LIPPINCOTT’S
EDUCATIONAL SERIES

EDITED BY
MARTIN G. BRUMBAUGH, Ph.D. LL.D.
PROFESSOR OF PEDAGOGY, UNIVERSITY OF PENNSYLVANIA, AND COMMISSIONER
OF EDUCATION FOR PUERTO RICO

VOLUME I

Lippincott Educational Series

EDITED BY DR. M. G. BRUMBAUGH

Professor of Pedagogy, University of Pennsylvania

VOLUME I

Thinking and Learning to Think

By Nathan C. Schaeffer, Ph.D., LL.D., Superintendent of Public Instruction for the State of Pennsylvania. 351 pages. Cloth, $1.25.

VOLUME II

Two Centuries of Pennsylvania History

By Isaac Sharpless, President of Haverford College. 385 pages. Illustrated. Cloth, $1.25.

VOLUME III

Kemp’s History of Education

By Dr. E. L. Kemp, Principal of East Stroudsburg Normal School. 385 pages. Cloth, $1.25.

VOLUME IV

Kant’s Educational Theory

By Edward Franklin Buckner, Ph.D., Professor of Philosophy and Education in the University of Alabama. 309 pages. Cloth, $1.25.

Lippincott’s Educational Series

THINKING
AND
LEARNING TO THINK

BY
NATHAN C. SCHAEFFER, Ph.D., LL.D.
SUPERINTENDENT OF PUBLIC INSTRUCTION FOR
THE STATE OF PENNSYLVANIA

PHILADELPHIA
J. B. LIPPINCOTT COMPANY
1906

Copyright, 1900
by
J. B. Lippincott Company

ELECTROTYPED AND PRINTED BY J. B. LIPPINCOTT COMPANY, PHILADELPHIA, U.S.A.

EDITOR’S PREFACE

The progress of educational thought during the closing years of this century has been marvellous. Professional schools have created a demand for professional teaching by giving an increasing group of skilled instructors to our schools. This professional activity has caused our leading cities to provide training-schools, as integral parts of the city system of education. Finally, our great universities have established departments of pedagogy for the higher training in education. As a result, the leading positions in higher schools and in supervision are more and more demanding professionally trained leaders.

In this auspicious awakening for professional leadership there has come an increasing demand for standard treatises upon the fundamental problems of education. Treatises upon the history, methods, principles, and systems of education have appeared with astonishing frequency. That many of these are commercial treatises—made to sell—is doubtless true. There is always a great temptation to profit by an active demand. Well-disposed but not always widely trained and broadly cultured teachers, who have achieved a local success with a method that owed its virtue to the personality of its author and not to its intrinsic worth, have been tempted into authorship. The wiser and nobler minds in the profession wait. The days of unrest and experimentation, breeding discord and confusion, have in part passed away, and the time has come when the products of all this divergent activity may be put to the test of clear analysis and adequate experience. This is especially true in the domains of historic and philosophic inquiry. In experimental activity, touching the problems of psychic life as related to its sensorium, much has been done in a tentative way. Much must yet be done to produce results of enduring significance.

This series of educational treatises is projected to give inquiring minds the best thought of our present professional life. Fundamental problems in education will be exhibited in the series from time to time by thoroughly trained leaders of extended experience. Teachers may confidently accept these as authoritative discussions of the cardinal questions of their profession.

The highest endowment of the human spirit on the intellectual side is the power to think. Learning to think is an essential process and end in all school work. Thinking is the intellect’s regal activity. In a vague way, all teaching appeals to the thought-activity of the pupil; but vagueness in teaching is as pernicious as it is common. To exhibit the value, scope, and process of thought is of inestimable service to the teacher. It gives specific direction to teaching processes, and saves the child from a thousand fanciful expedients.

In the craze of the passing decade for novelty in teaching, there has resulted an undue emphasis upon forms of so-called expressional activity. It has been, in many quarters, forgotten that education is noblest when it produces reflective activity. The power to analyze and synthetize thought-complexes is the most fruitful endowment of the intellectual life. Expression without adequate reflection is productive of superficiality.

We have been living a life of educational expedients. The path of educational advance is strewn with countless cast-off practices which once claimed attention largely because of the feeling among too many that the newest theory is the best. There has come, let us hope, the more rational resolve to test all new and loudly heralded theories by fundamental laws of mental activity. To emphasize the significance of this reaction, and to afford helpful criteria of educational processes, this volume will be found most stimulating, suggestive, and sensible.

For the purposes of the teacher thinking may be distinguished as follows:

(a) Clear thinking, by which one is to understand thinking the thing, and not some other thing in its stead. Much thinking is not clear. The power of recall is not fully developed. The mind acts, but is not able to assert confidently the accuracy of what it acts upon. Much needless criticism is heaped upon schools because pupils cannot spell correctly, solve problems accurately, recite a lesson in history or in geography properly,—in short, because the pupil’s knowledge is not clear. The first step in all true teaching is the step that makes clear to the pupil the thing he is to think.

(b) Distinct thinking, by which one is to understand thinking the thing in its relations. This phase of thinking is sometimes called apperception. It is the second, and not the first step in thinking. There is no value in teaching relations until the things to be related are first clearly apprehended. Perception must precede apperception. The pupil in the elementary school has been well taught if he has been taught to think clearly and distinctly.

(c) Adequate thinking, by which one is to understand thinking the thing in its essential parts. This is the analytic form of thought. The child at first cannot think adequately. His mind thinks things as wholes. He has not the power to think the whole and its parts, as parts of the whole, simultaneously. He must rise to adequate thinking only after clear and distinct thinking have become habits of mind. The fuller phase of this activity, by which these analyzed parts are synthetically wrought into an organic unity, is the process of concept-making,—the essential prerequisite of all high orders of thought. This power every teacher should possess. It is his surplus of knowledge, the possession of which makes him easily master in the teaching process.

(d) Exhaustive thinking, by which one is to understand thinking the thing in its causes. This is the highest form of thinking the thing. It gives perspective to thought-processes, and eliminates all accidental and misleading elements from the categories of thought. To achieve this, one must specialize. The teaching of the future must be more and more intensive in scope. The day of the encyclopædist is gone. The teacher of to-morrow must be a teacher who knows one order of truth exhaustively, and who possesses the skill to incite in others a permanent enthusiasm for that order of truth. Scientific progress is conditioned by such teaching.

The author has brought to this discussion the matured convictions of broad training in American and European systems of schools, and a wide and successful experience in teaching pupils and directing systems of education. The discussion takes on the modest but stimulating style of the public speaker. The author has for many years been among our foremost lecturers upon education. The temper of the discussion is moderate and constructive. There will be found here no wild excess, no straining after fanciful effect, no advocacy of sensational and ephemeral methods; nor is there a trace of pessimistic and destructive criticism of the earnest teachers who are conscious of limitations and are reaching hopefully for help. On the contrary, the discussion is full of real sympathy, founded upon personal experience with teaching in all its phases, and abounds in stimulating suggestion.

M. G. B.

October 1, 1900.

PREFACE

For a number of years it has been the author’s duty as well as privilege to lecture at county institutes on the difficult art of teaching pupils to think. This led to the request that the lectures be thrown into permanent form for publication. The lecturer who never publishes has no pet theories to defend; he can change his views as often as he sees fit; yet, in spite of this advantage, he cannot always escape or ignore the art of printing. One who gives his thoughts to the public without the use of manuscript and under the limitations of extemporaneous speech, made necessary by the large audiences which gather at teachers’ institutes, especially in Pennsylvania, runs the risk of being misquoted and misunderstood; he pays the penalty of being reported in fragmentary if not distorted forms. This ultimately drives him, in justice to himself and others, to write out his theories on education and to give them to his coworkers in print.

Portions of these lectures were delivered at the annual meeting of the superintendents of New England, before the State teachers’ associations of Massachusetts, Rhode Island, and Florida, before the Connecticut Council of Education, before the summer schools held under the auspices of the Ohio State University and the University of Wisconsin, and at several of the meetings of the National Educational Association. The favorable hearing accorded on these occasions induces the hope that the lectures will be kindly received by many who teach outside of Pennsylvania, and by some who give instruction in our higher institutions of learning.

Although no one can hope, on so difficult a theme, to say much that will be entirely satisfactory to leading educators, surely no apology is needed from any one who, after spending his best years in educational work, attempts to contribute his mite towards the solution of any of the problems which confront the teacher.

It is assumed that there is a body of educational doctrine well established in the minds of teachers, and that on many school questions we have advanced beyond the border line of first discovery. Those who assert that our educational practice is radically wrong and in need of thorough reformation should hasten to clarify their own views and ideas, to substitute constructive for destructive criticism, and to give definite shape to their reforms; otherwise a whole generation will grow to maturity and the reformers themselves will pass away before any of their reforms will have been accomplished. To give teachers the feeling that what they are doing is all wrong, and to leave them without anything better in place of what is condemned, robs them of joy in their work, makes them victims of worry and neurasthenia, and unfits them for the care of children. It is hoped that these lectures will be found to suggest a better way whenever criticism is bestowed upon existing methods of instruction.

No attempt is made to ridicule the arm-chair psychologists, or the advocates of child study, or those patient and painstaking workers who are honestly seeking to establish the facts of mind through experiments in the laboratory. He who has carefully reflected upon the art of making pupils think will not hesitate to admit that thus far he has received more light from the standard psychology than from the labors of those who claim to be the exponents of the new psychology. The latter can hardly write or talk without using the terms coined by the older students of mind; this shows their indebtedness to those who taught and speculated before laboratories of psychology were established. Sometimes the experiments have only served to test and give a reason for what was already accepted. Often they have brought to our knowledge facts of mind which could never have been discovered by the method of introspection. In either case the experiments have resulted in clear gain. Let the facts of brain and mind, of nervous and mental action, of human growth, maturity, and decay be gathered, questioned, tested, and classified; let their bearing upon educational practice be set forth in the clearest possible light: every resulting step of progress and reform will be hailed with delight by all who have no pet theories to defend.

The lecturer is limited by time, by the kind of audience which he addresses, and by circumstances largely beyond his control. These limitations drop out when he reduces his thoughts to writing, and a rearrangement at many points becomes possible as well as desirable. The expedients for relieving the strain of attention and winning back the listless can be omitted; and omissions that become necessary through the exigencies of the programme must be supplied for the sake of logical sequence. Moreover, the aims which those who engage the lecturer set before him frequently require a modification of the line of discussion, so that a course of lectures on a specific theme cannot always follow the same order of treatment, although substantially the same in content and scope. Hence the division into chapters has been adopted as preferable to the original sequence of lectures. Nevertheless, the style of the rostrum has not been altogether eliminated, because when oral discourse is thrown into new forms, and the phraseology is changed for the sake of publication, the loss in vividness, directness, and simplicity is greater than the gain in diction and fulness of statement.

Lecturing, as well as book-making, has its peculiar temptations. The lecturer must interest his hearers in order to hold them; he is tempted to play to the galleries, and to omit what is beyond the comprehension of the average audience. The book-maker, on the other hand, is tempted to display his learning, to make a show of depth and erudition. The student of pedagogy is supposed to be in search of profound wisdom. Those who write for him often dive so deep that their style becomes muddy. Unfortunately, some of the best treatises on education have been written in the style of the philosopher and wrought out on the plane of the university professor, although intended for undergraduates at normal schools, and for teachers whose meagre salaries do not enable them to pursue courses of study at institutions of higher learning. The lucid style of Spencer’s treatise on “Education” has done much to counteract this tendency. Yet many of the authors of our treatises on pedagogy seem to be haunted by a feeling similar to that of the German professor, who, on reading the opening chapters of a new book, and finding them to be intelligible to his colleagues, exclaimed, “Then I must rewrite these chapters; otherwise nobody will read my book through.”

