Class Lt Copyright}!" COPYRIGHT DEPOSIT. EXPOSITION AND ILLUSTRATION IN TEACHING THE MACMILLAN COMPANY NEW YORK • BOSTON • CHICAGO ATLANTA • SAN FRANCISCO MACMILLAN & CO., Limited LONDON . BOMBAY • CALCUTTA MELBOURNE THE MACMILLAN CO. OF CANADA, Ltd. TORONTO EXPOSITION AND ILLUSTRATION IN TEACHING BY JOHN ADAMS, M.A., B.Sc. PROFESSOR OF EDUCATION IN THE UNIVERSITY OF LONDON THE MACMILLAN COMPANY 1910 All rights reserved v^ COPYEIGHT, 1910, By the MACMILLAN COMPANY. Set up and electrotyped. Published January, 1910. Noriwaotj ^reS3 J. 8. Gushing Co. — Berwick & Smith Co. Norwood, Mass., U.S.A. g'CU^o^^Mjo TO MY OLD MASTER MR. JAMES LIDDELL Digitized by the Internet Archive in 2010 with funding from The Library of Congress http://www.archive.org/details/expositionillustOOadam CONTENTS CHAPTER TAGrS I. Nature and Scope of Exposition and Illustra- tion 1 11. Mental Content 37 III. Mental Activity 65 IV. Mental Backgrounds 91 V. Suggestion . 116 VI. Conditions of Presentation 145 VII. Beginnings in Exposition 167 VIII. Order of Presentation 187 IX. Exemplification and Analogy 228 X. The Story as Illustration 250 XL Elaboration 275 XII. Degree in Illustration 297 XIII. Material Illustrations 317 XIV. The Picture as Illustration 336 XV. The Diagram as Illustration 354 XVI. Dangers of Illustration 391 XVII. The Torpedo Shock 416 vii EXPOSITION AND ILLUSTEATION IN TEACHING CHAPTER I Nature and Scope of Exposition and Illustration Applying the principles to be laid down in what fol- lows, it is well to make a beginning in some region of knowledge that is common to all intelligent educated people. A good dictionary may be fairly taken to represent such a region. What the dictionary tells us about Exposition and Illustration will probably be admitted to be common property, and therefore a suit- able starting-point for a treatment that will introduce points of view that may be unfamiHar to the reader. In teaching, it is now generally admitted that we ought rather to lead up to a definition than to start from one. In what follows, the definitions as found in the diction- ary will not be treated as ends in themselves, but merely as the common basis from which reader and writer may make an intelligible start. This chapter will concern itself not so much with the explanation of the defini- tions which it borrows from the dictionary as with the elaboration of the connotation of the terms Exposition and Illustration in their relation to teaching. In Sir James A. H. Murray's ^'New English Diction- B 1 2 EXPOSITION AND ILLUSTRATION IN TEACHING ary on Historical Principles '* we find under the word expound f the following meanings : — 1. To set forth, declare, state in detail (doctrines, ideas, principles ; formerly used with wider application). 2. To explain, interpret : (a) gen. To explain (what is difficult or obscure) ; to state the signification of ; to comment on (a passage or an author) . (6) esp. To interpret, comment upon (Scripture, religious formularies, etc.) . Now chiefly with reference to homiletic exposition. We may safely neglect the more literal meanings attached to exposition, such as "putting out of," "ex- posure," "putting to public view"; just as we need not seriously consider the archaic use in Hudibras: "He expounded both his pockets," or Littre's "putting in the pillory." So far as the teacher is concerned, two of the accepted meanings stand out as of importance: "to set forth" and "to explain or interpret." In the ordi- nary practice of the schoolroom these two meanings are not usually distinguished from each other, because, as a matter of fact, the purpose of setting forth anything is to explain it to the pupil. If we set a matter clearly before another, we feel that we have explained it. If to a wayfarer we set forth his route, we feel that we have explained a matter about which he was in doubt. A clear statement of the Binomial Theorem is generally regarded as in some sort an explanation of that theorem. There are those who question whether the teacher can und^r any circumstances do more than make just such a presentation. Jacotot, the founder of the "Universal Method" of teaching, is usually true to his reiterated principle that "a teacher is never necessary to man," ^ > Enseignement Universel, p. 304. NATURE AND SCOPE 3 but in a moment of unusual generosity he admits that ''a teacher is useful to men, he is necessary to children, but a teacher who explains [uri maitre explicateur] is deadening [abrutissant\J^ ^ The negativeness of the teacher's work from this point of view is obvious. In the words of one of Jacotot's editors: '^In fact, the Founder limits himself to saying: ^Here is a book; learn Latin/ " But while the two meanings of Exposition — setting forth and explaining — to a certain extent overlap, they imply a real distinction that is worth the teacher's attention. While we are mainly interested in discover- ing how to present certain matters in the way best suited to render them intelligible to the pupil, we are none the less setting them forth. The first meaning of Exposition, in fact, implies the presentation of new matter, the second the explanation or interpretation of matter already known to, but not yet fully understood by, the pupil. The first meaning, ^^ setting forth," corresponds to what is usually understood in school and college by the verb demonstrate. This word, which literally means to show or point out, has acquired the added connotation of '^for a purpose.'' A demon- strator in a college is not a man who points out merely, but one who shows the meaning of what he points out. As the dictionary has it, he '' exhibits and explains." Still, the fact remains that in both the first meaning of expound and in the general meaning of demonstrate there is the notion of supplying new matter, so that this presentation of new matter may be regarded as an es- sential part of Exposition, though it need not be found at all stages of Exposition. We shall see when we come ^ Avant-propos de cette Quatrieme l&dition : De la Langue maternelle. 4 EXPOSITION AND ILLUSTRATION IN TEACHING to deal with Illustration that the same distinction arises between the introduction of new matter and the manip- ulation of old. It has to be observed that for our present purpose we are treating the subject of Exposition from the point of view of the teacher. It is possible to regard it entirely from the pupil's standpoint. When this is done, Ex- position is dealt with as a part of composition, and ranks as coordinate with narration and description. As such it enters into the ordinary school curriculum, and in many cases receives a considerable amount of attention. Naturally the principles of Exposition must remain the same whether practised by the pupil or by the teacher, but the conditions under which the princi- ples are applied in the two cases are so different that a separate treatise is required for each.^ It will be noted that the dictionary lays stress on the fact that the things to be set forth are '^doctrines, ideas, principles," the obvious inference being that Exposition has nothing to do with material things, that we can no more expound a steam engine than we can expound our pockets. But while it is bad English to speak of ex- pounding a locomotive, we may correctly speak of expounding the principles on which the locomotive works. This does not, after all, mean that the concrete is removed from the realm of Exposition, but merely that Exposition can deal with the concrete only in terms of ideas. The contributions of the senses must be taken for granted by the expositor. His business is so to arrange the mental results of sensations that they ^ For a treatment of the subject as a part of the curriculum, see Exposition in Classroom Practice, by Mitchill and Carpenter, the Mac- millan Co., New York, 1906. NATURE AND SCOPE 5 shall form a well-organised and therefore intelligible whole. From this point of view all Exposition is explanation or interpretation, though in order to com- plete the explanation it may be necessary to place the pupil in such a position that new matter may be as- similated. Sometimes the expositor can so arrange old matter that it becomes intelligible without the intro- duction of anything new, but frequently it happens that in the pupil's knowledge there is some link lack- ing, without which all the present material is necessa- rily unintelligible. To introduce the missing elements is clearly an essential part of Exposition. I have known a man who had a really excellent knowledge of French completely puzzled by a passage that pre- sented no apparent difficulty. He could make no sense out of it because he did not happen to know that Monsieur, when used absolutely, meant the eldest brother of the king of France. It is worth remarking that in this connection ^^ex- planation" has no reference to the ultimate meaning of the matter to be dealt with. It is not a metaphysical term. Accordingly, from the teacher's point of view. Exposition does not include the discovery of the true meaning of the matter to be expounded, but only the setting forth of that matter in such a way as to be in- telligible to the pupil. The facts and the explanation of the facts are for the teacher the data of Exposition. He may be misinformed about the materials he is deal- ing with, his facts may not be facts, his explanations of his facts may not stand the test of investigation, and yet his exposition may be excellent. As an ex- positor his business is so to present his facts that they shall carry with them the explanation that appeals to 6 EXPOSITION AND ILLUSTRATION IN TEACHING him as satisfactory. Too often it has been assumed that an intelHgent mastery of the facts to be presented is enough to quahfy a teacher for his work/ In reahty it is no more than the essential condition of his begin- ning to learn to apply his art. For our present purpose we shall assume that the teacher has acquired the necessary facts and has mastered their meaning. The problem remains to communicate these facts so that they shall convey to the pupil the meaning the teacher has accepted as the true one. The teacher may not only adopt a wrong interpre- tation of the facts, but may know that his interpreta- tion is false, and yet be an excellent expositor. Pro- fessor J. W. Allen ^ provides an admirable illustration. Taking the Reformation as subject, he gives three sep- arate expositions of its meaning, one from the Roman Catholic point of view, another from the Protestant, while the third is written from the standpoint of a critical Mercutio who calls for "a, plague o' both your houses. '^ By appropriate overemphasis and com- pression, each of the accounts, while not inventing incidents or what are commonly called ^^facts,^' con- trives to convey an entirely different impression from the others. So far as each is successful, it leaves the mind of the pupil with his ideas of the Reformation reconstructed in a particular way, a way that was first developed in the mind of the expositor, though, as we see, he has adopted at least two other modes of reconstructing the available elements. ^ Cf . De Quincey : " The t6 docendum, the thing to be taught, has availed to obscure or even to annihilate for their eyes every anxiety as to the mode of teaching." Essay on Style. Collected Writings (Masson, 1897), Vol. II, p. 160. 2 The Place of History in Education, 1909, p. 210. NATURE AND SCOPE 7 The test of the expositor is: does he produce on the mind of the pupil the impression he desires to pro- duce ? Literary style is sometimes tested by the clear- ness with which it conveys the author's meaning. But sometimes the author may not desire that his mean- ing should be understood. He may want his words to convey one meaning to one set of readers and another to another. From this point of view the test is: does he convey the meaning to each that he intended to convey ? Style is not so much a means of making an- other know what we think, as it is a means of producing a certain effect upon the mind of another. So in the case of the expositor, whether he be honest or dishonest, the result of successful exposition must be that there now exists in the mind of the hearer or reader a com- bination of mental elements that previously existed in the mind of the expositor. There may be many other ways in which the elements could be combined, and these possible combinations may all have been formed at one time or other in the mind of the expositor, but if he has succeeded in his present work, only one of these combinations is able to establish itself in the mind of the person he is dealing with. Exposition, therefore, comes to be, in the ultimate resort, the manipulation of the ideas of another. This gives a more definite meaning to the term ex- planation as used by the teacher. Some people do not see how things can be explained. They admit the ad- vantage of statement and demonstration, but cannot see how something that has been stated and demon- strated can be made clearer by writing or talking about it. They quote the case of the little girl who has won the good-will of all the teachers' common rooms in the 8 EXPOSITION AND ILLUSTRATION IN TEACHING world by her protest that she thought she could under- stand her arithmetic if only her mother would give up explaining it/ In his Modern Painters, Ruskin tells us bluntly: ^^Explanations are wasted time. A man who can see, understands a touch; a man who cannot, misunderstands an oration." The contrast between a touch and an oration is not very happy, as it might be held to imply a comparison between two different kinds of explanation — practical and verbal. But even if we limit the contrast to the cognate terms, a word and an oration, we have still the implied admis- sion that the word has done some good. In actual ex- perience it is often found that only a word is needed to estabHsh the proper relation among a group of ideas that need nothing but the help of this word to reduce them- selves to a combination intelligible to a person who otherwise is unable to understand them. It is quite possible for a man to have in his mind all the facts necessary to explain something that he does not under- stand, and yet be quite unable to make the necessary application of his knowledge. The facts must be put in a certain order before the true relation can be seen, and it is the business of the expositor, by means of words or otherwise, to arrange them in this order. One of the great difficulties at certain examinations is to keep candidates from getting just this kind of help from each other. A difficult problem in Perspec- tive or in Orthographic Projection often becomes quite easy to a candidate from a single glance at his neigh- ^ In his Charles Dickens, Mr. G. K. Chesterton says: Dickens "had one most unfortunate habit, a habit that often put him in the wrong, even when he happened to be in the right. He had an incurable habit of explaining himself." NATURE AND SCOPE 9 bour's completed drawing, though without that glance he could make no sense out of the problem as stated in words on his examination paper. He has all the knowl- edge needed to work out the problem, but he lacks the power of making the initial combination. At a certain examination in Applied Mathematics an industrious but not very original student found herself unable to understand a particular question on her paper till she chanced to see a fellow-candidate twirling her finger in a particular way. The motion of the finger at once suggested the idea of a left-handed helix, and the point of the question became plain. Both candidates hap- pened to be considering the same problem at the time, but there was no intentional signalling. The clever candidate did not know that she had helped the other. It has to be remembered that unless the duller student had had the necessary materials in her mind, no amount of finger-twirling would have been of the slightest use to her. In a similar way an uninteUigent plumber has often in his mind all the facts that are necessary to the mas- tery of a difficult job in a house, and is yet unable to apply his knowledge. The householder makes several suggestions, most of them futile, but happens to hit upon one combination that appeals to the practical but unintelligent workman, who then exclaims, ^^Ah, now that you put it that way — , '^ and proceeds to carry out a suggestion that he could not originate. In a certain sense the ignorant householder has explained matters to the plumber. What the householder has done more or less by chance, the skilful expositor must do deliberately. Exposition may well be described as a bipolar pro- 10 EXPOSITION AND ILLUSTRATION IN TEACHING cess. For our own ends we may regard it now from the point of view of the expositor, and now from that of the person to whom something is being expounded. But the process is working from both sides all the time. It is interesting to note that at the present moment psychologists are feeling keenly the need for double terms in the case of similar bipolar processes.^ In suggestion and imitation, for example, we have the two poles of the process and a term to describe only one of them. Suggester and imitator are words that stand for the persons who suggest or imitate; but we have no terms to denote those who are imitated or to whom suggestion is made. In the books we find rather clumsy references to the subject, the patient, the pattern, the model. Sometimes it is proposed to follow certain analogies and boldly introduce the two terms, suggestee and imitatee. But apart from the barbarous sound of expositee or expositatee, there is the serious objection that this form overemphasises the passive element. The person to whom an exposition is being made is to a certain extent more passive than is the expositor, but he is far from being quite passive. He is guided by the expositor, and to that extent plays a passive part, but if the exposition is to be successful, the person to whom the expositor appeals must bestir himself, and react vigorously on the material supplied by the ex- positor. In what follows we shall have to make constant reference to ^'the person to whom the exposition is to be made," and it is obvious that this cumbrous peri- phrasis cannot be repeated on every occasion. So with 'Hhe matter to be expounded." In both cases * Cf. Mr. W. Macdougall's Social Psychology, p. 325. NATURE AND SCOPE 11 we require a technical term. With regard to the matter to be expounded, we seem to have a word to our hand. Sheltering under the authority of De Quincey's use of TO docendum, the thing to be taught, we would sug- gest the term expositandurrij the thing to be expounded. By dropping the Greek to we render the term a little less formidable, and lose nothing in the way of accuracy. We have seen that no such convenient term suggests itself for the person to whom the exposition is to be made. Probably it will be best to retain the ordinary word pupil. To be sure, the word is not commonly applied to a person who has left school, and we must in these pages apply it on occasion to people of quite mature years and high attainments; but no confusion need arise if we clearly understand that by pupil we shall in this book indicate the person who in the process of Exposition occupies the pole that is the correlate of the expositor-pole. After all, a learned professor receiv- ing instruction from a street urchin how to find his way back to his hotel is, for the time being, a pupil. Our first business in preparing this ordinary term pupil for our use is to get rid of the lingering notion that it represents a purely passive side of the process of learning. It connotes rather that the person is being directed in his activities than that he ceases to be active. We are prone to regard listening as in itself a passive matter. The audience is conspicuously passive, while the lecturer or preacher is as conspicuously active. Preaching has, in fact, been defined as '^an animated dialogue with one part left out." But this part that is left out as spoken word must certainly be suppHed as inner thought all through the sermon; else the preaching is a complete failure. The difference be- 12 EXPOSITION AND ILLUSTRATION IN TEACHING tween teaching and lecturing lies just here. No fault is more common among inexperienced teachers than the tendency to do all the talking, and to treat the pupils as mere sleeping partners in the work of the class. '^Too much of a lecture'' is the hardest worked cliche in the Normal master's repertory of critical phrases/ In class work the one part must not be left out. There must be give and take ; the pupils must be allowed not only to be active, but to show their activity. In Ex- position the teacher may work either by the way of open dialectic, the rapid interchange of question and answer, or by the more sedate methods of the lecture. The important point to note is that the pupil must be equally active in either case. The psychology of listen- ing has not been sufficiently considered by teachers. To begin with, we are inclined to regard listening as more continuous than it really is. Psychologists are laying more and more stress on the rhythmic element in the phenomena in which they are interested. No- where is this rhythmic element more prominent than in listening, especially when long periods are considered. Trained listeners, such as students who have reached the postgraduate stage, are able to listen with a fair degree of continuity throughout an hour's discourse; ^ It is interesting to note that in England the inevitable reaction has come. So thoroughly have students in training been drilled into a distrust of lecturing that they are now said to be losing the power of sustained speech. "Few of our recently trained teachers," says Pro- fessor Mark Wright, " can make a well-arranged verbal presentation to a class for ten minutes, without asking questions." It would certainly be a pity if teachers lost the power of consecutive presentation, but of the two the loss of this power of lecturing would be much less seri- ous than the loss of the power of conducting class work on the Hues of a vigorous dialectic. Fortunately, in America, there is little danger of the loss of sustained speech. NATURE AND SCOPE 13 but your ordinary amateur listener, say the man who confines himself to a sermon a week and an occasional popular lecture, hears only in patches. Salient points in the discourse stand out, but each of these is a point of departure for trains of thought not bargained for by the speaker. The untrained listener rushes off from each salient point — and often from points that are not at all salient from the speaker's point of view — in a direction determined by the acquired content of his own mind, and he is recalled only by the emergence of another point in the lecture that catches his wandering attention. Fortunately, what is true in interstitial vision is true here. Just as the mind fills in a great many of the gaps that occur in actual vision, so it fills in a great many gaps that occur in the hearing of a discourse. Even dull people who are in earnest about the sermon go away with some fairly complete general idea of the whole (it is taken for granted that there is a general idea underlying the whole), but in many cases, no doubt, even after honest attention, the inexperienced listener goes away with only one or two prominent points, which are not by any means necessarily points in the main line ,of thought, but are more likely to be prominent points of illustration. A training in the art of listening is therefore an im- portant part of Exposition. Unless the expositor can assure himself that his pupils are doing their share of the work, he must be very doubtful about his success. In class-teaching he will, of course, seize every opportunity of making the pupils take an overt share in the work; but in the case of a more or less formal lecture this is difficult, sometimes, indeed, impossible; so the lecturer 14 EXPOSITION AND ILLUSTRATION IN TEACHING must do what he can to encourage the pupils to test their powers of continuous attention. An excellent test that they can themselves apply is to see how far they can anticipate what is coming. Certain lecturers resent such a test. I have known one quite lose his temper when this matter was brought before him. He did not put it that way, but his view obviously was that nobody could anticipate what he was going to say in any of his lectures. But the test implies no challenge of the lecturer's originality. No doubt at the very beginning of an isolated lecture by an unknown person, one cannot usually anticipate what is coming, and, further, at many points in the lecture one may be quite unable to guess what is coming next. But in an ordi- nary lecture or sermon the experienced listener is gen- erally able to anticipate a great deal of what is com- ing. When a halting speaker hesitates for a word, there are usually scores of his hearers who have already supplied it. What the psychologist points out to us in our ordi- nary reading of a book or newspaper is true in our listen- ing. In almost every case the incidence of attention is not on the word that occupies the centre of the field of vision.^ So in music we are familiar with the fact that the performer's eye is frequently bars ahead of the note he is actually striking, and in certain familiar combinations the conclusion of a passage seems to come of its own accord, even when the notes are not seen at ^ Dealing with reading aloud, Mr. E. V. Lucas, in The Avthor for July, 1909, writes the suggestive words: "Lacking the needful power of seeing two lines ahead (as John Roberts used to see two cannons ahead), I am continually falling into wrong stresses and misunder- standings, which annoy me like little stings." NATURE AND SCOPE 15 all ; that is to say, certain common endings will be played quite naturally by the performer, even if the notes oc- (cur on the page that has not yet been exposed. We are too apt to assume that our reading and our listening •are matters of word by word understanding. Our thinking is not carried on in this atomistic way. We work with much bigger units than the individual word or sound. We can never know the present except in relation to the past and the future. In the stream of thoughts that pass through our minds the present thought is the darkest in the whole series : — "The knowledge of some other part of the stream, past or future, near or remote, is always mixed in with our knowledge of the present thing." ^ When Shakespeare and Shelley agree in selecting as man's high prerogative the power of ^ booking before and after," they are building on a sound psychological foundation. The present can be understood only by reference to the past and the future. In listening, the pupil should always be using the past to anticipate the future. The beginning and ending of good listening is anticipation — being able to project ourselves towards the point up to which the lecturer is leading. We may not be able to anticipate the lec- turer sentence by sentence. It may be that we are unable to complete such a sentence as '^The most op- timistic writer on Education is ." Here it is prob- able that very few could add the missing word in the sentence as it thus occurs out of the blue. But sup- pose this sentence occurs in the middle of a lecture, a good lecture — that is, a lecture that has been thought * W, James: Principles of Psychology, VoL I, p. 606. 16 EXPOSITION AND ILLUSTRATION IN TEACHING out and organised — there would have been in all probability indications by the help of^ which an expe- rienced listener could infer at least the category under which the individual name is to be found. So far from being a reflection on the lecturer's originality, it is the highest compliment to him that his audience should be able to anticipate, within limits, what is coming. It is your careless, unprepared, unmethodical man who says the unexpected things. For remember, even with a professional dealer in paradoxes, it is quite possible, by the rule of contraries, or in extreme cases, when that rule fails, by the rule of contra-contraries, to anticipate what he is going to say. In other words, an organised lecture has a style underlying it that is all in the whole and all in every part, and that style can be surprised by a sympathetic listener. A merely capricious lecture, on the other hand, has nothing by which its develop- ment may be followed. Note further that the essential thing is not so much that the pupil is to be able to anticipate the very points to be raised, and how they will be settled, as that he must adopt the anticipative attitude. The pupil- mind must be feeling its own way into the problems that are being dealt with, and must keep on asking itself questions about the possibilities of the case. It may be thought that this stretching out of the mind towards what is to come will render it oblivious to what has gone before, that it will be so busy with the future as to lose sight of the past. On the contrary, it is only by relying upon the past that the mind has any chance of anticipating the future. The really active mind is playing all round the subject it is examining, and from what has been already presented, it gets all manner of NATURE AND SCOPE 17 impulses urging it to make tentative advances in this direction and in that. Each advance is not only sug- gested by what has gone before, but must be tested by its consistency with the facts that have suggested it. Assuming that the ultimate purpose of Exposition is to cause to arise in the mind of the pupil a combina- tion of ideas exactly corresponding to a combination already formed in the mind of the expositor, it is clearly of the first importance to find out what means are at our disposal to bring about this combination in the pupil's mind. This demands a study of the nature of ideas and the laws according to which they act. But before entering upon details, it is well to get a general view of the whole ground. In ordinary language we use the word Illustration as meaning the clearing up of something that is in itself obscure. This idea we found to underlie also the meaning of Exposition. In point of fact, there is a certain confusion in the popular use of these two terms, a confusion that has a good deal to justify it in the usage of capable writers. Appealing, as in the case of the term Exposition, to the disinterested verdict of the dictionary, and, in order to widen our outlook, selecting an American lexicographer, we find that Webster thus delivers himself on the meanings of the verb to illustrate : — 1. To make clear, bright, or luminous. 2. To set in a clear light ; to exhibit distinctly or conspicuously. 3. To make clear, intelligible, or apprehensible; to elucidate, explain, or exemplify, as by means of figures, comparisons, and examples. 4. To adorn with pictures, as a book or subject; to elucidate with pictures, as a history or romance. 5. To give renown or honor to ; to make illustrious ; to glorify. c 18 EXPOSITION AND ILLUSTRATION IN TEACHING The first meaning is purely literal, as shown in the line quoted from Chapman: ^^Here when the moon illustrates all the sky," and does not interest us here. The fifth meaning is also foreign to our present purpose, and besides is obsolete. The fourth meaning embodies only a special form of illustration. But when we deal with the second and third meanings, we come to close quarters with the distinction between Exposition and Illustration. It is quite obvious that if we set some- thing in a clear light, or exhibit it distinctly or conspicu- ously, we are really doing what we have included under the head of demonstration when treating of Exposition. In the third meaning the overlap between the two processes becomes particularly noticeable. The pur- pose of Exposition is just to make things clear, intel- ligible, or apprehensible; but the differentia may be found in the second part, ^Ho elucidate, explain, or ex- •emplify, as hy means of figures, comparisons, and ex- (amples.^^ Here we are led to see that Illustration is to be regarded as a branch of Exposition. A mere setting forth of principles may be fairly called Expo- sition, but could not be justly called Illustration. It is only when we proceed to supply examples, and to institute comparisons, or in some other way to elabo- rate our presentation, that we can be said to illus- trate. The secondary meaning, then, of Illustration, as found in the dictionary, but the primary meaning for our purposes, may be said to be the process of throwing light upon something that is assumed to be known already in a vague and more or less unsatisfactory way. There is always a principle or body of principles that may be regarded as given (though not, perhaps, neces- NATURE AND SCOPE 19 sarily given to the pupil at the beginning of the illustra- tive process), and as thus forming the datum of the problem of Illustration. This I should like the reader to permit me to call the illustrandum as a parallel tech- nical term to the expositandum. One part of the func- tion of Exposition we have seen is to present new matter, and another is the manipulation of matter that has been already presented. One is tempted to limit Exposition to the first function and to hand over all the rest to Illustration. Anything that we do or say to introduce a different arrangement of ideas already in the mind of the pupil would on this view be properly called Illustration. We are not to lose sight of the fact that Illustration is a branch of Exposition, and must not be surprised to find a certain overlapping in respect of the matters treated. In point of fact, both processes deal with both the new and the old. Yet there is a difference in their use of the two kinds of materials. The new ideas introduced by Exposition form an es- sential part of the subject-matter that is under discus- sion, while the new matter introduced by way of Illus- tration may have only a secondary connection with the subject-matter. An illustration may introduce new ideas, but these are not in this connection treated as of importance in themselves, but only as throwing light upon the ideas that are at the time being ex- pounded. When Mill states in his second canon — "If an instance in which the phenomenon under investigation occurs, and an instance in which it does not occur, have every circumstance in common save one, that one occurring only in the former, the circumstance in which alone the two instances differ is the effect, or the cause, or an indispensable part of the cause, of the phenomenon " — 20 EXPOSITION AND ILLUSTRATION IN TEACHING he is expounding; but he proceeds to illustrate when he goes on to say : — "li ABC, ADE, AFG are all equally followed by a, then a is an invariable consequent of A. li abc, ade, afg slW number A among their antecedents, then A is connected as an antecedent, by some invariable law, with a." ^ So far Mill can hardly be said to have introduced any new ideas by way of illustration. The letters are mere pegs ready to hang matter on when it is presented. When, in the following chapter of his Logic, he intro- duces a discussion of how '^arsenious acid and the salts of lead, bismuth, copper, and mercury" act as poisons, he is still illustrating the canon, but he is introducing a whole series of entirely fresh ideas that have no con- nection in themselves with the subject-matter under consideration, which is the logic of experimental method. In point of fact, he assumes that his readers know enough about chemistry to follow easilj^ his references to Baron Liebig^s theories. As a general rule it is unwise to use as illustrative material something that is very unfamiliar to the pupil. It is seldom good policy to use many new ideas in an illustration. In certain cases it may be justifiable to '^work up" an elaborate illustration out of new materials. But this is permis- sible only when it is possible to group into one mass a number of facts that are useful not merely as illustra- tive of certain points, but as themselves important elements in the organised whole that makes up the subject under consideration. Illustration will thus be seen to be, on the whole, rather a work of arrange- ment than of addition. 1 Logic, Book III, Chap. VIII. NATURE AND SCOPE 21 All the same, it is clear that illustrations of the na- ture of those submitted by Mill from Baron Liebig cannot but convey in passing a certain amount of new information. Not only do they make clearer and more definite the points that they illustrate, but they in- crease the mental content of the pupil. He may not know the principle of the lever any more accurately after a long series of illustrative examples, for it is quite possible to understand the principle from only one example, but he will understand it in a broader way. His experience has been enriched by the number of cases in which he has seen the principle exemplified. He does not know it more accurately, but he knows it more usefully. Hitherto we have been considering Illustration merely from the cognitive side, as a means to enable the pupil to understand something that is difficult. But our object is not always to make another under- stand something. It may be to make him realise more vividly, to appreciate, to enjoy. We must, therefore, make provision for the aesthetic use of Illustration. The importance of this aspect must not be underes- timated. An old clergyman, addressing an audience of beginners in his own profession, told them that they might preach over and over the same sermon at rea- sonable intervals, if only they took the precaution to change the text, and the illustrations.^ The congre- gation will remember the illustrations long after the expositions, the descriptions, and the exhortations * It is worth noting that young clergymen have complained that this gracious permission to use old sermons is no great relief. After all, they say, it is the illustrations that count, and if one has to work them up into the very warp and woof of the sermon, this practically means that the sermon has to be rewritten. 22 EXPOSITION AND ILLUSTRATION IN TEACHING have been comfortably forgotten. Herein lies one of the chief dangers in the use of Illustration. There is a strong temptation to use it for the sake of its own intrinsic interest, instead of for the interest it arouses in connection with the subject under discussion. Un- less an illustration forms part of the very nature of a lesson, unless it is worked into the very warp and woof of the whole, it is illegitimate.^ An illustration must not be used as a sedative. Its function is to stimulate. The teacher may think that he is entitled to introduce a story to brighten up a dull lesson. But he can pur- chase this privilege only by inventing a connection between the story and the lesson he is teaching. Some of the old English essayists supply capital examples of this justifiable combination of the didactic and aes- thetic functions of Illustration. Thomas Fuller, for in- stance, makes a very systematic application of this form. He has a habit of marking off his essays into short paragraphs, each beginning with an easily under- stood generalisation immediately followed by one or more illustrations that give it point. Thus, in his es- say, ^'Of Memory," we have the fourth paragraph running : — "Overburthen not thy memory to make of so faithful a servant a slave. Remember, Atlas was weary. Have as much reason as a ^ People who make a study of the art of advertising take the view that the main purpose of illustration in a newspaper or on a poster is to attract attention. The drawing may be bad ; it may not accu- rately represent the object advertised, but if it catches the attention of the passer-by or the indifferent newspaper reader, it has served its purpose: "Charles Austin Bates, the most successful advertisement designer of the day, has repeatedly asserted that the function of the illustrator is to attract attention, and not necessarily to illustrate." Illustrated Advertising, by F. W. Johnston, Ninth Edition, Toronto. 