires some modification. Said 28 HISTORY AND SCIENCE OF EDUCATION. early age, enabled to discipline themselves through pleasant employment; to submit to the will of the majority of their equals, on the one hand, or assert, on the other, their own free volition, if they can induce others to agree with them. Thus, they are to take their first lesson in moral self- government. Owing to the necessity of special skill and training in order to conduct a kindergarten efficiently, many persons who undertake this work fail, through want of preparation, to produce the results designed. In this way, spurious kindergartens have caused much complaint, and brought considerable discredit upon the system. The test of a good kindergarten is its obvious effect upon the pupils in exciting cheerfulness, intelligence, activity, and a fondness for the school work. If, on the other hand, the children dislike the school, it is an evidence that there is a want of Miss Brown, of Boston, in her paper on the " Application of Froebel's Principles to the Primary School " before the National Teachers' Association at Chicago; " In our schools there should be more of that wise winning, by which a child is led to do the right cheerfully and willingly. Still, even in the kindergarten, the little ones should feel the power behind the throne. We believe that children have an intense respect for law and order, however careless they may be themselves. It is right, it is imperative that a child shall feel himself obliged to do certain things, and refrain from doing others, because it is a required or expected thing. And if the kindergartner or teacher be as firm as she is winning, the children will not chafe under her little restrictions. There should be times in the kindergarten when the children are required to remain quiet for a time, while in some position not irksome. If such little devices are not employed, how else can the child be- come accustomed to the long sittings in the primary schools ? " Do not some kindergartners err from an excess of patience ? We have more than once seen the kindergartner stand over a naughty child for half an hour striving to win him to do a thing ; whereas a wise mother would have settled the matter in about thirty seconds by insisting upon prompt obedience both as duty and privilege. We believe most heartily in that wise direction of the will that secures a voluntary obedience from the child. Personal issues are to be avoided in the school and kindergarten as well as the home. Still, the child must realize that obedience is not always to be a choice with him ; that he owes it to others who have a right to expect that unquestioning, cheerful service. Some of our most loyal kindergartners have maintained that we do violence to the child's nature by insisting. Yet how shall he escape this great burden laid upon him by nature and life ? " THE KiNDERGARTEtr. ag tact and skill in its management. There may, indeed, exist in such a school all the occupations recommended by Froebel, and each may be used according to the estab- lished formula ; but if the spirit in which the exercises are to be conducted is missing, if the treatment is mechanical, all the moral influence which should spring from the cheerful self-activity of the child is lost. If, too, the teacher shows always the calm and dignified deportment of the ordinary class disciplinarian, instead of entering with all her heart into the harmless joy from which the child's self-government is to take a fruitful growth, and calming only the troublesome excess of this mirth by now and then a look, a word, or a gesture, she is not well-fitted for her calling. A genuine kindergartner will, like the best of mothers, take a lively interest in remedying, as far as possible, the bodily, mental, and moral defects of every child under her care — uncleanly and disorderly hab- its, want of attention, stammering, color-blindness, a bad gait or posture, imperfect articulation, etc. She will, in this way, earn the gratitude of the children and their parents, and exert a great moral influence. Her efforts in this respect are, in a great measure, facilitated by the plia- bility of the child's powers, as well as by its desire to avoid ridicule, and to enjoy the society of its comrades. Abun- dant experience teaches that there need be no incurable cases of the above kind among children who have the full use of their senses; that all children may learn drawing, singing, correct enunciation, and many other arts and accomplishments that are by common prejudice pro- nounced attainable by those only who are specially gifted. It is evident, therefore, that a kindergartner can hardly be too well educated; and, also, that no education repays so abundantly its cost. 30 HISTORY AND SCIENCE OF EDUCATION. ANALYSIS OF CHAPTER III. Various stages of life reckoned by different authors. The great natural division into the two periods of minority, and manhood or womanhood. Three divisions of minority: infancy, or childhood; boyhood or girlhood; and youth. The Period of Childhood : Extends to about the seventh year. Characterized by rapid growth. The Objective Stage. The prepara- tory period. Perceptive Faculties most prominent. The Conceptive Faculties also begin to play an active part. Memory peculiarly reten- tive. How this fact should be utilized. The mother the most natural educator of the very young child. When the primary teacher's aid becomes useful. Object teaching and instructive plays are better adapted to beginners than the usual school studies. Brief Account of the Kindergarten : Its fundamental idea is to render the child's powers self-active by free exercise. The child is thus trained to educate himself. Froebel studied the games of all times and nations, to select and arrange those most conducive to the happy and symmetrical develop- ment of the child. The kindergarten training was at first intended to be used both by mothers and teachers. The kindergarten should have a garden at- tached where the children may play and work. Kindergarten exercises consist of marching, singing, playing games, playing with the gifts, etc. The teacher must have a thorough special training. No abstract expressions are to be used. Discipline must not be maintained by authority — Some modification of this statement. No kindergarten which children do not enjoy is a good one. It should remedy personal defects and bad manners. The kindergartner needs special gifts, thorough training, and wide knowledge. SUPPLEMENTARY QUESTIONS. What is apt to be the influence on a child's character by removing him from his mother's care during a considerable portion of each day, before he is about five years of age ? THE KINDERGARTEN. 31 Can you trace any connection between this and the fact that the children of the very wealthy often turn out badly ? What about the children of the wretchedly poor ? Would you regard kindergartens for ordinary children, below the age of four or five, a blessing to the little ones or a misfortune ? What would you think of their influence on the wretched children of the streets, in the great cities, with no mother worthy of the name ? What of their influence on the children of the very wealthy and others whose children are so often given over to the care of nurses and other domestics ? What influence would their general introduction, at this tender age, be apt to have ? Why ? CHAPTER IV. HOW THE KINDERGARTEN SYSTEM MAY BE MADE SERVICEABLE TO THE ORDINARY SCHOOL. Froebel's Gifts — To carry out more practically his idea of inducing the child to educate itself through pleas- urable employments, commonly called play, Froebel de- vised a system of apparatus to be given to the children, as material for interesting and instructive occupation. Hence the name "gifts." Later teachers have improved and extended Froebel's "gifts," until the set now embraces twenty. They are here given for reference only : 1. Six soft balls of various colors, the use of which is to teach color (primary and secondary), and direction (forward and backward, right and left, up and down) ; also to train the eye, and to exercise the hands, arms, and feet in various plays. 2. Sphere, cube, and cylinder, designed to teach /«r«, by directing the attention of the child to resemblances and differences in objects. This is done by pointing out, explaining, and counting the sides, edges, and corners of the cube, and by showing how it differs, in these respects, from the sphere and the cylinder. The manipulation by the child should, of courss, precede this demonstration by the teacher. The child's self-activity will prompt it to place these forms in various posi- tions and combinations, so as to realize in its conceptions everything that is analogous or dissimilar in them. 3. A large cube divided into eight equal cubes, the object being to teach both form and number, also to give a rudiraental idea of frac- tions. 4. A large cube divided into eight oblong bloclis, designed to teach number s.nA a simple variety oi form (cube and parallelopiped). 5. A large cube divided into twenty-seven equal cubes, three of the (32) THE KTNDERGARTEM SYSTEM. 33 latter being subdivided into half cubes, and three others into quarter cubes (forming triangular prisms). This is a further continuation and complement of (3), but affording much ampler means of combination, both as to form and mimber. 6. A large cube so divided as to consist of eighteen whole oblong blocks, three similar blocks divided lengthwise, and six divided breadth- wise — a still further continuation of the ideas involved in (3). 7. Triangular and quadrangular tablets of polished wood, affording the means of further exercise in reversing the position of forms and combining them; and presenting, in addition, illustrations ol plane sur- faces, instead of solids, as in the previous gifts. This arrangement, placing the surfaces after the solids, recognizes an important principle of education — that we should pass from the concrete to the abstract, the square being a side of the cube, and the triangle deduced from the prism. 8. Sticks for laying : Wooden sticks, about thirteen inches long, to be cut into various lengths by the teacher or pupil, as occasion may re- quire. These sticks, like most of the previous gifts, are designed to teach numerical proportions. The multiplication table may be piacti- cally learned by means of this gift. The forms of the letters of the alphabet and the Roman and Arabic numerals, may also be learned. g. Rings for ring-laying, consisting of whole and half rings of various sizes, in wire, for forming figures ; designed to develop further ideas of form ; also to afford a means for developing constructiveness of the pupils, and practice in composing simple designs. 10. Drawing slates and paper, consisting of slates ruled in squares, and paper ruled in squares, for the purpose of enabling the pupil to draw or copy simple figures in a methodical manner, the ruling aiding them in the adjustment of proportions. 11. Perforating paper, ruled in squares on one sid»only, with perfor- ating needles, affording more advanced practice in producing forms and executing simple designs. 12. Embroidering material, to be used for tratisferring the designs executed on the perforating paper, by embroidering them with colored worsted or silk on cardboard. 13. Paper for cutting : Squares of paper are folded, cut according to certain rules, and formed into figures. The child's inclination for using the scissors is thus ingeniously turned to account, and made to produce very gratifying results. 14. Weaving paper : Strips of colored paper are, by means of a steel 34 HISTORY AND SCIENCE OF EDUCATION. or wooden needle of peculiar construction, woven into a differently colored sheet of paper, which is cut into strips throughout its entire surface, except a margin at each end to keep the strips in their places. A very great variety of figures is thus produced, and the inventive powers of the child are constantly brought into requisition. 