Huxley has well described the penalty which must be paid by those who speak or write for the purpose of being understood. These are his words:

“At the same time it must be admitted that the popularization of science, whether by lecture or essay, has its drawbacks. Success in this department has its perils for those who succeed. The ‘people who fail’ take their revenge, as we have recently had occasion to observe, by ignoring all the rest of a man’s work and glibly labelling him a mere popularizer. If the falsehood were not too glaring, they would say the same of Faraday and Helmholtz and Kelvin.”

One who can never hope to rival the style of Spencer and Huxley and those to whom the latter refers, will nevertheless do well to emulate their skill in making difficult things plain to people who are not specialists or experts. He who writes for the teachers in our public schools should put aside his ambition to be considered erudite or profound, and endeavor above all things to be understood. Vague theories are apt to beget a bad conscience in those who teach and to destroy the joy which every one has a right to feel while doing honest and faithful work. Hence the writer offers no apology for heaping illustration upon illustration in the effort to make his meaning plain to those whom he aims to help.

There is at present great need for clear thinking and luminous presentation of facts on the part of all who write on education for the people or for teachers in our public schools. By a process similar to that by which the mediæval imagination swelled the murder of the innocents at Bethlehem into a slaughter of thousands of children (there cannot have been many male children two years old and under in a small Judean village), the harm which some pupils suffer is magnified into a national crime at the feet of American parents; the evils which result from “Bob White” societies, from children’s parties, from church sociables for young boys and girls, are all ascribed to the school curriculum; and reforms in home study are proposed which never fail to provoke a smile on the face of a healthy boy.

The hygienic conditions of the average school are quite equal to those of the average home. The health of many children improves during their attendance at school. The pupils who are born with a sound mind in a sound body, who get healthful diet, enough sleep, and treatment from their elders which is not calculated to make them nervous or unhappy, show none of the illness from overwork, the dulness of brain from fatigue, and the exhaustion of nervous energy which are made to furnish the narrow basis of fact for vague and broad generalizations. The haze in which those who must furnish the printer a given amount of copy in a given time are apt to envelop whatever they write has an effect like that of misty air upon the size of visible objects. Travellers who have come into a cloud while ascending a mountain report that a small wood-pile then looks like a barn, a cow seems larger than an elephant, men appear as giants, and the surrounding heights assume threatening proportions. As soon as sunlight clears the atmosphere, objects are again seen in their true dimensions. The moment the light of common sense penetrates the haze and mist and fog and cloud which are used to heighten the effect of essays upon school work, the need of radical reform seems far less urgent; and teachers, instead of wasting their time in worry and uncertainty, begin with cheerful heart to impart that which modern civilization requires every child to know as a condition of bread-winning and complete living.

There is, of course, a worse fault than obscurity of style,—namely, dearth of ideas. The danger to which the lecturer is always exposed, that of losing his hearers and failing to be recalled (their minds may leave while they are bodily present), spurs to effort in two directions. Either he will try to say something worth listening to, or he will strive to entertain by amusing stories and incidents. If he be conscious of a lack of talent for humor, he will try to stuff his lectures full of sense. If the lectures here published lack in this respect, the writer is willing to acknowledge failure.

In preparing a course of lectures it is proper to bear in mind the difference between the lecturer, the orator, the poet, and the philosopher. The philosopher investigates ideas and truths, explores their essence and relations, and unfolds them in their deepest unity and in their greatest possible compass. When this has been done throughout the whole domain of thought, his mission is accomplished. The poet seeks to clothe his ideas in beautiful forms. When the idea is perfectly suited to the form and the form to the idea, his mission is accomplished. The orator aims to move the will; he quotes authorities, uses ideas, appeals to the feelings, and subordinates everything to the one end of gaining a verdict, winning a vote, or getting a response in the conduct of those whom he addresses. The lecturer seeks to impart information. He aims to get a response in the thinking of those whom he addresses. He tries to reach the intellect rather than the will. Beautiful language and exhaustive treatment are not essential parts of his mission. It is his province to elucidate the theme under consideration, to guide the efforts and inquiries of those who come to him for instruction, to direct them to the sources of information, and to furnish such incentives as he can towards independent study and investigation.

Since the data for pedagogy are derived mainly from kindred fields of investigation, the lecturer on the science and art of education has frequent occasion to cite authorities and to utilize the labors and conclusions of the men eminent in the sciences which throw light upon the growth of the child, more especially upon the development of mind and character. The most original writers quote very little, and those who are anxious to establish a reputation for originality refrain from quoting others. It is the business of the lecturer to lead the hearer to the sources of information. When anything has been so well said that he cannot improve upon the form of statement it is proper that he should quote the language, carefully giving the source whence it is derived. Without doubt, when the genius appears who will do for pedagogy what Aristotle did for logic and Euclid for geometry, he will so polish every gem he gets from others and give it a setting so unique and appropriate that the world will recognize the touch of the master and acknowledge the contribution as peculiarly his own handiwork. In painting and sculpture we look to the past for the greatest works of art. In music the century now closing has rivalled, if not surpassed, its predecessors. In the science and art of education the greatest achievements belong to the future. It is currently reported and sometimes believed that when the president of a celebrated university was asked why he had transferred a certain professor from the department of geology to that of pedagogy, he replied, “I thought the fellow would do less harm in that department.” If the story is not a myth, he probably meant less harm to the reputation of the university. When in our day a course in geology or logic or geometry is announced, one can foretell the ground that will be covered. No such prediction can be made with reference to a course of lectures on teaching. The prophet is yet to come who will fix the scope of the science of education and give it something like definite and abiding shape.

This volume is not designed to supplant systematic treatises on psychology and logic. Its aim is to throw light upon one important phase of the art of teaching. If it contributes but two mites to the treasury of information on the science and art of education, the labor bestowed upon it has not been in vain. Should any critic hint that two mites are all one has to give, it may be said in reply that it is better to give something than to give nothing at all, and that according to Holy Writ the smallest contributions are not to be despised if made in the right spirit. And it may add to the critic’s stock of ideas to be informed that a small English weight, called mite, outweighs very many of the current criticisms upon modern education, that of this small weight it takes twenty to make a grain, and that to a faithful teacher a tenth of a grain of helpful suggestion is worth more than many tons of destructive criticism.

CONTENTS

I
MAKE THE PUPILS THINK

The value of a thought cannot be told.

Bailey.

He who will not reason is a bigot; he who cannot is a fool; he who dares not is a slave.

Byron.

Reason is the glory of human nature, and one of the chief eminences whereby we are raised above the beasts in this lower world.

Watts.

Man is not the prince of creatures,

But in reason. Fail that, he is worse

Than horse, or dog, or beast of wilderness.

Field.

Man is a thinking being, whether he will or no. All he can do is to turn his thoughts the best way.

Sir W. Temple.

I
MAKE THE PUPILS THINK

A test of teaching.

For the purpose of testing the quality of gold alloy jewellers formerly used a fine-grained dark stone, called the touchstone. In the eyes of an educator good instruction is more precious than pure gold. The touchstone by which he tests the quality of instruction, so as to distinguish genuine teaching from its counterfeit, rote teaching, is thinking. The schoolmaster who teaches by rote is satisfied if the pupils repeat his words or those of the book; the true teacher sees to it that the pupils think the thoughts which the words convey.

Thring’s practice.

Thring, who, next to Arnold, was perhaps the greatest teacher England ever had, laid much stress upon thinking. Sometimes he would startle a dull lad, in the midst of an exercise, by asking, “What have you got sticking up between your shoulders?” “My head,” was the reply. “How does it differ from a turnip?” And by questioning he would elicit the answer, “The head thinks; the turnip does not.”

Views of others.

So important is thinking in all teaching that at the World’s Educational Congress, in 1893, one educator after another rose in his place to emphasize the maxim, “Make the pupils think.” One of the most advanced of the reformers shouted in almost frantic tones, “Yes, make even the very babies think.” After the wise men had returned to their homes, a Chicago periodical raised the query, “How can you stop a pupil from thinking?” And the conclusion it announced was that neither the teacher behind the desk nor the tyrant upon his throne can stop a pupil from thinking. Evidently, if that which sticks up between a boy’s shoulders is a head and not a turnip, if the pupil is rational and not an imbecile or an idiot, he does some thinking for himself; and the maxim, “Make the pupils think,” requires further analysis before it can be helpful in the art of teaching.

Thinking for one’s self. Relying on others.

We who teach are very apt to overestimate thinking in our own line of work and to undervalue thinking outside of the school. There is, perhaps, as much good thought in a lady’s bonnet as in the solution of a quadratic equation. A sewing-machine embodies as much genuine thought as the demonstration of a geometrical theorem. The construction of a locomotive or a railway bridge displays as much effective thinking as Hegel’s “Philosophy of History,” or Kant’s “Critique of the Pure Reason.” Most men think very well in doing their own kind of work; in many other spheres of activity they must let other people think for them. When the professor of astronomy discusses a problem connected with his science, he thinks for himself; but when he buys a piece of land, he gets a lawyer to think for him in the examination of the title and the preparation of the deed. The lawyer thinks for himself in the court-house; but when he goes home to dine, he expects his wife, or the cook, to have done the thinking for him in the preparation of the dinner. Grover Cleveland had the reputation of thinking for himself: many a politician found out that this reputation was founded on fact; but when the ex-President is sick, or has the toothache, he is willing to let a physician or a dentist think for him. In like manner, a pupil may think very well upon the play-ground; but if the teacher, whose very name indicates the function of guiding, fails to guide the pupil aright, the latter may become a mere parrot in the class-room. What, then, is involved in making a pupil think?

Thinking defined.

The difficulty in answering this question is increased by the diversity of meanings of the word thinking. The teacher who is not clear in his use of the term may employ exercises calculated to develop one kind of mental activity, and then accuse the pupils of dulness because they do not show facility in some other intellectual process. When a text-book on mental science defines the intellect as the power by which we think, the term thinking is used to designate every form of intellectual activity. The Century Dictionary defines thinking as an exercise of the cognitive faculties in any way not involving outward observation, or the passive reception of ideas from other minds. The logician defines thinking as the process of comparing two ideas through their relation to a third. Many exercises of the school are supposed to cultivate thinking in the last sense of the word, when in reality they cultivate thinking only in the widest acceptation of the term.

A faulty exercise.

The writer saw a normal school principal conduct an exercise in thinking, as the latter called it. Turning to one of the pupils, he said, “Charley, will you please think of something?” As soon as the boy raised his hand the principal asked, “Does it belong to the animal, the vegetable, or the mineral kingdom?” Then turning to the other members of the class, he said, “Who of you can think of the vegetable in Charley’s mind?” The names of at least forty different vegetables were given and spelled and written upon the black-board. At last a pupil succeeded in naming what was in Charley’s mind. Then there was a look of triumph upon the faces of the principal and the class, as much as to say, “Isn’t that splendid thinking?” At least one person felt like burying his face in his hands for very shame; for here was resurrected from the dead an old exercise of philanthropinism which was buried more than a hundred years ago. What should one call that kind of mental activity? Guessing. That is all it is. The exercise tended to beget a habit very difficult to break up after it has been formed.