1901. (Introduction.) NATURE AND SCOPE 23 Camel, to rise when thou hast thy full load. Memory, like a purse, if it be overfull that it cannot shut, all will drop out of it. Take heed of a gluttonous curiosity to feed on many things, lest the greedi- ness of the appetite of thy memory spoil the digestion thereof. Beza's case was peculiar and memorable; being above fourscore years of age, he perfectly could say by heart any Greek chapter in St. Paul's Epistles, or anything else which he had learned long before, but forgot whatsoever was newly told him ; his memory, like an inn, retaining old guests, but having no room to entertain new.'' This use of Illustration, common in Bacon, and in a less condensed form in modern essayists, is valuable in sermons and hortatory addresses, but must be used sparingly in lectures, and more sparingly still in les- sons. Essayists who follow more or less the method of Fuller are read largely for the interest of the illustra- tions. But, after all, the best essayists do make their generalisations the important points. All the rest of the matter centres round them. The illustrations may not be necessary to make clear the actual meaning of the thesis, but they at least illustrate. They form an organic part of the whole; they are not dragged in merely for the sake of their intrinsic interest. In a well- organised lecture or lesson it is possible that the illus- trations may occupy more space than the statements to be illustrated; but the main statements are felt to be the essential matters; the illustrations, however numerous, are organically interstitial. On the other hand, there are lectures and lessons, and even books, in which the illustrations are the main element, and the rest of the matter is worked in around them. The generalisations are interstitial; the substantive mat- ter is made up of what are nominally illustrations. Lectures on ''The Humour of Mark Twain," on ''The 24 EXPOSITION AND ILLUSTRATION IN TEACHING Blunders of School Children/' on '^Election Time in Texas/ ^ are all very likely to turn out to be series of illustrations with a few strenuously invented general- isations keeping them apart. The most popular form of book review is made-up mainly of interstitial matter, and lantern lectures have an almost irresistible ten- dency to resolve themselves into interstitial common- places that only a good set of slides can condone in the judgment of an intelligent audience. Some teachers may reasonably interpose here, and maintain that lantern lectures ought to be interstitial. There is a great deal to be said in favour of such a view. But to adopt it would be to change the standpoint from which we have been considering the whole matter. It is quite reasonable to maintain that the most valu- able part of a lantern lecture is not what the lecturer says, but what his slides show. Still, if the information conveyed by the slides is regarded as the primary matter, they can no longer be treated as illustrations: they have become the substantive matter of teaching. The interstitial remarks of the lecturer are really illus- trative of the slides. In the case of a literary lecture professing to give a critical estimate of a writer's works, it is illegitimate to depend for the main interest of the lecture on the intrinsic attraction of the quotations. The interest should be in the relation the lecturer is able to establish between his generalisations and the particular quotations that he uses to support his views. '^Note the beauty of this passage;" '^What could be more inspiring than the following;" ''If you wish to know what pathos means, turn with me to the Ode to ;" ''No one with a spark of humour in his compo- sition could refrain from chortling over the exquisite NATURE AND SCOPE 25 passage I am about to read to you;" all these are mere bits of padding that mark what may be called finger-post criticism. On the other hand, some of the finest passages of Shakespeare may be read with almost no interest in their primary meaning because they are being used to illustrate a point in the Shakespeare- Bacon controversy. It is quite possible for a lantern lecture to depend on the actual lecture that is delivered, so that the hearers recognise that the slides, however good they may be, would either have been meaning- less without the lecturer^s exposition^ or would have had quite a different meaning from that they actually took under his manipulation. It is clearly important for the teacher to distinguish between the values of certain materials as illustrations, on the one hand, and as the subject of actual teaching on the other. Finger-post criticism has its place in school. Indeed, it is probable that some readers of this chapter have got rather angry at the idea of spoiling Shakespeare by using his writings merely to illustrate an argument. But for our professional purposes it is important to keep apart the two uses of subject-matter, the one as illustration, the other as substantive matter of instruction. It is an excellent thing to read to a class a series of extracts from a standard author with only a few explanatory comments — probably a better thing for the class than to give it a seriously worked-out lecture in which only illustrative extracts are given. We have to remember that the purpose in the two cases is different. In the first we are giving the pupil the actual material; in the second we are entitled to as- sume that the pupil has the material, and all that we have to do is to manipulate that material in such a way 26 EXPOSITION AND ILLUSTRATION IN TEACHING as to enable him to acquire a better mastery of what he already possesses. Under ideal conditions in a lec- ture on the Humour of Tom Hood it may be assumed that the audience have all read Hood's works at least once. The lecturer has therefore no need to fall back on mere finger-post criticism; and on the other hand, he has no temptation to rely upon the intrinsic interest of the passages he quotes. In practice, however, it is impossible to attain the ideal, so the teacher has to combine in the most effective way he can the two uses of his material. In a lesson intended to deal with liter- ature as subject-matter, the teacher should seek to make himself as little prominent as possible. The matter is the important thing. So long as lantern slides are used as teaching matter (docendum), the pupils are entitled to attend to the teacher's explanations only so far as they feel the need of them. When the slides are used as illustrations, the incidence of attention should be reversed. The subject-matter of teaching illustrations is of con- siderable importance. In certain branches no problem emerges. Only one kind of illustration is possible, and the choice of the best material in that kind is really an essential part of the specialist's knowledge of how to teach his subject. But in many subjects illustrations may be sought from all parts of the field of knowledge, and the question arises whether it is better to select illustrations from matter that is cognate with that the pupils are dealing with, or to choose matter as different from that as possible. Generally speaking, it is better to keep to cognate subjects, as in this way the teacher may be teaching one branch substantively while illustrating another. On the other hand, there NATURE AND SCOPE 27 is the danger of weariness if the pupils are never allowed a change of venue. Teachers are beginning to realise, what pupils have realised some time ago, that it is possible to carry the method of correlation to such an extent as to exhaust all possible interest in certain matters. Illustrating in a circle is not quite so deadly as reasoning in a circle, but it has its serious defects. From what has gone before, it might appear to follow that in using Illustration we must always adopt the deductive method. The illustrandum is given as a sort of general statement, which the rest of the process works out and applies, as in ordinary deduction. But Illustration may sometimes be used in what may be fairly called an inductive way. Indeed, the methods used in applying Illustration vary between two ex- tremes. At the one end is the plan of depending mainly upon Exposition. Everything is stated in the plainest possible terms, and illustrations are introduced only where absolutely necessary, and are always stated to be illustrations. They are formally introduced by as, or some such word, or are actually named illustration or example. This all fits in with the deductive notion. At the other extreme are found those cases where the illustration is given almost without comment, and its meaning left to be inferred. Especially when many illustrations are given and the pupil is led to draw cer- tain inevitable conclusions, the resemblance to induc- tion is so great that the reader may not unnaturally say that it is induction and nothing else. The genders of Latin nouns, as gathered from inspection of their mere form, may be inculcated by a series of exercises to our pupils in which certain typical Latin nouns are system- atically called into play without any overt reference 28 EXPOSITION AND ILLUSTRATION IN TEACHING to their gender. But some may be inclined to question whether this is really Illustration. Is it not a process in which we teach rather than merely illustrate ? It is true that the illustrandum does not appear till the process is completed, but it has been in the teacher's mind throughout. It may not, therefore, be altogether unreasonable to regard the process as one of Illustra- tion, the teacher adopting the deductive attitude and passing from the generalisation to the particulars, and the pupils reversing this order. This view is worth elaborating a little, as it is not quite in harmony with the usual nomenclature. Sometimes, in ordinary experience, light is thrown upon some matter that nevertheless cannot be called the illustrandum, since, at the beginning, it is not pres- ent as such in the mind of either the pupil or the teacher. A person who knew no German was called upon to make a vocabulary that included over two thousand German nouns. She had to indicate in each case the gender, the genitive, and the meaning of the noun. Her method was the straightforward one of looking up each word in a standard German dictionary, and copying out the relevant details. As the work progressed, she found that she could anticipate with increasing accuracy the gender and genitive of each new noun as it presented itself; till towards the end she was strongly tempted to depend upon her general impression, without troubling to verify it by reference to the dictionary. A still more striking case is one that occurred under the deplorably bad system of payment by results, that used to obtain in England, in which the teacher's pro- fessional reputation depended upon the percentage of NATURE AND SCOPE 29 pupils he could contrive to squeeze through certain individual examination tests at the end of each school year. A harassed teacher, who had not enough time to attend to the dullards that under this system were the persons of chief importance, tried to get rid of the troublesome clever pupils in her youngest class by keep- ing them busy with long addition sums, while she de- voted all her energy to getting her dullards to work little sums with sufficient accuracy to obtain the coveted pass. Through much practice the clever pupils were able to work the long sums so rapidly that they were continually worrying the poor teacher by coming back for more. To save time in giving out fresh sums, she dictated only one line, say 987,526, and told the pupils to repeat that line on their slates another eight times, making nine lines in all, and then add the whole. The remarkable thing was that after some weeks of this in- genious labour-saving device, the poor teacher was more harassed than ever. The children appeared to have acquired a positively uncanny speed in addition. On investigation it was found that the pupils had gradually noticed that there was something peculiarly sym- metrical about the new sums the teacher was giving them. Some of the more intelligent among them began to see that it was a pity to waste time adding up a column of nine eights when they had added up such a column a little while ago. They began, therefore, to keep a note of results for future use, and gradually gave up adding at all, except in the matter of carrying from one column to another. The step from this to pure multiplication was easy, but as a matter of fact was not made by the pupils themselves; the secret of multiplication was communicated to them (for a con- 30 EXPOSITION AND ILLUSTRATION IN TEACHING sideration) by certain pupils in higher classes to whom the young experimenters had been talking about the peculiar sums they had lately been having. The net result was that those pupils learnt in a few weeks, and with great satisfaction, the full meaning of the multi- plication table and its application, matters that under ordinary circumstances take a whole school year to master. It might be argued that in these two cases the pupil passed from the illustration to the illustran- dum. But this is an unnecessary strain on the terms. It is better to restrict the term Illustration to those cases in which there is a deliberate attempt to throw light upon a given subject. Here, to be sure, light was thrown upon certain matters, but without any delib- erate intention on the part of either teacher or pupil. The learning, in fact, was carried on in the ordinary inductive way. The case is somewhat different when the teacher makes a deliberate use of the illustration before pre- senting the illustrandum. He is often able to arrange matters so that certain experiences of school difficulties that must occur at any rate among his pupils shall occur at certain stages that are convenient for him. He can, in short, modify the order of the development of the pupil's mental experience in such a way that the elements of this experience shall form certain combi- nations that from the point of view of the school are desirable because they lead to the pupil's coming to certain desired conclusions. To put it somewhat less abstractly, it is quite possible for a master who has taught the same school grade for several years to know very exactly how certain of the special points to be NATURE AND SCOPE 31 dealt with in that grade will affect certain minds. He is therefore in a position to arrange the matters to be presented in the order he thinks will best aid their proper assimilation. For example, the construction of the accusative with the infinitive in Latin involves problems for the young mind that are insoluble at cer- tain stages of knowledge. This subject may be illus- trated in advance by a carefully arranged series of lessons that have no apparent connection with the oratio ohliqua, as found in Latin. English grammar may be so taught as to pave the way, and even the use of brackets in algebra may be regarded as a prepara- tion, — as may be seen in the interesting little mono- graph on the subject by the Rev. J. H. Raven.^ In the ordinary sense of the term an illustration is expected to accompany the subject-matter to be illus- trated, so it must be admitted to be a little strain on the term to call such processes as those we have dealt with in the last paragraph Anticipatory Illustration. To be sure, the teacher always has the illustrandum before him as he prepares the exercises that are to throw light upon difficulties that have not yet arisen in the pupil's mind, and this gives a certain amount of justi- fication for the introduction of the term Anticipatory ^ " Do the two accusatives both feel the influence of the Transitive dicit, and so form a complex noun, governed by dicit, so that the analysis will be : He mentions the-enemy' s-coming f Key (Lat. Gram., § 911) seems to take a somewhat similar view to this. In analysing Ferunt Ccesarem rediisse, he has this original note : ' A mathematician might have expressed this by — Ferunt {Ccesar rediit)em, attaching the symbol of the accusative case to the clause. As the Romans were afraid to do this, adopting what under the circumstances was perhaps the best makeshift, they selected for the addition of the suffix the chief substantive.'" — Latin Exercises in the Oratio Ohliqua, by the Rev. J. H. Raven, p. 55. 32 EXPOSITION AND ILLUSTRATION IN TEACHING Illustration. But the real reason for seeking to use the phrase is that there is need for some term to desig- nate a process whose importance is now beginning to be appreciated in schools. Using Anticipatory Illustra- tion in such a way that pupils must reach certain gener- alisations, may be regarded as a form of inductive teach- ing. The pupil may be so fed with illustrative matter that he is practically coerced into reaching certain con- clusions. The heuristic method, in its healthier forms, is nothing more than a system of Anticipatory Illus- tration inevitably leading to a conclusion that already exists in the teacher's mind. It is a caricature of the method to describe it as a process of placing the pupils in the position of the original discoverer of a certain truth, and keeping them there till they discover it for themselves. We cannot put pupils in the position of the original discoverer. We can turn them loose in an orchard and let them watch the apples falling; but it would be difficult to say how much time we should give them before we come back to find them in possession of the theory of gravitation. The teacher on the heu- ristic method never lets go the guiding reins. He may hold them now loose and now tight, but he never drops them. He knows the course and he keeps his pupils in it — with the minimum amount of restraint, it is true, but the restraint is none the less real. It is, throughout, a system of Anticipatory Illustration. It is sometimes maintained that the heuristic method gives no real training in induction, since all the matter is so carefully arranged beforehand that the mind is not left free. But the mind, as a matter of fact, is, under no circumstances, ever left free. It must react upon what is presented to it, and it acts in the same NATURE AND SCOPE 33 way upon the material presented, whether that comes at haphazard or is carefully arranged in a definite order. The induction a pupil makes as the result of considering a number of anticipatory illustrations is as genuine as one that he makes in his ordinary experience. The fact that his ordinary induction is so often wrong, because the matter is not presented in a helpful order, is surely no advantage. So far as the intellectual pro- cess is concerned, there is no difference in the two cases. An induction either is an induction or it is not. A more plausible objection is that Anticipatory Illus- tration may be so arranged as to prevent the possibil- ity of error, and thus deprive the pupil of that prac- tice in dealing with deceptive cases that is so necessary as a preparation for the work of life. But here it is only necessary to remark that, in spite of the teacher's best endeavours, he will find it almost impossible to ar- range his anticipatory illustrations so that there is no loophole for error. Further, at later stages, the pupil is left more and more to his own resources. Under any system inductions must be verified, and this verifica- tion may be as well taught in connection with the heuristic method as with any other. All the needful precautions can be applied here as elsewhere. h As an example of the application of Anticipatory Illustration with the minimum possibility of error, take the case of teaching Euler's Theorem, that gives the formulae for the number of faces, corners, and edges of a pyramid or prism having a given geometrical figure as base. The data of the theorem may be so presented that the pupils must discover it for themselves. They are assumed to know what is meant by a face, a cor- ner and an edge. The teacher supplies the pupils with 84 EXPOSITION AND ILLUSTRATION IN TEACHING the sixteen solids named in the following table, but the numbers as they appear on the printed table are not inserted : — EULER'S THEOREM Pyramids Name op Solid Prisms Faces Corners Edges Faces Corners Edges 4 5 6 7 8 9 10 11 4 5 6 7 8 9 10 11 6 8 10 12 14 16 18 20 Triangular Square Pentagonal Hexagonal Heptagonal Octagonal Nonagonal Decagonal 5 6 7 8 9 10 11 12 6 8 10 12 14 16 18 20 9 12 15 18 21 24 27 30 n + 1 n + 1 2n n-gonal n +2 2n 3n Provided with this blank table and the necessary solids, the pupil is called upon to fill in the required numbers by the simple process of counting from the actual solids the number of faces, corners, and edges. All he is asked to do is to fill up the table as far as the decagonal solids. Naturally the generalised expres- sions in terms of n that occur at the end of the table are not even suggested to the pupil. It is the purpose of the lesson to lead the pupils to reach the generalisa- tions in n for themselves. To enunciate these at the beginning of the lesson would be what Professor Henry E. Armstrong calls *' criminal.'' ^ At first the pupils fill up the table in that conscien- tiously indifferent way that children have of dealing with easy routine exercises. By and by they begin to * The Teaching of Scientific Method, p. 254. NATURE AND SCOPE 35 note a certain symmetry, and their intellectual interest is aroused. It is an excellent plan to omit two of the figures, say the octagonal pyramid and the nonagonal prism, and invite the pupils to fill up the corresponding spaces by calculation. It will be found that fully half of the class will be able to do this directly they come to the place of the missing figure, and almost all the rest of the class will be able to fill in the blanks after they have completed the entries so far as they have solid figures to count from. The second stage consists in requiring the pupils to continue the table, filling in the non-technical terms in the name column, 11-gonal, 12-gonal, 13-gonal, and so forth down to 20-gonal. Experience showed that almost every pupil in a class of sixty boys of ten years of age could complete the table up to 20, and all this without one single word of explanation from the time the first number was set down till the 60 edges of the 20-gonal prism were recorded. Keeping to the case of the class just mentioned, the third stage consisted in setting the pupils to fill up the figures for a 40-gonal figure, then for a 60-gonal, then for a 100-gonal solid. Here there was a bigger percentage of breakdowns, and the method adopted was to write the correct line of figures on the blackboard after each solid had been attempted. In this way those who failed in the 40 solid saw how things went, and generally succeeded with the 60 or the 100 solid. The fourth stage consisted in a series of exercises such as : How many edges has a 45-gonal pyramid ? a 45-gonal prism ? How many corners has a 72-gonal prism ? The correct answer was in each case placed 36 EXPOSITION AND ILLUSTRATION IN TEACHING upon the board, and the pupils were thus enabled to correct any miscalculation. The fifth stage consisted in exercises that worked backwards: A ?-gonal solid pyramid has 41 corners ; how many faces has it? How many edges? What -gonal is it ? (That is, what number should go before the -gonal in the name column ?) The final stage consisted in an invitation to fill up the n-gonal figures. All that was explained was that n stood for any number, and that what was to be noted was whether the different numbers would be greater or less than n, and by how much. At the first exercise thirty-five boys wrote down the correct generalised form. They had won their generalisation. CHAPTER II Mental Content Teachers are now familiar with the phenomena of apperception. At the earhest stages pure sensation is possible to the developing human being, but very soon sensations are associated with meaning and become perceptions. Thereafter every stimulus that the mind has to deal with is modified by the results of previous stimulations. When we reach the plane of ideas, it is found that while every new idea presented is acted upon in accordance with the laws of mind, these laws can only be applied as conditioned by the other ideas at that time possessed by the mind. In other words, each new idea is acted upon by all the other ideas at that time available in the mind in question. This process is known as apperception. A given mind possessed of certain ideas must react in a determinate way when a given new idea is presented to it. Any one therefore who knows the general laws of mental activity and the content of a given mind may act upon that mind with a fair chance of being able to produce a desired mental result. In point of fact this is what the expositor does, for Exposition may be regarded as the process of guid- ing and directing apperception in another mind. The first assumption, then, underlying the art of Exposition is that it is possible for one mind to act upon another. Successful exposition implies that one 37 38 EXPOSITION AND ILLUSTRATION IN TEACHING mind has been able to produce a predetermined effect upon another. Now while our ordinary experience leads us to believe that this interaction between minds is continually going on, the slightest dip beneath the surface shows us that the matter is not nearly so simple as it appears. There is no direct communication between minds. Mind understands mind only by an elaborate system of interpretation. Philosophers puzzle themselves and their readers over the problem of the relation between the individual consciousness and what they call the general consciousness. But what- ever this relation may be it is one that does not admit of articulate expression. For all practical purposes each individual consciousness is insulated from every other. Consciousness is as impenetrable as matter: by no possibility can we penetrate into the conscious- ness of another. What goes on in that other conscious- ness can be understood by us only as the result of a process of inference from our own experience. The everyday act of influencing the mind of another, there- fore, acquires all the interest of a mystery. We may never be able to explain fully all that under- lies this mystery, but we can at least lay down certain conditions that must be complied with if we are to succeed in producing upon the mind of another a pre- determined effect. To begin with, we must be able to catch and retain the attention of the pupil. Next we have to acquire the power of manipulating his men- tal content so that there shall arise in his mind a com- bination of elements similar to a certain combination already existing in our own mind. To do this we must have a knowledge of the mental content of the pupil. The next condition of successful exposition is a knowl- MENTAL CONTENT 39 edge of the laws according to which mind in general acts. No doubt there are great varieties in the de- tailed working of individual minds, but there are cer- tain laws which are of a very general character, it is true, but which within the wide limits of their applica- tion are absolute. We cannot break these laws even if we try; it is according to these laws that the mind always reacts upon material presented to it. They are generally known as the Laws of Thought as Thought, and are more frequently found in books on Logic than in books on Psychology. So exceedingly general are they, that when they are stated, they sound particularly empty. But it has to be remembered that their empti- ness is the result of their universality. They run as follows: The first, known as the Law of Identity, is represented by the enlightening formula A is A. This again is explained to mean that everything is equal to itself, or the whole is equal to the sum of the parts. It has to be noted that this statement has noth- ing to do with either the whole or the parts, except in their relations as whole and parts. It is found to be an imperative law of our thinking that we shall, under no circumstances whatever, conceive the whole as being either more or less than the sum of the parts. Of the many meanings that have been given to the Principle of Identity perhaps the one most in point here is that supported by F. H. Bradley. This is that under identical circumstances the mind must reaffirm what it has once affirmed. For example, if I have once truly said that the sky is blue, I am bound to maintain the affirmation, even though the sky, as a matter of fact, is blue no longer. ^^Once true, always true; once false, always false." ^ ^ The Principles of Logic, p. 133. 40 EXPOSITION AND ILLUSTRATION IN TEACHING The Law of Non-contradiction is the second of these momentous laws. This is expressed in the formula: What is contradictory is unthinkable. Its shortened form is A = not-A = 0, or A - A == 0. To take a concrete case, a watch cannot be both correct and in- correct at the same moment, and tested by the same standard, A person cannot be at the same time guilty and not guilty. The third law introduces us to what is known as the Excluded Third, or the Excluded Middle. This com- pels us to think that of two repugnant notions that can- not both coexist, one or the other does exist. '^Of contradictory attributions we can only affirm one of a thing; and if one be explicitly affirmed, the other is implicitly denied. A either is or is not. A either is or is not BJ^ ^ A centaur either is or is not. Socrates either is or is not guilty. From our present point of view the fourth law is of less consequence than the others. It is known as the Law of Sufficient Reason, and limits itself to the asser- tion that we must infer nothing without a cause, or rather without a ground or reason, as cause is usually restricted to the region of the actual, and reason to that of thought. The very statement of this distinction is an explanation of the comparative unimportance of this law as illustrating the ultimate process of thought. The nature and origin of the idea of causation has been elaborately discussed, and when so much can be said in favour of the Associational origin of the idea of Causa- tion, it cannot be maintained that this law has the cer- tainty that marks the others. So unassailable are these three laws that the general ^ Sir William Hamilton : Lectures, Vol. Ill, p. 83. MENTAL CONTENT 41 feeling of every one who hears them for the first time is that they are superfluous, if not indeed a little silly. Why state them so ponderously when no one questions their truth. Are we any further forward when we have admitted that A is A, that A cannot be both A and not A, that a thing must be either A or not A? Yet it is because of our unanimity on these apparently unim- portant points that we are able to reason with one another in the full assurance that we shall come to certain inevitable conclusions, if only the facts are stated aright. Two minds that are given the same facts cannot but come to the same conclusion. Depending upon these laws, we are able to rely upon producing by our exposition a definite calculable effect upon the minds of others. Given certain facts, we can prophesy the mind's reaction upon them. Unfortunately the certainty of reaction is disturbed by the nature of the facts submitted to the mind. When dealing with quite abstract elements, as in formal logic and pure mathematics, the action of the mind can be depended upon. But unfortunately the greater part of our mental activity is carried on in connection with matters that are far from abstract. It is custom- ary to use a figure of speech and speak, as we have done once or twice already, of mental content. Naturally we must be on our guard against accepting this figure as expressing literal truth. The relation between the mind and mental content is not that between container and thing contained. For convenience of expression we speak of the mind and the subject upon which the mind acts, but the two terms are often very loosely understood. Occasionally we think about this subject as something outside of us altogether. For example, 42 EXPOSITION AND ILLUSTRATION IN TEACHING the mind may be said to act upon the colours when we watch a sunset. If this be so, the mind is acting upon something that is material. But it would be better to say that the brain through the medium of the sense organs is being affected in a certain way, and that as a result the mind is stirred to a particular kind of ac- tivity. The fundamental connection between mind and matter is fortunately no part of our present busi- ness; what we are interested in is the connection be- tween the mind and that upon which the mind acts. Speaking generally, the mind is said to act upon ideas.^ Mental content is usually regarded as being made up of ideas. It is a very convenient way of expressing our- selves to speak of the mind as a sort of force that acts upon certain entities called ideas. But ideas are not things from without that the mind takes into itself and builds up into useful combinations. Still less are they independent entities that act on their own initia- tive. Ideas are not so much things as forces. They are modes in which the mind manifests its activity. It is not so much that the mind has ideas as that the mind is ideas. It was formerly fashionable to speak of the mind as having a certain number of faculties; but recent writers regard the faculties as merely dif- ferent ways in which the mind shows its activity: they are sometimes spoken of as modes of being con- scious.^ This description might be equally applied to ideas, the difference being that the ideas are modes of consciousness more specialised than are the facul- ^ Cf. Locke's definition of an idea as "whatsoever is the object of the understanding when a man thinks." Human Understanding, Bk. I, Chap. 1, §8. 2 Cf . Professor Stout : Manual of Psychology, Book I, Chap. I. MENTAL CONTENT 43 ties. My idea of a table is my mode of being conscious of tables, but it has its peculiarities. My experience of tables has not been exactly the same as everybody else's, and my mode of being conscious of a table is affected accordingly. We must not be led into supposing that ideas always represent definite separate units such as we call things, or even that they always correspond to what are called the substantive elements of thought. It is found that the elements of thought may be roughly arranged into two classes : those upon which the mind may rest for at least a brief time, and those that are always on the wing and cannot be made by themselves the matter of thought, but must always be considered in relation to other thought-elements. The first class are called the substantive, the second the transitive, elements. Naturally these terms are not to be confounded with their equivalents in grammar. For the purposes of Psychology, for example, a verb may be regarded as a substantive. The mind can rest on the idea implied in the verb to walk, but it cannot deal with such a word as of unless it gets the help of other ideas. The dis- tinction between the substantive and transitive must not be pushed too far. We can in thought isolate tran- sitive ideas and — with the help of other thought-ele- ments — deal with them as substantives. Have we not erudite notes on such transitive elements as are indicated by fjLev and Se ? There is, in fact, always a strong tendency to turn the transitive elements into substantive. We are disinclined to let an idea act merely as a force. We want to pause over it, and wher- ever possible, analyse it. In actual experience, how- ever, we frequently fail to separate out the definite 44 EXPOSITION AND ILLUSTRATION IN TEACHING meaning of a word (which, of course, represents an idea), and yet we can use it quite accurately. We often find a difficulty in explaining the meaning of a peculiar turn in the mother tongue. We know that the expression is correct, and that it is the only expression that will meet the case, and yet we cannot explain to the en- quiring foreigner why. What is called the Sprachgefiihl represents this general sense of the value of certain of the transitive elements of thought. ¥/e recognise them as forces, though we are not always able to control them. The uneasiness we experience in dealing with the tran- sitive elements of thought results from a natural ten- dency we all have to endow abstractions with a more or less independent objective existence. There is, in fact, in the human mind a strong bias toward the '^ Thing'' stage, and this bias must be allowed for in our efforts to convey thoughts from mind to mind. The fundamental tendency of the human mind to treat thoughts as things is illustrated in the universal bias toward personifying the forces of nature. Poets spend a good deal of their time in this process of giving to airy nothings a local habitation and a name. But hypostasis, as this tendency to reify thoughts is called, is apt to induce confusion. It leads us to imagine, for example, that because we can remember and imag- ine and judge we must have faculties of memory, imagination, and judgment. A clock can tick, but no one thinks of endowing it with the faculty of tickibility. Yet if we had occasion to speak a great deal about a clock's power of ticking, we would almost certainly fall into speaking of its tickibility or its tickipacity. For expository purposes it is necessary to have a term to describe the various modes of being conscious, and so MENTAL CONTENT 45 long as we do not imagine that there is a thing corre- sponding to each of the terms, no harm is done in speak- ing of the faculties of memory, imagination, judgment, and so forth. It is obvious that there is the same tendency to hy- postatise the ideas as there is to hypostatise the facul- ties. Indeed the two — the ideas and the faculties — have so much in common that they must be distin- guished, not so much by their fundamental nature as by their reference. While both are, as we have seen, essentially modes of being conscious, a difference be- tween them may be said to be that while all men have the same faculties, — though perhaps not of the same quality, — all men are far from having the same ideas. The fact is that ideas are forces that have brought the. mind into touch with something outside itself. They therefore either directly, or at one or more removes, have a real connection with the outer world. They are, in consequence, to some extent dependent upon the nature of the environment in which the mind functions. The same thing, however, may be said about the facul- ties. Memory differs greatly according to the class of facts upon which it is exercised. We may all be said to have good memories for something. So with imag- ination and even reasoning. We always reason more easily when dealing with matters v/ith which we are familiar. This does not, of course, mean that the reason acts in one way in dealing with stocks and shares and in another in elaborating metaphysical theories. Simi- larly, there are general laws according to which the consciousness acts in forming ideas, — laws that are the same whether the idea has to do with the concrete or the abstract. 