15. Plaiting material, including sets of flats for interlacing, so as to form geometrical and fancy figures. 16. Jointed slats {gonigraphs), for forming angles and geometrical figures. 17. Paper for intertwining: Paper strips of various colors, eight or ten inches long, folded lengthwise, used to represent a variety of geomet- rical and fancy figures, by plaiting them according to certain rules. 18. Paper for folding, consisting of square, rectangular, and triangu- lar pieces, with which variously shaped objects may be formed. ig. Material for peas work, consisting of wires of various lengths, pointed at the ends, which are passed through peas that have been soaked in water for six or eight hours ; these are then used to imitate various objects and geometrical figures. Cork cubes are sometimes used instead of peas, as being more convenient. 20. Material for modeling : Modeling knives, of wood, and model- ing boards, by means of which various forms are modeled in beeswax, clay, putty, or some other soft substance. The Kindergarten Spirit -" What has the kindergar- ten to do with the work of the ordinary school ? " does some one ask ? Much, in many ways. First of al], it illustrates the great principle of the necessity of making school-work attractive to the little learners. If it only induces our teachers to put just a little of the kindergarten spirit into the primary work of the district school, it will repay a thousand-fold the little time we have here devoted to it. If it impresses on the minds of our teachers the fact that the child-mind deals with the concrete rather than the abstract, and if it induces them to conform their instruction to this fundamental principle, it will make them much better teachers of the little ones than the great majority of their predecessors. THE KINDERGARTEN SYSTEM. 35 If it succeeds in impressing the truth that activit)' is one of the Heaven-implanted laws of childhood, and induces our teachers to furnish employment for each little pair of willing; hands, it will bring joy and gladness to many a childish heart, and engender such a love for school that study will be a delight. If it impresses upon our primary teachers the utter unreasonableness of expecting the children to sit quiet three quarters of their school day, with nothing whatever to occupy their attention save looking into space's vacancy and doing their utmost not to think of any thing, it will have saved many a budding mind from blight. In addition to all this, it is believed by many of the most thoughtful educators that the highest utility of the kindergarten system is attained when it is applied in con- nection with primary school work rather than when entirely divorced from it. It is true that love for play is one of the chief attributes of the little learner's soul, and there can be small doubt that the Creator designed this attribute as much for an imple- ment of self -education to the child as for a means of letting sunshine into his little heart; but toward the close of the " Objective Period " of his career — the time from five to seven in the average pupil's life — more serious occupations, like those of the best primary schools, may well be inter- spersed. While it is emphatically true that " all work and no play makes Jack-a dull boy," it is doubtless equally true that all play and no work may tend to make him frivolous. The amount of kindergarten spirit, or actual kindergar- ten occupation, which can be interwoven with the ordinary school routine, will depend largely on the teacher's own originaHty — in fact, the success or failure of the work itself must rest to a very great degree on this, since many of the " gifts " admit of almost endless variety of application. Applications of the Gifts. — Let us glance at a few of 36 HISTORY AND SCIENCE OF EDUCATION. these variations — such as any bright teacher of a primary room in a graded school, or of a district school, may easily evolve if it is undertaken in the true spirit of a teacher. A few minutes' work of this sort occasionally would certainly be time well spent. Take, for example, the "third gift." These little cubic blocks may easily be used, not only to amuse and instruct the child by drawing his attention to their most obvious qualities, but they may also be employed to cultivate in him the sense of the beautiful and tasteful, as the result of order and harmony and symmetry. An important princi- ple of Froebel's system was to accustom the child to de- velop symmetrical forms and figures by slight changes and alterations, rather than by destroying the whole original figure, and then reconstructing it entirely anew. There is, indeed, much more in such a habit than at first appears upon the surface, as every scientist, or artist, or skilled me- chanic will affirm. Thus, as Mr. Hoffman so aptly illustrates, place first the eight cubes before the child as they stand in the box. Then induce him to place one of the upper layer to each of the four sides of the lower, beginning at the middle and proceeding to the right, as shown below : + Jr K f- ■#■ Fact to double Face to ^ace. Edge to edge. Face to face. Face to double /ace. /ace. Or such as the following ; First make an oblong, four blocks long and two blocks wide; and when alterations are made, let them be made with both hands on each of the two columns at once. Thus, take the two from the upper end of figure i and place them at the bottom, edge to edge, as in figure 2; then move two more from the top THE KINDERGARTEN SYSTEM. 37 with the two hands simultaneously, as shown in figure 3; then two more, evolving figure 4; and then, by the reverse process, the three preceding forms may be evolved from 4, and so on through an almost endless number of symmetri- cal forms, which any ingenious teacher may easily discover. i A A ^^ I. 2. 3. 4. The child not only loves play, but he loves dearly well to " make something," and this craving, to be of use in the world, should be early encouraged and cultivated. Let him, therefore, construct numerous forms of utility, his vivid im- agination supplying what the figures lack in detail. Thus, a key, (i), will, by slight changes, grow into an umbrella, (2); a goblet, (3); a candlestick and burning candle, (4); a fruit dish, (5); a hammer, (6); a sofa, (7); a wagon, (8); a bench, (9); a table, (ro); etc., etc., etc. t tYi Y 2. T 7. 8. 9. 10. With the fourth gift, these industrial forms may be ex- tended to a much wider range of objects, and the embryo architect, or smith, or sculpfor, may here find ample food for his inventive genius or occupation for his ever-willing bands. With the " fifth gift " a vast amount of arithmetical and 38 HISTORY AND SCIENCE OF EDUCATION. geometrical work may be introduced — much more than any ordinary primary school usually attempts to do. from these simpler forms the little ones may be led on, step by step, until they will have laid in a fund of informa- tion or experience that will make the transition to subjec- tive work or abstract reason natural and easy. It will not now be so difficult for the mind to look inward and study itself, for the obvious reason that it now finds something tangible to study there. And all this, if judiciously intro- duced by the teacher, need not interfere in the slightest with the pupils' regular school work; but, by breaking up its monotony and by supplementing it in various ways, will rather help it along, and lay a broad and deep foundation on which to build for the future. ANALYSIS OF CHAPTER IV. What has the Kindergarten to do with the Work of the Ordinary Teacher ? It shows the value of making school work pleas- ant. Impresses the fact that the concrete precedes the abstract, that activity is a necessity to a child — that it is cruel to make him sit still and do nothing. Many believe that kindergarten methods are of more value as aids to primary v^^ork than they are when used alone. The love of play as an educational force. With children from five to seven, work may well be interspersed with play. Much depends on the teacher's ingenuity. Uses that may be made of the Gifts in an Ordinary School : Use of the Third Gift to teach order and symmetry. New symmetri- cal forms developed by slight changes. Illustrated exercises with the eight small cubes. The child loves to "make something." How this desire may be gratified in the use of the Third Gift— in that of the Fourth Gift. Primary arithmetic and geometry may be taught with the Fifth Gift. Real progress that may be made by the use of these exercises. They will not interfere with regular school work. THE KIXDEEGARTEi^r SYSTEM. SUPPLEMENTARY QUESTIONS. 39 When primary teachers are exhorted to carry "the kindergarten spirit " into their work, what do you understand the injunction to mean ? When it is stated or implied in this chapter that the beginners in our district schools are often required to sit three fourths of the time with nothing whatever to do save trying to " keep still," are the facts at all over-stated ? How may the teacher very easily procure Froebel's Third Gift with- out buying it ? Can you suggest any other way by which the lesson on developing symmetrical forms and figures by slight changes may be impressed ? What other objects than the ones given in the figures may be made with the Third Gift ? With the Fourth Gift ? What other means than the ones suggested in the text can you sug- gest for encouraging the child's desire to be of use in the world ? (Let this subject have much more than a mere passing thought.) State some of the arithmetical and geometrical work which you think might be profitably illustrated by the Fifth Gift. What others of the kindergarten Gifts do you think you might use to advantage in primary teaching ? Should the games of the playground ever be utilized for educational purposes in any such way as are the in-door kindergarten occupations ? Why, or why not ? Is it true, as is often stated by the kindergarten teachers, that allow- ing a child to use any of the kindergarten Gifts carelessly — that is, without following out the purpose for which the Gift was especially designed — is detrimental to his habits of thought? Why, or why not? Would, or would not, the same objection hold against letting children play with building blocks, etc., at home? CHAPTER V. OBJECT LESSONS ESPECIALLY ADAPTED TO THE LAT- TER PART OF THE " OBJECTIVE PERIOD " OF THE CHILD'S SCHOOL LIFE. Object Lessons.— As before stated, the objective period of the child's life is the age of all others best adapted to Object Lessons. The reason is obvious : the little learner's mind has been principally engaged thus far in the reception of impressions of external objects through the senses, and he has, by the time he enters school, reached that stage of intellectual development when both the conceptive and perceptive faculties are in more or less active operation. He is now prepared to idealize and generalize his impressions more or less, and he naturally desires to clothe them in language. In most of our cities and towns, and in many of our country districts, too, for that matter, "Object Lessons "" will be found in the prescribed course of instruction. The framer of the course of study may never have seen a genu- ine object lesson given, and he may not know any one who has seen one; but the expression sounds well, and gives the course an air of "up-with-the-times,'' so it is put in on general principles. The result is, in many cases, that the teacher, who has never seen any thing of the sort, makes an attempt to carry out the requirements of the schedule, and succeeds about as well as one would in giving a lesson on the violin, without previous training on that much-abused instrument. These abortive attempts at giving object OBJECT LESSONS. 