A better plan.

Far better was an exercise which the writer witnessed in a graded school. The teacher had called the class in the second reader. As soon as all the pupils were seated she said, “You may read the first paragraph.” Instead of reading orally, the class became so quiet that one might have heard a pin drop. After most of the hands were raised she called upon one pupil to tell what the paragraph said. The second paragraph was read and the substance of it stated in the pupil’s own words. An omission was supplied by another pupil; an incorrect phrase was modified by giving the correct words for conveying the thought. In the course of the lesson it became necessary to clarify the ideas of some. This was accomplished by a few pertinent questions which made the pupils think for themselves. After the entire lesson had been read in this way she dismissed the class without assigning a lesson. Every member of the class went to his seat, took out his slate, and began to write out the lesson in his own language. The interest and pleasure depicted on their faces showed that it was not a task but a joy to express thought by the pencil. The teacher had given them something to think about; she had taught them to express their thoughts in spoken and written language; her questions had stimulated their thinking, and when, later in the day, the lesson in oral reading was given, the vocal utterance showed that every pupil understood what he was reading. There was no parrot-like utterance of vocables, but an expression of thought based upon a thorough understanding and appreciation of what was read. The silent reading was an exercise in thought-getting and thought-begetting, the language lesson upon the slate was an exercise in active thinking through written words, and the oral expression furnished a test by which the teacher could ascertain what she had accomplished in getting her pupils to think.

A suggestive reply.

The first thing necessary in making the pupil think is best shown by relating another incident. The catalogue of a well-known school announced that the teachers were aiming to get their pupils to read Latin at sight and to think in more tongues than one. A captious superintendent wrote to the principal, saying, “I envy you. How do you do it? We would be satisfied if we could make pupils think in English.” The reply was equally sharp and suggestive: “You ask how we make pupils think. I answer, By giving them something to think about. If you ask how we make them think in more tongues than one, I answer, By giving them, in addition to the materials of thought, the instruments of thought as found in two or more languages.”

The first essential.

The first step in training a pupil to think is to furnish him proper materials of thought, to develop in his mind the concepts which lie at the basis of a branch of study, and which must be analyzed, compared, and combined in new forms during the prosecution of that study. Just as little as a boy can draw fish from an empty pond, so little can he draw ideas, thoughts, and conclusions from an empty head. If the fundamental ideas are not carefully developed when the study of a new science is begun, all subsequent thinking on the part of the pupil is necessarily hazy, uncertain, unsatisfactory. How can a pupil compare two ideas or concepts and join them in a correct judgment if there is nothing in his mind except the technical terms by which the scientist denotes these ideas? The idea of number lies at the basis of arithmetic. How often are beginners expected to think in figures without having a clear idea of what figures denote! What teacher has not seen children wrestling with fractions who had no idea of a fraction save that of two figures, one above the other, with a line between them! How many of our arithmetics are full of problems involving business transactions of which the pupil cannot possibly have an adequate idea! Not having clear ideas of the things to be compared, how can the learner form clear and accurate judgments and conclusions?

Proper thought-material.

So essential to correct thinking is the development of the concepts and ideas which lie at the basis of each science, that we may designate the giving to the pupil of something to think about as the first and most important step in the solution of the educational problem before us. In other words, the furnishing of the proper materials of thought is the first step in teaching others to think. The force and the validity of this proposition are easily seen if we reflect upon the essential oneness of the manifold diversities of thinking as they appear at school and in subsequent years.

Thinking in the professions.

It is universally conceded that education should be a preparation for life. The thinking at school should be an adumbration of the thinking beyond the school. The possession of enough data, or thought-materials, for reaching trustworthy conclusions, which is the indispensable requisite of successful thinking at school, is likewise a necessary requisite of successful thinking in practical life. It behooves us to inquire into the nature and foundation of the thinking of men in the professions, and in other vocations, for the purpose of gaining further light upon the problem before us. Let us, then, inquire into the nature and foundation of the thinking of men eminent in a profession or prominent in some other vocation. The professional man may have less native ability, less general knowledge, less culture and education, less mental power than the client whom he advises or the patient for whom he prescribes; and yet his inferences and conclusions are accepted as more trustworthy than those of men outside of the given profession, because he has a knowledge of facts and data which they do not possess. If he be a physician, special training and professional experience have taught him how to observe the symptoms of different diseases; how to eliminate sources of doubt and error; how to reach a correct diagnosis of difficult cases, and how to apply the proper remedies. If he be a lawyer, he has been taught how to examine court records; how to detect and guard against flaws in legal documents; how to find and interpret the law in specific cases; how to protect the life and property of his client. The judge on the bench is learned in the law, though he may be ignorant of science, literature, agriculture, commerce, and manufactures. He is aided in arriving at correct conclusions by thought-materials which are not in the possession of laymen.

The thinking of experts.

Teaching not a trade.

How does the thinking of an expert differ from that of other men? Not so much in the processes of thought as in the data upon which he reasons. An ordinary witness may testify as to matters of fact; the expert is supposed to possess extensive knowledge and superior discrimination in a particular branch of learning or practice; hence he may be a witness in matters as to which ordinary observers cannot form just conclusions, and he is held liable for negligence in case he injures another from want of proper qualifications or proper use of the thought-materials necessary to form trustworthy conclusions. From this point of view we can see new force and beauty in the remark of Fitch that teaching is the noblest of the professions, but the sorriest of trades. The aim of a trade is to make something that will sell; its ultimate aim is money, a livelihood. Teaching and the other professions, although they cannot be sundered from money-making, have a nobler aim. This arises out of the thought-materials with which they deal. If a teacher’s mind does not busy itself with these, he sinks to the level of a tradesman. A very keen observer said of the head of a large boarding-school, that he had learned his trade from the principal of a large normal school under whom he had been trained. The remark, if true, was severe, but significant. It was an intimation that the substance of the thinking of these two men was business rather than education; that their conversation about the quality of the beef and mutton served, about the loaves of bread, the pounds of butter, and the bushels of potatoes consumed each week, indicated that they were thinking more of the stomach and the purse than of the things of the mind; that their aim was a large attendance and a large cash-balance at the end of the year rather than the mental growth and professional preparation of their students. Their thinking was efficient and trustworthy in the domain in which it was exercised. It partook of the nature of trade-thinking, and lacked professional quality because it did not concern itself with problems of mental growth and moral training, with the proper sequence of studies, with the educational value of different kinds of knowledge, and with the best methods of economizing the time and effort of their students.

Mysteries.

In several aspects teaching is like a trade. Every art has its mysteries, with which those who practise it must be familiar if they would succeed. Teaching is no exception; and if the annual institute or the school of pedagogy fails to clarify these mysteries by putting the teachers in possession of materials for thought and of methods of applying knowledge to beget thinking which are not within the ken of the average parent and the general public, then failure must be written over the outcome. A mystery is a lesson to be learned. A scrutiny of the mysteries which characterize every trade and every art will serve not merely to emphasize the necessity for furnishing proper thought-materials, but will be helpful also in paving the way for the consideration of another essential in training pupils to think. Let us view them in the concrete.

Examples.

A machinist, who was also a skilled mechanic, was compelled by circumstances to quit his trade and to accept a position as janitor. One day the pipe leading from the sink to the sewer was clogged. The teacher, in conjunction with a carpenter, worked a long time to fix it, but in vain. The janitor was called, who in a few moments overcame the difficulty by the application of a principle in natural philosophy on which the teacher could have talked learnedly, although he knew not how to apply it in the given case. The janitor related how the foreman in a foundry was baffled in the effort to bore a hole through a piece of iron until a workman, trained under a foreign master, suggested the purchase of two things at a drug-store by means of which the hole was easily bored. When the druggist asked about the use that was to be made of these chemicals, he was told that the use was one of the mysteries of the machinist’s trade.

Next, the carpenter fixed the mortise lock of a door which needed attention, and the others lauded the skill with which he handled his tools and applied his knowledge. Before the three separated, the janitor’s son came with a word which he could not find in his lexicon. With the aid of chalk and black-board and grammar, the teacher showed how to dig out the roots of a Greek verb and what beautiful changes occur in its conjugation. The turn had come for the tradesmen to admire the mysterious skill and power of the teacher.

In applying the principle of natural philosophy, the janitor made skilful use of one or two tools which the teacher and the carpenter had never seen. He could express thought through the tools of his own handicraft, in ways that they could not. Each one of the three men knew the tools and the mysteries of his own vocation. During the entire scene there was not a logical flaw in the thinking of any one of them. Probably there was little difference in their native ability; certainly none in the fundamental nature of their thought-processes. The practical difference resulted from the data at their command and from the tools they were using to express the thoughts peculiar to their several vocations.

Man, the tool-user.

Instruments of thought the second essential.

The power to use tools, instruments, and machinery lifts man above the brute creation. There is labor-saving machinery in thinking as well as in manual labor. The more perfect the tools with which we work the greater the results we can achieve without waste of effort. In thinking as well as in working we must use the best tools in order to attain the greatest facility and efficiency. Yonder are two wheat-fields. In one of them a giant is wielding the sickle of our forefathers; in the other a youth, not yet out of his teens, is at work. At the close of the day the work of the giant will not bear comparison with that of the lad, because the latter was sitting upon a self-binder. They had the same material to work upon, yet, in spite of his superior strength, the giant could not cope with his weaker though better-equipped competitor. In like manner, the youth who has mastered the algebraic equation, or the symbols and formulas of chemistry, is in many respects the superior of a much brighter man who is not in possession of these tools or instruments of thought. A boy of average capacity who goes through a good high school thereby acquires certain fundamental ideas and the accompanying instruments of thought by which he is enabled to solve problems entirely beyond the power of a much brighter boy who never studies beyond the grammar grade.

Confusion in thought and practice.

The instruments of thought are generally spoken of as symbols, whilst the materials of thought are the things for which the symbols stand. In thinking, the mind may employ the ideas which correspond to the things in the external world; or it may employ the symbols by which science indicates things that have been definitely fixed or quantified. Failure to distinguish the sign from the thing signified, the symbol from its reality, leads to confusion in thought and to the most disastrous results in mental development. Loss of appetite for knowledge must inevitably result from methods of teaching by which the pupil is expected to learn the sounds of the letters from their names, or musical sounds from the notation on the staff, or the ideas of number from the arabic notation, or a knowledge of flowers from the technical terms of a text-book, or a knowledge of chemical elements and substances from the definitions, descriptions, and formulas of a scientific treatise. The symbol is indispensable in advanced thinking; but to expect the learner to get the fundamental ideas of a science from words, symbols, and definitions is evidence that the teacher does not understand the nature of thinking. It may, therefore, be helpful to set forth clearly the important distinction between thinking in things and thinking in symbols; to point out their relative value in mental development; and to fix their place in a rational system of education.

II
THINKING IN THINGS AND IN SYMBOLS

The rote system, like other systems of its age, made more of forms and symbols than of the things symbolized. To repeat the words correctly was everything, to understand the meaning nothing; and thus the spirit was sacrificed to the letter.

Herbert Spencer.

Words are men’s daughters, but God’s sons are things.

Johnson.

For words are wise men’s counters,—they do but reckon by them,—but they are the money of fools.

Hobbes.

It is only by the help of language (or some other equivalent set of signs) that we can think in the strict sense of the word; that is to say, consider things under their general or common aspects.

Sully.

II
THINKING IN THINGS AND IN SYMBOLS

Lesson in geography.