46 EXPOSITION AND ILLUSTRATION IN TEACHING A convenient way of expressing the facts of the case is to say that some modes of being conscious are more general than others, and are called faculties; others less general and more affected by what they act on are called ideas. Since ideas are so much determined by our dealings with the external world, they may be said in some sort to represent the external world. This is how it comes about that ideas are often spoken of as if they were the material upon which the faculties act. We do not usually speak of the mind acting upon the imagination or the judgment — though, by the way, we sometimes hear expressions among those who pro- fess to improve the memory that seem to imply an action of the mind on the memory — while we do speak of its acting upon ideas. It is in this sense that ideas may be called the content of the mind, since they pro- vide a means by which the activities of the mind may be exercised. Memory, judgment, reasoning, and the other so-called faculties cannot exist unless they have something to exercise themselves upon. They cannot carry on their functions in vacuo. They depend upon the ideas to provide them with the necessary material to operate upon. This may be accepted as a useful form of stating the case, but it is necessary to be always on our guard against supposing that the ideas are in any real sense more material than the mind itself. They may be that upon the production and manipulation of which the activity of the mind expends itself, but it is only in this metaphorical sense that they can be re- garded as material. While we treat ideas as forces, we are still in danger of hypostatisation. They are forces, no doubt, but not independent forces. We sometimes speak of them MENTAL CONTENT 47 in a vague way as acting upon the mind. But this is always a mistake. They never act upon the mind for the reason that they themselves are only modes in which the mind acts. It has been suggested that an explanation may be effected by regarding the ideas as one part of the mind acting upon another part. To this no objection need be raised so long as it is clearly recognised that the normal healthy mind is after all one and indivisible. From its very nature as an or- ganism the mind must have action and reaction going on within itself, but it must never be forgotten that it always remains one organic whole. Ideas are really more or less stereotyped modes of being conscious, re- sulting from the more or less constant reaction to the same sort of conditions. A set of conditions that is continually recurring in absolutely the same way naturally causes a very definite reaction.^ This gives rise to what may be called an idea of great force, say, the idea of food. We can think of this idea and speak about it without really believing that there is an idea of food apart from any mind. When we say that the idea of food produces a certain effect on the mind, what we really mean is that the mind as a whole is experienc- ing a reaction resulting from its own activity in a cer- tain direction. When several ideas, say food, hunger, poverty, are said to act upon each other, what is meant is that the mind is correlating its various activities in relation to conditions that lie outside of itself. * A skilled mechanic's idea of a hammer is quite different from that of, say, a writer of novels. Foremen in works tell us that they know the really skilled workman by the way he lifts a hammer. His reaction is quite different from that of the casual user of the imple- ment. 48 EXPOSITION AND ILLUSTRATION IN TEACHING As a matter of phrasing, therefore, it may be per- missible occasionally to speak of ideas as forces acting and reacting upon each other. But it has always to be kept in view that this is only a mode of expression, a convenient figure of speech; and that the mind is the sole source of the activity of the ideas. From what has been said it follows that ideas are of different degrees of remoteness from the outer world. Certain ideas can be got directly from without and in no other way. The only way to attain to an idea of the scent called Eau de Cologne is to experience the sensation caused by smelling it. But the idea of scent as such is formed within. From without we can get such ideas as red, blue, yellow, and green; but we must look within for the idea of colour.^ Exposition is quite unable to make a congenitally blind person realise what blue is, though it may enable him to understand by analogy from certain other senses the sort of function that colour has in our interpretations of the outer world. A blind person may therefore be placed in the position of being able to behave quite intelligently in relation to certain questions involving colour. Since the essential purpose of Exposition is to cause to arise in the mind of the pupil a combination of ele- ments exactly corresponding to a combination at that time existing in the mind of the expositor, it is easy to see that in sensory matters, such as colour, taste, and smell, it may well happen that Exposition fails because the necessary elements are not present in both minds. ^ For a very graphic and intelligible account of the relation between ideas that depend on outward stimulus and those that arise within, see Huxley's Hume, p. 68 ff. The whole of the Chapter on The Con- tents of the Mind is very illuminating. MENTAL CONTENT 49 But there is a source of danger, even when all the elements are present in both minds. It is quite possible that the elements may be differently combined in the teacher-mind and the pupil-mind. Sometimes the combination formed in the pupil's mind is quite reason- able, and teacher and pupil may talk for long enough about the matter without discovering that they are dealing with combinations that do not agree. It was only by a chance statement in an examination paper that a teacher discovered that one of his best pupils had been for years under the impression that John Knox had been hanged. The cause of the error was a mis- interpretation of the remark made by the teacher in class: ^^John Knox was then sent to the galleys. '^ Not having heard of the galleys, and being familiar with the word gallows, the pupil made the natural enough assumption that Knox was hanged. The mis- take ought to have been discovered by a comparison of dates, but schoolboys are very willing to accept on trust a hypothesis that fits in with all the demands of a given lesson. Usually the combination of ideas in the pupil's mind is, as in this case, quite intelligible to the teacher as soon as it is exposed. But occasion- ally pupils who have had quite a different early train- ing from that of their teachers may make combina- tions that are unintelligible even when laid bare. An Enghsh Master could not understand the word smake that occurred in a Scotch boy's essay. He gathered from the context that it was something to eat, but could not accept the boy's confident explanation that it was a small steak. Careful enquiry brought out the fact that in the boy's family circle this was the accepted meaning, its origin being a corruption of the metrical 50 EXPOSITION AND ILLUSTRATION IN TEACHING version of the Hundredth Psalm. This had been taught to the children before they could read, by mak- ing them repeat the words after the nurse. Since they could not understand the real sense, they had, from a fundamental necessity of human thought, to supply a sense of their own. Know that the Lord is God indeed ; Without our aid he did us make : [did a smake] We are his flock, he doth us feed, And for his sheep he doth us take. [doth a steak] Custom legitimised the new substantive smake in the family circle, and the boy did not realise that it was not current in the outside world. Speaking generally, the best way of preventing serious misconceptions of the kind we have been dealing with is to encourage the interchange of ideas in class. This it is that to some extent justifies the otherwise unrea- sonable desire the teacher has for reproduction of knowl- edge by the pupil. But the best form of reproduction is that which applies knowledge already acquired rather than merely produces it for inspection. In the give and take of genuine class teaching there is every chance that misconceptions of all kinds will be exposed, not necessarily to the teacher but to the pupils them- selves. Many a brilliant howler is lost to the school because the pupil himself learns in time from the work that is going on in the class that the answer he would have given had he been unfortunate enough to be called upon is not exactly the sort of thing that would com- mend itself. The teacher has the further satisfaction of knowing that not only does this exchange of ideas serve the particular ends of Exposition, but is in itself MENTAL CONTENT 51 of such importance that it may fairly be treated as a fundamental part of the work of education. Mr. H. G. Wells, for example, lays it down that the chief function of education is to cultivate just this form of interaction: — "The pressing business^of the school is to widen the range of inter- course. It is only secondarily — so far as schooling goes — or at any rate subsequently, that the idea of shaping, or, at least trying to shape, the expanded natural man into a citizen comes in." ^ It is clear that for this improvement in intercourse there must be not only agreement in the methods in which minds work, but substantial agreement among the results of mental process. To put the matter baldly, there must be agreement between the mental content of teacher and pupil if there is to be communion between them. Exposition has for its aim the estab- lishment of this agreement. Even random intercourse between teacher and pupil will, if continued long enough, lead to the discovery of whatever disagree- ments exist between the two mental contents. But for satisfactory work it is necessary to have some com- mon standard to which both contents may be referred, so as to bring out inconsistencies. This standard is to be found in the outer world. Teacher and pupil alike may test their idea-combinations by comparison with what goes on in the world around us. After all, our mental content is primarily made up out of our re- actions upon the outer world, and the value of our com- binations of ideas may be tested by seeing how far they will work in relation to the state of things outside of us. The combinations in every normal mind can stand this * Mankind in the Making, p. 214. 52 EXPOSITION AND ILLUSTRATION IN TEACHING test of seeing whether they ^'work" or not in our or- dinary Hfe. Unless our inner world and the outer fit into each other, there is obviously something wrong. It is not perhaps too strong a statement to make that a great deal of exposition has for its object the build- ing up in the mind of the pupil of great combinations of ideas that correspond with the facts of the outer world. It is obviously of the first importance that we should carefully consider the nature of the two worlds, and particularly their relation to each other. The outer world is not only a standard by which to compare two inner worlds, — the teacher-world and the pupil-world, — but the source of the pattern upon which all inner worlds are built. The plain man has no difficulty in believing that there is a world outside of him, and that this world is full of objects upon which he acts and which in turn act upon him. He has no doubt whatever that he knows this outer world, and that it exists independently of him: that it has existed before he was born, and will exist when he has passed away. Some people, by reason of greater opportunities, may know more of this world than do others, but it does not occur to the plain man to doubt that it is possible to know it at all. This is left for certain philosophers who point out that all we can ever know is made up of our own sensations and the interactions and combinations of these sensations. Out of the elements of sensation each of us builds up a world of his own, but thinks that world exists outside. At first sight it appears easy to demonstrate the absurd- ity of a theory that maintains that there is no outer world at all, but that each of us makes up a world of his own. So soon as we try, however, we find that the MENTAL CONTENT 53 theory has a great deal of fight in it, and that the troublesome philosophers have much to say for them- selves. It is found that all our proofs ultimately come back to the evidence of our senses. We are confined within the circle of our own experience, and though we believe that there is an outer world we cannot prove its existence. Do I see a water carafe before me, or do I only ex- perience certain sensations of light and shade ? It makes matters no better when I stretch out my hand and feel the carafe. I only add a bundle of new sen- sations. Even when I pour out some water and drink it, I am no further forward. I have only multiplied sensations. I have not got beyond the range of my own personal experience. I believe that there is a carafe there, but I cannot get at it. There is the word carafe, and there is the complex bundle of sensations that make up my version of a carafe. But is there a real carafe, independent of me, — a carafe that exists when I am not there to perceive it, a caraf e-in-itself ? This problem of the existence of a Thing-in-itself apart from any perceiving being is of great importance in philos- ophy, but for the plain man it is an excellent problem to give up. Let us honestly beg the question. Let us acknowledge that we cannot prove the existence of an outer world independent of us, and let us at the same time take it for granted that there is an outer world. The very use of the words ''an outer world" implies the existence of a world that is not outer. With this inner world we are on friendlier terms. We feel at home in it. We seem to be free from criticism there. No one from without can penetrate within it. We are 54 EXPOSITION AND ILLUSTRATION IN TEACHING ourselves the only persons capable of passing judg- ment on its existence and nature. When we speak of the mind's eye we imply that there is an inner world that we can look upon after the fashion in which we examine the outer world. This would suggest a re- semblance between the two worlds. Most people when questioned would say that their inner world is a repro- duction of the outer, a sort of vaguer and less vigorous duplicate of what exists outside. As a matter of fact the inner world is in part ^ a reproduction of our experi- ence of the outer world. When we close our eyes and recall a past experience involving elements depending on the outer world, there is without doubt a reproduc- tion of what occurred in the past including those ele- ments; our present vague experience is similar to, though feebler than, our past. But this is not quite the same thing as to say that the inner world resembles the outer. Our mental picture of a water carafe, even when we are looking at it,, may not at all resemble the real carafe, the carafe-in-itself. All that we can say — but this is quite enough for the practical purposes of life — is that there is a corre- spondence between the inner and the outer worlds: they fit into one another, and both remain constant. Whatever the carafe-in-itself is really like, it always causes the same mental picture to arise when we look at it ; it always reacts in the same way to the different senses. So that after all what it is really like is not of any moment, since we can never by any chance get at this real appearance. ^ Part of our inner world is originated, if the expression may be permitted, "on the premises." Our feehngs and desires, for example, must be considered as essentially of the inner world alone. MENTAL CONTENT 55 We are apt to picture the inner world as made up of ghostly water carafes, tables, houses, mountains, seas, skies, clouds, all combined in an orderly way, — a sort of well-arranged storehouse of shadowy things that cor- respond to the things-in-themselves that form the real world. This view may be compared with that stage of thought that has been already referred to as the Thing stage. In this, the earliest stage of thought, the world is assumed to be made up of a great series of indepen- dent things, each existing by and for itself. The stage is illustrated in the drawings of children and savages. There each thing is drawn separately, and set down on the paper apart from the others. It is only when we begin to see the relations between the individual things that we realise that they are not so independent of each other as they seem. This marks the rise of the Law stage, at which relations are studied and reduced to order and classified. Most people pass through both the Thing stage and the Law stage. But com- paratively few reach the third stage known as System, in which the Laws themselves have their meaning brought out by being referred to great general prin- ciples that dominate them. The ^ things '^ that make up the inner world are some- times referred to as ideas, concepts, or images. The last name is applicable only when we are dealing with the direct reproduction of a particular experience. If I call up a mental picture of a particular table that I am familiar with, I have an image. But if I merely think about table in general, I can have no particular picture, for I do not know enough about it ; or if you like, I know too much. I do not know whether to picture the table as round or square, or with four legs or three 56 EXPOSITION AND ILLUSTRATION IN TEACHING or six, and yet I know that it may be pictured in any of these ways. This kind of general idea that cannot be reduced to a picture is the kind that is properly called a concept. It must be general enough to include all kinds of things that belong to its class. The concept table, for instance, must be ready to include all kinds of tables, — round, square, oblong, oval, hexagonal, — but it must never he any of these. It has to pay for its extreme generality by the loss of the power ever to become particular. The concept has the power of crystallising out into any particular example of that concept, but it possesses this power only on the condi- tion that it shall never exercise it, without the result ceasing to be a concept and becoming a generalised image or type. This generalised image or type stands between the mere image and the concept. If I look at a particular dog Ponto here and now present, I have a percept. If in the absence of the dog I call up in my mind a pic- ture of this very dog Ponto, I have an image. If now I call up in my mind a picture of a dog that is not a re- production of any particular dog that I have ever seen, but stands for a type of all dogs, a sort of pattern of dog in general, I have a generalised image of dog. This generalised image differs from the concept, since the latter cannot be represented as being any special kind of dog at all, but can only be thought about. The generalised image of a dog may be any species of dog, but it can be of only one species; it may have any colour I please (consistent with the possibilities of dog nature), but it must have some colour; and so on. The conceptual dog has all the qualities that are essential to all dogs : it must have four legs, a tail, two eyes, hair. MENTAL CONTENT 57 and so forth ; it must have colour, but no special colour; must have size and weight, but no fixed size and weight. Thus the concept gains in generality what it loses in definiteness. Even in reading about the concept one gets irritated at its extreme elusiveness, and in actual experience people fall back in despair upon the generalised image and do their thinking by means of that. We shall see later that some writers object very much to this more or less pictorial thinking, and certainly it has some disadvantages. We must not give up the freedom of thought that comes from the extreme generality of the concept, but on the other hand we need the sup- port of the generalised image to assist the mind in dealing with concepts. When we use the generalised image, we are really thinking of ^^dog in general, '^ but by means of a concrete particular dog — though which particular dog is irrelevant. The question may now be asked whether the inner world is made up of concepts or images. It would appear that there is room for nothing but images. How can one construct a world in which tables are not allowed to be any particular kind of tables, but only tables in general, that can be thought about but not represented ? This difficulty brings out the distinction between the static and the dynamic view of the concept. Each of the views is sound though each emphasises a different aspect. The static view of the inner world is that it is made up of a great mass of more or less attenuated represen- tations of ^'things," all arranged so as to fit into each other^s qualities and positions. But such a world is inert, dead. It exists only to be examined by logical 58 EXPOSITION AND ILLUSTRATION IN TEACHING persons who are concerned about definition and classi- fication. For the ordinary needs of hfe there must be the possibiUty of interaction among the elements that make up the inner world. It is here that the dynamic view has the advantage. The concept of a table is no longer to be treated as a mere group of the essential qualities of a table, but as a force determining particu- lar lines of action. If you ask an ordinary intelligent person what a table is, you will probably find that he has some little difficulty in saying precisely. Does this mean that because he cannot define a table he does not know what a table is ? Assuredly not. He is able to behave intelligently in relation to tables. To under- stand a term it is not necessary that one should be able to define it. Definition has no doubt its proper place. The moment we need to discriminate carefully between different terms, we have to define them more or less accurately, and more or less consciously. But we must not let the definition dominate us. If we are asked: what is chalk ? we may turn to the dictionary and find that it is "a soft earthy substance of a white, grayish, or yellowish white colour, ^^ etc., or we may simply say: it is something to write on a blackboard with, or to im- prove the head of a billiard cue with, or to make car- bonic acid out of. Some are inclined to say that these are purposes to which chalk can be applied, but that they do not tell us what it is. Chalk, they say, is a chemical compound represented by the formula CaCOs, that and nothing else. But chalk is as much a thing to write with as it is a chemical compound. This is a world in which we react upon chalk in various ways, one of them being a chemical way; but this way is no MENTAL CONTENT 59 more fundamental than the others. We must remember that classification is of the mind and not of the world. We find it necessary for our human needs to classify objects, but this is for our convenience, and is not at all binding upon nature. Among young students there is sometimes a certain impatience with Nature. They get their carefully prepared classification in books, and are not a little indignant with Nature when she does not see her way to fit into the arrangement in every case. For example, there is a troublesome little Aus- tralian mammal, called the ornithorhynchus anatinus, that is the despair of the taxonomist. It is a web- footed quadruped, with a bill like a duck ; and it lays eggs like a bird or reptile. There is no place for this creature in any of the recognised classes, and to make a new class for it by itself is extremely disconcerting. There is a touch of remonstrance even in the state- ment of the sober taxonomist : — "The lowest order of the Mammalia is that of the Monotremata, constituting by itself the division, Ornithodelphia, and containing only two genera, both belonging to Australia — namely, the Ornitho- rhynchus and the Echidna. '^ ^ This is not the place to show the value of such a hybrid specimen in leading us to discover the real nature of the different classes to which it might claim doubtful admission, and especially in making clear the relation between these classes. What is more germane to our subject is the question of what place is to be found in the mental content for such exceptional cases. Ruled out of the well-known bird and reptile classes and thrust into a little class of its own, the ornitho- rhynchus is still intelHgible to us ; we at least know what ^ H. A. Nicholson : Manual of Zoology, p. 630. 60 EXPOSITION AND ILLUSTRATION IN TEACHING we mean in speaking of it. Everyone who has read this chapter thus far has formed some sort of idea of the creature, and there are as many ideas of the ornitho- rhynchus as there are people who use the term. If the reader examines his idea, he will find that it is modified by what he knows about Australia, about ducks, about bills, about mammals, quadrupeds, eggs, birds, reptiles, and even Greek. In spite of all such troublesome exceptions there is a use for the exact classification that admits of no devia- tion from the strict marks that distinguish each group. Classification is of the mind, and so is the idea of the unclassifiable ornithorhynchus. But each represents a different department of mental activity. The limita- tions imposed by the laws of classification are logical; the additional materials supplied from individual ex- perience of exceptions to those laws have to be dealt with as psychological units. In the next chapter ideas will be treated as active. Here it will be enough to deal with them as the elements out of which certain combinations are to be formed. In Exposition the teacher has already in his mind a certain more or less elaborate combination of ideas, forming the expositandum. The pupil may have all the necessary ideas lying about loose, as it were. It is, then, the teacher's business to build up those ideas in the pupil's mind into the desired whole. It may be (in fact, this is the ordinary case) that the pupil has only certain of the needful ideas at his disposal. In this case the teacher has to present the necessary nev/ ideas as well as to arrange the ideas at present possessed by the pupil. Exposition may therefore be regarded as essentially MENTAL CONTENT 61 a constructive process, and under ideal conditions it need never be destructive. In building up knowledge, fact should be added to fact in such a way that it is never necessary to undo what has been done. A com- bination of ideas once formed should be for all time. Something approaching this ideal state of affairs may be reached in the case of subjects that are removed from the ordinary interests of everyday life. In certain branches of Mathematics, and in the higher reaches of many of the other school subjects, it is possible for the teacher so to dominate the presentation of entirely fresh matter that each new fact falls exactly into its appropriate place. In teaching Latin, for example, there is nothing to prevent the master from deliberately determining beforehand the exact order in which the various points shall be presented to the pupil. Yet even when, as in this case, the arrangement of the pres- entation is entirely in the hands of the teacher, it some- times occurs that in order to give complete understand- ing of a given fact two other facts must be presented simultaneously. Neither without the other will be capable of throwing light upon the point to be explained, and since in actual practice one must precede the other, it is occasionally necessary to present one because, on the whole, it is somewhat more relevant than the other, and yet the fact that has lost precedence may in cer- tain respects deserve to come first. Apart from this difficulty that is inherent in the na- ture of things, there is the ever present trouble that we can in almost no case start quite fair. We have very seldom indeed the clean sheet that ideal exposition demands. Our pupils generally come to us with their mental content already fixed with regard to many of 62 EXPOSITION AND ILLUSTRATION IN TEACHING the matters we have to deal with. Accordingly we cannot limit ourselves to the building up of new wholes out of entirely fresh elements. Our elements are not fresh, and there are wholes already in existence. Thus it comes about that there is a destructive as well as a constructive stage in Exposition. When the existing combination of ideas is not to our satisfaction, we must demolish it before we can begin to reconstruct it in the way we desire. We are all familiar with what takes place when a pupil changes from one teacher of the violin to another. Almost invariably the master is determined to have his style of execution adopted, and in order to secure this insists upon his pupil begin- ning again at the very beginning. When the violinist turns back his pupil in this way, his idea is to break up the previously formed coordination of muscular actions, and establish in its place a coordination that will fit in with the later complex movements demanded by the approved execution. In ordinary exposition it is seldom that we require to carry destructive work so far. It is usually unnecessary to reduce a given combination to its elements in order to correct some false colloca- tion. The pupil may have the view that the further south one goes the warmer it becomes. All his ex- perience warrants him in maintaining this view, and he holds it with some vigour. It is not at all necessary that the complex that corresponds to ^^ south" in his mind should be reduced to its elements and painfully reconstructed on correct lines. All that is necessary is to break up the existing unwarrantable connection between south and increasing temperature. To the pupil south still remains south in every other attribute, but the new element of relativity is introduced, and the MENTAL CONTENT 63 pupil learns that while moving to the south always in- volves change of average temperature, it does not al- ways involve the same kind of change. In ordinary exposition it is usually sufficient to stop far short of ultimate analysis, and to begin the reconstructive pro- cess with units that are not nearly the lowest possible. Further, it has to be noted that the destructive pro- cess may be necessary, not because the combination is in itself objectionable, but because there is a need for the elements of which it is composed, in order to build up a new complex. In a given combination certain ele- ments become so firmly welded together that their individual existence is overlooked, and it becomes the teacher's business to break up the fixed combination so that the elements may become available in other connections. In the ultimate resort, however. Exposition as Ex- position is a process of building up. The destructive process is no doubt important, and indeed essential, but it is none the less merely preparatory to the real work of Exposition which is constructive. Learning a subject means really the building up of various ideas into an organised whole in which each finds its appro- priate place. Ideas in this sense must be regarded as representing activities. It is only when fact has be- come faculty that we have really learned. It is clear that when we speak of a combination of mental elements, we give no indication of the extent to which the combination is carried. In Exposition we have frequently to seek out simpler ideas in order to explain those that are more complex. The unit of Exposition therefore becomes important. Naturally the ultimate unit is the individual idea. But in 64 EXPOSITION AND ILLUSTRATION IN TEACHING practice the simple individual idea is found to be very difficult to separate out and manipulate. It has always a strong tendency to take to itself other elements and appear as a complex. In what are called ^'Object Lessons'' in school there is a strong tendency on the part of the teacher to wander into an explanation of the qualities of objects, and to lose sight of the object itself. The teacher yields to the lust of analysis. Whatever the subject, the lesson is apt to drift into a discussion of the meaning of such terms as opaque, brittle, elastic, fluid, friable, metallic. But while the teacher's ten- denc3^ is thus towards abstraction, the pupils are in- clined the other way, and are found to be continually interpreting the abstract terms in connection with con- crete objects. When the teacher wishes to elicit the idea of whiteness, he gets from the pupil the answer chalk. ^^What do you mean by brittle?" asks the teacher, and the natural answer is glass. The unit of exposition must naturally vary with the stage of advancement of the pupil. As we progress in a subject the unit naturally grows bigger. Very many errors in exposition arise from using a bigger unit than the state of advancement of the pupils warrants. CHAPTER III Mental Activity The Laws of Thought as Thought are purely general and abstract. They take no account of the material upon which the mind acts. Yet this material is of the very essence of Exposition. We have seen that under certain reservations we may regard ideas as the material upon which the mind operates. This is their passive aspect. Ideas in this relation are regarded as the mere furniture of the mind, its stock in trade, its acquired possessions. So treated they are termed '^ presented content.'^ Ideas are also said to possess a certain degree of 'Tresentative activity,'^ which may be generally de- fined as the power to force an admission into conscious- ness. Every idea that has ever been in consciousness has by that very fact acquired a certain degree of this activity, and this amount is increased every time the idea finds its way back into consciousness. It is con- ceivable that at a given moment the presentative ac- tivity of every idea that has ever passed through a given mind should be tested and registered. If this practically impossible feat could be accomplished, we would have a systematic arrangement of ideas in order of their accu- mulated presentative activity for that mind. Now it is clear that if this state of affairs represented the whole truth, only a few ideas would ever get into the mind at F 65 66 EXPOSITION AND ILLUSTRATION IN TEACHING all, unless it were able to take in an unlimited number of ideas at a time. For naturally those with the great- est presentative activity would force their way into the mind and would resist all the attempts of the less power- ful ideas to dislodge them. As a matter of fact, how- ever, ideas with comparatively little accumulated pre- sentative activity may acquire a temporary power sufficient to dislodge for the moment all others. Sup- pose we are studying Shakespeare. The ideas called up by his plays have in the course of time acquired a great accumulation of presentative activity. Yet at the moment of our most intense study of As You Like It a sudden street call may displace Rosalind and Orlando from our thoughts in favour of shrimps or cat's meat. To be sure the Shakespearian ideas immediately resume their place in virtue of their greater accumu- lated activity as individual ideas, and also because of the support they give to one another as parts of an organised group. For ideas do not remain in the consciousness as iso- lated units. They are always bound more or less closely to the other ideas that happen to be present in the consciousness with them. It is, of course, impossible to say how many ideas may be in the consciousness at any one time. The number must vary greatly accord- ing to the degree of concentration that marks the moment. It may be said that if there are one or two particularly active ideas in the mind, there is no room for any others. The same fact may be more truly ex- pressed by saying that the consciousness is sometimes concentrated on a few points and sometimes spread over a large number. Except in pathological cases there are always more than one idea present in the conscious- MENTAL ACTIVITY 67 ness, and in normal cases there is usually a more or less uniform distribution of the available consciousness among the ideas presented. It is common to speak of the ^ Afield of consciousness '^ as representing the area within which ideas are active. This field is often re- garded as being round, perhaps from a more or less con- scious comparison with the field of vision as dealt with in linear perspective, where it is represented by the base of the cone of visual rays. Within this field some of the ideas appeal to us at a given moment much more than do others. We figure those ideas to ourselves as oc- cupying the centre of the field, and therefore we call them focal. Those somewhat removed from the centre may be called subfocal, those near the circumference submarginal, and those on the circumference marginal. The nearer an idea is to the centre, the greater its share of consciousness. It is obvious that the same fact may be expressed by saying that the ideas with the strongest presentative activity occupy the centre, and those of less activity have to content themselves with a place in the subfocal, submarginal, or marginal area. In other words we may speak literally of the distribution of con- sciousness, or metaphorically of the activity of the ideas. In order to make this figure workable it is probably necessary to assume that the field of consciousness is capable of more or less rapid change of area. Some- times it is very small and contains onh^ a few ideas. Under such circumstances the distinction between focal and marginal almost disappears; the few ideas present are practically all focal. At other times the area is wide, and the number of ideas correspondingly in- creased. Here the focal ideas are not so intense, as in the case of the smaller field, but they are much more 68 EXPOSITION AND ILLUSTRATION IN TEACHING intense than are those in the outlying regions. We have to assume that the total amount of consciousness avail- able at a given moment is limited, and that therefore the problem is largely one of distribution. There is danger of overrigidity in the figure. No exact line of demarcation can be drawn between focal and subfocal near the centre, and none between mar- ginal and submarginal near the circumference. The figure of the field has the advantage that it renders impossible the older view that really implied that only one idea at a time passed through the consciousness. In psychology it is frequently necessary to correct one metaphor by means of another. The 'Afield of con- sciousness" figure corrects the old linear view that con- fined itself to the seriatim procession of the focal ideas, but in its turn errs by confining itself to one plane. Professor James's ^ figure of the ^^ stream of conscious- ness" or the ^'stream of thought" with his various graphic illustrations emphasises the element of bulk or mass in our mental content. It has the further advan- tage of indicating a procession of force as well as mate- rial. In the field figure there is merely the suggestion of a place where the ideas may disport themselves. The stream figure, by its very nature, implies the crowding in of new matter and the passing away of old. Nat- urally the figure must not be too closely pressed, for in thought there is usually a core of preferred ideas that retain their place in the middle of the stream, while a great body of ideas pass rapidly along at the margins ; whereas in a real river the opposite is the case, for the water in the middle moves more rapidly than the water at the margins. * Principles of Psychology, Vol. I, p. 279 ff. MENTAL ACTIVITY 69 It will probably be well now to pass on to a more general statement of the case in less figurative terms. The word continuum is becoming more and more pop- ular as a term to describe the mental content at any given moment. The word indicates a great mass of ideas held before the mind; but the ideas are not re- garded as lying loose, they are bound to one another, they form a more or less homogeneous whole. The binding force may be said to be a common purpose or a common interest. The purposive interest that dom- inates the continuum may be concentrated, and may tend therefore to limit the number of elements; or it may be diffused, and may take in a large number of elements. But whether the elements of a continuum are few or many, they never remain long fixed in the same relation to one another. Constant change is of the essence of the continuum. There is a continuous coming and going of mental elements. When we are thinking steadily on a given subject, the core of the continuum will be fairly large in proportion to the whole, and will remain fairly constant ; whereas in easy general talk, or in attending to the details of ordinary life, the continuum is liable to violent changes in its elements, and the core is restricted to that minimum of common elements that ensures the preservation of our sense of identity. We have treated the elements that form a continuum as if they were separate from each other. No doubt in ultimate analysis the contents of any continuum could thus be reduced to independent elemental units; but in practice it is found that ideas have a tendency to group themselves. Under identical circumstances in the experience of the same individual certain con- 70 EXPOSITION AND ILLUSTRATION IN TEACHING tinuums are likely to have almost identical content. But even in a continuum that has never before invaded consciousness it will be found that its elements are more or less definitely arranged in groups. These groups of ideas, sometimes known as apperception masses, have been formed by the co-presentation in consciousness of the ideas in question. They must therefore have formed part of previous continuums, though their ac- companiments in any two of these continuums may never have been the same. In considering how these groups have been formed it will be well in the first place to begin from the side of the mind rather than from that of the idea, in order to counteract the tendency to regard the ideas as things independent of the mind. After the mental activity has been acknowledged there will be less harm in working out the attractive mechan- ism of apperception in terms of ideas. In the older fashioned theories of the Association of Ideas certain general principles were laid down that were useful enough so far as they went. But even when they were gathered up into one generalisation, as in Sir William Hamilton's Redintegration,^ they gave little help in the way of explaining the building up of great groups of ideas, though they certainly explained very ingeniously many mental phenomena after they had occurred. Fr. Paulhan, in his UActivite Mentale, works out a more active system of association which ultimately resolves itself into two great laws — a posi- tive and a negative. The positive law he calls the law of systematic association. It runs: — " Every psychical fact tends to associate to itself, and cause to develop, the psychical facts which may harmonise with it, which * Lectures on Metaj^hysics, Lecture XXXII, p. 238. MENTAL ACTIVITY 71 may strive with it towards a common goal or for complementary ends, which, along with it, may be able to form a system." ^ The negative law deals with inhibition or arrest : — " Every psychical phenomenon tends to prevent the production or development, or to cause the disappearance, of psychical phe- nomena which cannot be united to itself according to the law of sys- tematic association ; that is to say, which cannot be united with it for a common end." ^ These two laws, working under the impulse of purpose, secure that the various modes of being conscious that are of special value to the mind shall recur with suffi- cient frequency to establish an ease in reinstating them- selves whenever they are called for, and we have thus the beginning of the activity that results in the organi- sation of the mental processes in relation to the mental content. What we call organised groups of ideas or apperception masses may, from another point of view, be regarded as organised modes of being conscious. Treating the matter now from the point of view of the ideas, it is to be noticed that the two most important laws correspond in general with those of Paulhan. Ideas that are called contrary ideas, that is, ideas that belong to the same category but differ within that cate- gory (such as blue, green, and yellow, which come under the same category of colour, but differ inasmuch as they are different colours), arrest one another. This means that in the competition to enter consciousness contrary ideas oppose each other, do everything they can to eject each other, and finally as the result of the strife one or other succeeds in effecting an entrance and in expelling the other. It may be objected that two contrary ideas may occupy the consciousness at the same time. We ^ L'AcHvite Mentale, p. 88. 