41 lessons have, in many sections, brought the system into disrepute ; and there is undoubtedly much truth in the assertion that the object lessons, as conducted in the majority of our schools, are the most objectless of all lessons. Many, in attempting to conduct these exercises, seem to have no purpose in view further than that of complying with the requirements of the- course of study, and so the exercise becomes frivolous, and therefore positively harm- ful to the pupils' habits of thought and recitation. The exercise that leaves no definite impression of its object on the minds of the little ones is worse than a failure. It cultivates purposeless habits, creates in the minds of the children a distaste for the exercise, and in some cases a disposition to turn the whole matter into ridicule — a state of affairs which, it is needless to add, is in the highest degree detrimental to discipline. Misconception of True Purpose The failure in giving these lessons has been due in many other cases to a misconception of their real purpose on the teacher's part. In an examination which the author assisted in conducting some years ago, the applicants were asked to explain what they understood object lessons to be. The great majority answered, in substance, that they consist in holding up objects before the scholars and then telling them all about the objects thus shown. Such a lesson, while it might impart a little information, by the pouring-in process, would utterly fail in the real purpose for which these lessons are designed — that of cul- tivating the perceptive and the conceptive faculties of the little learners. The real object of these exercises should be to induce the children to see with their own eyes, hear with their own ears, feel with their own fingers, taste with their own tongues, then idealize these perceptions, and give their 42 HISTORY AND SCIENCE OF EVUCAJJUiv. conceptions expression in accurate language — first spoken, then written. It has been held by some educational writers that one of the prime purposes of the object lesson is the cultivation of the senses themselves. With all due respect for the opinions of these writers, the author does not believe that the amount of such teaching which our schools can give would be liable to sharpen the senses of our pupils to any appreciable degree. He does not believe that children, however carefully trained in object lessons, would have any sharper vision, any more acute sense of hearing, touch, taste, etc., in the ordinary sense of the terms, than have those who have had no training of the kind at all in the school-room. But there are " those who, hearing, hear not, and seeing, see not," in natural as well as in spiritual things. It is not the province of the object lesson to pro- vide our pupils with the senses themselves — Nature usually does this — but rather to give them skill in their use, to train them to give heed to the impressions which are made in the mind through the senses — to cultivate, in short, the conceptive rather than the perceptive faculties, though of course this must be done through the perceptive faculties. Conception — Imagination. — By the investigation of a few different substances containing any given property, the mind forms a conception of this property aside from, or inde- pendent of, any one of tHe objects considered. That is to say, the idea of its qualities, apart from the subject itself, becomes now a distinct object of contemplation. This men- tal process is what we mean by conception. The province of this faculty is to store the mind with ideas formed from its previous perceptions (impressions through the senses), through the aid of close attention and memory. These gen- eralizations of our perceptions have an elevating influence on the mind, and it is often disposed not to stop with the OBJECT LESSONS. 43 simple conceptions thus derived, but to go further and ex- tend these into creations more or less original. This fac- ulty is called imagination, though it is in reality only a higher developed form of conception. It is especially character- istic of the latter part of the objective period of the child's life, and it may be utilized by the skillful teacher in making the most commonplace subjects intensely interesting. To the average child of this age, the stick with a rag tied around it becomes a veritable living baby, a paragon of all the virtues, graces, etc., that usually belong to this most in- teresting object of juvenile contemplation ; while a crooked stick with a string for a bridle becomes a genuine prancing war-horse, of extraordinary speed and valor. It is the predominance of this faculty that renders the objective age so well adapted to the imparting of moral and religious impressions ; the conceptions derived from the perceptions are now so easily extended to the realms of the unseen spiritual world that they become ever after so real that it is next to impossible to eradicate them entirely from the soul. " Give me the training of your children until they are seven years old," said a distinguished ecclesi- ast, "and I will forever protect the great majority of them against the seductive teachings of the materialist," and this statement doubtless contains a large degree of truth. Ob- ject lessons may, by only a slight extension of the concep- tions, be so directed as to impress indelibly the deepest spiritual truths. Association. — The faculty of association, too, is now brought into play, and with the conceptions of new proper- ties, new forms, and new ideas of various kinds, certain arbitrary sounds and signs are associated. The name of the property, idea, or thing, whether spoken or written, be- comes associated with the idea itself, and inseparable from it thereafter. The object lesson, therefore, should always 44 HISTORY AND SCIENCE OF EDUCATION. be made a language lesson, both in the way of extending the pupils' vocabulary in a natural way, and for the purpose of cultivating accuracy of expression. As Mr. Tate so aptly expresses it : " This habit of clothing our conceptions in language is the highest exercise of the representative fac- ulty. It completely objectifies our ideas, and gives, as it were, a two-fold existence to the products of thought. Words and ideas exercise a reciprocal influence on each other : the visible representation suggests its correspond- ing idea, and the idea suggests the corresponding represen- tation." The whole matter is thus admirably stated in a work styled " The Cultivation of the Senses," * — a name which is, however, somewhat misleading, since, as before stated, it is not so much the senses themselves that are cultivated by these lessons as the faculties they supply with aliment. Classification of Object Lessons " Object les- sons for infant schools may be conveniently grouped into four classes, corresponding to the ages of the children : ist. Lessons in which the main purpose is to lead children to perceive the parts and the more obvious qualities of objects. 2d, Lessons calling attention to the less obvious qualities and uses of objects. 3d, Lessons involving an easy classi- fication of things. 4th, Lessons directing attention to the adaptation of means to ends, and thereby exercising the reason. The same subject may be treated in all these ways, the teacher remembering that the senses should be chiefly exercised first, the conceptive faculty next, and the reason- ing faculty last of all. " As far as possible, even in the primary school, lessons relating to connected and kindred subjects should be given in a series, so that the relations between things may be * " The Cultivation of the Senses.- Eldredge and Brother, Philadelphia. OBJECT LESSONS. 45 perceived, and in order that new knowledge may be linked on to the old. ' Alike in its order and its methods,' says Herbert Spencer, ' education must conform to the natural process of mental evolution ; there is a certain sequence in which the faculties spontaneously develop, and a certain kind of knowledge that each requires during its develop- ment; and it is for us to ascertain this sequence and sup- ply this knowledge.' Apparatus — " The teacher should in all cases take care to provide himself beforehand with the apparatus necessary for his lesson, the apparatus and the experiments made with it being, if properly used, in themselves the lesson, and the teacher merely a demonstrator, whose function is not so much to communicate knowledge by word of mouth as to direct and test the child's powers of observation and reasoning. Careful attention should be paid to the order in which the experiments are performed, and the specimens displayed. " If possible, the teacher should have the actual object on which the lesson is given placed before the children; and a specimen of it should be given to each child. For instance, if the lesson were on a daisy, each child should have a daisy, and should examine it for himself, under the teacher's direction, first taking off one part and then another, and laying each part carefully aside. An enthusiastic teacher will always be on the lookout for specimens for the illus- tration of his lessons, and will take advantage of times and opportunities to secure them. I recently heard a lesson on the bee, and found that the teacher had the forethought to secure a complete hive of dead bees, from which he was enabled to furnish every child a handful at the beginning of the lesson. " If the actual object can not be had, then a picture of it should be introduced; but it should not be forgotten that a 46 HISTORY AND SCIENCE OF EDUCATION. picture is only an imperfect symbol of the object which it represents. It is, of course, a more perfect symbol than a word, because it is not arbitrary, and bears some resem- blance to the real thing; but it is. addressed to only a single sense, and is very liable to mislead even that. It can give no idea, except by way of suggestion from the association of ideas, of resistance, weight, texture, etc. Pictures that are not on the same scale as the objects represented should contain some familiar object to furnish a standard for rela- tive measurement. A picture of a mouse should contain a cat. A picture of an elephant should contain a man. This rule should be invariably observed in lessons on Natural History. Use of Blackboard — "As an auxiliary to all other modes of illustration, the blackboard should be freely used. Every teacher should be able to draw rapidly and effect- ively before his class. An illustration may often be drawn on the blackboard when no other form of illustration is avail- able. Children love to see a drawing grow under their eyes. Moreover, a blackboard drawing enables the teacher to present a complex object little by little, and to exagger- ate the scale of important parts of an object that are too small to be clearly seen in a model or complete drawing. In lessons on subjects in which form plays an important part, as in botany, it is well to get the children to copy for themselves the forms set before them. New Words " In his desire to get children to acquire real knowledge, the teacher should not forget the impor- tance of their acquiring verbal knowledge commensurate with it. Words are indispensable as the symbols of knowl- edge, and should be taught as occasion requires, care being taken that the knowledge of the thing or quality takes precedence of the knowledge of the word designating it. There are some qualities that are common to large classes OJiJECT LESS0N5. 