Two kinds of thinking.

Within half a mile of the Susquehanna River a teacher was asking the class, “Of what is the earth’s surface composed?” “Of land and water,” was the reply. In answer to a question by the superintendent concerning the earth’s surface, one boy declared that he had never seen the earth. He had been acquiring words without the corresponding ideas. Turning to another boy, this official said, “Will you please show me water?” With a gleam of satisfaction on his face, the lad raised his atlas, pointed to the blue coloring around the map of North America, and said, “That is water.” “Will you please drink it?” The expression on the faces of teacher and pupils indicated that all felt as if some one had committed a blunder. Where did the blunder lie? Had the teacher taught what should not be learned? Surely, every child should learn how water is indicated on a map. Did the boy use language wrong in idiom? By no means; for, as every student who has handled a lexicon well knows, many words have both a literal and a tropical, or figurative, meaning. If, pointing to an object, the teacher says, “This is a desk,” he uses the word is in its literal sense. On the other hand, if he points to a division on the map of the United States, and says, “This is Pennsylvania,” he does not mean that the colored surface to which he is pointing is the real State of Pennsylvania (if it were, a political boss could pocket it, and carry it the rest of his days without further trouble). What is meant is, that a given space on the map indicates or represents Pennsylvania, the word is being used, in the latter instance, in a figurative sense. Whether the word is, in the expression, “This is my body,” should be understood in a literal or in a figurative sense has been discussed for ages in the Christian church. In the answer of the boy we strike a distinction in thought that lies at the basis of good teaching in all grades of schools, from the kindergarten to the university,—namely, the distinction between thinking in things and thinking in symbols. In one sense of the word, all thinking is symbolic; for the percepts, concepts, and images of external objects which the mind employs in the thinking process are symbolic of the things for which they stand. But in advanced thinking, and especially in scientific investigations, objective symbols, such as words, signs, letters, equations, formulas, technical terms and expressions, are utilized to facilitate the thinking process. Take the age questions in mental arithmetic that have been prematurely inflicted upon so many pupils in the public schools. So long as the mind consciously carries A’s age and the wife’s age, using the clumsy instruments of arithmetical analysis, the thinking is difficult indeed. As soon as x is made the symbol of A’s age, and y the symbol of the wife’s age, so that the conditions of the problem can be thrown into algebraic equations, the difficulty vanishes. In the algebraic solution the mind drops all thought of A’s age and the wife’s age while manipulating the signs and symbols of the equation, and restores the meaning of the symbols only when their value in figures has been found. The algebraic solution is a genuine specimen of thinking in symbols, and illustrates the labor-saving machinery which the human mind employs, more or less, in all the most difficult scientific investigations.

Symbol defined.

What is a symbol? It is a mark, sign, or visible representation of an idea. The mathematician uses the symbol to represent quantities, operations, and relations. The chemist uses the symbol to indicate elements and their groupings or combinations. The theologian applies the term symbol to creeds and abstract statements of doctrine. The grips, countersigns, and passwords of a secret society may be spoken of as symbols of the ideas, aims, and principles of the organization. Often the symbol is chosen on account of some supposed resemblance between it and that for which it stands, as when black is made the symbol of mourning, white of purity, the oak of strength, and the sword of slaughter. “A symbol,” says Kate Douglass Wiggin, “may be considered to be a sensuous object which suggests an idea, or it may be defined as the sign or representation of something moral or intellectual by the images or properties of natural things, as we commonly say, for instance, that the lion is the symbol of courage, the dove the symbol of gentleness. It need not be an object any more than an action or an event, for the emerging of the butterfly from the chrysalis may be a symbol of the resurrection of the body, or the silver lining of the cloud typify the joy that shines through adversity.” Frequently the symbol is chosen arbitrarily, or because it is the first letter of the word which denotes the quality, substance, thing, or idea for which the symbol stands. Generally the symbol is a visible representation, but it may also address the other senses, notably the ear and the sense of touch. The Standard Dictionary excludes the portrait from the extent or scope of the symbol, and confines it to the representation of that which is not capable of portraiture, as an idea, state, quality, or action. It is well to bear this limitation in mind during the present discussion.

Examples.

A few illustrations will serve to fix the sense of the word symbol. In some parts of America the tramps have a system of symbols of their own, a given mark on the front gate indicating a good place to ask for a meal, another indicating a cross dog in the rear yard. That which the tramp fears or likes is not the mark which he sees, but a very real thing which that mark suggests to his mind. A number of the apostles were fishermen by trade. The fish became a very significant symbol in the days of early Christianity. The letters in the Greek name for fish are the initial letters of the expression, Jesus Christ, God’s Son, Saviour. It is one of many instances showing how the human mind delights in heaping symbol upon symbol to conceal precious meanings from the uninitiated.

Symbols for water.

What was the mental condition of the lad spoken of at the beginning of this chapter? The boy knew the real thing long before he knew the first symbol for water. Without doubt he had tasted it, played in it against his mother’s will, been washed in it against his own will, for months before he learned the first symbol for water used in common by him and others, which was probably the spoken word. Up to that time he thought of water in some mental picture or image which had been formed upon the eye and then upon mind somewhat as the picture is formed through the art of the photographer. Up to the time that he learned the spoken word for water this liquid suggested mental pictures which constituted a thinking in things[1] rather than in symbols, using the latter term according to the limitation set by the Standard Dictionary. On entering school he was taught to read; he added to the ear-symbol the eye-symbol,—that is, the written or printed word, which he may have associated at first with the real thing, or with the spoken word; of course, very soon with both, if correct methods of teaching were followed. Next, he was taught the map-symbol. The blunder which the teacher on the banks of the Susquehanna had committed consisted not in teaching how water is indicated on a map, but in not pointing to the majestic river near the school-house, and associating the water in its channel with the representations of water on a map. If the boy studied Latin or Greek, he was taught new symbols for water in the corresponding words of these languages. If he studied chemistry, he early learned the composition of water, and was thenceforth taught to write it H₂O, a symbol enshrining a new truth and lifting him to higher planes of thought by giving him a new instrument as well as new materials of thought.

Sources of error.

Elementary instruction.

Half the errors in teaching arise from the fact that the teacher does not constantly bear in mind the distinction between the symbol and the thing for which the symbol stands, thus giving rise to confusion in the mind of the learner. A class was bounding the different States of the Union. At the close of the recitation the superintendent suggested that the class bound the school-house. It was bounded on the north by the roof, on the south by the cellar, on the east and west by walls. The geography classes of an entire city were caught in that way. Either the pupils had not been taught, or else they had forgotten the difference between the real directions and the ordinary representation of them on the surface of a wall map. Sometimes the confusion exists in the mind of the teacher as well as in the minds of the pupils. Then he expects them to learn one thing while he teaches them another. By the methods formerly in vogue the pupil was expected to learn the sounds of the letters from their names; the pronunciation of the word from the names of the letters which compose it; the names, forms, and sounds of letters from the word taught as a whole; the musical sounds from the notation on a musical staff; the ideas of number, of fractions, from the corresponding symbols; the units of denominate numbers and of the metric system from the names used in the tables of weights and measures; the flowers of the field from the nomenclature of the botany; the substances and experiments in chemistry from the descriptions and pictures of a text-book. Such teaching has given rise to endless lectures, editorials, and discussions upon the use of the concrete in teaching, upon the value of thinking in things, upon the importance of object-lessons, laboratory methods, and the like.

More advanced instruction.

But there is another side to the question. There comes a time in the development of the pupil when he must rise above the sticks and shoe-pegs and blocks of the elementary arithmetic, and learn to think in the symbols of the Arabic notation. Later he must learn to think in the more comprehensive symbols of the algebraic notation. He must learn to think the abstract and general concepts of science, and, in thinking these, to use the devices, technical terms, and other symbols which the scientists have invented to facilitate their thinking.

A parable.

Hear a parable. A teacher sat down to dinner. The waiter handed him the bill of fare. The proprietor followed the waiter to the kitchen, directed him to cut out the names of the eatables which had been ordered, and to carry these names on plates to the dining-room. “It is not these words,” exclaimed the guest, “that I desire to eat, but the things in the kitchen for which these words stand.” “Isn’t that what you pedagogues are doing all the time, expecting children to make an intellectual meal on words such as are found in the columns of the spelling-book and attached on maps to the black dots which you call cities? My boy gravely informs me that every State capital has its ring, because on his map there is always a ring around the dot called the capital of a country.” The teacher was forced to admit that there is, alas! too much truth in the allegation. In the afternoon he took revenge. Knowing that the proprietor had a thousand-dollar draft to be cashed, he arranged with the banker to have it paid in silver coin. When the landlord saw the growing heap of coin, he exclaimed, “If I must be paid in silver, can you not give me silver certificates?” “Did you not intimate to me,” said the teacher, tapping him on the shoulder, “that it is the real things we want, and not words and symbols which stand for realities?” The landlord was obliged to admit that in the larger transactions of the mercantile world it saves time and is far more convenient to use checks, drafts, and other symbols for money than it would be to use the actual cash. In elementary transactions, like the purchase of a necktie, it is better to use the cash, to think and deal in real money, but when it comes to the distribution of five and one-half million dollars among the school districts of Pennsylvania, it is better to draw warrants upon the State Treasurer, to use checks and drafts, and to think in figures, than it would be to count so much coin, and send the appropriation in that form all over a great commonwealth.

Its interpretation.

The parable hardly needs an interpretation. Its lesson points in two directions. On the one hand, it shows in the true light every species of rote teaching, of parrot-like repetition of definitions, statements, and lists of words which give a show of knowledge without the substance. It puts the seal of condemnation on most forms of pure memory work. It sounds the note of warning to all teachers who are trying to improve the memory by concert recitations. The boy whose class was taught to define a point as position without length, breadth, or thickness, and who, when asked to recite alone, gave the definition, “A point has a physician without strength, health, or sickness,” is but one of many specimens of class-teaching condemned by the parable. It says in unmistakable terms that all elementary instruction must start in the concrete, taking up the objects or things to be known, and resolutely refusing to begin with statements and definitions which to the children are a mere jargon of words.

Making blockheads.

On the other hand, the parable indicates how too long-continued use of the concrete may arrest development, and hinder the learner from reaching the stages of advanced thinking. It hints that the too constant use of blocks, however valuable at first, ultimately begets blockheads, instead of intelligences capable of the higher life of thought and reflection. A rational system of pedagogy involves proper attention to the materials of thought and proper care in furnishing the instruments by which advanced thinking is made easy and effective. In one respect the parable does not set forth the whole truth. It makes no account of differences in thinking due to heredity and mental training. The differences in native ability are, however, not as great as is generally supposed (unless the feeble-minded enter into the comparison); the differences due to correct training, or the neglect of it, are far more striking. The work expected of the pupil should, of course, tally with his capacity; otherwise it will force him to resort to pernicious helps, beget in him wrong habits of study, rob him of the sense of mastery and the joy of intellectual achievement, and destroy his self-reliance, his power of initiative, and his ability to grapple with difficult problems and perplexing questions. The power to think grows by judicious exercise. Here better than anywhere else in the whole domain of school work can we distinguish the genuine coin from its counterfeit, and discriminate between true skill and quackery, between the artist and the artisan. It is at this point that most help can be given to young teachers by a good course of lectures on learning to think and on the difficult art of stimulating others to think.

III
THE MATERIALS OF THOUGHT

A vast abundance of objects must lie before us ere we can think upon them.

Goethe.