2 75^^?^ p_ 22I. 72 EXPOSITION AND ILLUSTRATION IN TEACHING amy think of a geranium with green leaves and red petals. But here the ideas of red and green are not treated by the mind as mere colours, but only as aspects of a whole. We think of a geranium in fact, not of red and green. This brings out the distinction between the having of an idea and the realising of that idea. When we merely have an idea, or admit an idea to the mind, we treat it as a more or less representative ele- ment that embodies a meaning or is significant of something else. To realise the idea of red we must concentrate upon it all the forces that are appropriate to an idea of colour, and in so doing we are drawing off all the force that might otherwise have been concen- trated upon green or some other colour. In so far then as red and green as colours both retain their place in consciousness, neither is fully realised, and their relation to each other, and to the mind in which they are found, is one of unstable equilibrium, the force of each being spent in trying to further its own fuller development, and to eject the other from conscious- ness. The law of systematic association, on the other hand, applies to those ideas that are known as disparate. These ideas have no inherent relation to each other; they do not belong to the same category, and so can be formed into any sort of complexes that circumstances may favour. There is no inherent connection, so far as we know, between a grey overcoat, a white horse, and Napoleon I,^ yet by the actual collocation of these ideas in history they form a complex that has a certain sta- bility of its own. Taking that overworked example ^ If we could view these elements sub specie cEternitatis, no doubt we could discover a sufficient cause for their collocation. MENTAL ACTIVITY 73 of the psychologists, the orange, we find that its quali- ties are grouped together in the same way. All the ordinary complexes of life are built up in accordance with the law of systematic association, or the law of complication, as it may be called, when regarded from the point of view of the ideas rather than of the mind. Besides the two forces of complication and arrest there is a third that has to be taken into account in connection with the interaction of ideas. This is known as fusion. When an idea recurs in the mind it fuses with the traces it left at its previous visit. It is by this force of fusion that our elementary ideas acquire the stability that is so necessary as a founda- tion for the whole superstructure of ideas. In the case of two complexes being brought into conscious- ness together, all the similar elements in the two fuse, all the disparate elements proceed to form a new and more elaborate complex, while the contrary ideas arrest each other. It must not be supposed that fusion is limited to the substantive elements of thought. Similar relations that recur fuse as to their common elements, and strengthen the idea of their particular class of relation. The compelling power of analogy owes much to fusion. Fusion is always at work in the mind. For the com- mon elements in the different groups strengthen each other as elements, every time they appear in conscious- ness. Two ideas that are contrary to each other, and therefore seek to arrest each other, still so react upon the rest of the mental content that by fusing with sim- ilar elements in that content they really acquire each a little more strength; that is, increase their accumu- 74 EXPOSITION AND ILLUSTRATION IN TEACHING lated presentative activity, even while being driven out of consciousness for the moment by a stronger rival. Complication is obviously the converse of analysis. After we have broken up one group of ideas in order to reconstruct the elements into another, the rebuilding is largely a matter of complication. Naturally fusion is going on parallel with complication; for all the ele- ments common to the two groups, instead of forming a complex, merely go to strengthen each other. But arrest is also present in complication. Its main work in forming new groups is to prevent the accumulation of unnecessary details. Every idea seeks to introduce into consciousness all the other ideas with which it has formed connections. An idea therefore that forms a part of many apper- ception masses has a dangerous tendency to recall too many ideas with which it is allied in different groups. Of the ideas thus invited into the consciousness some set up a process of fusion, and others of complication, but a large number are cut off by the process of arrest. If it were not so, thinking would become impossible. The mind would be smothered under the crowd of ideas. Exposition consists fundamentally of the establish- ment of new combinations of ideas, or of the making clear and strong combinations that at present exist in a vague and feeble way. To give the new combinations strength we must have as great an amount of fusion as is possible under the circumstances. Richness and breadth depend upon complication. Clearness and definiteness are gained by arrest. That all three pro- cesses may produce their best results there must be many presentations of ideas and idea groups. But this is MENTAL ACTIVITY 75 largely the work of Illustration, and will be dealt with in later chapters. In addition to the Laws of Thought as Thought and the various laws of association with which we have dealt, there is another law of greater generality and of fundamental importance in the art of Exposition. It is, in fact, the ultimate impulse to mental activity, the equivalent in the mind to gravitation in the mate- rial world. It may be called the Law of Mental Har- mony. The ideas within the mind must be at peace with each other. The moment friction arises there must be ceaseless activity till the disagreement is removed. Consistency among the ideas is an essential to mind. All the mental content must be harmonised; there must be no contradiction in the arrangement that has been imposed upon the ideas. It does not, of course, follow that each mind must be able to resolve all the contradictions that occur in the course of thought, but the mind must try to reconcile them. This is of its very nature, and the necessity is not limited to the intellectual class. The mind of the sav- age is as sensitive to the need for internal peace as is the mind of the savant. On the other hand, the uni- versality of the need for internal peace is compensated for by the varying degrees of reconciliations that will satisfy it. What the savage cannot explain in terms of science he can in terms of superstition. In fact one of the main functions of superstition would seem to be the satisfaction of this imperious mental need. The invisible wind has no mouth to make the weird moan- ings that disturb him, so the savage is impelled to get rid of this apparent contradiction of the rest of . his ex- perience. Accordingly he personifies the wind and 76 EXPOSITION AND ILLUSTRATION IN TEACHING thus supplies it with the necessary apparatus, without rousing any further difficulty. At later stages, it is true, the latent difficulties appear, and the more sophisticated successor of the savage has to invent some other plausible explanation. The mind is exact- ing in its demand for some explanation or other; it is less exacting in the quality of the explanation it accepts. Herbert Spencer gives an interesting account of the stages by which he arrived at what he considered to be the truth ^ about the colour of shadows. At the first stage he regarded them as black, since he had been ac- customed to use India ink to represent them in his drawings. At eighteen he was told by a friend that all shadows are neutral tint, but ^4t was only after my friend had repeatedly drawn my attention to instances in nature, that I finally gave in.^' He held the neutral- tint view for some years, though he did observe 'Hhat the tone of the neutral tint varied considerably in dif- ferent shadows.'' The divergences, however, ^^were not such as to shake my faith in the dogma." His peace of mind was at last disturbed by a statement in a popular work on Optics: ^Hhe colour of a shadow is always the complement of the colour of the light casting it.'' He wanted to know " Why are shadows coloured? and what determines the colour?" As a result of his investigations : — "It became manifest that as a space in shadow is a space from which the direct Hght alone is excluded, and into which the indirect light (namely, that reflected from surrounding objects by the clouds and sky) continues to fall, the colour of a shadow must partake of the colour of everything that can either radiate or reflect light into it. » "The Valuation of Evidence," Essmjs (1891), Vol. II, p. 161. MENTAL ACTIVITY 77 Hence the colour of a shadow must be the average colour of the diffused light; and must vary, as that varies, with the colours of all surround- ing things. Thus was at once explained the inconstancy I had al- ready noticed ; and I presently recognised in Nature that which the theory implies — namely, that a shadow may have any colour whatever, according to circumstances. " Here, then, respecting certain simple phenomena that are hourly visible, are three successive convictions ; each of them based on years of observation ; each of them held with unhesitating confidence ; and yet only one — as I now beheve — true." Further, the mind does not go out of its way to seek for troublesome inconsistencies. So long as no ques- tions are raised it is quite content to accept things as they are. A teacher, giving a lesson to a young class on a bluebottle, asked how the creature made its famil- iar buzzing noise. When she received an answer, she told the children that she expected that answer. Of course they thought the bluebottle buzzed with its mouth because when they wanted to buzz they did it with their mouths. Accepting the teacher's word that they were wrong, the class had no peace till she told them that the buzzing was caused by the wings. This gave the children perfect satisfaction, as it did the teacher, till her Normal Master pointed out that if you remove the bluebottle's wings, it does not stop buzzing, but actually buzzes a little harder than usual. It was now the teacher's turn to be worried, and it was not till she had learned about the special little buzzing organ * that she could drop the subject and be at peace once more. Every mind contains a large number of contradic- tions that give rise to no trouble because they are not ^Discovered by Landois. T. H. Huxley: Anatomy of Inverte- brated Animals, p. 377. 78 EXPOSITION AND ILLUSTRATION IN TEACHING perceived. The two sets of facts lie apart, and are never brought into contact with each other, so the mind is content with its erroneous correlation. It was an experienced M.D. with a tincture of literature who con- fessed that he had just discovered the true meaning of a ^' flash in the pan.^' He had all along associated the proverb with the frying pan. He knew quite as much about flintlocks as about frying pans, but he had never had occasion to connect the proverb with the firearm. The same sort of thing is seen in relation to our precepts of religion and of business. We usually keep them carefully apart. Indeed it is the business of the earnest and faithful clergyman to bring face to face the pre- cepts from the two spheres and ask his congregation to reconcile them. His success is measured by the degree of discomfort he is able to introduce into the minds of his hearers. So soon as he has introduced dispeace among the elements of the mental content he has pro- duced a disturbance that cannot be set at rest till in some way or other the exposed contradiction is recon- ciled. No doubt churchgoers are often very successful in effecting a superficial reconciliation, but this must be honestly satisfactory so far as it goes, if the person affected is to get any peace. There is no such thing as deliberate self-deception in our attempts to restore harmony between apparent contradictions. The wish no doubt is often father to the thought, but in the cases we have in view the con- tradiction is assumed to have been brought to light and placed clearly before the consciousness, so that the wish cannot generate the thought, much as the mind may desire it. When Shakespeare says of the false Duke Antonio, — MENTAL ACTIVITY 79 "Who having unto truth, by telling of it, Made such a sinner of his memory, To credit his own lie, — he did believe He was indeed the duke,"^ he is describing what Antonio would have liked to believe, rather than what he did believe. No doubt the usurper was full of arguments to justify himself in ousting his brother, and these arguments probably gave him a great deal of consolation, but they could never convince him that ^'he was indeed the duke.*' As a matter of fact the greater the efforts he made to deceive himself, the less likely would he be to attain his end, for he would only be keeping more prominently before consciousness the contradiction that he wished to remove. In his efforts to deceive himself he would be doing what the good expositor is continually doing when he seeks to break up a false combination of ideas in order to substitute a true one. For this co-presen- tation in consciousness of ideas that are really con- tradictory to each other is an essential part of the process of Exposition. It may be called Confrontation^ since it implies the bringing face to face of ideas that cannot live peaceably together. In Confrontation it is assumed that both terms of the contradiction are known to the person concerned. If this is not the case, no real confrontation can take place. I once tried to prove to an Arran farmer that the earth is round. I did not succeed. He was in the wrong, no doubt, but his was a mind of the most vigor- ous kind, a mind that worked admirably within its limits. These limits excluded all the scientific ideas that make it necessary to believe that the earth is » The Tempest, Act I, Sc. 2. 80 EXPOSITION AND ILLUSTRATION IN TEACHING round. All the ideas that had access to the farmer's mind were on the most friendly terms with all the other ideas to be found there. So soon as anyone is able to introduce into that man's -mind an idea that is incon- sistent with the flatness of the earth, a disturbance will be set up that may lead to the true arrangement of his ideas on this subject, but is more likely to lead to a rear- rangement which shall explain the particular inconsis- tency of which he has been made conscious, without necessarily corresponding with what we call fact. The principle of Confrontation is nowhere better illustrated than in the Socratic method. It was the custom of Socrates to begin his discussions by a demand for a definition, which in his ironical way he often rep- resented to be a help to himself in getting at the true meaning of the subject under discussion. It was not long before he proceeded to confront the ideas put for- ward by his interlocutor with certain other ideas that he knew formed a part of that interlocutor's mental content. The opposition thus disclosed gave an excel- lent opportunity of stimulating that enquiry that was always Socrates' aim. The method, in fact, has almost always three stages. First there is confidence without proper foundation; next as the result of Confrontation there arises doubt and desire to attain to the truth; then in the third place comes certainty founded on legitimate grounds. It is true that in some of the actual Socratic dialogues the third stage is not attained, the master contenting himself with the disturbance that he had set up, well knowing that the interlocutors could not settle down till they had reached some sort of conclusion, which if not perhaps so satisfactory as one that could have been supplied, had at any MENTAL ACTIVITY 81 rate the compensating advantage of having been at- tained by the effort of the thinker himself. This method of unfinished exposition may be permissible in the case of advanced pupils, but with the ordinary schoolboy it is generally better to carry the dialogue to its legitimate conclusion. The work of the ordinary school affords many opportunities to apply the method of Confrontation. To illustrate, take the case of that constant diffi- culty at the early stages of composition, the incomplete sentence. Pupils brought up in illiterate homes are very apt to make a relative clause stand by itself, with no other help than the original grammatical sub- ject. In schools where the pupils come from homes in which grammatical English is habitually spoken, there is not so much danger of this particular form of error, but every teacher in a school for the poorer classes is unpleasantly familiar with such a sentence in a pupil's exercise book as — John who broke the window The following is a verbatim reproduction of a lesson actually given to a class of about sixty-five rather dull boys of average age 11 J. The sentence had occurred in one of the class exercise books, and was placed on the blackboard, as it had been written, with the addition of a comma after the word John} ^ The class had gone through a regular course of instruction on the nature of the sentence, and knew in theory all about sentence making, and the distinction between a sentence and a mere phrase. The pur- pose of the lesson, therefore, was not so much to communicate new ideas as to give a meaning to ideas already known, and to increase their presentative activity by co-presenting them to the consciousness in their proper connections. G 82 EXPOSITION AND ILLUSTRATION IN TEACHING Teacher. Now what did John do ? Pwpil (confidently). Broke the window. T. Then what did ly/io do ? P. Broke the window. T. Were there two windows, then ? - P. No, sir. T. Then who broke it ? P. John. T. And what did who do ? P. (doubtfully). It says ^who broke the window.* T. Did it take two to break the window ? P. No, sir. T. Then which of them did the breaking ? (Pupils puzzled. No answer.) T. How many people were there altogether ? P. (cautiously). John and who. T. Now, which was bigger, John or who f P. They're both the same. T. Then there was only one person there ? P. Yes, sir. T. And what was his name ? P. John. T. And what did he do? P. Broke the window. T. Then, would it not be enough to say, ' John broke the window ' ? P. Yes, sir. T. Is that what it says on the blackboard ? P. No, sir : it says, 'John, who broke the window.' T. And John and who are the same person ? P. Yes, sir. T. Then, they both have the same right to the verb ? P. Yes, sir. T. Which of them is nearer the verb ? P. Who. T. What mark is between John and the verb ? P. A comma. T. Now if only one of the two can claim the verb, which has the better right to it ? P. Who. MENTAL ACTIVITY 83 T. And every noun and pronoun that is a subject must have a verb? P. Yes, sir. T. Then if who gets ' broke, ' what verb is left for John f P. None. T. How many subjects are there here ? P. Two. T. And how many verbs ? P. One. T. And every subject must have a verb ? P. Yes, sir. T. How many verbs do we need, then, besides ' broke ' ? P. One. 7^. Give me one. (No answer.) T. John (who broke a window) did something, or was something. What would you do if you broke a window ? P. (promptly). Run away, sir.^ T. Finish it, then. John, who broke a window ? P. Ran away. T. Which are the two verbs now ? P. ^Broke'and'ran.' T. Which belongs specially to who f P. Broke. T. And to John? P. Ran. In this and in all other applications of the Socratic method the teacher is really leading, though he seems to be following. He knows from the beginning the goal he desires to reach. He knows, further, the ideas the pupil already possesses, and feels that it is his business ^ In the actual lesson this answer led to the inevitable moral rebuke from which the teacher returned to the main subject as above. As a matter of fact the teacher was severely criticised for not substituting in the final part the moral " paid for it, " instead of the discreditable "ran away." It does seem a pettifogging distinction, but I am in- clined to think the critics are right. 84 EXPOSITION AND ILLUSTRATION IN TEACHING SO to manipulate those ideas that they shall ultimately form the combinations he desires. But when we say that the pupil possesses certain ideas, we do not mean that these ideas are necessarily present in the consciousness of the pupil when the les- son begins. At any moment in a given mind only a very limited number of ideas can be functioning. The mind is capable of being conscious in a great variety of ways, but is not capable of being conscious in all those ways at one and the same moment. When we say that a mind possesses a certain idea, we mean that that mind has a permanent potentiality of acting uniformly under certain identical conditions as often as those conditions recur. An idea not in consciousness may therefore be regarded as a permanent possibility of appropriate response to certain stimuli. The field of consciousness is limited, and unless an idea happens to be within that field at a given moment it would seem to be powerless, and indeed practically as if it did not exist. While we are thinking at this moment about consciousness and activity, myriads of ideas that in ordinary speech we may be said to possess are lying dormant, and exercise no influence upon the ideas that are at present in consciousness. Our ideas about rock crystals, for example, are as if they had no existence. But the important point has to be consid- ered : Are all our ideas that are not within consciousness at a particular moment equally inert? When a man is thinking of the power of ideas, for example, are his ideas about rock crystals and his ideas about John Locke equally ineffective ? He is not thinking about either Locke or crystals, but we have the general feel- ing that Locke is nearer to his thoughts at the present MENTAL ACTIVITY 85 moment than are the crystals. Though Locke is below the threshold of consciousness he somehow seems nearer that threshold than do the crystals. Is there then a differentiation among the ideas that are out of con- sciousness corresponding to the differentiation we have seen to maintain within consciousness? It would seem that between the conscious and the unconscious there is a clear dichotomy. We are either conscious of an idea or we are not; anything that is below the threshold is therefore out of consciousness. Perhaps our trouble arises from a too rigid application of our figure of the threshold. There is something extremely definite in the idea of a threshold. A visitor either has or has not crossed it. He is either in our house or he is not. But if we are expecting him, or if we chance to see him coming up the walk we are influenced by him before he is actually in the house. The figure is not perhaps a very illuminating one, as it amounts, after all, to an illustration of consciousness by an appeal to con- sciousness. But since it is impossible to transcend consciousness, it is difficult to see how this community of subject-matter can be avoided. Even if we could justify the rigidity of the threshold figure, there would still remain a certain vagueness about the mental content in the marginal area. Ideas are in constant motion about the threshold of conscious- ness : now on the line, now above, now below. An idea that is at the present moment below the threshold, but a moment ago was above it and in another moment will be above it again, may be said to exercise a certain influence on the continuum on the borders of which it wavers. It is to meet cases of this kind that the term subconscious is used. Of course an idea must either 86 EXPOSITION AND ILLUSTRATION IN TEACHING be in consciousness or not; accordingly we must regard a subconscious idea as in some way or other within consciousness. Yet from the way in which the term is used one would almost be led to think that it meant that certain ideas are in the consciousness without our being conscious of them — a clear contradiction in terms. By the Law of Excluded Middle there seems to be no place for the subconscious between the con- scious and the unconscious. Yet it is obvious that there is a difference between an idea that is hovering on the verge of consciousness, and one that is lost in the limbo of unconsciousness and may never again return to consciousness. Logic may rule out the sub- conscious, but Psychology must find it a place. To begin with, it has to be admitted that ideas that are not present in the consciousness exercise a certain influence upon ideas that are in the consciousness, and if an absolute distinction is demanded, it may be satis- factorily put for practical purposes as : At any given moment an idea may be said to be subconscious if without being itself within the consciousness it exercises an influence on ideas that are at that moment within the consciousness. It is easy to see that an idea that has just left the consciousness may leave behind it an influence that does not cease the moment it passes over the threshold. So with an idea that is coming up towards consciousness, it may not be very difficult to persuade people that it may cast its influence before it, and thus to some extent act within the mind before it appears. But we must go further, and admit that ideas may exercise an influence within the mind even if they do not reach the consciousness at all on the particular occasion that we examine. When we are dealing with a MENTAL ACTIVITY 87 difficult and complicated problem, for example, we call into the consciousness a large number of relevant ideas and carefully examine them in relation to each other, and to the problem we are working with. But as we shall see more fully later ^ we cannot at will recall all the relevant ideas. By skilful manipulation we may gather together most of the significant ideas, but some at least remain outside consciousness. Are these un- called witnesses without influence on our decisions? The answer would appear to be that ideas in the sub- conscious region do exercise an influence upon ideas within consciousness, even though on the occasion in question they do not emerge at all above the threshold. The mind is dealing with a knotty problem in some such dangerous subject as Political Economy — noted for its pitfalls. The ideas at present in the continuum seem to fit into each other quite naturally; there is therefore internal harmony, and the problem seems to be solved. Yet the mind is not satisfied. It has an uneasy sense that there is a flaw somewhere, and goes on calling up all the available ideas connected with the subject in order to discover some possible error. For long nothing adverse turns up; but by and by an idea rises above the threshold and breaks down the hypoth- esis that was in all other respects satisfactory. This belated idea may be reasonably supposed to be sub- conscious at the time that the hypothesis was formed, thus causing the disquieting vague impression. Fur- ther it would have been none the less subconscious even if it had not come up in time to break down our hypoth- esis, or had never come into the consciousness at all. It might quite well have caused the uncomfortable 1 P. 104. 88 EXPOSITION AND ILLUSTRATION IN TEACHING feeling in the mind without coming up in time to warn the thinker. When the thinker's critics point out the flaw, the subconscious idea rises into consciousness and the thinker recognises that it had given him a vague warning though it did not reach his conscious- ness in time to prevent the blunder. The phenomena of the subconscious may be readily correlated with certain of the theories of brain action. If the associations formed among ideas correspond to interrelations established among certain neural systems through their functioning in a systematic way in re- sponse to certain stimuli, it may well be assumed that when certain systems are stimulated to the necessary extent, certain corresponding ideas rise into the con- sciousness. This stimulation has the natural tendency to spread among the other systems, but naturally it will spread more easily among systems correlated with ideas that have formerly been connected with the ideas at present in consciousness. It may plausibly be sug- gested that within the brain there is a sort of physical replica of the field of consciousness; certain neural systems are in a high state of excitement — these cor- respond to the focal ideas. Systems in various de- creasing degrees of excitement may well correspond to the various degrees of obscuration of the ideas till tracts are reached that, though stimulated by the gen- eral impulse that affects all the system we are dealing with, are not sufficiently stimulated to cause a definite idea to rise into consciousness. Such tracts will corre- spond to the ideas that are in the subconscious state. If the neural system concerned is thoroughly well organised, as must be the case with regard to the sj^s- tem that regulates our thinking on any subject of which MENTAL ACTIVITY 89 we have an intelligent knowledge, it will be impossible to stimulate some of the tracts up to consciousness pitch without at the same time stimulating all the cor- related tracts into some degree of activity. Accord- ingly, even the most remote relevant ideas will be raised to at least the subconscious state, and the whole system so energised that its elements require only a very slight additional impulse to send them up into consciousness. This additional stimulus is what we seek to give them by our ordinary methods of dealing with problems. We put ourselves in the way of stimulating certain ideas. We turn to books where we know such ideas are treated. This gives us the primary set of ideas. The systems corresponding to these primary ideas stimu- late a great many other systems at the secondary and tertiary degrees of remoteness. If our system of ideas is perfectly coordinated, then the neural tracts will inevitably be stimulated in their proper order and the corresponding ideas will present themselves to con- sciousness, just as they are required for purposes of thought. This indeed is what happens in well-regulated minds when dealing with subjects in which they are quite at home. It goes without saying that this parallelism between the physical and the mental in no way commits us to materialism. Even if we could correlate every idea that passes through the mind with a definite corre- sponding cell in the brain, we would be no nearer than we were before to the solution of the problem of the relation between mind and matter. The physical parallel has been introduced here mainly because it gives a certain confirmation of the view taken with regard to the place of the subconscious in mental process. If 90 EXPOSITION AND ILLUSTRATION IN TEACHING the theory adopted with regard to the subconscious fits in with the hypotheses of certain physiological psychologists, there is the greater likelihood of its being true. In any case the analogy serves as a useful illustration, and after all, if analogy is not always itself a reliable argument, we are told that it often indicates that a reliable argument exists. CHAPTER IV Mental Backgrounds Painters are familiar with the phenomena of what they call Turbid Media. Colours vary according to the colour tone of the material upon which they are laid. This is what the Hon. John Collier has to say on thfe subject: — " Rub a little ivory black thinly over a white canvas, it will ap- pear a distinct brown ; mix the same colour with white, it becomes a neutral grey ; brush this grey thinly over a black ground, it will have a distinctly bluish tinge ; so that the same pigment can vary from a warm brown to a blue grey without admixture with any other colour but white, merely in accordance with the manipulation it receives. Yellow ochre gives similar results ; when lightly brushed over a white ground it seems a rich orange, when brushed in pre- cisely the same way over a black ground it seems a sort of green." So with the mind. The same idea has to harmonise itself with quite a different tone according to the nature of the background against which it is projected. The groups of ideas that give body to the stream of con- sciousness may be, without too violent a figure, com- pared with a background, which like every other back- ground has a powerful influence on our view of any element worked into the foreground. Naturally the analogy is more complete when we deal with the af- fective aspect of thought or speech. Public orators of a sentimental turn are not uncommonly guilty of * Primer of Art, p. 59. 