47 of objects. It is not necessary to introduce these into every lesson on objects possessing them. Once well learned, the teacher may assume the knowledge of them, and direct his attention more particularly to distinctive qualities. All the new words should be written on the blackboard, and an abundance of examples should be given and required in which the words occur. " Teachers can not be too careful in performing experi- ments, in handling and arranging specimens, and in draw- ing and writing on the blackboard, to set an example of neatness, order, and symmetrical arrangement. Clumsy ex- periments, disorderly heaps of specimens, bad drawings, illegible writing, and confused blackboard work, have nec- essarily a bad moral and intellectual effect on the minds of the children before whose eyes they are constantly pre- sented." ANALYSIS OF CHAPTER V. The "objective period" the time for object lessons. The child's perceptive and conceptive faculties are active; he is competent to form general ideas, and express them in language. " Object Lessons'' often placed in courses of study because they are fashionable. Attempts to give them by those who have never learned how. The result spiritless and indifferent at best, often ridiculous and subversive of discipline. Common misconception that object lessons consist in description of objects by the teacher. On the contrary, the real aim is to lead the pupils, first: to observe; second, to express their observations. The object of such lessons is not to cultivate the senses, but the capa- bility of the mind to use them— to train the conceptive faculties through the perceptive ones. The process and the province of conception. Imagination ready and vivid in children. This fact may be utilized in producing profound moral and religious impressions on the child's mind. The faculty of association comes into play in teaching the child the spoken and written word that belongs to each new idea. 48 HISTORY AND SCIENCE OF EDUCATION. The object lesson should always be a language lesson. The reciprocal influence of words and ideas upon each other. Object lessons for infant schools : Divided into four classes ; 1st, perceiving the more obvious qualities ; 2d, the less obvious ; 3d, classification ; 4th, adaptation of means to ends. Connected subjects should be given in a series. Apparatus should be prepared and experiments tried beforehand. Have the actual object, if possible. Precautions to be observed when pictures are used. Use of the blackboard. Language lessons. Neatness and order. SUPPLEMENTARY QUESTIONS. Did you ever give object lessons to your pupils? If so, what were some of the principal difficulties you encountered ? Did your pupils seem to enjoy the exercise, and did it seem to you, upon the whole, that it was profitable ? How frequently do you think such lessons should be given, and how long should they be ? Through how many years of the pupil's school-life should pure object lessons be continued ? AVhat distinction would you draw between object lessons and object teaching ? When a child sees an object for the first time, what kind of a faculty is he exercising — perceptive or conceptive ? When you ask him such a question as " How many legs has a fly?" — he having no specimen before him — what kind of faculty is brought into play ? Is it possible for us to think without language ? CHAPTER VI. OBJECT LESSONS CONTINUED AND AMPLIFIED. In giving object lessons, the subjects first selected should be of the simpler kinds — those whose parts or prop- erties are most obvious— but the lessons should at the same time be made difficult enough to impress upon the minds of the pupils the fact that they are learning some thing, or at least turning their previous knowledge to some account. To spend the whole time of an exercise in impressing upon the class the astounding fact that the table has four legs, does not tend to cultivate their respect for the system. It is well, in the beginning, to introduce such lessons as will afford the little ones some opportunity to gratify their love of activity, as was illustrated in the earlier kindergarten gifts. In the second Stage common objects should be introduced — bearing in mind the neces- sity of directing the attention of the pupils to such facts as may have escaped their observation. The most interesting classes of subjects are those con- nected with natural history. Here there is so much that even children of an older growth usually fail to see that the lesson, when skillfully conducted, becomes intensely in- teresting. It is wonderful how much the sharp eyes of the little tots may be led to discover in such an object as a feather, a bee, a fly, etc., etc. The more prominent parts of the human body may also be made of interest, and the exercises on these may be 4 (49) 50 HISTORY AI^D SCIENCE OF EDUCATION. turned to the most practical account in connection with such subjects as temperance physiology. We now pass to a more practical illustration of the con- ducting of this most important school-room exercise. A SYSTEMATIC SERIES OF OBJECT LESSONS ON THE HEAD AND ITS MORE OBVIOUS PARTS OR ORGANS. Points to be developed : ist.^ — The position of the head. 2d. — Its general shape. 3d. — The parts on the right-hand side. 4th. — The parts on the left-hand side. 5th. — The fact that the two sides are just alike. 6th. — The covering of the head, and its use, care, etc. yth. — The eyes — their parts, position, care, use, etc. 8th. — The nose — its position, care, use, etc. c)th. — The ears — their position, shape, care, use, etc. loth. — The mouth — its position, use, abuse, etc. nth. — The fact that all the organs of the head are placed in the. best possible position for the purpose for which they are designed; the lesson which this teaches, etc. First Lesson. — The teacher, laying her hand on Lucy's head, asks the class : " What part of Lucy is this, scholars ? " The answer comes promptly, " It's her head." If they are disposed at first to answer in too loud or too boisterous tone, it must be checked, and the answer must be given again in the proper tone. There must be proper freedom in connection with all such exercises, or they will lose much of their spirit and sparkle, and consequently much of the purpose for which they are designed will be lost ; but at the same time, the familiarity of the exercises must not under any circumstances be permitted to degenerate into rudeness or insolence. The interest and enthusiasm must OBJECT LESSONS AMPLIFIED. 51 be natural if permitted to transgress the ordinary bounds of school-room decorum. The tone of assurance in which some will be disposed to answer the first question may indicate that they regale mental discipline ? Explain your statement by reference to the culties it cultivates. Can you give any other reasons than those given in the text in favor cultivating the verbal memory? Can you give any reasons aside from those quoted from Mr. Tate 'ainst it ? As a matter of fact, is it possible to " drop " any thing intentionally om the memory ? Can we forget at will ? Should a child's first exercise in drawing be from nature or from mod- s? Why? Will he learn easier from imitation, or from analysis ? How will these statements apply to his learning to write? To speak ? o read ? What method, then, of teaching reading to young children seems to )U the most philosophical ? CHAPTER IX. THE THIRD STAGE OF INTELLECTUAL DEVELOP- MENT. Understanding It will be remembered that the third stage of intellectual evolution is that point at which we may- be said to "understand," in the higher sense of the term, a principle or proposition. In one sense we have this fac- ulty from the earliest dawn of our mental being ; but it is in the spontaneous exercise of our primitive judgments — it is an act of unreasoning judgment, more instinctive than intellectual in its nature. We know things with ab.solute certainty, but we can hardly be said, in the higher sense of the term, to understand them until we have arrived at this understanding by the exercise of some of our intellectual faculties. During the earlier stages of intellectual development the mind has been laying in a large store of material. It has worked up its perceptions of the external world into a vast number of conceptions, or idealized forms of existence; and now, by its inherent energy and acquired strength, it is able still further to investigate the conceptions stored up, as well as to direct its attention more critically to the external world, and to classify, arrange, and systematize whatever falls under its observation. When it arrives at conclusions now, it must of necessity understand them, since it has worked them out for itself. Forming Conclusions While this faculty is usually well developed with regard to most matters outside of his studies at a comparatively early stage of the pupil's school- (78) THE THIRD STAGE. 79 ;, he is often only half sure of even the most obvious jpositions connected with his recitations. He arrives at 1 conclusions by legitimate means, perhaps, but he has ne it in such a half-hearted and purposeless way that he often ready to abandon these conclusions without an ort to defend them. It is obviously the teacher's duty endeavor to break up this half-hearted, uncertain habit long boys and girls, and, as far as possible, to cultivate them the habit of rational assurance in their conclu- ns; not, of course, that brazen kind which is the out- )wth of mere egotism, but the modest certainty of those o have not jumped at their conclusions, but have arrived them by careful thought, and who feel, therefore, that ;y have reason to believe themselves right, and to hold their convictions until evidence be adduced to the con- ry- The teacher who rebukes a pupil for asking an explana- n of why he is wrong, when there is occasion to correct Y of his statements, makes a grave mistake — provided fays that the pupil does not ask in an insolent way. It is :Ler rather to encourage his rational assurance by question- \ him in the Socratic fashion, until he is led to discover own mistake, and thus arrive at the proper conclusion methods at least partly native to himself. This will train Q in habits of correct thought, and thus give him each y more and more reason to have faith in his conclusions, [t is well for a class to have confidence in the infallibility their teacher's judgment, but it is vastly more important it they be led to exercise such care in arriving at con- sions that they will have intelligent faith in their own Igments. The class of scholars that change their answer ;hout a moment's hesitation, on the slightest mark of non- luiescence on the teacher's part, are not being educated any proper sense of the term. 8o HISTORY AND SCIENCE OF EDUCATION. Cognitive Faculties. — For the reason that the faculties involved have now to do with knowing, or comprehend- ing, by the aid of the understanding, their general char- acter is said to be Cognitive, as shown in the table on page 58. The more important of the individual faculties involved are, as shown in this table, abstraction, classifica- tion, generalization, explicit comparison, analysis, and judg- ment. By this it is meant to be stated that the capability of the mind in doing these special acts, or its susceptibiHty of being in these states, is now to be employed in attaining to intellectual understanding. Abstraction is the withdrawal of the mind from certain things or phenomena for the purpose of concentrating it upon other things or phenomena. The objects of pheno- mena thus singled out for consideration are said to be ab- stractions. " The utility of abstraction," says Schuyler, " is evident : for by it we avoid the distraction and confusion which would result from considering many things at th% same time. But it is not asserted that the mind can not at the same time attend properly to more than one things. An illustration of abstraction is found in the philosopher, who, absorbed in thought, walks the crowded street, obliv- ious of what is going on around him. He is in a state of abstraction." Abstraction is not only necessary in order to concentrate the mind on any given subject or phenomenon, for the pur- pose of investigating it, apart from the distracting influences of others, but it is also necessary to efficient study under any circumstances. It is here as much as anywhere else that the principle of " learning to do by doing " has appli- cation. The habit of abstraction is only acquired by its practice. The teacher can, however, make it more practi- cable on the pupil's part by her general management of THE THIRD STAGE. 