The young have a strong appetite for reality, and the teacher who does not make use of that appetite is not wise.

J. S. Blackie.

The child’s restless observation, instead of being ignored or checked, should be diligently ministered to, and made as accurate as possible.

Herbert Spencer.

What do you read, my lord?

Words, words, words.

Hamlet.

You have an exchequer of words, and I think no other treasure.

Two Gentlemen of Verona.

III
THE MATERIALS OF THOUGHT

Words without thoughts.

The hotel man was right in his criticism of teachers who expect their pupils to make an intellectual meal on mere words. For three hundred years educational reformers have been hurling their epithets against this abuse. Has it been banished from the schools? By no means. It crops out anew with every generation of teachers and in every grade of instruction from the kindergarten to the university. During the years in which a child acquires several languages without difficulty, if it hears them spoken, the mind is eager for words and often appropriates them regardless of their meaning. The child learns rhymes and phrases for the sake of the jingle that is in them, and cares very little for clearly defined ideas and thoughts. So strong and retentive is the memory for words that the child finds it easier to learn by heart entire sentences than to think the thoughts therein expressed. Like a willing and obedient slave, the verbal memory can be made to do the work of the other mental powers. The merest glimpse at a picture may recall all the sentences on the same page, so that the pupil can repeat them with the book closed or the back turned towards the reading chart. The recollection of what the ear has heard may thus relieve the eye of its function in seeing words, degrade the child to the level of a parrot, and thereby greatly hinder progress in learning to read. Very frequently the memory is required to perform work belonging to the reflective powers, because the learner is thereby saved the trouble of comprehending the lesson and expressing its substance in his own language. Moreover, the accurate statement of a truth is apt to be accepted as evidence of knowledge and correct thinking. The average examination tests very little more than the memory. If the answers are given in the language of the text-book or the teacher, the examiner seldom supplements the written work by an oral examination. Thus there is a constant tendency on the part of teachers and pupils to rest satisfied with correct forms of statement; and the pernicious custom of feeding the mind on mere words is encouraged and perpetuated. Exposed in plain terms, this abuse of words is condemned by everybody; yet it is as easy at this point to slide into the wrong practice as it is to fall into the sins forbidden by the decalogue. Like Proteus, this abuse assumes diverse and unexpected forms; instance after instance is needed to put young teachers on their guard and to expose its pernicious effect upon methods of instruction and habits of study. To cry “words, words, nothing but words,” will not suffice to correct the evil, for words must be used in the best kind of instruction. Line upon line, precept upon precept, example after example is needed to expose the folly of learning words without corresponding ideas, of teaching symbols apart from the things for which they stand. No apology is needed for citing laughable and flagrant instances in point; ridicule sometimes avails where good counsel fails.

Spelling.

A superintendent who advocates spelling-bees and magnifies correct orthography out of all proportion to its real value startled a class in the high school by asking for the spelling of a word of five syllables. Not receiving an immediate answer, he referred to the Greek. This made the spelling easy for at least one pupil. A year later he accosted this pupil, saying, “You are the only person that ever spelled psychopannychism for me.” “What does it mean?” was the question flashed back at him in return for his compliment. He could not tell, because he did not know. For years he had worried teachers and pupils with the spelling of a word whose meaning he had failed to fix accurately in his own mind.[2] What more effective method could be devised for destroying correct habits of thinking?

Eyesight.

There is a time in the life of the child when it is hungry for new words. The habit of seeing words accurately and learning their spelling at first sight is then easily acquired, provided there is no defect in the pupil’s eyes. In cases of defective eyesight the first step towards the solution of the spelling problem, as well as the first condition in teaching the pupil to think accurately, is to send him to a skilled oculist (not to a so-called graduate optician or doctor of refraction, who must make his living out of the spectacles he sells, and whose limited training does not enable him to make a correct diagnosis in critical cases). Correct vision will assist the pupil not merely in learning the exact form of the words which he uses in writing, but also in forming correct ideas of the things with which the mind deals in the thought-processes. Although great stress should be laid upon the orthography of such words in common use as are frequently misspelled,—daily drill upon lists of these should not be omitted at school while the child’s word-hunger lasts,—yet it is vastly more important to acquire an adequate knowledge of the ideas, concepts, and relations for which the words stand. To spend time upon the spelling of words which only the specialist uses, and which are easily learned in connection with the specialty by a student possessing correct mental habits, is a form of waste that cannot be too severely condemned. It is far better to spend time in building concepts of things met with in real life.

The meaning of very many words is, of course, learned from the connection in which they occur. This, however, is not true of sesquipedalian words like the one mentioned above, nor of the technical terms by which science designates the things that have been accurately defined or quantified.

Fundamental ideas.

Technical terms are used to denote the ideas which lie at the basis of science. These fundamental ideas are appropriately called basal concepts. Since basal concepts cannot be transferred from the teacher’s mind to the pupils’ minds by merely teaching the corresponding technical terms, they must be developed by appropriate lessons. If this be neglected, there may be juggling with words and a show of knowledge; but close, accurate thinking is impossible. This seems to be so self-evident that one would hardly expect to meet violations of such a simple rule in the art of teaching. And yet it is related of the professor of physics in one of our largest universities that he began his course of lectures in this wise: “A rearrangement of the courses of study deprived you of the usual instruction in elementary physics. That is your misfortune, and not my fault.” Thereupon, he began his lectures on advanced physics as if the preparation of his class to think the concepts at the foundation of his science could be ignored without detriment to the progress of the student, as if confused minds and unsatisfactory thinking were not the inevitable outcome of juggling with technical terms apart from the concepts which they denote. A master in the art of teaching would have started on the plane occupied by the students. By development lessons he would have lifted them to the plane of thought on which he intended to move. He would have considered their mental progress of more consequence than the course of lectures which he was in the habit of delivering. The student, and not the study, should have held the chief place in his professional horizon.

Abuse of text-books.

In another State university the professor of physics applied to an influential member of the board of trustees for an appropriation for apparatus. “Teach what is in the text-book; then you will not need apparatus,” was the reply. It seems almost incredible that a trustee of a modern university should fail to see the difference between an experiment actually performed and a description of the experiment in a text-book. More incredible still does it seem when we hear of professors who see no difference between an experiment made in the presence of a student and an experiment made by the student himself.

Apparatus and experiments.

Agassiz.

Pictures of apparatus and descriptions of experiments should, of course, not be despised or neglected. They are helpful in forming concepts of that which cannot be brought before a class. When made by the learner himself, as a result of his own work, they serve to clarify his thinking, and furnish a sure test of the pupil’s progress and of the teacher’s skill as a guide and instructor. A drawing, or even a statement in the pupil’s own words, is often an astonishing revelation of the crude notions which pictures give. The city lad who said that a cow was no bigger than a finger-nail because he had often measured its size in the First Reader is a typical example. The ability to interpret pictures and descriptions comes from actual knowledge of things similar to what is depicted or described. The noted teacher, Agassiz, made a difference in his directions to beginners and advanced students. To the former he would give specimens, with directions to study them without referring to a book. Having taught them how to use their eyes, he would gradually lead them to the method of interpreting and verifying the statements of an author. And when the advanced student was set to work at original investigations, he was told to study certain books, as it would save much valuable time. One of his pupils writes, “I shall never forget a forceful lesson given me by the great Agassiz, when I studied with him in the Museum of Cambridge. I worked near a young man from Cleveland, Ohio, who has since achieved distinction as a teacher of biology. I was comparatively a beginner, however, while he was well advanced in his studies. On a certain day Agassiz came sauntering by, and stopped long enough to tell me not to use the library so much, but to confine myself to observations of the specimens on hand and the writing of my observations and comments. Passing on a little farther, he spoke to my friend and said, ‘Albert, when you go home, this summer, to Cleveland, I wish you would make a special study of a certain kind of fish found in the harbor there. It is not found plentifully anywhere else in the world. Take a row-boat and go three hundred yards northeast of the point of the breakwater, and you will find them in abundance. Before going home, get the only three books ever written on this fish from the library here and read them. It will save your time to read them before beginning to study the fish itself.’”[3] Agassiz was as anxious to teach the right use of books as is the professor of literature; but he adapted his directions to the degree of advancement which his students had attained, and did not neglect the formation of the basal concepts and the habits of study needful in the sciences he taught.

Botany.

How little the exhortations of our educational reformers have been taken to heart by some teachers is evident from the recent experiences of a normal school principal, who had great difficulty in finding a satisfactory teacher of botany. The students could invariably answer the questions of the State Board of Examiners by filling pages of manuscript with technical terms. In the field they could not distinguish one plant from another. In despair, the principal said to his teacher of psychology, “Why can we not apply common sense to the teaching of botany? Can we not plant seeds, watch their growth, and study the growing specimens instead of the pictures in a text-book?” “If you will give me the class in botany, I will try it,” was the reply. Before the next class took up botany, every chalk-box was emptied and every flower-pot utilized in the planting of seeds. In no long time there appeared on the fences of neighboring farms sign-boards with the inscription, “Trespassing on these fields is forbidden, under penalty of the law.” The members of the class were traversing the country, studying the real flowers, the growing plants, instead of the technical terms of a text-book. At the next final examination, the herbarium which each one had prepared, together with the accompanying analysis and drawings of parts which could not be described, including colorings in imitation of the actual colors of the flowers, gave evidence of real knowledge, and served to satisfy the examiners, although the array of technical terms was far less formidable.

If violations of the fundamental laws of teaching occur in our higher institutions of learning, what may we not expect in the lower schools where the teaching is intrusted to young people of limited education? Nevertheless, it is a notorious fact that the worst forms of teaching are found in our higher institutions of learning, where many of the professors seem to know as little of the science of education as the motorman knows of the science of electricity; otherwise they would make impossible the use of “ponies, coaches, and keys,” by means of which the student taxes the memory rather than the understanding, and ultimately loses all power of independent thought and investigation. Such helps arrest mental development, destroy the power of original thinking, and do more harm than the practice of feeding the mind with mere verbal statements which in course of time may acquire content and meaning. The study of the sciences which classify minerals, plants, insects, birds, fishes, and other animals may degenerate into a mere study of words, even when the student acquires some familiarity with the specimens to be classified. The scientific name is the one thing about a flower with which the Creator has had nothing to do, and if the recognition of the scientific name is the chief or sole aim of the student of botany, it is a genuine case of feeding the mind on words.

Words as material for thought.

Geometry as thought-material.