91 92 EXPOSITION AND ILLUSTRATION IN TEACHING falling into a rhapsodical mode of expression, a sort of '^Ah!" strain, that renders them blind to the real mean- ing of the ideas they use. The emotional background is too strong for the ideas that are projected against it. Next morning in cold blood the orator usually sees his mistake; indeed there is a danger that the cold daylight criticism may go too far in the other direction, for it has always to be remembered that there are occa- sions when the value of an idea must not be judged too closely by the logical standard. Still there is some- thing wrong when the emotional background retains its paralysing power even through the callous period of proofreading. The following occurs at the end of a sermon-tale to children by a well-known London clergy- man, who published it along with other sermons in book form in 1891. "And away down in 81st Street a woman was stitching what seemed like a httle nightgown, but ah me ! it was not that — it was something sadder still, for her little dear baby had died; and the mother's heart was full, and the tears would flow." Apart from the background of this sad sermon-tale no one would think that '^a little nightgown" was a .particularly sad object, only less sad, in fact, than a little shroud. Yet so powerful is this background of sentiment, that not only did it blind the preacher at the time, but completely deceived two different classes of divinity students to whom I had occasion to lecture, and upon whom I took the liberty to experiment. My subject was the preparation of sermons for the young, and I read the passage — naturally beginning a little bit before the dangerous passage in order to give the background its proper effect — to illustrate a psychological principle. In both cases the implicit MENTAL BACKGROUND 93 absurdity escaped detection, though, when it was pointed out to them, the young men were much cha- grined that they had allowed it to pass. But the figure of a background in mental matters is not limited to the affective tone. It has a useful application on the ideational plane. We have found that each idea that occurs to the mind must make itself at home there. It must harmonise itself with its sur- roundings; and must take a different meaning accord- ing to the mental background against which it is pro- jected. The presented content may be quite neutral or it may have a positive tone of its own. In both cases the new idea or ideas must submit to a modification of tone or meaning from the effect of the background. Take some such colourless sentence as Think of him, and note the difference effected by projecting it against the following backgrounds. A picture in Life of a low-class photographer trying to encourage a pleasant expression on his female sitter's face. A widow laying flowers on a grave and addressing her little girl. A religious revival meeting. A French schoolmaster during the Franco-Prussian war pointing to a portrait of the first Napoleon. A conspirators' meeting where a traitor's name has been men- tioned. A crowd of starving " unemployed " watching the Mayor pass from his carriage to a City Banquet. The same thing applies to an idea dealing with a con- crete object, say a fish. Note how the emotion aroused varies according to the background. Against a back- ground that includes the Early Christians and the Catacombs it arouses either a deeply religious or a mildly antiquarian interest. Try it now against a 94 EXPOSITION AND ILLUSTRATION JN TEACHING background of Astronomy, Sport, Bread-winning, Geography, Art, Science, Slang, Heraldry, Asceticism. Most of the honest, that is, unmalicious, misunder- standings of life, are the result of failing to make al- lowance for the background in the mind of another. When the same ideas are presented against different backgrounds, the consequent confusion is so inevitable that common speech includes a special phrase to ex- press this particular form of misunderstanding. When people are at '^ cross purposes, '' they are dealing with the same words in different connections, which is the same as saying that the meanings are modified by the backgrounds. Here we have passed beyond mere tone, and have reached the region of relation among the ele- ments that make up the content of mind. The care- less, unreflective man takes it for granted that the idea he sends forth from a given background will find a cor- responding background in the mind of his hearer or reader. Fortunately his expectation is usually jiisti- fied. By the very fact that two minds are in com- munication, they are placed in such a relation as to encourage the development of the same backgrounds. But at the very beginning of a conversation there is sometimes a little difficulty. The preliminary talk between two persons, before coming to the real point, is a sort of tuning up, a kind of mental feeling for the proper pitch. This preliminary talk has sometimes been compared to the few passes that a pair of fencers make before coming to the real business of the en- counter. But the figure of finding the pitch is perhaps nearer the truth. Many people — particularly young people — are irritated at what they call ^'beating about the bush." MENTAL BACKGROUND 95 No doubt the principle in medias res is admirable, if we are sure that we and our interlocutor are to be in the middle of the same res. If two men meet to discuss the same subject, they are probably provided with the same backgrounds, or at any rate closely similar backgrounds; but even then a certain amount of harmonising may be necessary. It is quite possible that each may view the subject against a background quite differently made up, though composed of the same elements. People who argue for the sake of arguing, people who write to the newspapers, almost in- variably deal with ideas in the light of their own back- grounds, and refuse to take the trouble to discover the mental backgrounds against which the same ideas are projected in the mind of the person with whom they debate. If we desire to convince another person that his view is wrong, we must endeavour to find out exactly what that view is; we must discover what sort of back- ground his ideas are projected against. The reason why we are so seldom at cross purposes is that we rarely move out of our own set. All societies are made up of sets or coteries, each of which is marked by the possession of a common series of backgrounds. In dealing with those of our own set we have no diffi- culty, and dealing with our own set makes up the greater part of life for most of us. It is when we have communication with our political opponents, with members of a different church, with foreigners, even with members of some of the ordinary ^' Anti'' societies, that we realise that our ideas do not seem to have the effect upon our interlocutors that we intend. Teachers in a more or less conscious way feel the need of bringing their own backgrounds into harmony 96 EXPOSITION AND ILLUSTRATION IN TEACHING with those of their pupils. Young teachers in particu- lar soon discover that their questions do not produce the answers they were intended to elicit. A question is asked, for example, the answer to which is known to be within the range of the pupil's knowledge. There is no doubt about the matter. The teacher knows, from immediately preceding experience, that the answer is in the pupil's mind only waiting to be drawn out. Indeed the question may be fairly regarded as nothing more than a stage in the process of making clear and distinct an idea that the pupil already possesses, though in a vague way. The question is, however, so expressed that the pupil, with the best intention in the world, cannot discover against which background he is expected to project the ideas concerned. Accordingly he projects them against the first available background, in the hope that this may be the right one. ^^ Where was St. Paul converted?" asks the teacher, speaking from a geographical background. ^^In the ninth chapter of the Acts," responds the pupil, from a background of textual reference. In testing the in- telligence of a class the inspector asks, ^' Where do you find gates?" The pupil, from a background made up of puzzling experiences of the Socratic method, answers : ''We don't find gates, we make them." From an his- torico-geographical background the inspector desired to elicit the deleterious effect of a large town on the purity of a river. He brought out the fact that Robert the Bruce spent his latter years at Roseneath on the Clyde in Scotland, and that as a recreation he very probably — according to the inspector — fished in the river. The question that was to incriminate those who were re- sponsible for the pollution of the Clyde took the form : MENTAL BACKGROUND 97 ''Why couldn^t the Bruce fish there now?'' From a background of plain common sense came the reply: ''Because he's dead." It is manifest that what we are here calling mental backgrounds correspond to what we have already spoken of as continuums ; but we are now treating them from a new point of view. Hitherto we have been con- cerned with the relative clearness or obscurity of the elements that make up the continuum; now we are interested in the varying effects of the same idea ac- cording to the continuum in which it is found. Instead of considering the effect of the diffusion and concentra- tion of consciousness on the composition of the con- tinuum, we now examine the change produced on a given idea by the company in which it finds itself. The management of mental backgrounds is clearly an important part of the process of Exposition: ac- cordingly we must study the mechanism of these back- grounds; we must look into the problem of mental scene-shifting. With regard to the elements out of which the back- grounds are worked up there is probably a greater uni- formity than would at first sight be expected. The ultimate elements, the products of sense-perception, are practically uniform, though no doubt even here there are differences corresponding to the physical con- ditions of the sense organs. But even admitting the general uniformity of elements there remains a vast possibility of differentiation through variety in com- bination. Given a hundred minds with precisely the same ideas as presented content, it is probable that no two of them have the ideas arranged in the same way. The order in which the ideas were originally presented, 98 EXPOSITION AND ILLUSTRATION IN TEACHING and the circumstances of the different persons con- cerned, have brought about a necessary variety in the combinations. It is obvious that it is impossible to make a classification of minds on a basis of mental con- tent without practically attempting to ^^ exhaust the universe/' though a rough and ready classification may be very serviceable for practical purposes/ But with respect to the mechanism by which combinations are effected there need not be the same difficulty. Minds may be divided into three classes according to the degree of stability they establish among the elements as components of complexes. Naturally there are certain complexes of ideas that are formed to correspond to certain complexes of objective phenomena. These complexes owe their stability to the uniformity with which they react satisfactorily upon the conditions of actual experience. But certain other complexes de- pend for their stability upon the quality of the mind in which they are formed. From this point of view the first kind of mind may be named the rigid. It is marked by the close connec- tion that is maintained among the elements that go to form a given background. Instead of moving freely among themselves the individual ideas form a complex once for all, and can hardly be separated from each other. The rigidity may result from the emotional tone; we may refuse to break up our complex because we prefer to have the elements arranged in that way. This is the case with the stubborn little cottage girl ^ Such studies as Dr. Berthold Hartmann's Die Analyse des kind- lichen Gedankenkreises als die naturgemdsse Grundlage des ersten Schulunterrichts (Leipzig, 1896) show that a good beginning has al- ready been made in this kind of classification. MENTAL BACKGROUND 99 who in Wordsworth's poem refused to break up the combination of herself and her brothers and sisters into a group of seven, merely because two of them were dead. The poet does his best to break up the com- plex: — " ' But they are dead ; those two are dead ! Their spirits are in heaven ! ' 'Twas throwing words away ; for still The httle maid would have her will, And said, ' Nay, we are seven ! ' " The extreme case of this rigidity is to be found in that form of insanity that bears the name of Videe fixe. Very frequently the natural tendency of certain minds towards rigidity is intensified by bad teaching, teaching for the sake of immediate results rather than for the sake of the power that comes from the organization of ideas. It seems to save time to present ideas in ready- made boluses. Education, however, should be free from the trammels of such time conditions. The ultimate result is the only thing worth considering. We are not here concerned with the practical difficulties of supply- ing the best possible equipment for life's work in the limited time at the disposal of the teacher in the case of the average child. Few questions are of greater importance than that of making the most of the short school time available for the artisan class. But at present our aim is to get at the best ideal state. Once this has been determined, educators may be in a posi- tion to discuss what compromise, as a compromise between what ought to be and what is, will lead to the best result. Obviously we must know the best possible, before we can examine how closely we can approach it without attempting to overstep the limits of our powers. 100 EXPOSITION AND ILLUSTRATION IN TEACHING The backgrounds formed by rigid minds may be termed fixed. Naturally no background can remain permanently fixed, except perhaps in the case of the insane, but in ordinary life we find modified forms of Videe fixe. Your dull, matter-of-fact man regards all things of the same class against the same unvarying background. He finds the greatest possible difficulty in knowing what nimbler-witted people mean. The same ideas are presented to him and to them. He can- not understand why they produce such a different effect in the two cases. We shall see later that up to a certain degree of elabo- ration, it is a distinct advantage to have fixed complexes of ideas, but beyond that degree fixity is a thing the teacher must fight against. In the case of rigid minds it is obviously of prime importance that the first presenta- tion of a given complex of ideas shall be properly made, since any change at a later stage will be exceedingly difficult. To prevent the evil effects of rigidity, then, the best means is to present the component elements in as simple a form as possible. This does not mean merely in the easiest forms, but as nearly as may be in the forms resulting from ultimate analysis. The mind we appeal to ought to do its own combinations. It does not, of course, follow that the mind we deal with will form a different complex from that we have our- selves formed. The skilful teacher will in fact manipu- late his facts so that the pupil will form precisely the same complex as the less skilful teacher would present as a ready-made bolus. But the fact that the bolus-fed pupil and his better-taught compeer form the same final complex, in no way proves that the resulting know- ledge is of the same value in the two cases. There is a MENTAL BACKGROUND 101 fundamental psychological difference between ideas grouped by the mind itself, and the same ideas in the same grouping when that grouping has been presented ready made as the result of the operations of another mind. It is true that even when the mind has made its own complexes of ideas, there may be unhealthy rigidity in the result. Some minds are naturally in- elastic. That class of mind that Roger Ascham calls harde wittes ^ is inclined to be unduly rigid. Great care must accordingly be taken that the true complex should be suggested at an early stage, and further, continual exercise should be given in dealing with the same ideas in different connections. Exercises of all kinds have their uses in this way. Every time that the teacher is able to satisfy the reproach that is implied in the complaint ^'But you said so-and-so, '^ he is loosening the too rigid bonds that unite ideas. After all, harde wittes form capital material for the teacher to exercise his skill upon, and it is not difficult to see that old Roger has a warm side to this class of pupil. But every teacher dislikes the opposite type of mind that, for want of a better name, may be called the fluid. In this case there is no fear of too close a con- nection among the ideas that form a background. They are allowed to roll about in the mind pretty much as the molecules of a liquid mingle with each other. Some complexes must, of course, be maintained in a position of comparative stability, else the mind would fall to pieces altogether. But the complexes are at any time easily broken up. To this type of pupil one com- plex is as good as another. But even here we must ^ The Scholemaster : The first booke tep.chyng the brynging up of youth. Arber's Reprints, p. 34. 102 EXPOSITION AND ILLUSTRATION IN TEACHING try to get the mind to do its own combining and building up. No doubt we shall have to use stronger induce- ments, and we must find better and firmer bonds. Above all we must keep on repeating those connections that we seek to impress on the pupil-mind. Instead of seeking out exercises in which the individual ideas are exhibited in different connections we must confine ourselves to those that illustrate the working of the ideas in the same connection though under different aspects. The complex must as before be made by the pupil himself; but, once made, it may be greatly strengthened by the outside influence of the teacher. The fixed background is in general more character- istic of mature life; the unstable background is common in school. The necessity of childhood to grow as well as to live makes it imperative that material for growth should be gathered from all parts. Accordingly it is an arrangement of nature that children should be rest- less in body so as to secure an all-round physical de- velopment, and restless in spirit in order that they may derive materials from all their environment. A child may have a more or less strong inherent tendency to develop fixed backgrounds, but at early stages it is unusual to find this tendency very prominent. Our great difficulty is the instability that characterises the youthful background. We are never quite sure that the ideas of this minute will be projected against the same background as the ideas of last. Among grown-up people those who are silly, giggling, flippant, are usually those with unstable backgrounds. What is often called the Associative mind is of this class. No doubt the force of association tends to make ideas cohere. But in the case of fluid minds association MENTAL BACKGROUND 103 exercises its power rather in promoting a flow of ideas than in consoUdating ideas into organised groups. A word is enough to divert the stream of thought. Dame Quickly is the emeritus example of a mind of this sort — though, unfortunately, we do not need to go so far afield for abundant examples of the type. The background against which the ideas of Dame Quickly project themselves can hardly be called stable. It is more like a rapidly moving panorama than an or- dinary picture. The third class of mind, as characterised by its back- grounds, is the desirable one that may be named the 'plastic. This type of mind forms its own complexes with fair ease, and at the same time is able to retain them in that state that prevents deliquescence on the one hand and rigidity on the other. The resulting backgrounds are mobile. They remain steady as long as they are required to be steady, but are ready for immediate change if that is found desirable. They are stable enough to allow of very gradual change, and mobile enough to submit to sudden fluctuations if need be. Nimble-witted people are marked by a high degree of mobility of background. To illustrate the working of mental backgrounds, take the cases of a congregation listening to a sermon, students listening to a lecture, and a person reading a poem. In the sermon, as a rule, there is no call for vio- lent change of background. Frequently, indeed, the lines are laid out beforehand, the heads are given, and the work of the preacher is to develop these heads, the work of the listener to supply the appropriate and slowly changing background. So with the instructive lecture. Fact after fact is introduced, but for each fact a place 104 EXPOSITION AND ILLUSTRATION IN TEACHING has been prepared. At the very start of the lecture the teacher, if he knows his business, has referred to some fact that he is sure Ues within the knowledge of his hearers. This prepares the way for a background different from that which previously existed in the students' minds. As a rule that previous background is not of much consequence. It is usually made up of floating ideas of the campus or stairs or notebooks or whittling pencils. If the students have just come from an examination, or from a college row, or even from a specially interesting lecture, the power of the back- ground they bring with them may be much greater, and much more difficult for the new lecturer to deal with. Under adverse circumstances like these, the teacher has two courses open to him. He may begin with a particularly striking sentence, in the hope of causing a rapid change of background, in which case he makes an assault upon the attention in the hope of taking it by storm. Or he may begin by saying noth- ing to which he attaches much importance during the first five minutes, in the hope that the old background will gradually give way, and enable him to establish a new one as soon as he begins to deal with the real matter of his lecture. This latter method is, on the whole, more likely to succeed. Replacing the old back- ground item by item is a much more hopeful proceed- ing than an attempt to wave the conjurer's wand. A background cannot be called up at will. Recall is not quite the same thing. It is perhaps not very difficult to reinstate the background of a previous lecture. Indeed, it ought to be easy, for all the help students usually get is the dry paragraph that follows the colorless opening: ^^ Gentlemen, in^our last lecture MENTAL BACKGROUND 105 . . .'^ But a real beginning is different. Why is it that the experienced railway reader prefers to start his journey with a ^' begun'' novel? And if it is a little irksome to make a beginning of a novel, why is it still harder to begin to read a play ? The answer is clearly that in both cases there is no background, and that in the case of the play the background is more remote than in the novel, where the author at least does his best to help the reader in supplying a background. In reading a poem we are often called upon to make rapid and violent changes of background. This does not mean that we must suddenly change the whole body of thought that corresponds to James's stream. In reading a well-constructed poem, the main body of thought remains constant in spite of the rapid changes called for by the accumulated figures of speech. The as of the figure suspends the main interest of the reader till the corresponding so releases it again. At Virgil's invitation^ we leave the two Trojans and accompany him to the teeming bee-hive, but when the visit is over, we gladly return to ^neas and his friend. While we are with the bees, what has become of the Trojans and the Tyrians ? Has the background of country life dis- placed entirely the background supplied by the surging city? Are our thoughts with the bees or with the Trojans and the Tyrians? Different minds act dif- ferently here. The rigid mind prefers to remain with the Trojans and the busy city-builders: it resents this interruption, looks at the bees with disapproval, waits impatiently till the poet sees fit to return to his proper work. The fluid mind, on the other hand, accompanies the poet gladly, forgets all about the Trojans, and 1 ^neid, Book I, 430. 106 EXPOSITION AND ILLUSTRATION IN TEACHING revels in the new scene. The man of plastic mind read- ily supplies the new background that is necessary, but does not forget the old. His enjoyment of the new background is affected by the fact that it has a relation to the old one. The country scene has a different charm for him here, compared with what it would have had it occurred, say, in Wordsworth, where it would appear for its own sake. It is a case of turbid media. Some minds treat such temporary backgrounds as ends in themselves, others as a mere part of a wider whole. Some keep the Trojans before their minds all the while they are considering the bees. The interest for minds of this class lies mainly in the relation be- tween the two sets of ideas. The toiling Tyrians are set over against the busy bees. Other minds can sus- pend, for the time being, the background of Dido's new city without letting it disappear altogether. The charm of comparison comes after the figure has been enjoyed for its own sake. Yet even while the figure is present it cannot be treated quite as if it were an independent subject of thought. It lies on the sur- face of the stream of thought, it is true; it cannot be denied that it is focal, but the influence of the whole undercurrent of the stream is felt; the subconscious body of the stream influences our treatment of the surface current. It is in the practical affairs of life that there is a call for sudden and more or less complete changes of back- ground. The different business calls a man receives in his office every day need not involve a greater change of background than we have seen in the case of read- ing a poem. There is usually sufficient continuity to MENTAL BACKGROUND 107 maintain the connection between the parts. But if a man is interrupted in his business by household cares, or by, say, church concerns, the difficulty of main- taining a stable background is greatly increased. A man called away suddenly, after a hard bargain with a business rival, to deal with a case of conscience can hardly make the necessary change of background with the required rapidity. In this case there has to be a complete change in the body of the stream of conscious- ness before the required background can be attained. What happens as a matter of fact is that at the beginning of the new interview there is a good deal of confusion of thought. The new background is not distinct. It is affected according to the laws of turbid media by the background that has not yet had time to disappear. After a little, thought becomes clearer, ideas are grad- ually rearranged, the old background becomes so dim as not to interfere with the new, and the change is effected. So far we have been dealing with backgrounds as wholes. But the elements that make up a given back- ground are not combined as simple and independent units. They are all grouped together more or less firmly into different complexes, and these complexes form the real units of combination. In all descriptive writing and speaking it is assumed that the reader or hearer has the necessary complexes at hand ready-made. The more cultured the audience with reference to a par- ticular subject the greater the degree of complexity the expositor is entitled to assume in the combination unit. When a novelist sets his scene in a medissval castle, he assumes that his readers have a complex of ideas that corresponds to his own. He does not begin with the 108 EXPOSITION AND ILLUSTRATION IN TEACHING elementary ideas of portcullis, barbican, moat, draw- bridge, keep, bailey; he assumes these to be present and arranged in a particular way. If the novelist uses the words '' Norman castle," he assumes what he has assumed before, but limits the possible combinations of the elements. If he mentions the century in which the castle was built, he makes a still higher demand on his readers' ability to conform to standard in form- ing complexes. If the novelist thereafter feels called upon to expand into description, he concerns himself entirely with those parts of the castle in question that are more or less peculiar to it. As a matter of fact, we have all a large supply of ready-made complexes that are in themselves invariable and may be used as composite units to build up any desired whole. The skill of the poet, the teacher, and the novelist is shown in the way they manipulate these complexes to form the whole that suits their immediate purpose, i The first general remark to be made about these ready-made complexes is that they owe some of their characteristics to the preferred sense of the person in whose mind they are formed. It is well known that minds differ in the class of impressions that affect them most. There are those who depend mainly upon the eye. These are termed visuals.^ For them every- thing that is comfortably assimilated by the mind has been treated in terms of form, size, and colour. Audiles, on the other hand, prefer to deal with sounds. An audile enjoys being read to; a visual is unhappy unless he can read for himself. At the play the visual is most impressed by the scenery, the dresses, the gestures; the audile by the dialogue, the songs, the music. Those ^ Some writers prefer the term visiles. MENTAL BACKGROUND 109 that are known as tactiles reduce everything as far as possible to impressions of the sense of touch. When we speak of a cat, the visual has an impression of its size, form, and colour; the audile remembers its purring or its caterwauling; the tactile reproduces in his conscious- ness the pleasant feel of its fur. The senses of smell and taste are not usually included in this classification : we do not, as a rule, speak of gustatives or olfactives. This is probably because these senses are of inferior importance in the building up of knowledge. There is no doubt, however, that they also have a considerable effect in modifying the way in which different people regard the same thing. A caution is here not out of place. We must not make the distinction too promi- nent. It is not to be supposed that an audile gets most of his information through the ear, but only that that is the best way to get at that particular person. He prefers to have his knowledge come through the ear. It is quite possible that the psycho-physicists may by and by be able to arrange the senses in their precise order of merit as knowledge-providers. But even if this absolute order of merit were to be published to- morrow, it would in no way affect the fact that people have their preferred sense. An audile may learn abso- lutely more from the sense of sight than from the sense of hearing, and be an audile none the less. In dealing with mental backgrounds most of us have the prevailing impression of sight. For this there are obvious reasons. There are more visuals than audiles in the world; and in addition, the very word back- ground drives us by association to visual impressions. Moreover, for the purpose of school, visual back- grounds are more useful than any others, for the very 110 EXPOSITION AND ILLUSTRATION IN TEACHING sufficient reason that we can, to some extent at least, compare them with each other through the intermediary of an external standard. If the pupil is asked to think of a country town, a picture at once rises in his mind. This is his picture of a country town. If it is analysed, it will be found in all probability that it owes most of its characteristics to one particular town with which he is familiar, or in connection with which he made his first acquaintance with country towns. Further, the fewer country towns the pupil has seen the clearer is the picture that rises in his mind. To one who has seen a great number of such towns there is a vagueness about the picture. The peculiarities of the different towns are contrary ideas, and therefore arrest each other. Accordingly there is a struggle going on all along the line, and only the absolutely common elements remain clear. If, now, the man of many country towns is determined to have a clear picture, he can usually suc- ceed; but the price that he pays is the loss of the pic- ture of a country town in general, and the adoption of a particular town. His town is the pictured image of what he has actually seen. Indeed this is the most common form. Instead of having a vague background ready-made, most people have more or less vague mem- ories of backgrounds that actually exist. At first sight it may seem that there is no harm in this, and some may even be prepared to say that these pictures are better than vague generalised outlines. But when it comes to supplying backgrounds to ideas presented by another, it will be found that misunderstandings are apt to arise from the detailed character of the pic- ture. The teacher's exposition may not fit into the pupil's picture because some detail in that picture is MENTAL BACKGROUND 111 inconsistent with something the teacher has said. This detail is not essential to the general background de- manded by the teacher, and should therefore be elim- inated. In a description, for example, the teacher may speak of the church as being on the north of the market-place, while in the pupil's picture it is on the east. The pupil's mind resents this, and a wrong atti- tude results. With a purely generalised picture of the village the church can be put anywhere without rous- ing opposition. A very interesting as well as useful exercise is to take the catalogue of an art exhibition before seeing the pictures, and try to realise what sort of picture corre- sponds to each of the descriptive titles. The man of many galleries succeeds fairly well. His mental picture of even such a tantalising description as '^Portrait of a Lady" is not usually far wrong. But to the ordinary lay mind there will be little but disappointment. ^^Chill October," ^^With Daisies Pied," ^'In Spate," ''Where the Bee Lurks," ''Boors Drinking," "The Village Wedding," all raise pictures in our minds that do not correspond to what we find in the frames. Yet we cannot blame the painters: in each case we are constrained to admit that the picture justifies the name, and in most cases we are prepared to acknow- ledge that the painter's idea is better than ours. But for all that, the two pictures, his and ours, are not the same. So with description. However carefully a town may be described to you, — in words, — you will always find that when you reach the town itself it is not quite what you had pictured it to be. You cannot accuse your friend of describing it falsely or carelessly. Everything he has told you is justified by what you see. 112 EXPOSITION AND ILLUSTRATION IN TEACHING You admit that it is exactly as he described it to you — only it is different. Now if practical issues depend upon this description, how easily you might be misled. Your picture corre- sponds at all the points of contact with the description, but at all other points your picture is independent of the reality, and has no guidance. Let us not forget that the very vagueness of our backgrounds may have its use. It is this quality that enables us to fit them into so many different frames. If any discrepancy arises, it can be readily remedied, while as for the remain- ing unexpressed details they do not matter, so long as they do not imply a hidden contradiction. We some- times forget how much work the reader or hearer has to do as the apparently passive partner in the process of Exposition. The writer no doubt brings his ideas together and lays them before us with more or less skill ; but the reader has to supply his own backgrounds, and see that they agree with the ideas projected against them. Sometimes it happens that a discrepancy arises because in the mind of the writer the idea was originally projected against a false background, and the error is detected against the more accurate back- ground supplied by the reader.^ More frequently the reader's faulty background is exposed by the process of projecting the writer's ideas against it. A schoolboy who had never been in Edinburgh objected to his lesson book for describing an attempt on Edinburgh Castle made from the steep cliff on the west side. His argu- ment was that the steep cliff was on the east side. When asked to justify his criticism, he had nothing to say but a reiteration that the account must be wrong; ^ This is worked out in greater detail in Chap. XIV, p. 344, MENTAL BACKGROUND 113 this seemed to him self-evident. It was only when hard pressed by his teacher, who pointed out that the access was quite easy from the east, that the boy scorn- fully explained that climbing a high cliff out of small boats was not what he considered an easy approach. The mention of boats led to further enquiries, when it came out that the boy was dealing with the only castle he had seen, which happened to be Dunnottar Castle in the northeast of Scotland, where certainly his objection held. He had simply taken the word castle to connote all the elements of the single castle he had seen. Apart from the errors arising from different concep- tions of the content of the mental backgrounds, there is another source of danger. Exposition may fail because of what may be called mental parallax. The teacher and the pupil may project the same ideas against identi- cal backgrounds and yet come to different conclusions, because they view the ideas from different standpoints. The teacher may project a given idea against one part of the background, and the pupil against another. Much depends upon the point of view. Nothing is more important in Exposition than the selection of the proper point of view and the securing of the coincidence of the pupil's standpoint with the teacher's. The danger of a wrong point of view may be illus- trated from our own adult experience when reading novels. Sometimes the author takes it upon him to keep us for several chapters in the company of the vil- lain and his accomplices. Gradually we begin uncon- sciously to look at things from the villain's standpoint. There is, of course, in this case no real harm done; it is only a matter of tone. But the effect is quite per- 114 EXPOSITION AND ILLUSTRATION IN TEACHING ceptible. By and by, when some virtuous person in the story comes along and interferes with the villain's plans, we experience a distinct, if momentary, an- noyance/ It must not be supposed that the point of view is limited in its effects to the tone value of a lesson. It is equally important in Exposition that deals with the cognitive side. In the more practical parts of our teaching, in which imitation is largely reHed upon, we find the point of view of the first importance. In the various exercises in which the teacher shows the pupils by example exactly what they are to do, there is a special form of confusion that arises from difference in the point of view. This is the distinction between right and left. In ordinary Hfe it is common to find a certain amount of confusion between the right and the left. Every stranger who asks his way in a great city has abundant evidence of the existence of this con- fusion. It is always well to test each direction at every turning. For 'Hhird turning to the right" we have frequently to read 'Hhird turning to the left." This arises partly from the confusion that inevitably occurs in an appreciable percentage of cases when we are dealing with two opposed directions. We have the same confusion to a less degree between east and west on a map, but not nearly so frequently between north and south. There may be other causes for the differ- ence, but there can be little doubt that east and west are more readily confused because of their connection with the right and left of the map. The fact that the wayfarer and the policeman who is directing him usually stand facing each other may have ^ For further illustration, see Chap. X. MENTAL BACKGROUND 115 something to do with the resulting confusion. The wayfarer's left is the policeman's right. This source of error is not absent from school. The drill-master and the sewing mistress standing in front of their class and trying to illustrate some motion run serious risk of confusion. They sometimes meet the difficulty by facing the same way as the class, and doing the best they can under the circumstances. The position is awkward for both pupils and teacher, but is found to be, on the whole, the best way out of an almost impossible situation. An alternative is to stand facing the class, and then give the demonstration with reversed arms; that is, the teacher uses the right arm when he wishes the pupil to use the left, and vice versa. This naturally requires special training on the part of the teacher. CHAPTER V Suggestion in Exposition We have seen that the process of influencing another mind acquires all the interest of a mystery, and the wonder of our being able to act upon the mind of an- other at all is increased when we discover that our own minds are far from being entirely at our own disposal. Psychologists are fond of pointing out that we cannot call up ideas at will; ^ that we are more or less at the mercy of chance recall; ^ that if ^^ activity seems to be self-caused change/' ^ then we have no such thing as mental activity; * that even the inventor has to wait for ^ " Volition has no power of calling up images, but only of rejecting and selecting from those offered by spontaneous redintegration. But the rapidity with which the selection is made, owing to the familiar- ity of the ways in which spontaneous redintegration runs, gives the process of reasoning the appearance of evoking images that are fore- seen to be conformable to the purpose. There is no seeing them be- fore they are offered; there is no summoning them before they are seen." — Shadworth H. Hodgson : The Theory of Practice, Vol. I, p. 400. 