8 1 the school.* The less there is to distract the pupil's atten- tion from study, the easier will it be for him to abstract his mind from his surroundings and concentrate it upon the theme or subject under investigation. But valuable as this faculty is for purposes of study, it may be cultivated in a wrong direction, and become a veritable mon.strosity. The person is then said to be "absent-minded." For the teacher, especially, this is most unfortunate, since his pupils will soon detect it, and take advantage of it to work annoyance. The properly edu- cated man is the one that can devote his undivided atten- tion to any theme of consideration without losing con- sciousness of whatever else is going on about him. Unless he retains the power of rousing himself at any moment, he is unfitted for the practical duties of life, and will certainly be imposed upon. Generalization is that faculty by which the mind is enabled to examine its own conceptions, discover their * Many a pupil wastes much the greater part of his time from the fact that his attention is distracted by his surroundings. It is often his own fault, no doubt, but the teacher's efforts to Iceep " order," or noisy methods of conducting reci- tations, are often the most distracting element in the school. A misdemeanor of some kind has been committed, or is supposed to have been committed, and instead of watching quietly to discover the offender, the teacher disturbs the whole school by inquiring in a loud tone of voice, '* Who dropped that pencil ? " " Who IS studying so loud ? " or who did this, that, or thither real or imaginary mischief. Every pupil in school is now interrupted in his study, his line of thought is broken, and it may take him some time to get down to quiet work again. Especially will this be true if, in addition to this general inquiry, the teacher stops to deliver a long lecture on the general depravity of the pupils, or administers cor- poral punishment to some one in the presence of the rest. For this reason, as well as for many others, it were better that when punishment must be administered it be done in private. Then, again, it is exceedingly difiScult to abstract the mind from its surroundings when the teacher habitually speaks in a loud and unnatural tone of voice in con- ducting the recitations. The author has a vivid recollection of a school he once visited, in which the teacher's tones in shouting out words to the spelling classes were actually startling. If they really succeeded in abstracting their minds from the teacher^s habitual racket, they must afterward have found small difficulty in meditating m a nail factory. 6 82 HISTORY AND SCIENCE OP EDUCATION. common properties, and group them into more general classes. It also has reference to the mind's power of exer- cising similar judgment with reference to external objects of contemplation. Thus the child, from having seen a great many dogs, forms an idealized conception of that, to him, most interesting animal; in the same way he forms a conception of the cat, the sheep, the cow, the horse, the pig, etc. Now, by a further examination of these various conceptions, he discovers one general point of resemblance — they each have four legs. He thus has evolved the idea of a quadruped. Again, he may observe a number of figures, or different forms, like the following : They are very unlike in shape and size, but if he has been properly trained to use his eyes, the pupil will detect almost at a glance their one point of resemblance, and be able to refer them to a common class. He sees that they each have four sides, and he thus evolves the general notion of a quadrilateral. This he should be led to dis- cover for himself, and when he has done it he is apt to "understand " wttat a quadrilateral is. He should then be encouraged to give a definition of it in his own words. If the definition prove faulty, the teacher should not correct it, but should lead the pupil to correct it himself by asking him questions after the Socratic * fashion. Thus, if he should frame his definition from looking at (i) alone, he might say that a quadrilateral is a figure bounded by four equal straight lines and having four equal angles. The teacher should then, instead of correcting him in the * For illustration of tlic Socratic method, see Cliapter III., Second Part. THE THIRD STAGE. 83 ordinary way, ask whether (2) is then a quadrilateral. A little reflection will lead him to see that one part of his defi- nition is wrong, since this figure has not four equal sides. He may then possibly say that it is a figure having four straight sides and four equal angles. If so, the teacher may ask him whether his definition applies to (3). He now discovers that the angles are not necessarily equal, and he is thus enabled to construct a perfect definition. This is the way that definitions should generally be evolved. The pupil should be led to a full comprehension of the idea, and should then be asked to describe it. When he has done this, he may fairly be said to know or understand it, and until he has done this his understanding of it may be safely doubted. Comparison is the simultaneous examination of two phenomena for the purpose of deducting resemblances and differences. It is a most valuable educational agency, and it may be illustrated by reference to any two of the foregoing figures. Thus, in (i) and (3), for example, the pupil should be led to discover the following points of resemblance : i. They are each enclosed by lines. 2. All the lines in each are straight lines. 3. The opposite sides of each are parallel. 4. They each have four angles. 5. The opposite angles of each are equal. Points of difference: i. While all four of the angles of (i) are equal, only the opposite angles of (3) are equal. 2. They are of unequal altitude. 3. They are of unequal area. 4. They are of different form or shape. 5. While the angles of (i) are all right angles, those of (3) are all oblique. When this faculty is applied to the investigation of phenomena other than objects it may become much more involved, but this will be sufficient to illustrate its applica- tion in arriving at an intellectual understanding of facts. §4 HISTORY AND SCIENCE OF EDUCATION. ANALYSIS OF CHAPTER IX. The third stage of intellectual development, where we really under' stand. This power of understanding principles distinguished from the pri- mitive understanding of the infant. The mind has now accumulated a considerable store of conceptions, and is able to work out conclusions, to classify and systematize. The lack of confidence in their own conclusions frequently shown by pupils. The teacher should endeavor to cultivate a reasonable assurance in pupils and should not rebuke them for asking respectfully why they are wrong, when correcting their statements, but lead them, by judicious questions, to see and correct their errors. It is of great importance that pupils should learn to reason so care- fully and clearly that they may feel confidence in their conclusions. The Cognitive Faculties : Enumeration of the more important ones. Abstraction — defined — illustrated — necessary to successful study — how the habit may be formed — how the teacher can provide favorable conditions for its cultivation. How some teachers interrupt their pupils' studies and render abstrac- tion impossible by noisy and meddlesome methods of discipline, by scolding, by administering corporal punishment in public, by conduct- ing recitations in an unnaturally loud tone. Dangers of excessive abstraction. This is peculiarly unfortunate for a teacher. The properly educated person is he who can concentrate his mind on a subject, and yet not lose consciousness of his surroundings, or the power to rouse himself promptly when necessary. Generalization — the classifying power. Illustrated by the child's observations of domestic animals, by his study of quadrilaterals of dif- ferent shapes. Leading the child to form definitions, and to correct them when faulty, illustrated by the quadrilaterals. Comparison — defined — value as an educational factor — illustrated by comparing two of the quadrilaterals. SUPPLEMENTARY QUESTIONS. Does the bee " understand " the nature of the cells it so perfectly constructs ? By what power does it work ? THE THTRD STAGE. 85 Does a boy "understand" the law of atmospheric pressure when he lies down to drink from a spring ? By what power, or faculty, then, does he know that the water will rise into his mouth in opposition to the force of gravity ? Has it been your experience that the mind is directed only to the external world during the earlier stages of its existence ? Why is it that the knowing, in the sense of the understanding facul- ties, are apt to take more vigorous hold of matters outside of school than inside ? How may the teacher check undue egotism on the part of a pupil with- out weakening his rational assurance ? Can you name any other school-room transactions than those men- tioned in the text that would be liable to distract attention ? Is it good logic to say that pupils must be accustomed to study in the midst of distracting exercises, since in after life they will often be obliged to abstract their thoughts amidst the most distracting surround- ings? What are some of the logical conclusions from the above statement, if valid ? What was the theory of the old-fashioned " loud school " ? What arguments can you advance in favor of administering necessary &sc\p\ine in the presence of the school? What arguments can you ad- vance against it ? Did the public punishment of culprits in the ' ' good old times " tend to increase or to diminish crime ? Can you give other illustrations of the employing of the faculty of generalization ? Give other applications of comparison. What is meant by analysis? Give illustrations. What is the reverse of analysis called ? Give examples. CHAPTER X. THE FOURTH STAGE OF INTELLECTUAL DEVELOP- MENT. INDUCTIVE REASONING AND ITS APPLI- CATION TO TEACHING. We discovered in the last chapter a great advance of the mind's intellectual grasp in the third or cognitive stage of its evolution. We saw how it acts by its reflective power upon its former stores of information, and molds these into general principles and abstract truths. We saw, also, how it may reach outward, and by comparison, abstraction, analysis, and other powers, classify, systematize, and arrange until order is made to appear where to the less developed understanding seems confusion. We have seen that the human mind, by the exercise of these faculties, rises far beyond the realms allotted to the brute creation, who have not this god-like power of seeking after, finding out, and knowing general truths. Reason. — But exalted as this stage of intellectual evolu- tion is, it is not the highest. There is still a loftier height to which the soul may climb, and the path by which its feet ascend almost to the celestial gates is Reason. Step by step it climbs, its horizon widening until its vision well-nigh sweeps the universe and scans the lurking-place of many a hidden world; it makes the solar waves its toys and play- things, using them in sportive picture-making; it grasps the waves of light that journey from the very verge of space's shoreless sea, and forces each to tell the secrets of its far-off home; it reaches forth its subtile hand to grasp (86) THE FOURTH STAGE. 