By those who are fond of scientific pursuits the dead languages are sometimes despised as though the study of them were learned playing with mere words. Among people who begin their education somewhat late in life there is a strong temptation to estimate linguistic studies very far below their true value as a means for disciplining the reasoning faculty. When pursued in the right way, the study of the classical languages furnishes as much good material for thought as the natural sciences. Huxley may charm an audience by a lecture on a piece of chalk; the philologist can excite equal interest by a lecture on the word chalk. Words grow and undergo changes according to well-defined laws which furnish as much food for thought as the laws governing the union of atoms or the motions of the heavenly bodies. The words of a lexicon contain as much of precious interest in the sight of man as the manufactured gases or the plucked leaves and dissected flowers of the laboratory. Greek and Latin roots have more vitality in them than the collections of stones, stuffed birds, and transfixed bugs in the museum. The endings of nouns, adjectives, pronouns, and verbs furnish ample opportunity for observation, comparison, and reflection; their functions in the syntax of the sentence furnish splendid exercises in formal and qualitative thinking. If, however, the time of the pupil is entirely consumed in mastering the hundreds of exceptions to the rules of gender and case, of declensions and conjugations, of syntax and prosody, it is another sad instance of feeding the mind on mere words. The pupil who begins the study of any foreign language before he has reached his teens should acquire the power to read the language at sight; otherwise there has been something faulty in the methods of teaching or of study, or in both. A man is as many times a man as he knows languages; and the comparison of the idioms of two or more languages furnishes most excellent material for careful and accurate thinking. In translating an author like Plato the student must think the thoughts of a master mind, weigh words so as to detect the finer shades of meaning, and arrange them in sentences that shall adequately express the meaning of the original. The value of pure mathematics, especially the Euclidian geometry, as a means for the cultivation of thinking, lies in the limited number of fundamental concepts which must be clearly fixed and in the nature of the reasoning by which the truth of the theorems is established. The axioms are few in number and easily grasped; the quantities to be defined can, without difficulty, be set in a clear light before the understanding; the chain of proof compels the mind to join ideas by their logical nexus, and if the learner persists in memorizing the demonstration, he is at once detected. And yet when, as sometimes happens, he goes over several books of geometry without clearly perceiving the difference between an angle and a triangle, it must be a genuine specimen of acquiring words without the corresponding ideas.

S. S. Greene’s views.

The words of S. S. Greene deserve the attention of every teacher anxious to prevent the formation of vicious habits of thought by the pupils in our schools and colleges. Years ago he wrote as follows: “While an external object may be viewed by thousands in common, the idea or image of it addresses itself only to the individual consciousness. My idea or image is mine alone,—the reward of careless observation, if imperfect; of attentive, careful, and varied observation, if correct. Between mine and yours a great gulf is fixed. No man can pass from mine to yours, or from yours to mine. Neither, in any proper sense of the word, can mine be conveyed to you. Words do not convey thoughts; they are not vehicles of thought in any true sense of that term. A word is simply a common symbol which each associates with his own idea or image. Neither can I compare mine with yours, except through the mediation of external objects. And, then, how do I know that they are alike; that a measure called a foot, for instance, seems as long to you as to me? My idea of a new object, which you and I observe together, may be very imperfect. By it I attribute to the object what does not belong to it, take from it what does, distort its form, and otherwise pervert it. Suppose, now, at the time of observation we agree upon a word as a sign or symbol of the object or the idea of it. The object is withdrawn; the idea only remains,—imperfect in my case, complete and vivid in yours. The sign is employed. Does it bring back the original object? By no means. Does it convey my idea to your mind? Nothing of the kind; you would be disgusted with the shapeless image. Does it convey yours to me? No; I should be delighted at the sight. What does it effect? It becomes the occasion for each to call up his own image. Does each now contemplate the same thing? What multitudes of dissimilar images instantly spring up at the announcement of the same symbol!—dissimilar not because of anything in the one source whence they are derived, but because of either an inattentive and imperfect observation of that source, or some constitutional or habitual defect in the use of the perceptive faculty.”

J. P. Gordy’s statement.

Pestalozzi’s reform.

Dr. J. P. Gordy, to whom credit is due for the preceding quotation, further says, “Words are like paper money; their value depends on what they stand for. As you would be none the richer for possessing Confederate money to the amount of a million dollars, so your pupils would be none the wiser for being able to repeat book after book by heart, unless the words were the signs of ideas in their minds. Words without ideas are an irredeemable paper currency. It is the practical recognition of this truth that has revolutionized the best schools in the last quarter of a century.... In what did the reform inaugurated by Pestalozzi consist? In the substitution of the intelligent for the blind use of words. He reversed the educational engine. Before his time teachers expected their pupils to go from words to ideas; he taught them to go from ideas to words. He brought out the fact upon which I have been insisting,—that words are utterly powerless to create ideas; that all they can do is to help the pupil to recall and recombine ideas already formed. With Pestalozzi, therefore, and with those who have been imbued with his theories, the important matter is the forming of clear and definite ideas.”[4]

Sight and insight.

It was a remark of Goethe that genius begins in the senses. With equal truth we may say that thinking begins in the senses. Like unto the genius, the thoughtful man perceives and interprets what has escaped the notice of other people. To sight he adds insight. That which he sees is subsumed under the proper class or category, and is viewed from different sides until its significance is discovered, and a place is assigned to it in the intellectual horizon and in the external world. Every fact thus seen in its relation to other facts serves as a basis for further observation, reflection, and comparison. Not merely the genius, but every other person whose thinking is above the average in vigor and accuracy, has the power to perceive things which escape the eyes and ears of other people. Through habits of careful and correct observation he fills his mind with images, ideas, concepts of the objects of thought and of the relations which exist between these objects, and thereby acquires the materials for the comparisons which constitute the essence of good thinking. If the strength of a student is exhausted in gathering and storing the materials for thought, his mind becomes a wilderness of facts; if he reasons without the facts, his conclusions are more unreal than the figments of the imagination.

Truth the proper thought-material.

Truth is the best thought-material for the mind to act upon. The possession of truth is the aim and the goal of all correct thinking. Knowledge of the truth implies the conformity of thinking with being. The world within should be made to correspond with the world outside of us.

The laboratory and the library.

Aristotle.

Fortunately, the self-activity of children is towards the objective world of things which they can see, hear, smell, taste, and handle. From inner impulse their thinking is directed towards the cognition of objects. One of the functions of nature study is to beget habits of careful and accurate observation. This is a characteristic feature of the laboratory method as distinguished from the library method. A training in both is essential to a complete education. The library stores the treasures of knowledge which the human race has gathered and makes them accessible to the learner. The laboratory shows him by what methods truth is discovered and tested and verified. The German professor who declined to visit a menagerie, asserting that he could evolve the idea of the elephant from his inner consciousness, may have spent much time in reading books and in speculation; but he certainly never worked in a laboratory; nor had he taken to heart the lessons which he might have learned from the sages of antiquity. Aristotle knew the importance of asking nature for facts, and he induced his royal pupil, Alexander the Great, to employ two thousand persons in Europe, Asia, and Africa for the purpose of gathering information concerning beasts, birds, and reptiles, whereby he was enabled to write fifty volumes upon animated nature. After teachers had forgotten his methods they still turned to his books for the treasures which he had gathered. In the ages in which men hardly dared to ask nature for her secrets, fearing that they might be accused of witchcraft, they turned to Aristotle as if he were an infallible guide—so much so that when Galileo announced the discovery of sun-spots a monk declared that he had read Aristotle through from beginning to end, and inasmuch as Aristotle said nothing about spots on the sun, therefore there are none. This book-method of studying science has not entirely disappeared from the seats of learning. Books like Tyndall’s “Water and the Forms of Water,” Faraday’s “Chemistry of a Candle,” and Newcomb’s “Popular Astronomy” may, indeed, be read or studied as literature, and thus prove a means of culture; but to accept the facts and statements of a text-book without verification is the lazy man’s method of studying science; and as a method it fails to lay the foundation upon which a solid superstructure can be built. The correct method starts with observation of the things to be known, develops the basal concepts which lie at the foundation of the science under consideration, ends by teaching the pupil how to make independent investigations, how to utilize the treasures which have been preserved in our libraries, thereby furnishing an adequate supply of proper materials for thought.

Productive minds.

The habits of men who have surprised the world by their intellectual and professional achievements are very suggestive. Spurgeon kept his mind filled by constant reading. Goethe was fond of travel and utilized what he learned from others. Emerson visited the markets regularly, conversed with the men and women from whom he bought, and sought to learn their views on current events. Study the greatest thinkers the world has known, and you will find their memories to have been a storehouse of thought-materials which they analyzed, sifted, compared, and formulated into systems that win the admiration of all who love to think.

IV
BASAL CONCEPTS AS THOUGHT-MATERIAL

Thought proper, as distinguished from other facts of consciousness, may be adequately described as the act of knowing or judging of things by means of concepts.

Mansel.

We cannot learn all words through other words. There is a large and rapidly increasing part of all modern vocabularies which can be comprehended only by the observation of nature, scientific experiment,—in short, by the study of things.

Marsh.

The question we ask of each thing (and of the whole experience) is, What are you? You have qualities which I find everywhere else; your color I find in other things; your texture and hardness and odor and form I find in other things; but they are combined in you in such a way as to make you a thing by yourself, and not anything else. And I want to know what you truly are,—in short, what is your essence, which is also your idea, and the purpose or τέλος of your existence.

Laurie.

IV
BASAL CONCEPTS AS THOUGHT-MATERIAL

Building concepts.

The head may be likened unto a walled city, with comparatively few building materials on the inside, and with a limited number of gate-ways through which all other materials for building purposes must pass. The walls are not made of brick or stone, but of bone; the gate-ways are the different senses through which knowledge enters the mind. The building materials on the inside are intuitive ideas which take shape in conjunction with the entrance of materials from without. The structures which are built up out of the ideas within and the sense-impressions from without are individual and general concepts. Take an orange. Its shape, color, parts, are known through the eye. Its flavor, as sweet or sour, is ascertained through taste; its odor through smell; its temperature, shape, and some other qualities through touch. These various sense-impressions, giving the mind a knowledge of essential and accidental qualities and attributes, are combined in the idea of a particular orange. If the object were a bell, its sound, parts, uses, and qualities would make impressions through different gate-ways of knowledge; the builder inside would combine them into the more or less complete idea of the object presented to the senses. From each sense-impression the mind may get a percept; the synthesis of these percepts produces the individual concept or notion.

It is helpful at this point clearly to distinguish between essential and accidental attributes. The orange may have been kept in the open air when the temperature is low. To the hand it feels cold, and this quality enters into the idea of the first orange which the child has. As other oranges which have been in a warmer atmosphere are brought to the child, the attribute cold is seen to be accidental,—that is, it is not a necessary quality of oranges in general. On the other hand, the qualities which are found in every orange—many of them hard to describe in words—become fixed in the mind as essential attributes of the orange. In course of time many objects of the same kind are presented to the senses, cognized by comparison so as to retain the essential attributes and to omit the accidentals. By this process the general notion or concept is formed.

Gate-ways of knowledge.

It is self-evident that the mind’s comparisons and conclusions are unreliable in so far as the gate-ways of knowledge are defective. Few persons have perfect ears; many can never become expert tuners of pianos or reliable critics of musical performances. The man who is color-blind is not accepted in the railway service or as an officer in the navy. The man who is totally blind is never selected as a guide in daylight. On the other hand, the blind girl spoken of by Bulwer could find her way better in the darkness of the last days of Pompeii than other people, because she was accustomed to rely upon the data furnished by the other senses in making her way through the city, and had improved these as gate-ways of knowledge beyond the needs of those gifted with sight.

From things to symbols.

From sign to thing or idea.

The sense to be addressed.