2 See the whole of the section on "Command of the Thoughts" in Professor Alexander Bain's The Emotions and the Will, pp. 369-382, particularly the famous passage (pp. 376-377) in which the mind is compared to a wild beast waiting to spring upon its prey, as soon as it appears, but quite unable to hasten that appearance. 3 F. H. Bradley : Appearance and Reality, p. 64. ^ G. F. Stout : Analytical Psychology, Vol. I, p. 155 : " It seems clear that if our whole conscious existence is so constantly and thoroughly dependent on factors extraneous to it, there is no room anywhere within it for purely immanent causality. It is impossible to find any bit of mental process which is determined purely from within." 116 SUGGESTION IN EXPOSITION 117 some outside spark to touch off his loaded inteUigence.^ If we are distrustful of the evidence of the professional psychologists, we may turn to the evidence of the intel- ligent layman. The following is the view of a writer, not a professional philosopher, whose name is a house- hold word on both sides of the Atlantic. The passage occurs in a private letter to the author : — "A curious thing is the mind, certainly. It originates nothing, creates nothing, gathers all its materials from the outside, and weaves them into combinations automatically, and without any- body's help — and doesn't even invent the combinations itself, but draws the scheme from outside suggestion. . . . " It does seem a little pathetic to reflect that man's proudest pos- session — his mind — is a mere machine ; an automatic machine ; a machine which is so wholly independent of him that it will not take even a suggestion from him, let alone a command, unless it suits its humour ; that both command and suggestion, when offered, origi- nate, not on the premises, but must in all cases come from the outside ; that we can't make it stick to a subject (a sermon, for instance) if an outside suggestion of sharper interest moves it to desert ; that our pride in it must limit itself to ownership, ownership of a machine — a machine of which we are not a part, and over whose performances we have nothing that even resembles control or au- thority. It is very offensive. Any tramp that comes along may succeed in setting it in motion, but you can't. If you say to it : ' Examine this solar system, or this Darwinian Theory, or this potato,' you can only say it or think it when the inspiration has come to you from outside. And to think that Shakespeare and Watt, and we ^ F. Paulhan : Psychologie de V Invention, p. 10. Taking Newton as a typical case, Paulhan deals with the two essential elements, (1) the total results of Newton's previous thinking, and (2) the fall of the apple (or its equivalent) as the immediate cause of the discovery: "L'un indique la preparation lente de Tinvention, la tendance qui travaille a se completer, I'idee confuse cherchant 1' element qui la precisera; I'autre signale Toccasion venue, Telement nouveau qui se presente engage dans la perception (ou dans I'idee) d'oil I'esprit saura I'ab- straire, et determine la synthese nouvellC; la creation intellectuelle." 118 EXPOSITION AND ILLUSTRATION IN TEACHING others can't even combine our idea-catches on plans original with ourselves, but that even the combination-scheme must come from the outside — gathered from reading and experience. " Meantime, which is I and which is my mind f are we two or are we one? However, it is not important, for if we say, 'I will think/ neither I nor the mind originated the suggestion — it came from outside." All this may be very depressing and even ''offensive" to the ordinary man. To the teacher it is full of en- couragement. For it must be remembered that in the process described he plays the part of the tramp. He does the stimulation from the outside. Archimedes prayed for a fulcrum for his lever, and promised that if his prayer were answered he would move the world. But as he could not step off the earth, the ttoO o-rw he desired remained an aspiration. The prayer that was refused to Archimedes in the physical world has in the mental been granted to the humblest teacher. So far from complaining that we are ''prisoned in sepa- rate consciousness'^ and cannot share the consciousness of our pupils, we ought to rejoice that we are enabled to stand outside the mind-world of our pupils, and from our vantage ground there move that world. To what extent we can move it is a different question. For here we come to an aspect of the matter that restores our self-respect as human beings, though it diminishes our power as teachers. The writer just quoted is un- duly depressed. It is true that the tramp can for the moment direct our attention this way or that at his will and against ours. But the amount of attention we give depends not on the tramp, but on the nature and content of the mind he seeks to manipulate. The power of the teacher, like the power of the tramp, is SUGGESTION IN EXPOSITION 119 limited to directing the mind's attention. The deter- mination of the amount and the duration of the at- tention hes with the mind attacked. For the comfort of the teacher, and the discourage- ment of the tramp, it is well to remember that the time element is very important to the full understanding of this matter. The ordinary tramp can command im- mediate but only momentary attention to a particular topic. If he happens to know the sort of things we are interested in, and is able to talk intelligently about them, he no doubt is in a position to retain our atten- tion for quite a long while. But in doing so he ceases to form a part of mere external nature. He is no longer a mere tramp acting at haphazard. He is acting deliberately, and with a knowledge of what he is about. He is really usurping the teacher's place. Nor can we reasonably resent the exercise of the power he has over our minds. After all, it is we who have put this power into his hands. It is because we are what we are that he is able to manipulate us. To a certain extent he can make us act according to his will, but he can do this only by obeying the laws of our nature, by appealing to what he knows to be in us. He must adapt himself to us. He must respect our individuality. He must stoop to conquer. Having learnt the lesson of the tramp, it is now our business to discover what means we have at our dis- posal to manipulate effectively the mental content of another mind. Immediate recall in which an idea forces its way into consciousness by the mere strength of its accumulated presentative activity offers no difficulty, and mediate recall that takes the form of sense stimulation, as in the case of sights, smells, and 120 EXPOSITION AND ILLUSTRATION IN TEACHING sounds reestablishing a whole that formerly existed, is almost equally free from trouble. But in the ordi- nary case in which one idea recalls a whole mass we have a notable complication. For an idea usually belongs to several groups. Certain ideas, it is true, are for most minds restricted to one definite mass. They have nothing whatever to do with any other mass. It is the function of technical terms to limit such ideas to their proper mass, and thus prevent confusion. The word ohm is, I believe, restricted to the science of elec- tricity, and for the ordinary person has no connection with any other group of ideas. Even here, however, I have no doubt that in the mind of a competent elec- trician the idea of ohm will have connections with sev- eral masses.^ Speaking generally, every idea forms a part of several masses. When an idea, then, obtains admission into the field of consciousness and proceeds to introduce others by mediate recall, the question arises: Of the various masses with which it is connected, which will it favour, which will it tend to reinstate ? At first sight the obvious answer is the strongest mass; that is, the mass that is richest in elements, is best arranged, and has the greatest accumulated pre- sentative activity. Reflection shows that if this were so, then in a given mind at a given stage the same idea must always call up the same mass. But experience proves that this is not the case. It has to be observed 1 On making a testing, casual reference to the term in conversation with a distinguished physicist, Dr. WilKam Garnett, Educational Adviser to the London County Council, I found that in his mind it formed part of an historical mass, an economic mass, an educational mass, a laboratory mass, a workshop mass, a literary mass — at this point we were interrupted. SUGGESTION IN EXPOSITION 121 that we are not here deaUng with the effect of the same idea on different minds. It is easy to guess the mass that a given idea will recall in the case of chosen types of men. The idea of vine will naturally recall his green- house to the retired merchant who is fond of garden- ing, to the hon vivant his favourite wine, to the devotee the fifth chapter of St. John, to the man home from Europe the slopes of the Rhine or of Burgundy, to the art-lover certain pictures and schools of painting, to the botanist some particularly long words. All this is plain sailing. But suppose we take the case of a man who combines the six conditions. It is surely not im- possible to find an old gentleman eager about his green- houses, fond of wines and pictures, an enthusiastic amateur in botany, full of memories of happy walking tours on the continent, and withal a constant church- goer and Bible-reader. He would be a rash man who, without knowing the old gentleman, would venture to predict which of the six masses the idea of vine would call up. Even if we made his acquaintance and dis- covered which masses had the greatest power in his consciousness, we would have only a slight probability in our favour in guessing the strongest mass as the one to be recalled. On the other hand, if we learn that the idea was brought before him while walking in his garden on an autumn evening when he had just become aware of the first appearance of frost for the year, we may with more confidence foretell the direction of his ideas. Yet even under these circumstances, if the old gentle- man had during the afternoon given instructions about heating the greenhouses, and so had his mind easy on the practical side, and if the friend with whom he was walking in the garden had been recaUing escapades 122 EXPOSITION AND ILLUSTRATION IN TEACHING during their old Burgundy tramp, the chances are that the idea of vine would rouse the geographical and reminiscent mass. Before we can foretell the course of recall, we must know (1) the contents of the mind in question and the relative accumulated presentative activities of the masses; (2) the conditions under which the mediating idea is presented; (3) the actual contents of the con- sciousness immediately preceding the presentation. It is obvious that this is no mere theoretical problem. We are here dealing with the fundamental problem of Exposition. We desire a given mind to act in a given way. Our first step must be to learn the laws accord- ing to which it acts, and the conditions under which these operate. Having acquired this knowledge, we are able to interfere effectively with the course of thought in the mind of another. In ordinary life we are continually doing this, often quite unconsciously. Our every action in relation to others cannot but modify the course of thought in those others. Our very pres- ence often accomplishes such a modification without our even being aware of the existence of the person upon whose mind we have exercised an influence. For we have seen that we are all to a great extent at the mercy of external suggestion. In applying suggestion for our special purposes, then, the first consideration in presenting a new idea is to discover against which background it is likely to be projected. Apart from any special circumstances that may complicate individual cases, there are certain backgrounds that may be called the normals for cer- tain ideas. If this mark 1 3 be placed upon a black- board, we are entitled to assume that it will be projected SUGGESTION IN EXPOSITION 123 against a background of numerals and read as thirteen. But if we place the word Ethel before it and the word Jones after it, we may be certain that it will be thrown against a literal background, and read as the initial of one of the names of a person. In nearly every case there is a preferential background against which an isolated idea will be normally projected. Naturally this varies according to the content of the individual mind. But examination will show that there is a gen- eral as well as a personal preferential background for each idea. It is useful for teachers to look into these preferences both personal and general. Take the case of homonyms. If the word one is uttered, most people who hear it will project it against a numerical background, though some will connect it with win. So with the word two : the numerical back- ground prevails, though in this case there are three homonyms to choose among. It is clear that it is not mere familiarity with the word that determines the choice here, for to occurs more frequently in ordinary reading and writing than does two. Speaking generally, a substantive meaning has the preference over a tran- sitive ^ meaning. I should have been inclined to make the statement without the reservation, had it not been for the results of certain experiments that I made to verify my general impression, which was based on ordinary observation. I selected five homonyms and pronounced the sounds ^ to various classes of pupils who were instructed to write down without hesitation the word that occurred to them. I have classified the 1 See p. 43. 2 The invariable sequence of the sounds, as dictated, was : one, he, rain, by, to. 124 EXPOSITION AND ILLUSTRATION IN TEACHING results into three groups. Group I (representing the work of about 600 pupils) includes only pupils between 9 and 10; Group II (about 2500 pupils) represents the work of pupils of ages varying from 11 to 15, the ages being pretty evenly distributed; Group III (close on 500 persons) gives the reactions of under- graduate students of ages ranging from 19 to 22 : — Homonyms Group I Group II Group III Percentage Percentage Percentage One . Won . 99.1 .9 96.3 3.7 92.7 7.3 Be . Bee . Borb^ 96.6 3.4 73.6 26.4 47.1 40.0 12.9 Rain . Reign Rein . 99.4 .6 76.8 22.1 1.1 86.0 11.2 2.8 By . Buy . Bye . 96.6 1.7 1.7 69.0 25.1 5.9 52.7 38.1 9.2 Two . To. . Too . 3.7 92.6 3.7 43.4 43.4 13.2 77.2 12.6 10.2 ■r» J 1 1 '11 1 Till ^• rr> 1 / Practical teachers will have little difficulty in ac- counting for the differences in the various groups. The little children took the point of view of the dicta- tion lesson, and if they did happen to know any other form than the obvious one, preferred to stick to what ^ Groups I and II had been warned that words were expected; this accounts for the absence of the mere letters in their case. SUGGESTION IN EXPOSITION 125 they were quite sure of. The increase in the percent- age of less-known words is quite uniform as one moves up the school, and closely corresponds to the school standing of the pupils. With those who were quite free in their choice — that is, Group III — there is a steady preference for the substantive element ^ in every case but in that of By, It is this exceptional preference for a transitive element that made me qualify my general statement. There is nothing sur- prising in this preference for the substantive elements ; these form the natural resting-places of thought. Besides, the other words that do not carry a substantive element depend for their meaning on some relation, and relationship is discounted in this case by the fact that the sounds are by the conditions of the problem presented in isolation. Accordingly, non-substantive words are less likely to arise in the mind as compared with the words indicating substantive ideas, and on that account carrying an environment with them. In the case of homonyms both of which represent substantive elements, there is a preferential back- ground in favour of the more familiar. Thus, Rain clearly outstrips Reign, and that again Rein. We more naturally think of a containing vessel than of an eastern potentate when we hear the sound can (Khan). So with the word vessel that has just been used; when taken by itself, its natural background is the sea. On the other hand, with a given background we have ^ As a matter of fact, I got a higher percentage of Bee's in a post- graduate class (average age twenty-three) than I did with any of the undergraduate classes ; but the numbers are too small (43 Bee's from a class of 70 students) to permit of our drawing any satisfactory con- clusion. 126 EXPOSITION AND ILLUSTRATION IN TEACHING no hesitation at all in predicting the exact sense in which a given word will be accepted. The background, then, is of fundamental importance in suggestion. In- deed, suggestion often implies nothing more than the calling up of an appropriate background. The mind does the rest for itself. When we come to consider more exactly the nature of suggestion, we find the usual differences of opinion among psychologists. To begin with, we must keep clearly before our minds that we are concerned not with pathological cases but with normal, healthy people. There is a wholesome naturalness that is very attractive in the view supported by Mr. W. Macdougall,^ following G. Tarde, that suggestion may be regarded as a direct manifestation of the mode of behaviour called ^^imita- tion." But while many educational applications may be made on this basis, we are not much helped by it in the way of Exposition. There appears to be a very general agreement among psychologists that suggestion is ultimately based upon association, and it is probable that Mr. Macdougall's view is not inconsistent with the recognition of association as a necessary part of the development of suggestion. Wundt tells us that '^ suggestion is an association ac- companied by a concentration of consciousness on the representations engendered [angeregten] by the asso- ciation." ^ He limits the application of the term to ''only those states of consciousness excited within us which are strong enough to resist — at least for the ^ Social Psychology, p. 325. ^ As I do not have the German text by me at the moment, I quote from Keller's French translation, Hypnotisme et Suggestion (Alcan), p. 72. SUGGESTION IN EXPOSITION 127 moment — the contrary states of consciousness that tend to destroy them." When we come to educational applications of the term, we find that Professor P. Fehx Thomas prefers to define it as: ^'The inspiration of a belief, the true grounds for which escape us, which with greater or less force tends of itself to realise itself." ^ Thomas supports this view by a reference to J. M. Guyau's definition: ^Hhe introduction of a practical belief that of itself realises itself."^ Baldwin regards suggestion as ^Hhe tendency of a sensory or an ideal state to be followed by a motor state," ^ and quotes Janet's formula : ^'a motor reaction brought about by language or perception."^ This tendency towards realisation in action is very commonly implied in the use of the word suggestion; but surely it is not neces- sary to assume an impulse that issues in an overt act. We may surely suggest a line of thought as well as a line of action. If not, then suggestion is of very limited use to the mere expositor. Sometimes he desires his exposition to lead to a certain line of action, as we shall see in the chapter on the Story as Illustration. But it will frequently happen that he desires no more than mental activity. This, however, should satisfy the psychologists. It appears to satisfy Mr. Macdougall, who gives us: ^^ Suggestion is a process of communica- tion resulting in the acceptance with conviction of the communicated proposition in the absence of logically adequate grounds for its acceptance." ^ Later in the ^ La Suggestion son Role dans V Education, p. 20. 2 Education et Her Mite, p. 17. 3 Mental Development in the Child and the Race, p. 105. * Aut. Psy., p. 218. ^ Social Psychology, p. 97. 128 EXPOSITION AND ILLUSTRATION IN TEACHING chapter we shall work up to a fuller description, but in the meantime it must be understood that by suggestion we mean the manipulation of the ideas of our pupil so as to produce a predetermined result, whether in thought or action. For success in our work we must depend upon the Wundtian concentration of conscious- ness on associations. The inspiration that leads to the concentration of con- sciousness may originate from within or from without. If it comes from within, we have what is commonly called auto-suggestion. It is sometimes questioned whether auto-suggestion is possible. The lay witness quoted on page 117 would certainly deny the possibility. For him suggestion necessarily comes from without. Professor Stout would at first sight seem to be on the same side, if we identify mental activity with the power of initiative. According to him, mental activity implies that mental process is determined purely by previous mental process.^ But even if we cannot produce a single '^bit of mental process that is determined purely from within,'' it does not follow that we have no power of initiation. We may never get rid of a certain resid- uum of stimulus from without, but all that this im- plies is that we are always kept in touch with the outer world, a condition that is in itself desirable. We may be able to remain open to all manner of external sug- gestion, and yet have the power to concentrate our con- sciousness in the manner Wundt demands; and this concentration may fairly be said to determine the suc- ceeding process in consciousness. Now according to Professor S. Alexander: ^^ What I have called mental activity is, in the usual language of psychology, cona- ^ Analytical Psychology, Vol. I, p. 148. SUGGESTION IN EXPOSITION 129 tion." ^ Auto-suggestion may therefore be said to occur when we will to concentrate our consciousness on certain associations. We know what those asso- ciations are, and we have a schematic knowledge of whither they are likely to lead. We may not be able to call up directly just the ideas we desire, but we can put ourselves in the most favourable situation to en- counter them. We can go where certain classes of ideas are to be found, and we may have the full as- surance that particular ideas, of which we are at the time of beginning our quest only vaguely conscious, will by and by sort themselves out and become focal. Probably pure auto-suggestion is a very rare phenome- non; but in any case it does not directly concern us here, for the suggestion that we are interested in is that which works from without, ^'foreign suggestion,'^ as it is called by Wundt and others. A certain confusion between auto-suggestion and foreign suggestion sometimes occurs through neglecting the point of incidence of the external influence. Some- times this is so far removed from the point at which suggestion begins to act that the subject has forgotten all about the external force (if, indeed, he ever observed it as such), and regards his action or thought as self- suggested. Some writers accordingly regard the term auto-suggestion with suspicion, and one ^ at least would like to use the descriptive term pseudo-auto-sugges- tion, were it not so intolerably cumbersome. A knowledge of the working of auto-suggestion may no doubt help the expositor in his preliminary examina- tion of the mental content of his pupils. A skilful ^ Proceedings of the Aristotelian Society, 1908, p. 222. 2 M. M. Keatinge, Suggestion in Education, 1907, p. 55. 130 EXPOSITION AND ILLUSTRATION IN TEACHING observer like E. A. Poe's Dupin may be able to antici- pate the developments of a mental train self-origi- nated in another mind/ but as a matter of fact the ex- positor is almost entirely interested in trains of thought that he has himself originated. His interest is prac- tically confined to foreign suggestion, though it has to be remembered that the false auto-suggestion is in- cluded under this term. In fact, this false auto-sug- gestion is by far the most effective form. It greatly increases the power 6f suggestion, if what is really external suggestion should appear to the pupil to be auto-suggestion. The further back we can throw the incidence of the external influence the better the re- sults. Indeed, the root principle of the skilful use of suggestion is to make the mind of the pupil do as much of the work as possible. Why is it that suggestion is regarded as so much more dangerous in morals than direct statement or demonstration ? It is because sug- gestion merely starts a process; the mind carries it on, and in carrying it on is apt to think that it is acting on its own initiative. There is nothing so pleasant in mental process as self-activity,^ and if the mind can be made to feel that it is carrying out its own processes in its own way, it works with its maximum vigour. The further back the impulse from without can be thrown, the greater the chance of the pupil thinking that in a given case he is acting on his own initiative. ^^ Hus- band, voter, or pupil, they willingly follow a suggestion ^ Though even here the ingenious Dupin really owes his success to his power of anticipating the effects on the given mind of the various external stimuli to which he observes it to be exposed. 2 Compare Whately's explanation of the fact that the metaphor is more popular than the simile : " All men are more gratified at catching the resemblance for themselves than in having it pointed out to them." SUGGESTION IN EXPOSITION 131 whose origin is so well concealed that it seems to be their own." ^ A pupil who can make no headway with a difficult rider in geometry may be helped by the teacher bluntly suggesting that the solution of the problem lies in the demonstration of the equality of two angles, CDE and RPQ, which, from their position on the drawing, do not seem to have any connection with each other, and certainly do not appear to be equal. But if the teacher, by shifting about the paper on which the drawing is made, is able to place it so that the equality of the angles is likely to strike the pupil's eye, he will set up a much more vigorous reaction than by merely stating the fact. The speaker who makes his conclusion fol- low immediately on the statement j of two premises saves time, no doubt, but does not have the same effect upon his hearers as the man who gives one premise at one time and the other a little later, and does not give the conclusion at all, but takes it for granted, and uses it in a further development of his theme. This is the method of the successful popular lecturer, and cannot be so usefully applied in the case of diffi- cult subjects presented to listless pupils. Even in such adverse circumstances, however, it will be found that an obvious inference is better left to the reluctant pupil. After all, he finds it less disagreeable to draw his own obvious conclusions than to have them thrust upon him from without. From what has gone before, it will be seen that there is nothing humiliating to the pupil in being thus ma- nipulated; for when all is said, the success of the manipulation depends entirely upon the nature and ^ W. Mitchell, Structure and Growth of the Mind, p. 145. 132 EXPOSITION AND ILLUSTRATION IN TEACHING content of the pupil-mind. If the pupil responds to the external stimulus, it is because the stimulus appeals to his nature. He responds to the stimulus because it has been so prepared as to respect his individuality. All the same there is a very natural objection to a system that may be in any sense described as ^'Educa- tion by deception.'^ Dr. Johnson is very angry with those who seek to manage other people in this way. Nobody likes to realise that he is managed by other people. It is true that Mr. Keatinge tells us in his book on Suggestion that ''Boys like to be managed," ^ but he certainly knows too much about boys to mean that they like to be managed in this insidious way. What he means is probably just the opposite. Boys like to feel that they are in the hands of a master, though this, again, is a little difficult to reconcile with the stress he lays upon the " contrariant " characters of the French psychologists. These characters are said to respond in the opposite sense to that sug- gested. In the case of rigid contrariants there is no difficulty, since all the suggester has to do is to change his suggestion from the positive to the negative, and the desired positive results will follow. With the more intelligent contrariants the attempt to use sug- gestion resolves itself into a trial of wits between the suggester and the subject, each trying to find out what the other really wants. It is because of the prev- alence of this contrariant spirit that the incidence of the external suggestion has to be so carefully watched. Dr. Sidis, in fact, goes the length of regarding the con- trariant attitude in our unhypnotised state as the nor- mal one, and enunciates the law of human stubborn- ' p. 70. SUGGESTION IN EXPOSITION 133 ness: ^^ Normal suggestibility varies as indirect sugges- tion, and inversely as direct suggestion.'^ ^ An important consideration for the teacher is that suggestion works in only one way. It is positive, not negative. By suggestion we may cause another person to think or act in a particular way; we cannot directly cause him not to think or act in a particular way. The power of the little word not is greatly overrated by some teachers. They are apt to think it is more efficacious to say, ''Don't use non with the imperative in Latin; use ne," than to say, ''With the Latin imperative, when we wish to signify negation, we always use ne.'^ What we wish to impress on the pupil's mind is that ne is the proper word to use under certain circumstances. Accordingly, we ought not to bring in the word non at all. With regard to conduct, the word not is very weak as a suggestion. In the early part of last century there was a town and gown riot in Aberdeen, and the students were not having the best of it. When they were driven within their own quadrangle, and had no available weapons the old principal, disappointed at this result, came out of his house, and shaking his fist at the stu- dents, shouted that they must not pull up the palings to use as clubs. Even had the old gentleman meant the negation seriously, it would have had no effect. There was only one suggestion in his remark, though there were two possible lines of conduct. Moral questions are not, however, urgent in the use to be made of suggestion in Exposition. Our interest is rather in the manipulation of ideas than in the particu- lar ideas to be manipulated. For our purpose it may be permitted to regard suggestion as a force applied ^ Psychology of Suggestion, p. 89. 134 EXPOSITION AND ILLUSTRATION IN TEACHING from without so as to bring into action organised powers latent in the mind of another, and by utihsing our knowledge of their organisation to cause these powers to act in a direction desired by the operator. A static result is not enough. If we bring under the notice of another person some of the elements of a back- ground that we know has previously existed in his mind, the likelihood is that this background will be thereupon reinstated. If this is all, we have an ex- ample of redintegration, and the process may not be recognised by some people as suggestion at all. It may be held that suggestion must lead to a definite line of mental activity^ and not to a mere reestablishment of a previous state. As a matter of fact, the redintegra- tion of a background materially affects the direction of the immediately succeeding activity. A reasonable description of the function of suggestion in Exposition is to say that it is the bringing of external influence (by means of words, signs, pictures, models, or what not) to bear upon a given mind so as to make it ap- perceive certain ideas in a way predetermined by the suggester. Since apperception is an active process, this description should meet the case. In teaching, as opposed to education, suggestion may be regarded as the process of initiating by more or less indirect means certain mental processes that have been so organised that when once begun they are carried out automatically. It may be said to be the tapping of the forces stored up by habit, the drawing of a cheque on the paid-up mental capital. We cannot suggest a process that has never before occurred in the mind. We fail just as we have failed when we have a cheque returned to us from the bank with the legend, ''No SUGGESTION IN EXPOSITION 135 funds. '^ The crudest example of this class of didactic suggestion is to be found in the blunt giving of a few words that form part of the desired answer. Plain prompting is a kind of suggestion. Teachers some- times adopt a sort of disguised prompting that seems to give them satisfaction by saving them from the dis- grace of having to tell something that they feel in honour bound to elicit. The pupils in one case could not be persuaded to answer the question, ^^ Which English statesman was responsible for the loss of the American colonies?" The teacher encouraged them by telling them that they knew quite well if they would only think. They thought; but without success. At last the teacher had an inspiration, and asked, ^^What is the opposite of south?' ^ She was rewarded with the unanimous reply, ^'Lord North.'' ^ The teacher must not lose sight of the fact that, in addition to the deliberate and accidental suggestions of the moment, there are certain general lines of sug- gestion that work in a more permanent way. Most of these are what medical men would call benevolent, but some are malignant, and deserve special atten- tion. It is a desirable thing that when certain ideas are recalled there should at once arise by suggestion certain of the important elements implied in the con- notation of these ideas. But if only trivial elements are suggested, there arises the danger of a false concep- tion of the idea as a whole. The following extract from ^ At a drawing-room meeting of a branch of the Parents' National Education Union, a very distinguished London physician maintained that he saw nothing wrong with this example of the use of suggestion. On the contrary, he believed it to be an excellent illustration, and a capital way of bringing the young people to the point. So hard is it to be efficient in two professions. 136 EXPOSITION AND ILLUSTRATION IN TEACHING a clever novel ^ of journalistic and artistic life well illustrates this permanent suggestion of superficial ele- ments. The scene is a pubhshing office, and Mild- may, the art editor, is discussing with Martin, the literary editor, the illustrations submitted for an Egyp- tian story in a magazine. Martin begins : — "Where's the Sphinx?" *'Not mentioned in copy, '^ said Mildmay, moving a little farther behind Martin's chair. '* Where are the Pyramids ? " "The story contains no reference to the Pyramids," said Mildmay, quietly. "But — but — but — you know better than that, Mildmay ! " the editor protested, shocked and trembling. "But — but — my dear chap ! Here's a story about Egypt, and not so much as a Sphinx or a Pyramid or anything at all to suggest Egypt in it." "The chap who drew that, Martin, was on the Condor, and at Kassassin and Tel-el-Kebir." "Then he ought to know better than to send us a drawing like this:' An example of the most malignant form of the per- manent suggestion is to be found in the denominators of vulgar fractions. These have a peculiarity that is often disconcerting. They carry over to their frac- tional functions the associations of their integer con- nections, with the result that they suggest false estimates of the values of fractions. Some highly intelligent adults suffer from this permanent suggestio falsi. Most of us have come across men who believed that their club was more select than another, because ^ Little Devil Doubt: by Oliver Onions, p. 290. SUGGESTION IN EXPOSITION 137 it was necessary to have only a fifth of the balls black before rejection followed, while in the other club it required a tenth. Underlying the idea of percentage is the permanent suggestion of considerable numbers. Not infrequently illustrations in percentages convey a false impression on this account — not always unintentionally. Un- scrupulous persons quote the actual figures in all cases where they are large and imposing, and when they are unpleasantly small represent them by percentages. Grave injustice is sometimes done by the necessity of expressing certain official returns in uniform tables. A country teacher finds, for example, that her eighth grade is listed as having 100 per cent of failures in a certain examination. This reads like a complete breakdown of the school, whereas all that it means is the complete breakdown of dull John Brown, who happens to constitute the whole of the eighth grade for that year. Wherever the numbers concerned are very small, the permanent suggestion should be corrected by a statement of the actual figures. The following quatrain from Beranger's Les Gueux proved unexpectedly difficult in an examination in French : — "Vous qu'affiige la detresse, Croyez que plus d'un heros, Dans le Soulier qui le blesse, Peut regretter ses sabots." On investigation I found that the cause of the trouble was the force of the permanent suggestion of the word un. Though the students all knew, of course, that the word could mean one as well as a or an, the suggestion 138 EXPOSITION AND ILLUSTRATION IN TEACHING of an article before a noun was so overpowering that most of the pupils had to make the best they could of the article-sense, and as a consequence they rang the varia- tions on ' ' more of a hero. ' ' A similar suggestion played havoc with a class called upon to read at sight a passage which they had not before seen from the Twelfth Book of the Mneid : — '' Ardentes oculorum orbes ad moenia torsit Turbidus, eque rotis magnam respexit ad urbem." Since the class had never encountered the enclitic que in this collocation with e, the horse-suggestion was over- mastering, supported as it was by the accompanying rotis. The majority of the pupils more or less in- geniously apostrophised a hypothetical horse. It sometimes occurs that relative terms acquire a permanent suggestiveness that leads to error. Towns on the east coast acquire a suggestion of easterliness. Most people, for example, who have not had their attention specially called to the matter, are under the impression that Edinburgh is farther east than Liver- pool, which does not happen to be true. It is difficult to believe that a place ^'west of the Andes" maybe ''east of New York." The expositor must be continu- ally on his guard against these permanent suggestions. We have seen that the range of suggestion is limited to the mental content of the pupil. We can suggest to him new combinations of old elements of experience ; but we cannot suggest new experience. Further, we may be quite aware of the mental content of the pupil, and yet be unsuccessful in suggesting the proper ideas. We are familiar with the story of the American who in France did not know the word for mushrooms, but made SUGGESTION IN EXPOSITION 139 a sketch of one, and had the mortification of being offered an umbrella. Palaeographers tell us that the early iconographs and ideographs are exceedingly sug- gestive. But when tested by application to modern pupils, it is not found that they make the proper suggestion. The accompanying two drawings are re- FlG. 1. productions of early Chinese iconographs. They are merely different ways of representing the same thing. But though the pupil has thus a double chance, it becomes clear on making the experiment with a class that none of the pupils can guess what the drawings ought to suggest. Yet the palaeographer tells us that this is regarded as ''an exceedingly clever abbreviation of a pictorial representation of flame." ^ The following are regarded also as particularly suggestive, but to English pupils, at any rate, they have proved quite unintelligible. WINDOW GARDEN CONSTELUATiON Fig. 2. Accompanied by the interpretation, all these icono- graphs are intelligible enough, and the symbolism is ^ M. J. B. Silvestre: Paleographie Universelle. 