87 the all-destroying thunder-bolt, and makes it tame to do its will and bear its messages around the earth with speed that makes the flight of Puck in Shakespeare's dream seem ordinary. Aye, more than this, it turns the pages of the ponderous stone-clasped volumes of creation's genesis, and reads the records of a million years ago; and who shall say what deeper hidden mysteries it may yet solve ? It is this tremendous force, this inner power of man that laughs at time and space, and penetrates the secrets of the deep; it is this untamable, resistless spirit, throned within a little mass of living clay; it is this most subtile, most ethereal essence — most like himself of all that the Creator trusted to man's care — it is Reason, with its bound- less possibilities, that is now for a season to be trusted to your hands, to set in order or to disarrange, to plume for loftier flights or to clip its wings, to leave it groveling in the dust, companioning with creeping things or wallowing with swine ! Deduction and Induction. — Reasoning is of two gen- eral kinds or, more properly speaking, it assumes two gen- eral forms: In the exploration of a great river system, one may start at the mouth of the main stream, and by follow- ing it up, explore in turn its countless tributaries, with all their branches; or, pursuing the reverse process, we may start at the beginning of the various rivulets, and trace them downward to their common mouth at the great ocean. In the one case we have reached the smaller through the greater, the special through the general; while in the other we have reversed the process, and arrived at the greater through the less, the general through the special. The former method is called Deduction; the latter. Induc- tion. Inductive Reasoning Induction, or the Inductive Method of Reasoning, may be further illustrated thus: 88 HISTORY AND SCIENCE OF EDUCATION. Two bodies of very unequal weight, as a coin and a feather, are placed at the same height in a long glass tube from which the air is carefully extracted by an air-pump. When let fall, they are both seen to strike the bottom of the tube at the same instant — that is, they both have fallen through this space in the same time. The noticing of the fact that these two bodies fall through this particular space in the same time is a fact of observa- tion. I may infer from this observation that should I re- peat the experiment, under the same circumstances, at an- other time; or that, should I use any other coin and any other feather; or that, should I use any other two substances whatever, the conditions as to the vacuum remaining the same, the same results would follow. Such a conclusion, or supposition, is known as an Inductive Inference, or as an Induction. Let us now examine the grounds for such inference. Law of Universal Causation Our object in per- forming the experiment has been to satisfy our minds as to whether bodies of different weights, or different specific gravity, will fall equally fast if acted on by gravity alone. We know of but one thing that could interfere with their free motion, and that is the resistance of the air. By pump- ing out the air we have "isolated the phenomenon," and may now observe the effect of gravity alone. We are assuming that there is a cause for the falling of these objects, that nothing can happen without a cause, and that no changes in the happening can take place with- out being preceded or attended by circumstances which, if rightly understood, would fully account for them. This principle, though we may not frame it in words, is what is known as " The Law of Universal Causation; " and it is acted on by rational men in all the practical affairs of life. THE FOURTH STAGE. 89 No doubt this law is in part the result of our deductions, drawn from our earliest experiences, but it is also a neces- sary condition of our thought — an intuition. Law of Uniformity of Nature We have tried the above experiment with only one coin and one feather, and at only one time; why should I infer that if I used differ- ent coins and feathers, or performed the experiment at dif- ferent times, the result would be the same ? By another law, as deeply seated in our nature as the one above con- sidered, we know instinctively that the same causes or com- bination of causes will invariably be followed by the same effects or combination of effects; or, to state the proposi- tion in different words, that " Wherever the same antece- dents, and none others, are introduced, the same conse- quents will invariably follow. This principle is known as The Law of the Uniformity of Nature." Thus, it will be seen, we have arrived at a general truth from the investigation of a particular phenomenon. Induc- tion is, therefore, seen to be the legitimate inference of the general from the particular. Converse of the Law does not Hold It is neces- sary to observe, and to impress upon the minds of our pupils the fact that the converse of the Law of the Uni- formity of Nature does not hold, though, of course, we should use none of this technical language. While it is always true that the same cause (no counteracting circum- stances) will produce the same effect, it does not follow, by any means, that the same effect is necessarily produced by the same cause, though much of the reasoning among children, and even among children of a larger growth, is apt to be of this fallacious nature. We may illustrate its absurdity in some such way as this : A given dose of poison may be sure to produce death iinless its effects are counteracted; but it >vould be piost 9° HISTORY AND SCIENCE OF EDUCATION. absurd to assume, for this reason, that wherever death occurs it is due to poison. It must also be observed that an effect is not necessarily due to one cause alone. It may require the combined action of several to produce it. Thus, death may be the result of an enfeebled con- stitution, in conjunction with some sudden illness or over-exertion or any one or more of a score of other causes, no one of which alone would have proved fatal. So, too, it must be ever borne in mind that the success or failure of a pupil may not be wholly or even principally due to the cause we happen to have in mind at the moment, even though we may be certain that it was in operation; neither can we affirm with certainty that the general success or failure of school is due to any given method. In arriving at legitimate conclusions in matters of this kind the greatest care must be observed. Many of the tests to be applied will naturally suggest themselves to the keen-witted teacher, but in order to be able to guide pupils safely it would be well to read carefully some good work on Inductive Reasoning. Induction and Science. — Most of the physical sci- ences are based so largely on observation and experiment that the Inductive Mode of reasoning is especially adapted to them and, for the same reason, they are especially adapted to its cultivation. By performing a few simple experiments in natural philosophy, with the aid of such apparatus as any intelligent teacher may extemporize, enough of the general laws of nature may be illustrated to start the mind of many a thoughtful boy or girl to thinking and investigating for itself. The author well remembers an evening spent at the home of a friend in a rural district, where the intelligent teacher had that afternoon been giving a few such experi- ments in homespun science, The heads of the boys were THE FOURTH STAGE. 91 full of it, and it was late before their intelligent discussions of the principles involved were ended. Inductive Method should not be too strictly fol- lowed A strict adherence to the Inductive Method, in our ordinary teaching, would require that instead of teach- ing definitions, principles, and rules, and afterward illus- trating them by facts, we first call the pupil's attention to a sufficient number of facts to establish the principle, or rule, or definition, and then require him to make it for him- self. Undoubtedly this is the more scientific way, but it will be observed that the books which profess to be written on the Inductive Plan usually state the principle in the blackest of full-faced type at the beginning of the section devoted to its discussion. The reason is that this gives the pupil something definite to work to, and the principle is, therefore, often mastered in a much shorter time, and stated in clearer terms, than the pupil would be apt to work out wholly by himself. The stating of a principle first, or the giving of a defini- tion before its explanation, is not objectionable, in case the full explanation immediately follows. It is the giving of definitions, and the statement of principles and rules, with- out explanation or illustration, that made the old system of Deductive Methods so void of good results. The Deductive Method of reasoning is not without its value, even in common-school education, and our next chapter will be devoted to illustrating the rational combi- nation of the two methods in teaching. ANALYSIS OF CHAPTER X. Lofty character of the third stage of mental development. The much more exalted nature of the fourth stage, or Reason. Brief summary of some of the more wonderful achievements of the human reason. Two general forms of reasoning — Inductive and Pedugtive. Illus- 92 HISTORY AND SCIENCE OF EDUCATION. trated by exploring a river system, beginning at its various sources, or beginning at its mouth. Deduction proceeds from the general to the particular; Induction from the particular to the general. Inductive Reasoning • Illustrated by the falling of a coin and a feather in a vacuum. The inductive inference from this experiment. Examination of the grounds of this inference. Principle of Universal Causation. We know this principle both by intuition and by experience. The Law of the Uniformity of Nature. Statement of the chain of inductive reasoning from which we infer the law of falling bodies in a vacuum. This shows how the general may be legitimately inferred from the particular. The converse of the Law of the Uniformity of Nature does not hold ■ — illustration. An effect is not necessarily due to one cause alone. The success or failure of a pupil or a school will probably depend on a combination of many causes. The greatest care necessary in considering whether we have found all the causes of any effect. The Inductive Method of reasoning specially applicable to the Physi- cal Sciences. The study of these sciences especially adapted, therefore, to train minds in inductive reasoning. Excellent and far-reaching results that may follow from showing children a few experiments in natural philosophy. We do not strictly adhere to Inductive Methods in our ordinary teach- ing, because, while their use is stimulating to the mind, yet their exclu- sive use makes the way too hard for the little learner, forcing him to find everytliing out for himself, instead of giving him the benefit of what older and wiser people have learned by ages of research. It is not objectionable to state the principle first, if its explanation immediately follows. It is rules without explanations that should be avoided. The Deductive Method is not without its value, even in common- school work. SUPPLEMENTARY QUESTIONS. Can you mention any other wonderful things, aside from those men- tioned in the text, that have been discovered or accomplished through roan's reason f THE FOVkTH STAGE. 