In building concepts of objects in nature it would be a great mistake to begin with the word instead of the thing. Just as little as a blind man can conceive the qualities color, light, darkness, through mere words, so little can children conceive classes of objects which have never addressed the senses. Hence great stress has been laid by educational reformers upon the cultivation of habits of observation, upon the supreme necessity of teaching by the use of objects, or so-called object-lessons. First, things, then words, or signs for things, was at one time a favorite maxim in treatises on teaching. Consistent application of the maxim would have banished the dictionary from the school-room, or at least its use as a means for ascertaining the meaning of words. In consulting the dictionary for the meaning of a word, we pass not from the thing to its sign, but in the opposite direction,—that is, from the sign to the thing signified, from the symbol to the idea for which the symbol stands. The main essential in good instruction is that the words be made significant. In primary instruction this is best accomplished by passing from the idea to the word; but in advanced instruction it is of less importance whether we pass from the word to the idea or from the idea to the word. The meaning of very many words is acquired from the connection in which they are used. For the meaning of the larger number of words in our vocabulary we never consult a dictionary. The finer shades of meaning we get not from definitions, but from quotations taken from standard authors. This fact should never tempt the teacher to trust to words, definitions, and descriptions in the formation of basal concepts. He should seek to give unto himself a clear and full account of the things or ideas which cannot spring from mere words, however skilfully arranged in sentences. The music-teacher who complained of the public schools because a seven-year-old child did not grasp his meaning when he spoke of half-notes, quarter-notes, eighth-notes, sixteenth-notes, should have known that many children of that age have never been taught fractions, and that the idea of a fraction is obtained not from sounds (who distinguishes between half a noise and a whole noise?), but from objects which address the eye. Instead of complaining about the school which the pupil attended, a teacher acquainted with the mysteries of his art would have started with the comparison of things visible; and after having developed the idea of halves, quarters, eighths, sixteenths, by the division of visible objects into equal parts, he would have applied the idea to musical sounds.

Different gate-ways for different ideas.

Integers.

In seeking to build in the mind of the learner the concepts which lie at the basis of a new branch of study, it is a legitimate question to ask by which of the gate-ways of knowledge the materials or elements for the new idea can best be made to enter the mind. At the basis of arithmetic lies the idea of number,—an idea that is evoked by the question of how many applied to a collection of two or more units. Taste and smell must be ruled out from the list of senses which can be utilized to advantage. Three taps on the desk are as easily recognized as three marks or strokes on the black-board. The sense of touch is helpful in passing from concrete to abstract numbers. To think a number when the corresponding collection of objects is not visible, but is suggested by tactile impressions, helps to emancipate the thinking process from the domination of the eye; in other words, it helps to sunder the thinking of number from a specific sense, and thus aids in the evolution of the idea of number apart from concrete objects.

Fractions.

As already indicated, there are some basal concepts, like that of a fraction, in the development of which only one sense can be utilized to advantage. Whilst imparting the idea of a whole number, the appeal may be to the eye, the ear, and the sense of touch; the instruction designed to impart the idea of fractions to the normal child is limited to visible objects. In the instruction of the blind the other senses are addressed from necessity. The extent to which touch can supply the function of sight is full of hints to teachers in charge of pupils possessing all the gate-ways of knowledge.

Teaching decimals.

Moreover, not all units are equally adapted for imparting the first ideas of a fraction. Half of a stick is still a stick to the child, just as half of a stone is still called a stone in common parlance. The half should be radically different from the unit; hence an object resembling a sphere or a circle is best adapted for the first lessons in fractions. In teaching decimals the square or rectangle is better than the circle. It is difficult to divide a circumference into ten equal parts. On the contrary, the square is easily divided into tenths by vertical lines, and then into hundredths by horizontal lines, thus furnishing also a convenient device for the first lessons in percentage.

Basal concepts.

John Fiske on symbolic conceptions.

It is one of the aims of the training-class and the normal school to point out the best methods of developing the different basal concepts which lie at the foundation of the branches to be taught. Many of these are complex, and require great skill on the part of the teacher. The difficulty is well stated in John Fiske’s discussion of Symbolic Conceptions. He says, “Of any simple object which can be grasped in a single act of perception, such as a knife or a book, an egg or an orange, a circle or a triangle, you can frame a conception which almost, or quite exactly, represents the object. The picture, or visual image, in your mind when the orange is present to the senses is almost exactly reproduced when it is absent. The distinction between the two lies chiefly in the relative faintness of the latter. But as the objects of thought increase in size and in complexity of detail, the case soon comes to be very different. You cannot frame a truly representative conception of the town in which you live, however familiar you may be with its streets and houses, its parks and trees, and the looks and demeanor of the townsmen; it is impossible to embrace so many details in a single mental picture. The mind must range to and fro among the phenomena, in order to represent the town in a series of conceptions. But practically, what you have in mind when you speak of the town is a fragmentary conception in which some portion of the object is represented, while you are well aware that with sufficient pains a series of mental pictures could be formed which would approximately correspond to the object. To some extent the conception is representative, but to a great degree it is symbolic. With a further increase in the size and complexity of the objects of thought, our conceptions gradually lose their representative character, and at length become purely symbolic. No one can form a mental picture that answers even approximately to the earth. Even a homogeneous ball eight thousand miles in diameter is too vast an object to be conceived otherwise than symbolically, and much more is this true of the ball upon which we live, with all its endless multiformity of detail. We imagine a globe, and clothe it with a few terrestrial attributes, and in our minds this fragmentary notion does duty as a symbol of the earth.

“The case becomes still more striking when we have to deal with conceptions of the universe, of cosmic forces such as light and heat, or of the stupendous secular changes which modern science calls us to contemplate. Here our conceptions cannot even pretend to represent the objects; they are as purely symbolic as the algebraic equations whereby the geometer expresses the shapes of curves. Yet so long as there are means of verification at our command we can reason as safely with these symbolic conceptions as if they were truly representative. The geometer can at any moment translate his equation into an actual curve, and thereby test the results of his reasoning; and the case is similar with the undulatory theory of light, the chemist’s conception of atomicity, and other vast stretches of thought which in recent times have revolutionized our knowledge of nature. The danger in the use of symbolic conceptions is the danger of framing illegitimate symbols that answer to nothing in heaven or earth, as has happened first and last with so many short-lived theories in science and in metaphysics.”

The word conception as used in this quotation is synonymous with concept, but elsewhere it is also used in two other senses,—namely, to signify the mind’s power to conceive objects, their relations and classes, and to name the activity by which the concept is produced. Hence the term concept is preferred in this discussion.

Concepts of distance.

Large cities.

To give a full account of the development of the basal concepts in the different branches of study would require a treatise on the methods of teaching these branches. All that can be attempted is to draw attention to some of the typical methods and devices adopted by eminent teachers in the development of the concepts which Mr. Fiske calls symbolic conceptions. Distance is one of the concepts at the basis of geography and astronomy. To say that the circumference of the earth is twenty-five thousand miles, that the distance of the moon from the earth is two hundred and forty thousand miles, and that the distance of the sun is ninety-two and one-half millions of miles may mean very little to the human mind, especially to the mind of a child. Supposing, however, that a boy finds a mile by actual measurement, and that he finds he can walk four miles an hour, he can gradually rise to the thought of walking forty miles in a day of ten hours, or two hundred and forty miles in the six working days of a week. In one hundred and four weeks, or two years, he could walk around the globe. To walk to the moon would require a thousand weeks, or about twenty years. It is by the method of gradual approach that concepts of great distance, of immense magnitudes, of the infinitely large and the infinitely small, must be developed. To this category belong large cities like New York and London, quantities denoting the size of the earth and its distance from the sun and the fixed stars, the fraction of a second in which a snap-shot is taken, or an electric flash is photographed; such quantities are apt to remain as mere figures or symbols in the mind of the learner unless the method of gradual approach is adopted. Starting with a town or a ward with which the pupil is familiar, several may be joined in idea until the concept of a city of fifty or sixty thousand population is reached. It takes about twenty of these to make a city like Philadelphia, and five cities like Philadelphia to make a city like London. A lesson on how London is fed will add much to the formation of an adequate idea of such a large city.[5]

Shape of the earth.

An adequate idea of the shape of the earth can be formed only by gradual development. The three kinds of roundness (dollar, pillar, ball) must be taught; then the various easily intelligible reasons for believing it to be round like a ball may follow in the elementary grade. As the pupil advances he may be told of the dispute between Newton and the French, the former affirming it to be round like an orange,—that is, flattened at the poles,—the latter asserting that it resembled a lemon with the polar axis longer than the equatorial diameter; and how, by measuring degrees of latitude and finding that their length increases as we approach the poles, the French mathematicians, in spite of their wishes to the contrary, proved Newton’s view to be correct. The same lesson might be taught by starting with the rotation of the earth, showing by experiment the tendency of revolving bodies to bulge out at the equator, and then drawing the inference that the degrees of latitude are shortest where the curvature is greatest, and that they are longest where the curvature is least. Either method is strictly logical; but the method which follows the order of discovery, whenever it is feasible, is calculated to arouse the greater interest in minds of average capacity. The teacher who is a master of his art will supplement the historical lesson by a lesson passing from cause to consequence, so as to fix and clarify the concept formed by passing from the ground of knowledge to the necessary inference. Finally, by drawing attention to the fact that the equatorial diameters are not all of the same length, he will build up in the pupil’s mind a concept of the real shape of the earth,—a shape unlike any mathematical figure treated of in the text-books on geometry. The attempt to give a complete idea of the shape of the earth in the first lessons on geography would have ended in confusion of thought; the wise teacher develops complex concepts gradually and not more rapidly than the learner is able to advance. This process may be called enriching the concept. The successive concepts, although only partial representations of what is to be known, are adequate for the thinking required at a given stage of development; the number of complete or exhaustive concepts in any department of knowledge is small indeed.

The order of discovery and of instruction.

Instructive as it often is to follow the order of discovery, it must not be inferred that this is invariably the best order of instruction. What teacher of astronomy would be so foolish as to lead a student through the nineteen imaginary paths which Kepler tried before he discovered that an elliptical orbit fitted the recorded observations of Tycho Brahe![6]

Much may be learned from the methods pursued by eminent teachers. It will abundantly pay any teacher of science to study Faraday’s lectures on the chemistry of a candle,—a series which for models of developing the fundamental concepts of chemistry is unsurpassed. The devices used by such teachers are often very suggestive. For instance, in teaching the concept of the new geography that the earth revolves not like a body with a liquid interior, but like a body with an interior as rigid as glass, Lord Kelvin suggests a comparison of the spinning of a hard-boiled egg and of an egg not boiled at all,—an experiment easily made in every school-room.

Ideas of great distances.

A few quotations from the astronomer Young will show how concepts of great distances can be developed so as to be more than a numeral with a row of ciphers annexed:

“If one were to try to walk such a distance, supposing that he could walk four miles an hour, and keep it up for ten hours every day, it would take sixty-eight and one-half years to make a single million of miles, and more than sixty-three hundred years to traverse the whole. If some celestial railway could be imagined, the journey to the sun, even if our trains ran sixty miles an hour, day and night, without a stop, would require over one hundred and seventy-five years. To borrow the curious illustration of Professor Mendenhall, if we could imagine an infant’s arm long enough to enable him to touch the sun and burn himself, he would die of old age before the pain could reach him, since, according to the experiments of Helmholtz and others, a nervous shock is communicated only at the rate of one hundred feet per second, or one thousand six hundred and thirty-seven miles a day, and would need more than one hundred and fifty years to make the journey. Sound would do it in about fourteen years if it could be transmitted through celestial space, and a cannon-ball in about nine, if it were to move uniformly with the same speed as when it left the muzzle of the gun. If the earth could be suddenly stopped in her orbit, and allowed to fall unobstructed towards the sun under the accelerating influence of his attraction, she would reach the centre in about two months. I have said if she could be stopped, but such is the compass of her orbit that to make its circuit in a year she has to move nearly nineteen miles a second, or more than fifty times faster than the swiftest rifle-ball; and in moving twenty miles her path deviates from perfect straightness by less than one-eighth of an inch.”[7]

Professor Young uses a very suggestive device in his astronomy for showing the comparative sizes and distances of heavenly bodies:

“Representing the sun by a globe two feet in diameter, the earth would be twenty-two-hundredths of an inch in diameter—the size of a very small pea or a ‘twenty-two caliber round pellet.’ Its distance from the sun on that scale would be just two hundred and twenty feet, and the nearest star (still on the same scale) would be eight thousand miles away at the antipodes.”[8]

Sometimes the employment of a new unit aids in realizing the idea of very great distances. The ordinary astronomical unit is the distance of the sun from the earth; it is not large enough to be convenient in expressing the distances of fixed stars. Hence astronomers have found it more satisfactory to take as a unit the distance light travels in a year, which is about sixty-three thousand times the distance of the sun from the earth. The tables of fixed stars give distances in terms of this unit from 3.5 upward. A glance at these figures fills the mind with an idea of the infinite grandeur of the universe and with feelings of awe and sublimity akin to those which must fill the soul on approaching the throne of Almighty God.