140 EXPOSITION AND ILLUSTRATION IN TEACHING quite apparent, but in themselves they suggest nothing. With the two following drawings as they stand V Fig. 3. I had no success whatever in eliciting the meaning from a class of intelligent students of average age 22. But when the help was given that they pictured male human beings who stood in a certain family relationship to one another, and that the silhouettes were taken from early Chinese writing, nearly half of the class were able to respond to the suggestion, and declared them to be father and son, the suppliant attitude of the son and the protecting attitude of the father being quite what one would expect, in view of what one hears of the filial relation in China. A similar difficulty in applying Suggestion is experi- enced in attempting to reproduce in graphic form certain states of mind. No doubt Sir Charles Bell ^ and others have succeeded in representing very faithfully some of the stronger emotions. But unobservant people fre- quently misunderstand excellent graphic presentations of human facial expression, and when we deal with less skilful presentations, even intelligent readers do not always respond successfully to the suggestions offered. M. Maurice Castellar, in illustrating the practical side of expression, gives nine photographs of persons whose at- titudes and facial expressions are supposed to indicate ' Anatomy of Expression in Painting (1806). SUGGESTION IN EXPOSITION 141 certain states of mind that are set forth in the explana- tory letterpress that accompanies them in his book/ There are in all seventeen individual figures, and in only four of these did an inteUigent class of students hit upon the state of mind that was described in the ex- planatory letterpress. Still, when the letterpress was read, the students were willing to admit that the photo- graphs might be said to represent quite well what was wanted. In the use of suggestion it is obviously of importance to discover the least possible amount of energy to be used to produce a given effect. We must seek out the minimum suggestible. It is sometimes discussed how much of a given complex must be presented before the whole is suggested to the mind. There can be no quantitative answer. We have no standard. Every- thing depends upon our familiarity with the complex in question. The case is sometimes put: How much of the stag must appear above the crest of the hill before the hunter is certain that he is dealing with a stag ? Clearly, it all depends on the hunter. There are some hunters who would require to see pretty nearly the whole animal before they would be certain, while others respond to suggestion at the first appearance of the tip of the antlers. With an object for which we are not prepared (the stag-hunter is assumed to have been waiting for a stag), we cannot say which element it is that suggests the complex. It does not come to us piecemeal, but as a whole. Going along a crowded street, we find ourselves thinking of a certain friend. Suddenly we become con- scious that there he is, a few steps in front of us. The * UArt de VOrateur: Paris, 1906. 142 EXPOSITION AND ILLUSTRATION IN TEACHING thought of him has been suggested to us by the appeal of some of his physical qualities. If we are asked how we knew it was he from the mere appearance of his back, we find it difficult to say, and what we say, remember, is pure theory. The fact that it is we who have seen and recognised the man gives our evidence no more authority than that of anyone else; for the recognition was not made deliberately. Very probably the peculiarities that we select as distinguishing our friend had little to do with our recognition. We did not observe this thing and that, then reason out that it must be So-and-so; So-and-so sprang ready-made into our consciousness.^ The fact seems to be that if the different elements of a complex are firmly welded together, that complex can be suggested only as a whole. If we wish to recall to the mind of another the idea of a cow, we can do so by appealing to various senses, but so soon as the cow appears she appears as a whole; it is not a matter of one part appearing and being followed by another. Further, the cow that does appear is always the same cow for the same mind. We have all only one avail- able cow as idea. This idea may be aroused at any moment by the sight of the word cow, or by the pro- nunciation of that word, or by the lowing of some unseen animal, or by the peculiar odour that we associate with cowsheds, or by the sound of a peculiar kind of bell. However aroused, the resulting idea of cow in our mind is the same, if it be allowed to develop to its full extent. The preferred sense will no doubt have its effect in the * For an ingenious theory that does not agree with the above, see Dr. W. T. Harris's Psychologic Foundations of Education, Chaps. IX and X. SUGGESTION IN EXPOSITION 143 setting in which the cow will be found, but the cow itself will be the same, however recalled. To be sure, this ideal cow is capable of improvement. Increasing experience of cows gives the idea greater content. But such a change is gradual. It remains true that for a given stage the available mental cow is constant for the individual. For suggestion this is the only cow. Changes can be effected only by supplying means of observation. The question is sometimes raised whether we are morally justified in using suggestion in such a way that the person operated on does not know that sug- gestion is being used. Note that stress is laid on the fact that the person affected is not aware that he is the subject of suggestion. But as a matter of fact, if the person knows that suggestion is being used, it is no longer a case of suggestion. If we openly advise a man to follow a particular line of conduct, we may be said in a certain sense to make suggestions. We may even put our advice in the very form of, ^^Well, I would suggest — " But this is quite a different process from that we have been considering in this chapter, — the problem of the sanction of suggestion solvitur ambu- lando. Whether we will or no, we are continually using suggestion in the sense in which we understand it here. It is true that we may use it sometimes more, sometimes less, deliberately. But even so, the problem has to be carried a step farther back before it is worth discussing. Not the use of suggestion, but the pre- paring the mind for suggestion, is the responsible work. Suggestion is powerless to do anything but set in motion forces that are latent but none the less ex- istent. The sight of means to do ill deeds makes ill 144 EXPOSITION AND ILLUSTRATION IN TEACHING deeds done, only when the ill deeds are already within the mental content of the person tempted. Sugges- tion is powerful only in so far as it follows the laws and takes account of the content of the mind operated upon. This is the psychological explanation of the saying that to the pure all things are pure. No amount of sugges- tion can evoke from the mind ideas that are not there. Still, it cannot be denied that suggestion is capable of illegitimate applications. It is significant that the word is only now emerging from a very discreditable association in the dictionary, and even still the adjec- tive suggestive connotes a special and particularly vile class of things to be suggested. But the fact that the process is recognised as preeminently dangerous is only an argument the more for the educator seizing this specially powerful means of influencing his pupils. If it can so easily lead pupils wrong, it is surely our duty to learn how to use it on the side of right. There is no reason why evil should monopohse suggestion. From the moral standpoint, the purpose of education is really to make the pupil suggestible to certain in- fluences. The good boy is the boy who responds to suggestion in the way that his teacher regards as right. In intellectual instruction the same may be said. The boy who knows a subject really well is the boy who can be depended upon to respond loyally to suggestion in his subjects. Suggestion, while a valuable means of Exposition, is also in itself one of the goals of intellec- tual education. CHAPTER VI Conditions of Pkesentation Peesentation is one of the Five Formal Steps that are now the common property of all who deal with method in teaching. The very name Formal Steps implies two underlying assumptions. It takes for granted, in the first place, that it is possible to separate form from matter in teaching. One may be a little surprised to find in these steps that originated with Herbart this emphasis on the formal side. The usual criticism against him and his followers is that they attach undue importance to the nature of the matter to be presented to the pupil. According to them a man is what he is because he knows what he knows. When we find, then, that the Herbartians commit themselves to form at all, we may take it for certain that the matter to be taught is not neglected. The Formal Steps are a statement of the process of teaching, with the minimum reference to the nature of the matter to be taught. We can never entirely elimi- nate consideration of the subject-matter of instruction, but in the formal steps it is maintained that the separa- tion of form and matter has been carried to the ulti- mate point. By following these steps it is claimed that the teacher will best guide the pupil in the process of learning, and that with the minimum consideration of the nature of the matter to be learned. L 145 146 EXPOSITION AND ILLUSTRATION IN TEACHING The second assumption is that instruction should proceed by definite steps. Comenius warns us with some energy, and not a httle repetition, that nature never proceeds by leaps, but always by steps. Herbart has taken this warning to heart, and has systematised the steps in teaching that he believes nature would have us follow. We must not confound the need for step- wise progression with the speed with which progress is accomplished. Whatever nature may do, children certainly sometimes appear to proceed by leaps in their thinking. We often accuse them of jumping to con- clusions. But this does not show that they have not proceeded stepwise, unless by stepwise we mean that every step must be deliberately taken. The fact that I go upstairs three steps at a time does not prove that I am not going upstairs. I proceed stepwise, though I take big steps, and though I do not take every indi- vidual step that I might. The clever pupil may pass over many steps that the teacher may feel called upon to deal with in class, and the stupid pupil frequently requires additional steps to be interpolated between what may be regarded as the normal steps; but both kinds of pupils are proceeding along in the same direc- tion, covering the same course, though the one has to touch the ground much more frequently than does the other. The number of steps to be taken is one ques- tion, — and in itself a very important one, particularly in relation to class-work, — the order in which these steps have to be taken is another. It is mainly with the order of the steps that Herbart deals when he speaks of the Formal Steps. As a matter of fact. Presentation does not occur among the steps originally suggested by Herbart. These were CONDITIONS OF PRESENTATION 147 only four, named respectively, Clearness, Association, System, Method.^ These names are not very suitable as descriptions of processes, so later writers have in- troduced certain changes. The first step, that which leads to clearness in the pupil's mind, is really made up of two processes, and may therefore be regarded as a double step. The first of these processes consists of analysis: the contents of the pupil's mind must be analysed so that he may be prepared to receive the new matter. The second consists in a synthesis of the new matter with the old. The analytic step has been named preparation, and the synthetic, presentation. It may not be amiss here to emphasise the fact that prepara- tion in this sense means preparation of the pupil's mind, not the teacher's. There has been a good deal of dis- cussion about the naming of the different steps. Prob- ably the most widely accepted nomenclature of the five steps now generally recognised is. Preparation, Presentation, Association, Generalisation, and Applica- tion.^ It is sometimes held that in the first two steps we are working on the perceptual plane. Certain elements of our past experience have been combined with certain new elements; but that is all. The new wholes thus formed are yet mere units, though they are in them- selves complex. They must now be brought into rela- tion with other wholes. At this stage we are not very particular which other simple or complex units they are brought into relation with. What we want is to ^ Allgemeine Pddagogik, Book II, Chap. 2. ^ For a tabular presentation of the various classifications of the Steps by the followers of Herbart, see p. 139 of Charles de Garmo's Herbart in the Great Educators Series. 148 EXPOSITION AND ILLUSTRATION IN TEACHING bring the new unit into relation with as many other units as we have at our disposal. To bring this about, the best means is easy discussion, not in the sense of argument, but rather in that of free conversation. The teacher can work up the association of a subject in different ways. He may suggest as many similar ideas as he can, and thus encourage comparison, with a view to bringing out resemblances. Or he may call up as many contrary ideas as the experience of his pupils sup- plies, and thus lead to arrest by force of contrast within the same field. Or he may change the point of view from which the newly presented ideas are to be viewed, and thus show them up against different backgrounds. The purpose of this third formal step — called Associa- tion — is to find the true place of the new combination in the nature of things as represented by the present content of the mind in question. The associations formed at this stage may be of a purely accidental character. Naturally most of the ideas with which the newly acquired elements are compared or contrasted have something in common. But in turning over ideas in the mind, combinations of purely disparate ideas must frequently be formed. The complexes thus formed are at this stage not of primary consequence, though they should all be able to bear the test of comparison with an objective standard. What is at present aimed at is the familiarising of the new elements with their surroundings in the mind. The next step, called Generalisation, goes further. Like association it implies the grouping together of the elements of experience, but this time the grouping is no longer a matter of chance or arbitrary choice. We have to advance from mere grouping to system. CONDITIONS OF PRESENTATION 149 Association supplies us with the materials for forming concepts, but it is the work of the Generahsation step to develop the concept. This is why the step is variously named System, Concentration, and Gener- alisation. Underlying each of the elements joined to- gether at the step of Association, there is a deeper meaning than appears at the first casual glance. At the associational stage we regard this chair and that as self-existing objects. They are no doubt related to other objects inasmuch as they all coexist in time and space. But the essential oneness of all chairs is really perceived at quite an early stage. The child behaves intelligently towards a chair that he has not seen before if he has already had dealings with a few chairs, or even with only one if the new chair is not too unlike the first. But he does not realise this oneness till he has had it brought to consciousness by a process of generalisation. The process of generalisation is apparently a very complicated one, and when we reflect that it implies as a necessary preliminary the process of abstraction, we seem to have ruled it out of court altogether so far as young pupils are concerned. But as a matter of fact it is not necessary to go through the complete process of philosophical generalisation in the junior school- room. Without, of course, knowing of the existence of such a thing as the self-conscious level, the very young- est pupils generalise with ease. It is indeed the fatal ease with which they generalise that calls for such care- ful treatment. It is not the difficulty in getting them to generalise that need concern the teacher, but the difficulty of preventing them from generahsing wildly. Children begin to generalise in their nurse's arms. When a child calls a cat a bow-wow, or a dog a pussy, 150 EXPOSITION AND ILLUSTRATION IN TEACHING we say he generalises rashly. As a matter of fact he is guilty of an undistributed middle. But the appeal to reason at this stage is out of the question. Not rea- soning is wanted, but experience. To avoid rash generalisations the association step must be carefully made. Ordinary experience secures that in the great majority of cases the association step is sufficiently elaborated to prevent at least such rash generalisations as are dangerous. In actual teaching the association step can be so manipulated as to meet the special needs of the generalisation about to be made in the next step. For instance, if the teacher is afraid that the pupils are likely to fall into Sir Thomas Browne's rash generalisation and maintain that no quadruped lays eggs, the conversation at the associa- tion stage may be directed to frogs, crocodiles, and such troublesome exceptions to an otherwise unobjectionable generalisation. The value of the conversational method lies in the fact that it turns attention in a great variety of directions, and thus brings forward collocations of facts that produce healthy contradictions, and prevent generalisations that otherwise might have passed mus- ter. The greater the knowledge the teacher possesses of the content of the minds of his pupils, the more effectively can he direct the course of the association step. But even with the best-informed teacher there must always remain a vast unexplored region of the pupil-mind which can be best dealt with by the free course of conversation. Once the generalisation has been obtained, there is room for ingenuity in the way of fixing it in the memory of the pupils. The apt phrase, the epigrammatic definition, the broad general rule are all here in place. CONDITIONS OF PRESENTATION 151 Even the moral, if well expressed, may have its claims recognised on the condition that it has been worked for by the pupil. When once the moral has been worked for and expressed in the pupil's blundering language, there can be no harm in translating his halt- ing sentences into crisp English. The final step is named Application. We must not rest content with imparting facts, correlating them with facts already known, and deducing from them the underlying meaning. They remain as mental lumber till they are applied in actual life. It is one thing to know: it is quite another to be able to use knowledge. A very useful classification of our pupils may be made on this point. There are those who have much more knowledge than they can make use of, and those who could make use of much more knowledge if they had it. We are familiar in school, and perhaps more familiar still in ordinary life, with the person that can make a little knowledge go a very long way, and also with the person that is full of knowledge and cannot make any use of it. A good method of Exposition must do some- thing towards bringing these two extremes together. The earlier of the formal steps provide the knowledge in the best form : the final step sees that this knowledge gets a field on which it can be exercised. It is quite possible for the pupil to have a piece of knowledge without being at all able to use it. In several hundred classes I have held up a six-inch foun- tain pen and invited the pupils to tell me how long a half of three-quarters of it was. I had but a small percentage of answers. Yet the moment the prob- lem was stated on the blackboard as ^^Find the value of one-half of three-fourths of six inches, '' most of the 152 EXPOSITION AND ILLUSTRATION IN TEACHING pupils were indignant at being asked such an easy one.^ This final step, then, is the place for exercises of all kinds. Till the pupil has applied his knowledge in some way, it is not really knowledge to him. It is something inert, dead, useless. When the application step has been completed, the knowledge is living; fact has been turned into faculty. This may not unfitly be described as the aim of the whole series of formal steps. They have served their purpose if they have so presented and manipulated the facts that they have become faculty. Two common lines of error in the application of these Formal Steps have done much to diminish their usefulness. In the first place there is a tendency among the more matter-of-fact teachers, those who are just a little above the rule of thumb, to emphasise unduly the second step. To such ultra-practical teachers Presentation is the only step that need be seriously considered. It is the one bright gleam of light in an otherwise dark system. To present new ideas to the pupil's mind : that is teach- ing. All the other steps are more or less pedantic refinements, but Presentation is something real, some- thing that commends itself to a man of common sense. Yet as a matter of fact complete Presentation is pos- sible only in so far as all the other steps are taken. It may seem trifling to say that the mind can accept only what it has been prepared for; but the constant neglect of this commonplace is the cause of much unsuccessful teaching. The practical teacher is right in seizing upon Presentation as being the most important of ^ As illustrating the power of the mere form of expression, it is interesting to note that I got somewhat better results when I asked for o?2e-half than I did when I asked for a half. CONDITIONS OF PRESENTATION 153 the five. It may not unreasonably be maintained that the whole five steps are only different aspects of Presentation in its wide sense. But we must not con- fuse a special aspect of Presentation separated off from the others and labelled the second step, with Presenta- tion as a name for the whole process that cannot be completed without the whole five steps. The view that all teaching resolves itself into the direct giving of information, the telling the pupil something new, has produced a natural reaction which leads to error in the application of presentation, or rather by the elimination of presentation. From their studies in theory young teachers are inclined to avoid anything in the form of direct presentation. The second step, while still monopolising their atten- tion, is regarded with suspicion. What is contemp- tuously called ^' telling'^ is regarded by these young teachers as in the highest degree unintelligent and un- scientific, and they fall into ludicrous errors in their efforts to avoid it. Everything must be, in the words of their text-books, ^^ elicited from the pupil by skilful questioning. '^ They do not realise that there are two kinds of knowledge: one that must be communicated directly, and another that may be worked up from materials already in the mind. We want very badly a couple of words to keep these two kinds of know- ledge from getting mixed. I cast covetous eyes on the two words information and instruction. The first would very well represent the communication of new facts, the second might stand for the rearrangement of facts that are already known to the pupil-mind in one way, but that by being recombined may produce knowledge that was latent, if you like, but that certainly 154 EXPOSITION AND ILLUSTRATION IN TEACHING would never have come to light at that stage, but for the intermediation of the teacher. It is information to tell me the Japanese word for a tree. If I do not happen to know the word, no amount of skilful questioning will ever elicit it from me. On the other hand the generalised formulae of Euler^s Theorem ^ may be said to be implicit in the pupiPs mind before he approaches the problem. All the teacher has to do is to arrange that certain ideas shall be grouped in a particular way, and the formulae issue of themselves. The meaning of instruere, that our dealings with Caesar have familiarised us with, comes in very appositely here. The general draws up the line of battle, now making one formation, now another. In every case the men, like the ideas, are given. Information is as different from Instruction as recruiting is from drilling. The second error in the application of the Formal Steps is just the opposite of what we have been consider- ing. Instead of being tempted to overestimate one of the Steps and neglect the others, the teacher may be impelled to insist too rigidly on the individual rights of each step ; in other words, to insist pedantically on the Steps, the whole of the Steps, and nothing but the Steps. For long, students in the training colleges of Great Brit- ain arranged their Notes of Lessons in three columns, at the top of which stood the words Heads, Matter, Method, respectively. The Formal Steps came along and introduced a welcome elasticity into the form of note-making. Unfortunately the new system is rapidly settling down into the old rigidity. The student first of all makes the mistake that every lesson must exem- plify the whole of the Steps, forgetting that the teaching * See p. 34. CONDITIONS OF PRESENTATION 155 unit does not necessarily coincide with the lesson unit. It may take several lessons to complete the cycle of the Steps in respect of some important section of a subject. Besides, all the Steps are not always of the same importance. Particularly the two steps, Associa- tion and Generalisation, have very different values according to circumstances. It is no uncommon ex- perience to find a student coming to her Mistress of Method with the distressing news that she ^^ simply can't get a generalisation for this lesson." As a matter of fact, the one important thing is that a subject should be so presented that when the lesson is over the new matter shall have been worked into the very warp and woof of the mental content of the pupils. In the process the Formal Steps give very useful guidance, but that guidance must be of a general kind. Application, for example, need not be kept entirely to the end of the process. Frequently it comes in very appositely along with Association. Sometimes generalisation may force itself in before association has had time to complete its work, and sometimes there may be no need of gener- alisation at all. The Steps meet the case of the normal mind under normal conditions, but they have been formed on experience of how the mind acts, and are not something above the mind, and therefore something that the mind must obey. Most people who have had to do with the training of teachers have had experience of the complaint expressed to a class that is answering ahead of what the teacher's notes arranged for: ^'But you don't know that yetJ^ This means that the pupils have anticipated what, according to the teacher's calculations, is not due for several questions yet. In such cases it may still be desirable, for the sake of the 156 EXPOSITION AND ILLUSTRATION IN TEACHING duller members of the class, that the teacher should insist on going through what he had intended. But he must realise that there is no absolutely fixed rate at which pupils learn. All the same, it is not a matter of indifference in what order facts are presented to the pupils. Old facts that have to be recalled, and new facts that have to be pre- sented, cannot be put forward haphazard. It may be impossible to lay down any fixed law according to which presentation must always be made, for some- times one fact and sometimes another may be the best to bring forward first. Everything depends upon the mental content of the pupil, and the purpose the teacher has in view at the time. It is conceivable that the same matter might have to be presented by the teacher in quite a different order to the same class, according as the lesson is to be given at the beginning, the middle, or the end of a given session. Indeed, so important is this question of order, that as soon as we have dealt with some other of the conditions of presentation, we shall devote a couple of chapters to it. One of the most popular problems in examination papers for teachers is to work out the relation between the inductive and the deductive methods of teaching. The orthodox answer seems to be that we should begin with the inductive, and end with the deductive. But obviously the two methods cannot be dissociated in a wholesale way. No doubt in dealing with a particular part of a subject one method or the other has the prefer- ence, but when we view the field of school work as a whole, we find that there is a place for both, all through the pupil's course. Speaking generally, new matter is acquired by inductive methods and applied by deduc- CONDITIONS OF PRESENTATION 157 tive. But in the application by means of deductive methods we put ourselves in the way of learning at least some new matter as well as establishing what we have already mastered. It is not that we are inductive at the beginnings of our subjects and deductive later on. The two processes interlace even at the beginning. Some law must be laid down, some datum given even at the start. Thus in making a beginning of the teaching of Latin, we may either give a few rules of construction and a few Latin words with their meanings, and set our pupils to read a bit of Latin; or we may give our pupils a bit of Latin and tell them its general meaning, then set them to find out the meaning of the individ- ual words and to learn the meaning of case, number, person, and what not, from their experience of the way in which words behave in Latin passages. The first method would be generally described as deductive, the second as inductive.^ Obviously there are inductive and deductive elements in both. The alternation between the two methods characterises the whole course by which the boy acquires a mastery over his subject. This alternation of the different methods is paralleled by a different form of rhythm that is characteristic of Exposition. This is the alternation between the con- centration beat and the diffusion beat. Viewed from the standpoint of psychology, this is usually regarded as the rhythm of attention. But it is not a matter merely of greater and less attention, but rather a change in the area of the field within which attention is dis- tributed. There is a tendency among teachers to ^ For the Inductive Method in Latin teaching, see Bennett and Bristol's The Teaching of Latin and Greek, p. 80 ff. 158 EXPOSITION AND ILLUSTRATION IN TEACHING confound intensity of attention with the narrowness of the range within which it is exercised. A pupil may attend as intently to a wide field that he has under observation as he does in concentrating his atten- tion on the tip of a blade of grass in that field. In practice it is found that there is need for continual change of what may be called the focus of attention, and of this changing focus the expositor must take careful heed. Microscopic work affords us a useful parallel. The observer usually begins by using the low power, say 70, to get a general idea of the specimen under examination. By and by he wants to get a more detailed view of some part. Accordingly he uses a higher power and turns on perhaps the 350 objective. Some part of the new field he desires to examine in still further detail, and in consequence he uses the 700 objective. But while working with these high powers, he begins to get a distorted view of the object as a whole, and to correct this he returns to the lowest power of all. It is because of this need for continual change from one power to another that the double nozzle and the multiple nozzle are supplied to microscopes, so that with the minimum outlay of time the field of vision may be changed according to the degree of detail the observer desires. In Exposition we are continually changing our focus, and there is a certain danger that the expositor's focus may change without a corresponding change on the part of the pupil. The Expositor may be working with the 700 objective while the pupil is working with the 70. The tendency in Exposition as in microscopic work is to use the higher powers too freely, or rather too frequently, without reference to the low powers. It CONDITIONS OF PRESENTATION 159 is natural to suppose that the higher the power, the more the pupil will learn. There is the misleading '^permanent suggestion'' ^ of the word thorough. To know a thing thoroughly is generally understood to mean to know it in great detail. But it is not unusual to find a person who knows a subject in great detail and yet has no command over that subject, because he has not correlated the details to the broad general principles. In Exposition the teacher must concentrate now on this point, now on that ; but he must never fail to correlate the minute points of the concentration beat with the broad outlines of the diffusion beat. He must learn from the painter who goes close up to his canvas to peer into it and put in a delicate stroke or two only to step back a few paces so as to get the general effect. The painter is attending as keenly at the long range as he is at the short one, and doing quite as valuable work. It is obviously of the first importance that expositor and pupil should be at each moment working with the same power. This is sometimes secured by the ex- positor making use of certain conventional expressions, such as '^speaking very generally," ^Haking a wider view we find," '^coming now to details we see." Apart from specific verbal cautions, the best way to maintain identity of power is to use the material in such a way as to lead to difficulties if it is presented along with material that belongs to a different grade. This may be best illustrated by the case of history, where we have the possibility of a geographical background. Besides, we are able, by the kind of characters we introduce, to indicate the general scope of our Exposition. We may » See p. 136. 