93 Can you give a clear, original illustration of the difference between induction and deduction ? To which class does reasoning from analogy belong ? Give an illus- tration. Is there any difference between induction and empiricism ? If so, what? Can you give some other illustration of the fact that we instinctively assume the law of universal causation ? Can you give other illustrations of the fact that we assume the law of the uniformity of nature ? What are some of the mistakes or errors most liable to be made by the careless in the application of this law ? Give other illustrations of the fallacy of assuming that the same effect is produced by the same cause. Why does the same cause not always seem to produce the same effect ? Mention a few of the more simple experiments that may be performed by the teacher in order to wake up the mind and set pupils to investi- gating the laws of nature by the inductive process. CHAPTER XI. THE RATIONAL COMBINATION OF THE INDUCTIVE AND THE DEDUCTIVE METHODS IN TEACHING. It was stated in the last chapter that the Inductive Method of reasoning starts from the observation of the particular, and by the application of the Laws of Universal Causation and Uniformity of Action in Nature, arrives at general principles. It was also stated, but without ex- tended illustration, that the Deductive Method follows the reverse course — starting with the general and leading back to the special. How the Inductive precedes the Deductive.^It will be seen that the general principle must be established before the Deductive Method can be applied, and that un- less this general principle be intuitive, like the axioms in mathematics, for example, the Inductive must necessarily precede the Deductive. Thus, the surgeon, from having dissected a few bodies, or from having seen them dissected by others, learns the science of Anatomy. In the few sub- jects he has examined he has observed that each internal organ has its special locality, shape, relation, size, etc. He therefore reasons by induction, not only that the members of the human race generally have the organs he has found in the individuals investigated, but that these organs will have the same general locality, shape, size, etc., in all in- dividuals, except in such few cases as, owing to counter- acting circumstances, have had the uniform course of nature interrupted, and are, therefore, exceptional or ab- (94) hYDUCTIVE AND DEDUCTIVE METHODS. 95 normal. His faith in the fact that the cases he has exam- ined are the normal rather than the abnormal is greatly strengthened, and amounts to positive certainty when he compares the results of his own observations with the re- corded observation of a multitude of others. He now rea- sons deductively, when any individual of the human species requires surgical treatment, that this subject, being a mem- ber of the human race, must have such or such an organ in such or such a place, and must not have it located an inch or two inches above or below this point, or to the right or the left of it. On this evidence he stakes the life of the patient, and thrusts his lance, knowing that he will not pierce a vital organ or sever any of the larger veins or arteries. His reasoning, reduced to the form of a syllogism, is something as follows : " In the human body the organ O is located at the posi- tion L; it is N inches in diameter. This patient is a mem- ber of the human race; therefore he has the organ O in the locality L, and with the diameter N. Consequently, if I pierce this wound or ulcer at the distance of more than one half of N inches from the center of L, I will not strike the vital organ O." Should he now be ignorant of the fact that the large artery A runs just above the center of O, and should he sever this with his lancet, causing the death of the patient, he would be held responsible in the courts for the death of the person in question. Not having all the facts of Induc- tion which he should have had, it has been impossible for him to make the necessary Deduction, and the result is death to the patient and ruin to the surgeon. If such a rigid enforcement of justice were to be applied to the Doctors of the Mind and Surgeons of the Soul, how many of us would be outside of prison walls ? Probably only those who had already been hanged. 96 msTOkV AND SCIENCE OE EUUCATjujv. Necessity of Thorough Knowledge. — The anatomy of mind is quite as much a science as is that of physical organism; and, like the latter, it is an Inductive Science, all that is valuable in it being the result of observation and experiment; and though it may not be possible for each one of us to make all these observations and conduct these experiments ourselves, before beginning the work of teach- ing, the results of the observations of thousands of compe- tent observers have been recorded, and we should, as far as possible, avail ourselves of them before presuming to thrust the lance among the subtile tissues of the soul. If it is criminal negligence for the surgeon not to have suffi- cient inductive knowledge of the human system to enable him to make the requisite deductions as to where it is dan- gerous to probe, or how to dress and treat a wound, what must be said of those of us who attempt to teach, in utter ignorance of the anatomy of mind and soul ? The mutual relation of the Inductive and the Deductive may be further illustrated by, and applied to, our ordinary school-work in arithmetic. Deduction without Induction. — By courtesy of the publishers of this work, the author has before him a copy of one of the first arithmetics ever printed in the Eng- lish language. It is called "The Schoolmaster's Assist- ant," and is dedicated "to the Reverend and Worthy Schoolmasters in Great Britain and Ireland," by Thomas Dilworth, Schoolmaster in Wapping, 1742. It is further stated that the work is a " Compendium of Arithmetic, both Practical and Theoretical." But in spite of this state- ment, there is not the slightest attempt at the explanation of a principle from beginning to end. The principles are all stated dogmatically, in the form of rules, and the pupil is then set to work to apply these, deductively, in the solution of problems. More than this, the rules are often so blindly INDUCTIVE AND DEDUCTIVE METHODS. 97 Stated that it is difficult to see how pupils were enabled to follow them. Here is the way subtraction is treated, and it is a fair illustration of the way all other subjects were handled, be- fore the Inductive methods came into use: Q. What is the use of Subtraction ? A. By taking a less Number from a greater, it shows the difference between botli. Q. How many Sorts of Subtraction are there ? A. Two : Simple and Compound. Q. What is Simple Subtraction ? A. Simple or Single Subtraction is the finding a difference be- tween any two Numbers whose Signification is the same; as, the Differ- ence between 6 yards and 4 yards, is 2 yards. Q. How are Numbers to be placed in Subtraction ? A. With Units under Units, Tens under Tens, &c., as in Addition. Q. What Rule have you for the Operation of Subtraction in gen- eral ? A. When the lower Number is greater than the upper, take the lower Number from the Number which you borrow, and to the differ- ence add the upper Number, carrying one to the next lower Place. Q. What Number must you borrow when the lower Number is greater ? A. The same which you stop at in Addition. Q. How do you prove Subtraction ? A. By adding the Kemainder and the lesser Line together, which will always be equal to the greater Line. Or, By subtracting the Remain- der from the greater Line, and that Difference will always be equal to the lesser Line. Q. What is Compound Subtraction ? A. Compound Subtraction produces a difference between any two Sums of divers Denominations. And then, without so much as even an attempt at illus- trating the mechanical solution of a problem, the pupil is gi'ven a long array of examples, both in simple and com- pound subtraction, couched in language which fairly bristles 7 98 HISTORY AND SCIENCE OF EDUCATION. with the dictatorial air of the old-time schoolmaster — like the following : There were 4 Bags of Money, containing as follows, viz. The First Bag 34/., the second Bag 50/., the third Bag 100/., and the fourth Bag 150/., which were to be paid to several persons ; but one of the Bags being lost, there were but 234 /. paid ; / demand which Bag was want- ing ? This is an example of teaching entirely by the Deductive Method. The idea that pupils could be led to understand the rules they employed does not seem to have found lodg- ment in the heads of the school-masters of the good old days. How pupils ever managed to follow, even in the most mechanical way, such rules as the following is a mystery : Q. How do you reduce a Fraction of one Denomination to the Frac- tion of another, but less, retaining the same value ? A. Multiply the given Numerator, by the Parts of the Denominators between it, and that Denomination you would reduce the fraction to, for a new Numerator, and place it over the given Denominator. Possibly most of us could still work such a problem, in spite of this rule, but it is safe to say that very few of us could follow the rule. Yet this is just what our great-grand- fathers were compelled to do, and it would doubtless have been a painful experiment for one of them to have at- tempted to solve a problem by any other means than by the rule laid down, or to have asked why he did so and so. It was all-sufficient that the rule said so; and the worst of it is that this method of teaching is not yet wholly obsolete. The author must not be understood as condemning utterly the use of rules. He will illustrate presently how they may be rationally employed; but it is the habit of requir- ing children to work blindly by meaningless rules that is objected to, especially in cases where they might easily be INDUCTIVE AND DEDUCTIVE METHODS. 99 led, by Inductive methods, to a clear conception of the prin- ciples involved. Deductions derived from Induction. — Let us sup- pose that the pupil, wholly unfamiliar with the subject, is given such a problem as this : " Divide f by f ." The teacher may go on and explain inductively the process leading to the required solution, and this is a very good way, but not the best. Rather so direct the minds of the pupils, by skillful questionings, as to lead them to discover the principle or rule in part for themselves. The teacher may question them somewhat as follows: " How many times are 5 men contained in 10 hours ? " They will answer in substance that 5 men can not be said to be contained at all in 10 hours, because they are not the same kind of things. Their attention has been drawn to this fact long before, but it is well to have them keep it fresh in mind. Changing the question, " How many times are 2 gallons contained in 40 quarts ? " After a few mo- ments' hesitation, most of the pupils will correctly answer, " Five times." When asked to explain how they obtained this result, they will say, in substance, that 2 gallons equal 8 quarts, and that 8 quarts are contained in 40 quarts, 5 times. "What did you have to do, then," they may be asked, " before dividing ? " They will say that they had to " make the numbers alike," or to "change them to the same name," or something else that means about this. The teacher may then say that we commonly speak of this as " reducing them to the same denomination." Then might follow some such question as, " How many times are | contained in 4 ? " As they have had previous drill in this kind of work, they should promptly answer, " Six times," and when asked for an explanation, they will loo HISTORY AND SCIENCE OF EDUCATION. say that 4 is equal to twelve thirds, and two thirds are con- tained in twelve thirds six times. Then, again, in answer to the question, " What did you really do, before dividing ? " they will say that they re- duced the two numbers to the same denomination. It is then asked: " What must we really do before divid- ing I by |- ? " Some of the class will see that we must, in fact, reduce them to a common denominator — an opera- tion with which they are already familiar. The members of the class may then be permitted to perform this reduction, and they will soon have the results — | = W and \ = Jf. They will now have no difficulty in seeing that fourteen twenty-firsts are contained in fifteen twenty-firsts i^ times, for the same reason that 14 bushels are contained in 15 bushels, or that 14 things of any kind are contained in 15 things of the same kind i Jj times. They could now, undoubtedly, work any other example of this kind by following out the same Inductive Method of reducing to a common denominator, and dividing, as we have here done; but this would be much too slow for prac- tical purposes; so, now that the pupils understand what they must really do, the teacher may pursue these induc- tions a little further to evolve a very practical general statement or rule. In reducing the above two fractions to a common de- nominator, let the pupils only indicate the multiplication by means of the proper signs, without actually performing the work — that is, by multiplying both terms of each by the de- nominator of the other. Thus : ^ = ^-^^ and - = ?