Time of snap-shot.

Scientists assert that the infinitely great is more easily conceived than the infinitely small; that quantities represented by billions and trillions are more easily grasped than fractions of a unit with a million in the denominator; that ages of time are more easily comprehended than fractions of a second. In a lecture delivered at the International Electrical Exhibition, Professor Charles F. Himes employed a very ingenious device for giving an idea of how a “snap-shot” may be made, or a photographic impression taken of an electric spark, or a flash of lightning. He exhibited a photograph of the sparks of a Holtz machine, which are of shorter duration than any instantaneous drop or slide could be made to give. “They impressed themselves upon an ordinary collodion plate as they passed. Suppose we assume one-twenty-thousandth of a second as the time, and we will be within bounds. That is a fraction difficult to comprehend. Our mental dividing engine fails as we work towards zero. The twenty-thousandth of a second is so small that it eludes our mental grasp.... Looking at it from another point of view, let us regard the effect as a space-effect instead of a time-effect. Light has a velocity, in round numbers, of one hundred and ninety thousand miles per second. That would be one hundred and ninety miles in one-thousandth of a second, nineteen in one-ten-thousandth, or, say, ten miles in our one-twenty-thousandth of a second. Ten miles of light drive in upon our plate in that time; or, if we held the corpuscular theory of Newton, a chain of these little pellets ten miles long would have delivered themselves upon the sensitive surfaces. Ten miles is comprehensible, one mile is, so that we could easily conceive of an effect in one-tenth of the time allowed to our electric sparks. But let us take another look at it. Light is not corpuscles, but undulations, tiny wavelets, ripplets of ether, eight hundred million million in a second for violet, a number we can easily understand, as Sir William Thomson[9] has told us. That would make eight hundred thousand million in one-thousandth, eight thousand million in one-ten-thousandth, or forty thousand million impulses striking our sensitive molecules in our one-twenty-thousandth of a second. Surely that number should produce an effect. We can readily conceive that one thousand million wavelets would produce an appreciable effect. They would represent one-eight-hundred-thousandth of a second, say one-millionth of a second. That would seem, then, to be ample time to produce a photographic effect.”[10]

Idea of total depravity.

Many teachers of science spend all their spare time in reading scientific literature and in posting themselves upon the latest achievements in their specialty. It might be to them a less delightful occupation if they traversed fields of investigation already well explored for the purpose of seeing how the student can be led over these most expeditiously and with minimum expenditure of time and effort. Thought bestowed upon the best way of imparting the elements of science would have a most beneficial effect upon their methods of instruction, and would greatly increase their skill in teaching. Many of the most abstruse and complex ideas can be resolved by analysis into their elements, and thereby be made intelligible to people of ordinary training. An eminent teacher of theology felt called upon to impart to a promiscuous audience an idea of the doctrine of total depravity as taught by the Church. He started by referring first to the popular mistake that the doctrine teaches the utter depravity of the human race, then to the ancient heresy that the depravity of human nature resides in the body, and not in the soul, and, finally, to the meaning of total as signifying not that man is as bad as he can become, but that he is depraved, or has a tendency towards sin not merely in his physical body, but in the totality of his being. Analysis prepared them to see that by total depravity is not meant that men are as bad as they can be, nor that they do not have in their natural condition certain amiable qualities or certain laudable virtues; that the doctrine means that depravity, or the sinful condition of man, infects the whole man,—intellect, feeling, heart, and will,—and that in each unrenewed person some lower affection, and not the love of God, is supreme. Such analysis of a complex concept into its elements, the explicit setting forth what it is and what it is not, followed by the synthesis of the parts into a thought-unit, is the plan pursued by the best teachers in teaching difficult subjects. By analysis we resolve complex concepts into their elements, which may be simple percepts or their relations. Things are separated in thought which go together in time, space, motion, force, or substance. Every essential attribute or constituent can then be viewed by itself until the mind has gone around it with the bounding line of thought, grasped its nature and essence, and explored it in its different aspects and relations. In this way the most abstruse subjects are shorn of their difficulties, the most complex problems are solved and elucidated.

Value of analysis.

The bearing of all this upon the art of teaching is easily shown. A teacher of geometry, whose mind was quite logical, failed, through lack of power, to make things plain. If the class did not grasp the demonstration of a theorem, he invariably started at the beginning, tried to throw light upon every link in the chain of proof, and by the time he reached the point of difficulty the members of the class were thinking of something else. A younger colleague pursued a different plan. Starting some pupil upon the demonstration, he detected the difficulty, and by a few words of explanation, or by a well-framed question, he focussed attention upon the simple elements, into which he resolved the difficulty, and frequently surprised the class by showing the simplicity of what had puzzled their minds. Under the clarifying light of analysis half the difficulties and half the sophistries of human thinking vanish like dew and mist before the morning sun.

The moral nature.

For the purpose of making an impression upon the moral nature word-painting is sometimes very helpful. All the text-books on physiology and hygiene intended for use in the public schools seek to teach the evils of strong drink by showing the effect of alcoholic stimulants upon different parts of the human system. Yet the most exhaustive lessons on how whiskey is made, and what are its exhilarating and its pernicious effects, cannot equal the effects of the word painting of Robert Ingersoll and the paraphrase by Dr. Buckley. In making a gift to a friend the former penned the following eulogy on whiskey:

“I send you some of the most wonderful whiskey that ever drove the skeleton from the feast or painted landscapes in the brain of man. It is the mingled souls of wheat and corn. In it you will find the sunshine and the shadow that chased each other over the billowy fields, the breath of June, the carol of the lark, the dew of night, the wealth of summer, and autumn’s rich content, all golden with imprisoned light. Drink it, and you will hear the voice of men and maidens singing the ‘Harvest Home,’ mingled with the laughter of children. Drink it, and you will feel within your blood the starlit dawns, the dreamy, tawny dusks of perfect days. For forty years this liquid joy has been within the staves of oak, longing to touch the lips of man.”

This was Dr. Buckley’s statement of the other side:

“I send you some of the most wonderful whiskey that ever brought a skeleton into the closet, or painted scenes of lust and bloodshed in the brain of man. It is the ghosts of wheat and corn, crazed by the loss of their natural bodies. In it you will find a transient sunshine chased by a shadow as cold as an Arctic midnight, in which the breath of June grows icy and the carol of the lark gives place to the foreboding cry of the raven. Drink it, and you shall have ‘woe,’ ‘sorrow,’ ‘babbling,’ and ‘wounds without cause.’ Your eyes shall behold strange women, and ‘your heart shall utter perverse things.’ Drink it deep, and you shall hear the voices of demons shrieking, women wailing, and worse than orphaned children mourning the loss of a father who yet lives. Drink it deep and long, and serpents will hiss in your ears, coil themselves about your neck, and seize you with their fangs; for at the last it biteth like a serpent and stingeth like an adder. For forty years this liquid death has been within staves of oak, harmless there as purest water. I send it to you that you may put an enemy in your mouth to steal away your brains, and yet I call myself your friend.”

The languages.

There comes a stage of development of the learner at which the word itself becomes the object of thought. Words are then classified as parts of speech, and their function in sentences is studied. Their properties and endings must be learned and compared. There is abundant room for thought in the eleven hundred variations of the Greek verb. The variations of words by declension and conjugation can be made the material for thought, and as these are always at hand in the text-book, no excursions to the field being needed to secure specimens, and no preparation of difficult experiments being required on the part of the teacher, the ancient languages have held their own in the schools with most wonderful tenacity. The study of language has not merely the advantage of supplying material for thought in the words, grammatical forms, and sentences which are always at hand in the text, but through the classics it brings the learner into intellectual contact with the best thoughts of the best men in ancient and modern times. To translate an author like Virgil or Demosthenes is to think the thoughts of a master mind, to weigh words as in a most nicely adjusted balance, and finally to arrange them in sentences that shall adequately convey the meaning of the original text.

Science.

Science is, of course, a product of the human mind, quite as much as the so-called humanities, and answers the same purpose when studied as literature; but then it ceases to have the value of training the intellect in the rigid methods of original research and scientific investigation. Whilst it is the function of the laboratory to initiate the student into the mysteries of the methods by which new discoveries are made and verified, and thus to enable him to avail himself of the labors of others through their publications, it does not bring the student into living contact with human hopes, emotions, and aspirations as do the poems of Goethe, Schiller, and Shakespeare.

History.

History deals with what man has achieved. The materials for thought which it furnishes are mostly in the shape of the testimony of eye-witnesses and other original sources of information. The incidents, the achievements, the struggles, the victories and the defeats, the thoughts, feelings, and experiences of historic personages, are an inexhaustible supply of material from which authors, editors, and orators draw illustrations, figures of speech, and other matter for their thinking. Here is a field which must not be neglected by those who would influence their fellows or figure as leaders of men.

Vigorous thinking.

Some minds are slow at gathering materials; yet they think vigorously. They look at facts and ideas from every possible point of view, explore their nature and relations, their content and extent, and point out their bearing upon other things by the conclusions they reach. Sometimes they go astray because they do not have sufficient data to warrant a conclusion. Their condition resembles that of the King of Siam, who did not believe that water could become solid because he had been in the nine points of his kingdom and had not seen ice.

Intellectual gluttony.

Other men are intellectual gluttons. They keep pouring into themselves knowledge from every quarter, carry it in their minds as the overloaded stomach carries food, and end in mental dyspepsia. Better the man with few ideas, who can apply these in practical life, than the man of erudition who cannot apply his knowledge.

Too little food produces inanition and starvation; too much food brings on dyspepsia and a host of other ills and distempers. The haphazard selection of studies by inexperienced youth from the large list of electives offered by a great university is apt to result either in mental overfeeding or in intellectual starvation. The mind can be rightly formed only when it is rightly informed. To expect satisfactory thought-products when the mind lacks proper materials to act upon would be as irrational as to expect good grist from a flour-mill whose supply of grain is deficient in quality and quantity. In the process of making flour very much depends upon the instruments employed. The rude implements of antiquity, the buhr-stones of our fathers, and the improved machinery of the roller process make a difference in the product, even though the same quality of grain is used. In the elaboration of the thought-material the well-educated man uses instruments which may be likened to our modern inventions for saving labor in the domain of the mechanic arts. These instruments of thought will next claim our attention.

V
THE INSTRUMENTS OF THOUGHT

But words are things; and a small drop of ink

Falling, like dew, upon thought, produces

That which makes thousands, perhaps millions, think.

Byron.

Constant thought will overflow in words unconsciously.

Byron.