-^ . The teacher next re- .7 7x3 3 3x7 minds the pupils that since these fractions have now a com- mon denominator, the first of them is divided by the second by dividing its numerator by the numerator of the second INDUCTIVE AND DEDUCTIVE METHODS. loi — that two thirds are contained in four thirds twice, etc. etc. Consequently, 7~x^ "^3^ "i"st be the same as (5 x 3) H- (2 x 7); or, stated in the fractional form, ?^^. 2x7 Now, by inspecting this result it will be seen that the numerator is made up of the product of the numerator of the dividend and the denominator of the divisor; and that the denominator of the answer is the product of the denom- inator of the dividend and the numerator of the divisor. That is, the upper part of the dividend has been multi- plied by the lower part of the divisor, and the lower part of the dividend has been multiplied by the upper part of the divisor — the same result we would obtain by inverting the terms of the divisor, and then multiplying the numerators together for a new numerator, and the denominators to- gether for a new denominator. This principle should be further illustrated by the solution of other problems. Thus : ^ H- §- = •^ — - ~ ? — '- = ■^ , the same result as 7 8 7x8 8x7 5x7 would have been obtained by inverting §, making it |, and then multiplying s. by it. Or, in other words, - -h^ = ~x- — ^^ ■ 7 8 75 7x5 From this and other illustrations it will be seen that to divide one fraction by another, we invert the terms of the divisor and then multiply, or proceed as in multiplication, or multiply the numerators together for a new nu7nerator and the denominators for a new denominator. This same rule may, of course, be arrived at by other methods of induction. The pupils having now fairly reached the rule by legitimate inductions, should be permitted to employ it ever after in their practical work. To require the pupil to re-explain I02 HISTORY AND SCIENCE OF EDUCATION. every principle every time he uses it is nearly, if not quite, as illogical as to require him to use it without any expla- nation at all. The making of the rules is Induction; the applying them to the solution of problems is Deduction. The actual course of reasoning which the pupil employs, though he does not frame it in words, would be: "Any problem in division of fractions may be solved by invert- ing the terms of the divisor, and proceeding as in mul- tiplication. This is a problem in division of fractions; therefore it may be solved by inverting the terms of the divisor, and then proceeding as in multiplication." General Observations on the Use of both Methods in Teaching. — In most cases the rule will be reached by much simpler induction than in the case of division of frac- tions, and in many cases the inductions are so obvious that the intelligent pupil sees the method of solution at a glance, and needs no rules. This is true in most of the cases of percentage and its applications, and rules in such cases serve rather to confuse than to help the pupil: here he works best by employing only deductive methods. But there are many other cases, such as multiplying or divid- ing one fraction by another, finding the greatest common divisor and the least common multiple, multiplying or divid- ing one decimal by another, square and cube root, arith- metical and geometrical progression, simple and compound proportion, and most of the problems in mensuration, where, without the use of derived rules or formulae, his progress would be much too slow for the practical purposes of a stirring age. More than this, there are even a few cases where it be- comes necessary to employ the deductive method, and work by rule without having made the inductions and deductions on which the rules are based. Thus, every pupil should know how to find the circumference, or area, of a circle from its diameter, but he can not understand lohy he multiplies the INDUCTIVE AND DEDUCTIVE METHODS. 103 diameter by 3.1416 to find the circumference, or why he multiplies the square of the diameter by .7854 to find the area, until after he has studied geometry and been drilled in the higher applications of deductive reasoning employed in demonstration. No more can he understand many of the other rules of mensuration, such as finding the contents of a sphere, a cone, a pyramid, etc. But these are exceptional cases, not the rule by any means, and the teacher must see that in cases where the rule can be reached through induc- tive reasoning, the pupils do no blind, unthinking work. For reasons similar to the ones given here, both methods should be employed in grammar, spelling, and their kindred branches; and we will greatly err in teaching if we do not lead our pupils to draw many valuable deductions from their rich stores of inductive inference in history, geog- raphy, and other branches. ANALYSIS OF CHAPTER XI. Restatement of the Inductive Method. The Deductive follows the reverse course. A foundation must be established before the Deductive Method can be applied, unless it is intuitive. The Inductive, therefore, usually precedes the Deductive Method : This illustrated by the case of a surgical operation. How, in his inductive studies, the surgeon determines that the cases he has examined are the normal, rather than the abnormal — His responsibility. How the teacher would fare if held equally responsible for mischief done. The anatomy of the mind, like that of the body, is an inductive science. How we may supplement our own personal experience. Teaching is largely a deductive science, based on the inductive scienee of the mind. Illustration of the Folly of using the Deductive alone, FROM "The Schoolmaster's Assistant": (i) All its principles and rules stated dogmatically and blindly. (2) Illustration from the subject of subtraction. (3) Reduction of fractions to lower denominations. (4) 104 HISTORY AND SCIENCE Ur ilUUCAiiuiv. What our great-grandfathers had to contend against. (5) This method not yet wholly obsolete. The combination of inductive and deductive reasoning in teaching further illustrated — in relation to the problem of dividing one fraction by another. By inductive processes, directed by the teacher's questions, the pupils are led to see clearly that this can be done by reducing both to a com- mon denominator. By further inductions, they are led to evolve the short-cut of the common rule. The reason of a rule once understood, the pupil should not be re- quired to explain it whenever used. Division of fractions involves much more difficult reasoning than most problems in arithmetic. In many cases the inductions to be made will be seen at a glance by a bright pupil. This is especially true in Per- centage. In such cases it is best to use no rules. In many cases, how- ever, rules are necessary; but they should, as far as possible, be led up to inductively. There are a few rules, however, that can not be explained in common school work because they depend on the higher mathemat- ics. Examples of such rules. Both methods of reasoning should be employed in teaching other branches than arithmetic : as language, history, and geography. SUPPLEMENTARY QUESTIONS. Can you show, by deductive reasoning, that Illinois and Iowa must be largely engaged in raising hogs ? Make a statement of the process by which a pupil should arrive at such a conclusion, even though his geography said nothing on the subject. Is it wise to have pupils memorize the productions of each State and Territory ? Why, or why not. Illustrate how the pupil should be led to determine, by induction, the industries and products of New Mexico, of Wyoming, of Idaho. To what extent can they be led to determine, by induction, the habits, customs, and general characteristics of the future population of these various sections ? When we say of a person that "he is a far-sighted business man," do we mean that he reasons from induction or from deduction ? Give illus- trations. Can the man who measures the circumference of a circle by a tape line, and finds that it is 3.1416 times the diameter, be said to have estab- INDUCTIVE AND DEDUCTIVE METHODS. 105 lished the fact by induction ? What is such a process commonly called ? Is it better, in an educational way, than no proof at all ? Why, or why not? Is it, or is it not, true that from having inspected a geometrical series, and observed the fact that the 2d term is found by multiplying the ist term by the ratio, the 3d by multiplying the 1st by the square of the ratio, the 4th by multiplying the ist liy the cube of the ratio, etc. , we do not \-aof! positively that the loth term will be found by multiplying the ist by the gth power of the ratio ; or, in general, that the «th term will not be found by multiplying the ist term by the (» — i)st power of the ratio' What process of reasoning is this ? Does it arrive at an absolute dem- onstration of the rule ? CHAPTER XII. THE MORAL FACULTIES AND THEIR CULTIVATION. Our Moral Faculties may be said, in general, to be those powers of the soul that are called into operation in know- ing the right and the wrong, in discriminating between them, and in determining our actions with regard to them. Conscience That there exists such a thing as abstract goodness or rightness is a fact of which the soul is intui- tively conscious, and it is impossible for us to conceive of it being otherwise. For any rational being to believe that truth is a vice and that falsehood is a virtue, or that dis- honesty is right and that honesty is wrong, is as far beyond our power of conception as that he should be so constituted as to believe that two parallel lines can forK an angle with each other, or that effects may exist without causes. There is such a thing as right, and truth, and virtue, and the knowledge of this fact is as inseparable from us as is our very being. It does not follow from this, however, that we intuitively know that any given act, or motive, or line of conduct is right or wrong. Before determining this, the mind must compare the given motive or action with the intuitive model its Creator has provided, to see whether or not the two agree. The determining of the rightness or wrongness of any specific act or motive is, therefore, seen to be a matter of judgment, and it is as liable to error as are matters of judgment on questions in which the moral ele- ment plays no part. The faculty which makes this com- (io6) CULTIVATION OF MORAL FACULTIES. 107 parison of the Tightness or wrongness of an act or motive with the perfect model is called Conscience. Dependent on Judgment — Let us thoroughly under- stand this point before proceeding further, since a great amount of misunderstanding exists regarding it. Every rational creature knows intuitively that honesty is right, and that dishonesty is wrong. But every person is often uncertain where to draw the line between prudence and dishonesty in business affairs. If his judgment dictates that he can not conduct a certain line of business with a less profit than 20^, his conscience will dictate that his duty to his family will not allow him to charge less than this; but if, on the other hand, his judgment dictates that \o