160 EXPOSITION AND ILLUSTRATION IN TEACHING have half a dozen historical manuals all of the same size, yet dealing with widely different fields of history. We may have one dealing with Ancient History, another with The History of the United States; a third may be An Epitome of the History of the World, while a fourth is The History of Partney Parish. We have here four quite different powers, and while a certain number of events are common to two or more of the volumes, the importance of those events is entirely different in the various volumes. The Renaissance might be treated in four different powers at different times, with the same advanced class. Under the 70 objective we might treat of the great movement that north of the Alps culminated in the Reformation and on the south of the Alps in Humanism. The 200 objective would give scope for a lesson on the state- ment that '' Modern History begins with the reign of Henry VII.'' Under the 500 objective there would be enough detail to work out The Effect of the Renais- sance on the Public Schools of England. ^^The Renaissance is epitomised in Erasmus" would be a theme that could be satisfactorily treated only under the 1000-power object-glass. This sliding scale of focus emphasises the relativity of everything that can be said on the subject of Expo- sition. There is a natural desire for a standard of some sort to which different cases may be referred. The ordinary thermometer with its two fixed points of departure — the freezing and boiling points of water — rouses our envy and challenges competition. In attempting to set up two points as a basis of comparison in Exposition it must be remembered that we are work- ing on the subjective side, and that therefore the points CONDITIONS OF PRESENTATION 161 will vary with each individual treated. It is com- paratively easy to standardise the expositandum, the matter of Exposition, but so soon as we enter upon the subjective consideration of that matter we must be prepared for difficulties; we must face the problem of the individual mind. It is possible to obtain two points that are fixed for any given individual at a given time. They change in the course of the pupil's development, and they do not coincide exactly in the case of different pupils at approximately the same stage of development. But they are fairly definite within the experience of the in- dividual, and the coincidence with corresponding points in pupils of the same standing is sufficiently close to give the points a certain practical value. The first may be called the Inference Point. It marks the stage in any given subject at which the pupil has to go through a process of inference, however slight. Up to this point everything in that subject that is presented to the pupil is accepted at its face value. If on glancing at the sky a man remarks, ^^I see it is going to be a fine day to-morrow, '' he is dealing with a matter that is below his Inference Point. No doubt he is really making an inference and not merely record- ing an observation. He does not see that it is going to be a fine day, but from what he sees he infers that the day is going to be fine. So closely related, however, are the facts observed and the deduction drawn from them, that the whole process is practically one. When a number of facts and deductions from facts are so welded together as to become independent organised groups, the mind requires merely to observe them in order to accept them as wholes without criticism. M 162 EXPOSITION AND ILLUSTRATION IN TEACHING Wherever this happens, the mind in question is working below its Inference Point. But when the Inference Point has been reached, it is necessary to do conscious work. Ideas have to be compared and correlated, and deliberate deductions drawn from previous expe- rience. A medical student at a clinical examination is working well above his Inference Point. The case may be an easy one, but the student is quite aware of the processes by which he reaches his conclusions. A mere glance at the patient tells the examiner all that it is necessary to know. The few perceptual impres- sions that act on the examiner's mind call up at once certain groups of ideas with which they have become in his mind so closely associated as to form one whole which represents the disease from which the patient is suffering. Obviously the Inference Point in a given subject which the student is studying is continually rising. What he has to reason out painfully at the earlier stages becomes a part of his being. As soon as a fact becomes faculty, it falls below the Inference Point. With growing experience fact after fact takes its place in complexes that remain below this point. The num- ber of groups of ideas that may be accepted at their face value is always increasing. Botanists tell us that at the tip of each twig there is what they call '' the growing point." The plant as a whole increases by the multiplication of cells according to their special fashions, by budding, fission, gemmation, or what not. But in whatever way the}^ multiply they always produce cells of exactly the same kind. Sap cells produce sap cells and no other kind, bast cells other bast cells, wood cells other wood cells, and so on all round — except at the growing point. There the CONDITIONS OF PRESENTATION 163 cells are undifferentiated and multiply so as to produce cells that are fitted to become at need sap cells, or cam- bium cells, or bast cells, or whatever other kind the plant stands specially in need of at the time. The range above the Inference Point corresponds to the growing point of the plant, is indeed the growing point of the mind. It is in this region that the nurture of the mind takes place. It would seem as if there could be no limit to the region within which inference, conscious inference, is exercised. But there is an upper limit to the region of Inference when the matter is considered from the point of view of teaching and learning. The Infer- ence Point marks the limit of paid-up mental capital. All the matter that lies below it may be called upon at a moment^s notice, with the full assurance that it will come at once and behave as it is expected to behave. It is organised almost to the automatic level. Above the Inference Point the matter on which the mind acts is still organised, though the organisation is less com- plete. In certain directions the organisation is more and more to seek, and a stage finally comes at which the subject cannot be said to be organised at all. When this stage has been reached in a given subject, we may be said to have attained the Gaping Point. It indi- cates the limit of organisation of the mental content. Up to this point everything is dealt with under definite categories. The mind is prepared to manipulate the matter in certain definite ways : it puts certain standard questions and knows how to deal with the answers. If, however, some matter is presented that the mind does not know at all how to deal with, the Gaping Point has been reached. All that the mind can do is to turn 164 EXPOSITION AND ILLUSTRATION IN TEACHING over this new matter in various ways, look at it from this point and from that; in fact, gape at it. A mineralogist has a new substance presented to him for examination. It is not sufficiently characteristic to be at once classified by inspection. Accordingly it rises above the Inference Point. He proceeds to apply this test and that according to his system. He observes its colour, its crystalline form, and its gen- eral texture. He strikes it with his hammer to hear how it rings. He breaks off a piece to discover its fracture. He pounds a small portion to get the colour of the powder. He tests its hardness compared with his standard minerals. Then he goes to his laboratory and discovers its specific gravity, its chemical compo- sition, its reaction to heat, electricity, and other things. All this while he has kept on asking certain definite questions. He knows exactly the sort of information he wants. His examination has been guided by pre- vious experience, and therefore admits of experiment. If now, in consequence of his investigations, he finds that not only does the result not fit into any system of classification with which he is acquainted, but that several of his individual results contradict each other, he has come very near the Gaping Point. It remains for him to consult his books and his friends. If as the result he finds that the mineral remains a mystery, he has actually reached the Gaping Point; for not only does he not understand the mineral, but he does not know how to go about discovering its meaning. Everyone who has had experience in working riders in geometry has had experience of the Gaping Point. At first we treat the problem in certain definite ways dictated by previous experience. This proposition CONDITIONS OF PRESENTATION 165 and that will be applied. But if after a time every- thing we know has been applied in vain, all that can be done is to gape at the problem, and wonder whether anything will turn up to suggest new lines of investi- gation. We look at our drawing upside down, side- ways, obliquely, any way that may enable us to surprise the hidden meaning; just as we do in that typical case when we are reduced to the Gaping Point by the very bad handwriting of a friend. Like the Inference Point the Gaping Point is not stationary. After many illegible letters from our friend we begin to know that certain tiny scratches mean the; that a particular wriggle always means ing, another wriggle ation, and a third ly; that what looks like e is always a; and that of is always omitted. Out of this we form a system by means of which we can pro- ceed scientifically to deal with the body of the letter, though probably at the end there will be a small por- tion still left at the Gaping Point. But if it is important to remember that our Inference and Gaping Points are continually changing, it is much more important to realise that our pupils' Points are quite different from ours. What is below the teacher's Inference Point is often at the pupils' Gaping Point. No better way of testing a teacher's skill in manipulat- ing the two Points could be found than an examination of the use he makes of the word therefore. With mat- ter below the Inference Point of his pupils the teacher is entitled to bring his therefores closely together, but in subjects within the pupils' Inference zone the teacher should see that a good deal of matter is placed between each therefore. We have all met the brilliant mathe- matician who puts down one line of algebraic symbols 166 EXPOSITION AND ILLUSTRATION IN TEACHING on the board, immediately followed by another, the only bridge from the one to the other being this ag- gravating word. Sometimes it takes pages of close ^ ^ figuring ouf before a pupil contrives to bridge the gulf that his teacher has dismissed with a therefore. CHAPTER VII Beginnings in Exposition Accepting the view that Exposition consists essen- tially in producing among the elements of the mental content of the pupil a combination that coincides with the combination existing in the mind of the teacher, it is obvious that there must be a double process of analysis before a beginning can be made. First the teacher must review his own mental content so as to discover which elements are of importance for the pres- ent purpose. Naturally all the necessary ideas can- not be called up at once; but all the salient elements will readily come into consciousness and the presenta- tive activity of all the other relevant ideas will be quickened by the presence in consciousness of those that have actually risen above the threshold. The subconsciousness is filled with ideas bearing upon the subject. The mental content of the teacher is there- fore in a favourable condition for entering upon the work of Exposition. Next we have an analysis, as far as this is possible, of the pupil's mental content in relation to the matter about to be presented to him. This process obviously corresponds to the beginning of the Preparation Step, dealt with in our last chapter. Before we can prepare the mind of the pupil we must discover which parts of its content are relevant to the subject in hand. The 167 168 EXPOSITION AND ILLUSTRATION IN TEACHING regular teacher of a class has obviously a great advan- tage in this particular. From his previous dealings with the pupils he has a very effective knowledge of the ideas which he can rely upon finding at their disposal. With a new subject, or an entirely new branch of an old sub- ject, there is a certain danger of fogginess about the available mental content. But even under such cir- cumstances the class teacher need seldom wander far afield in order to find connecting ideas. A teacher with an entirely new class has, of course, to feel his way by questions and careful observation of the effects of what- ever presentations he ventures to make. With a fairly distinct knowledge of the ideas to be conveyed to the minds of the pupils and the com- plexes to be formed in those minds, and a less clear but still adequate knowledge of the ideas and complexes at present existing in the minds of the pupils, the teacher is prepared to enter upon the next stage, which consists in comparing the pupil mental content with the teacher mental content, and selecting a starting-point for the exposition. It will be found that the two mental con- tents overlap each other to some extent. There may be a larger or a smaller common segment, but in every case where Exposition is possible there must be some elements common to the two contents. If no common element can be found. Exposition is out of the question. Very frequently with a new or difficult subject the teacher has to cast about for a little before he finds the overlap that is necessary to secure a starting-point. Sometimes, on the other hand, the two mental contents coincide. In other words the pupils have all the ele- ments necessary for the full understanding of the matter in hand, though these elements may be at pres- BEGINNINGS IN EXPOSITION 169 ent SO arranged as to give a different result from that desired by the teacher. The complexes in the pupil- mind may be all wrong as tested by an objective stand- ard; as, for example, in the first two stages of Herbert Spencer's progress towards a true theory of the colour of shadows/ In such cases the teacher's business is to break up the false complex by Confrontation and replace it by a better. But it sometimes happens that the pupil's complex is true so far as it goes, or true in certain connections, and yet there are other com- plexes to be made that are equally true, or that are true in a wider sense. In cases of this kind it is not necessary to break up the first complex. It may be temporarily analysed in order to separate out the ele- ments so that they may be built up into the new com- plex that for some reason or other the teacher regards as necessary for the pupil. But there is no need to introduce dispeace into the original combination of ideas; it may quite well coexist along with the new one, as a permanent part of the pupil-content, though the elements of which it is composed may now be cap- able of forming a totally different whole when required. For example, the complex ^^ primary colours" is made up of the elements red, blue, and yellow. But while this is found to be a true collocation so far as pigments and their manipulation are concerned, it is unsatisfac- tory when colours are treated from the standpoint of psychology. What are primary colours from the one point of view are not primary from the other. But the pupil who has had the psychological primary colours — red, violet, and green ^ — firmly grouped together ' See p. 76. 2 Cf. A Primer of Art, by the Hon. John Collier, p. 44. 170 EXPOSITION AND ILLUSTRATION IN TEACHING as the result of later exposition, need not dispense with his old pigment combination of red, blue, and yellow. Both complexes are useful, each in its place. As a matter of fact, for the ordinary needs of life, we have to adopt still a third complex, for we have even psycho- logical authority for the statement that: ^'The pri- mary colours for the mind are the four principal colours — red, yellow, green, and blue.^' ^ When we begin to study chemistry and form new combinations of ideas, these need not in any way interfere with our old com- binations as represented by such familiar phrases as '^acid drops,'' or '^ table salt." The chemist may call these ^ trivial or irregular names,'' ^ but they represent wholes that are as real as those represented by his systematic terms. The rainbow complexes found in Genesis and in lyrical poetry need not be broken up because we have formed new combinations under the heading ^'ihe refraction of light." It is seldom that the teacher needs to use up every individual element in a given complex in order to build up another complex. The much more common case is that there has to be a general analysis of the pupil- content in order to get the elements necessary to build up a desired complex. In the process, it frequently occurs that certain elements necessary for our new com- plex are found to be lacking, and must be supplied by the teacher before any progress can be looked for. In any case the beginning must be made in that part that is common to the pupil-content and the teacher- content. Frequently there are many possible starting- points within the common area, and the selection must ^ Lightner Witmer : Analytical Psychology, p. 181. ^ Dr. Edward Frankland : Lecture Notes for Chemical Students, p. 11. BEGINNINGS IN EXPOSITION 171 be determined by the purpose the teacher has in view, and the Hne he intends to follow. While it is admitted that the teacher must, at the beginning of his exposition, know definitely what his purpose is, it does not necessarily follow that this pur- pose need be communicated to the pupil. As a matter of fact at present serious consideration is given to this problem among the German teachers. There is much that is of interest in the discussions that centre in what they call the Zielangabe ; that is, the giving or state- ment of the purpose of the lesson at the very start. The term is usually closely associated with the name of Tusikon Ziller,^ though his critics spend a good deal of time in proving that the idea of stating clearly at the beginning of a lesson the purpose of that lesson is none of his invention,^ and is in fact of very venerable antiquity. The text of a sermon, the title of a book, the heading of a chapter are referred to as familiar ex- amples of the Zielangabe in ordinary life. But such cases do not always supply a parallel. Frequently the text and the title are used to whet curiosity rather than to indicate purpose. Indeed the misleadingness of titles is a cause of increasing complaint among readers. When the student of elocution punctiliously begins his recitation with '^Barbara Frietchie, a poem: by John Greenleaf Whittier," his introduction can hardly be classed as an example of the Zielangabe, ^ See his AUgemeine Padagogik, dritte Auflage, p. 162 ff. ^ While there is httle difficulty in finding examples of the applica- tion of the principle of the Zielangabe, it is not so easy to give cases in which it is deliberately applied as an educational principle. As far back as 1780, however, we find E. Ch. Trapp using in his Versuch einer Padagogik (p. 315) the term Zielsetzung, which he uses in quite the Zillerian sense. This reference I found in Karl Richter. 172 EXPOSITION AND ILLUSTRATION IN TEACHING But when in our peculiar idiom a lecturer tells us that he '^proposes'' to do certain things in the hour at his disposal, we have a genuine Zielangabe. The very fact that writers on Education have thought it worth while to use the word as a technical term, and to discuss its exact meaning and function, marks it out as indicating a noteworthy stage in the develop- ment of the theory of presentation. It indicates among other things the more or less conscious adoption of the heuristic attitude in opposition to the Socratic, as most suitable for the teacher to take up. By the very fact of recognising the necessity for the pupil to know the object of the lesson, the teacher proclaims that he ex- pects his cooperation; in other words, the activity of the pupil is assumed. He is not merely to be supplied with facts and conclusions; he is to be made to work out conclusions for himself. The goal of the lesson is set before him as something to be attained; the means of attaining it are not specifically indicated. A great part of the value of the lesson would be lost if this were not so. Misapplications of the heuristic method supply illustrations of the abuse of the Zielangabe. ^'To dis- cover the chemical composition of water ^' is a legiti- mate Ziel or aim to set before a class ; but when we find in a pupil's note book that the matter is put: ^'To find the chemical composition of H2O," we realise that something has gone wrong. On the other hand: ^'To prove that water is composed of Oxygen and Hy- drogen'' is quite a legitimate Ziel. It is clear that the Zielangabe cannot be limited to the lesson-unit. It would be inconsistent to maintain that the pupil must know definitely the purpose of each lesson, and yet be kept in ignorance of the purpose of BEGINNINGS IN EXPOSITION 173 each part of the lesson. One Ziel is not enough to guide throughout a whole lesson. There must be many inter- aims, or as Campe calls them, Zwischenziele} But if there are to be inter-aims, there must be inter-units. We must have our matter cut up into sections, at the beginning of each of which must appear an inter-aim or Zwischenziel. Each of these sections must be com- plete in itself, the completeness being determined in relation to purpose. They need not by any means be of the same length; the one condition is that they must be little wholes.^ Sometimes the Zielangahe becomes a mere matter of pedagogic routine, and exercises no real influence on the lesson. This is specially true of lessons that form part of a course. Here the whole matter dealt with by the teacher is so closely connected together that it is some- times neither possible nor desirable to cut it up even into lesson-lengths, not to speak of smaller sections. The general amount of work to be done at each class meeting must, of course, be determined, but it does not follow that the whole need be separated into purpose units of uniform magnitude. The purpose of one les- son has frequently to be carried over into the next. Accordingly, we find that sometimes the German teacher who is loyal to the theory of the Zielangahe finds him- ^ " Soil die Jugend auf demselben nicht ermiiden, so muss man ihn durch viele Zwischenziele verktirzen und angenehm machen. Auch ohne Riicksicht auf Erieichterung fiir die Jugend hat dieses Zielsetzen einen grossen Nutzen." (Campe: Allgemeine Revision des gesammten Schul- und Erziehungswesens, 8 Teil, 1787, S., 180 ff.) Quoted by- Karl Richter. 2 Amongst certain "long-known rules of teaching" Diesterweg in- cludes "Lass das Kind kleine Ganze auffassen; gieb ihm kleine Ganze." 174 EXPOSITION AND ILLUSTRATION IN TEACHING self forced to begin with the ludicrously attenuated Ziel: ''Our object in to-day ^s lesson is to see what hap- pens next/' ^ What leads to this absurdity is the notion that the Zielangdbe is a sort of pedagogic rite to be gone through at the beginning of each lesson- period. The theory of the Zielangahe does not demand that the time-unit and the purpose-unit must be iden- tical. The essential point is that the pupil should know whither he is going, so that he may cooperate with the teacher, and do his fair share of the work.^ It is true that there may be occasions when it is not only unnecessary but unprofitable for the pupil to be told the exact purpose of a lesson. In many lessons given on the Socratic Method, for example, the very essence of the teaching is the unexpectedness with which certain conclusions are reached. It is well that the pupil should not know that the purpose ^ " Ja nach einer Bemerkung in den ' Erlauterungen zum Jahrbuche von 1883/ die also nach Zillers Tode erschienen sind, hat Ziller spa- ter selber stillschweigend zugelassen, dass das Thema z. B. fiir eine Geschichtsstunde auch so formuliert werden konne: 'Wir wollen sehen, wie es weiter geht.'" Karl Richter: Die Herbart Zillerschen Formalen Stufen, p. 131. 2 " Nicht nur der Lehrer muss wissen, was er in dieser Stunde er- reichen will, sondern auch die Schiller sollen es wissen, dass ein be- stimmtes Ziel gesteckt ist, iiber das sie am Schlusse der Stunde miissen Rechenschaft geben konnen. Dadurch wird der Gedanken- gang konzentriert, es wird das Gefiihl der Erwartung und Spannung, die Lust und Freude zur Losung der gestellten Aufgabe erregt. Fehlt Jenes Ziel, so wird der Schiller wie ein Blinder mit verbundenen Augen vom Lehrer gefilhrt, und eine eigene Willensanstrengung ist un- moglich. Die Schiller miissen am Schlusse der Stunde eine bestimrate Antwort auf die Frage geben konnen : Was habt ihr heute gelernt ? Wovon habe ich gesprochen ? Schlimm ist es wenn sie keine Ant- wort geben konnen, oder vielleicht sagen : Wir haben allerlei gehabt." Ferdinand Leutz : Lehrbuch der Erziehung und des Unterrichts, 4 Au- flage, Zweiter Teil, p. 40. BEGINNINGS IN EXPOSITION 175 of the lesson is to make him aware of certain gaps in his knowledge. In the Socratic Method the pupil is working towards two ends: one that he knows he is working towards, and one that is known only to the teacher. It does not follow that pupil and teacher are working at cross purposes. We are deahng here with the educational effects, and these are best produced without the pupil's conscious cooperation. His coopera tion is, of course, essential, but the teacher loses his position of advantage as an external influence if he explains to the pupil the educational effect to be pro- duced, and urges him to assist in being educated. Even in matters of mere knowledge it may sometimes be an advantage to omit a statement of the Ziel. It is largely a matter of the distribution of interest. When the Ziel is given, the interest Hes in the means of attaining it; when it is withheld, the interest lies in the process itself, particularly in relation to the suspense as to what it is going to lead up to. This contrast between the place of the Zielangahe in the Heuristic and the Socratic Method will, if carefully investigated, lead to the conclusion that the real dif- ference lies in the magnitude of the purpose unit. No teacher would suggest that his pupils should be kept entirely in the dark with regard to the purpose of the work he is engaged in. The question always is: How wide an outlook is it advisable to offer them? With advanced pupils ^ we can give much wider aims than those that apply to each lesson as it comes round. It is probable that teachers are too easily content with ^ Campe tells us: "So wie die Jugend heranwachst, kann man die Hauptziele nach Monaten, Viertel-und halben Jahren stecken." Allgemeine Revision as above. 176 EXPOSITION AND ILLUSTRATION IN TEACHING the mere Zwischenziele : it is certain that the pupils are. So long as the pupil is allowed to go on dealing with each step as an independent unit, he is usually quite content to work away without looking for any wider or deeper meaning. Pisgah views are not to his liking, and he will certainly not climb the mountain unless under pressure, or at least under encourage- ment. One of the redeeming features of school ex- aminations is that they bring into occasional promi- nence the main aims (Hauptziele), that give meaning to the Zwischenziele with which the pupil is too apt to be content. Teachers of arithmetic are now laying great stress on the need for clearly imaged ends in the minds of the pupils before beginning to work out problems. The pupil must not be left merely to multiply and divide in the hope that somehow the answer will come out. The following extract gives a graphic account of a state of mind that is too common in our schools. It is taken from a school story called The Rickerton Medaly which is the work of a practical teacher. The scene is a a class room in an elementary school. Mr. Leckie, the teacher of the class (Standard VI, average age about 13), propounds a problem in arithmetic: — " If 7 and 2 make 10, what will 12 and 6 make ? " A look of dismay passed over the seventy-odd faces as this apparently meaningless question was read. Everybody knew that 7 and 2 didn't make 10, so that was nonsense. But even if it had been sense, what was the use of it ? For everybody knew that 12 and 6 make 18 — nobody needed the help of 7 and 2 to find that out. Nobody knew exactly how to treat this strange problem. Fat John Thomson from the foot of the class raised his hand, and when asked what he wanted, said : — " Please, sir, what rule is it ? " BEGINNINGS IN EXPOSITION 177 Mr. Leckie smiled as he answered : — "You must find out for yourself, John; what rule do you think it is, now ? " But John had nothing to say to such foohshness. "What's the the use of giving a fellow a count ^ and not telling him the rule ? " — that's what John thought. But as it was a heinous sin in Standard VI to have "nothing on your slate," John proceeded to put down various figures and dots, and then went on. to divide and multiply them time about. He first multiplied 7 by 2 and got 14. Then, dividing by 10, he got If. But he didn't like the look of this. He hated fractions. Besides, he knew from bitter experience that whenever he had frac- tions in his answer he was wrong. So he multiphed 14 by 10 this time, and got 140, which certainly looked much better, and caused less trouble. He thought that 12 ought to come out of 140; they both looked nice, easy, good-natured numbers. But when he found that the answer was 11 and 8 over, he knew that he had not yet hit upon the right tack; for remainders are just as fatal in answers as fractions. At least, that was John's experience. Accordingly, he rubbed out this false move into division, and fell back upon multiphcation. When he had multiplied 140 by 12, he found the answer 1680, which seemed to him a fine, big, sensible sort of answer. Then he began to wonder whether division was going to work this time. As he proceeded to divide by 6, his eyes gleamed with tri- umph. "Six into 48, 8 an' nothin' over, — 2-8-0 an' no remainder. I've got it ! " Here poor John fell back in his seat, folded his arms, and waited patiently till his less fortunate fellows had finished. James ^ knew from the "if" at the beginning of the question that it must be proportion ; and since there were five terms, it must be ^ Scotice : any kind of arithmetical exercise in school work. ' The clever boy of the class. N 178 EXPOSITION AND ILLUSTRATION IN TEACHING compound proportion. That was all plain enough, so he started, following his rule. " If 7 gives 10, what wiU 2 give ? — less." Then he put down 7 :2: :10: "Then if 12 gives 10, what will 6 give? — again less." So he put down this time 12:6 Then he went on loyally to follow his rule: multiplied all the second and third terms together, and duly divided by the product of the first two terms. This gave the very unpromising answer If. He did not at all see how 12 and 6 could make If. But that wasn't his lookout. Let the rule see to that. The problem of beginning is often complicated by the fact that it is not recognised as a problem. It seems so easy. There are so many possible beginnings that it would appear that one could hardly fail to hit upon something that will exactly meet the case. Some teachers, in fact, deliberately minimise the importance of the beginning. Too much time is spent over con- siderations of beginning, they maintain, and advise their pupils to get to work anyhow. The important thing, they say, is to get a start. It does not matter how you begin, so long as you get begun. There is perhaps a certain justification for all this impatience. An experienced editor, in engaging a brilliant young man to assist him in preparing for the press manu- scripts that had been accepted for his magazine, gave this advice: ''In many cases, particularly with essays, you will find it a good plan to cut out the first paragraph. The author gets down to business in the second. You will, of course, be prepared to have all the authors complain that the first paragraph is the best in the essay, the fact being that they have given so much time BEGINNINGS IN EXPOSITION 179 and care to the beginning that they have lost all sense of its true value." What the editor objected to here is not so much beginnings as ^^introductions.'' No one is more tired of formal openings than the experienced trainer of teachers. He of all men is fully convinced that introductions are excellent things to omit. But the lesson must be begun all the same, and the problem of the beginning remains. It may not be a logically justifiable statement that there are many degrees of beginning, but it contains a definite meaning. We have indeed the whole range from the beginning of an entirely new subject to the begin- ning of a new sentence. There is a certain rhythm in teaching, and each new beat in this rhythm implies a new beginning. Obviously, the longer the beat the more important the beginning. It is, however, only at the bigger divisions of a subject that any serious prob- lem arises. At the subordinate divisions the begin- ning is practically determined by what has gone before. In dealing with a subject, the teacher acquires a swing that carries him on over all the smaller breaks in con- tinuity. A lesson in the middle of a course has to a certain extent determined its own beginning with regard at least to matter, and often with regard to form as well, inasmuch as the reaction between teacher and pupil throughout the course has led to the development of the teacher- and pupil-content in such a way as to estabhsh a more or less inevitable interaction between them. But the very beginning of a new subject, and especially when the teacher is new to his class, presents a very different problem. It involves the breaking in somewhere or other into the pupils' circle of thought, and it is often of material consequence 180 EXPOSITION AND ILLUSTRATION IN TEACHING where this irruption takes place. The subject-matter may be approached from many different points, and nothing but a fair knowledge of the pupils' mental content can determine which it is best to select. That this difficulty in beginning is not an imaginary one originating in an excess of refinement in method is proved by the trouble often experienced in ordinary life when we set about explaining anything that is in the least complicated. We often toss about for a while, seeking the most suitable starting-point. Sometimes, indeed, we actually put our difficulty into words, and ask: ''Well, now, where shall I begin?" And it is to be noticed that we do this even in what we are apt to regard as the simplest case, that is, in the telling of a story. When a Frenchman does not follow a confused story as it is being told to him, he is apt to say to the story-teller: '' Si tu voulois commencer par le commence- ment." The reference is to Anthony Hamilton,^ the brilliant Irish writer of French fairy tales. In one of Hamilton's stories Moulineau the giant calls upon the ram (who, of course, is one of the speaking kind) to cheer him up by telling some pleasant tale : — " The ram, after having meditated for a little, began in this way : — 'After the wounds of the white fox, the Queen had not failed to pay him a visit.' 'Ram, my friend/ said the giant, interrupting him, 'I understand nothing of all that. If you would begin at the beginning, you would give me pleasure ; for all those tales that begin in the middle only confuse the imagination.' 'Very well,' said the ram; 'I consent, against the custom, to put everything in its place ; accordingly the beginning of my story [histoire] will stand at the head of my narrative [recit].' " ' Died 1720. BEGINNINGS IN EXPOSITION 181 Here Moulineau takes it for granted that it is a self- evident proposition that we should always begin at what he calls the beginning. No doubt there are intellects for which this rectilineal arrangement is the best possible. Moulineau would have been at home in China, where, we are told, the drama begins with the birth of the hero, and goes straight on. Even in Eng- land there is room for the orthographic story of the Robinson Crusoe type: — "I was born in the year 1632, in the city of York, of a good family, though not of that country, my father being a foreigner of Bremen, who settled first at Hull . . .," etc. but there is also a place for the Iliad, Paradise Lost, and the modern complicated novel that begins in the middle of the plot. Yet Moulineau is right in insisting upon beginning at the beginning : his mistake lies in suppos- ing that chronology is the only element that determines what a beginning is. Time is, of course, of fundamental importance in thinking, but it must not be allowed to dominate the expositor in his selection of material. He must be guided in every case by the purpose he has in view. In dealing with Moulineau it is clear that the proper order is chronological; in dealing with a jaded pubhc, tired of the ordinary and in search of excitement, the ram's successors are entitled to neglect the chrono- logical order, and to adopt the chronological middle or end for their purposive beginning. The expositor wishes to produce a certain arrangement of ideas in the mind of another: the beginning that lends itself best to the production of this arrangement is the best. The teacher in an English school begins, for instance, with a blackboard full of figures from the Board of 182 EXPOSITION AND ILLUSTRATION IN TEACHING Trade returns for the past ten years, from which the pupils are invited to discover which are Britain^s best customers in the matter of buying her goods. Various ups and downs are noticed, and causes sug- gested. One sudden fall is unaccounted for. Tow- ards the end of 1906 Italy began to buy a good deal less from Britain. The fall is not temporary, for there has been no corresponding rise since. Italy is not hostile to Britain: rather the contrary. The cause must be sought elsewhere. More figures are sub- mitted, from which it appears that what Britain has lost Germany has gained. But why this sudden change ? Germany is no nearer Italy than it was before; there has been no quarrel with British goods; the Germans may be better at pushing goods, but there was no sudden increase in their superiority at that time. Gradually the search is narrowed down to something peculiar that belonged to that year, and the opening of the Simplon Tunnel in May, 1906, is suggested. Since this beginning occurs in a lesson in commercial geography, the tunnel is approached from the proper point. Moulineau would have insisted upon start- ing with the tunnel. A problem of this kind is often an excellent way of beginning an exposition. Instead of starting straight- way with the subject of the difference between the development of the Feudal System in England and in France, the problem might be suggested : Why are there hedgerows in England and not in France ? In answer- ing this interesting question all the essential points of difference emerge, and the incentive of a well-defined purpose is maintained throughout the lesson. The problem of beginning is important not merely BEGINNINGS IN EXPOSITION 183 because of its relation to the interest aroused, but also because it practically fixes the order in which the lesson must afterwards proceed. In a lesson on the development of the butterfly, we may begin with the egg, or with the imago, with the grub, or with the chrysalis. If we begin with the egg, we would satisfy Moulineau, and follow the development up- wards. If we begin with the imago, we follow the development backwards. In both cases we have no break in the time series. If, now, the start is made with either of the intermediate states, there must be a double progress, one part forwards, the other back- wards. At first sight it would appear that there is only one way of beginning this exposition properly. The egg seems the only natural beginning. But most pupils have seen a butterfly, while comparatively few have seen a butterfly^s eggs. In most cases, though the egg would form a part of the teacher's mental content, it would not form a part of the pupil's, and therefore would not prove a suitable commencing element. On the other hand, if the teacher possesses specimens of the eggs of butterflies, he might quite well start with the idea of egg in general, which, of course, forms a com- mon element in teacher- and pupil-content, and then present the specimen eggs as new matter to be correlated with the old. Out of the common elements it is always the teacher's business to select those which will lead to the desired result with the minimum expenditure of time and energy. In certain subjects the difficulty of choos- ing the proper elements is much greater than in others. In mathematics, for example, there is much less liberty of choice than in, say, history and geography. The connection among the different points in the subject 184 EXPOSITION AND ILLUSTRATION IN TEACHING is SO close that it is impossible to present them in any but one order. Yet even in mathematics there is great diversity of opinion as to the order in which certain elements should be presented. At what stage, for example, should the idea of an equation be introduced in the teaching of algebra ? Should decimal or vulgar fractions come first in the teaching of arithmetic? Again, the whole of the propaganda for what is called the new geometry is an exemplification of the impor- tance placed on the beginnings as determining the after processes. As there are many beginnings throughout the course of a lesson, so there are many endings. Every beginning implies an ending of the same degree of im- portance as itself. Naturally the ending of a lesson or a section has to be as carefully considered as the begin- ning. In point of fact, they must be considered together. Indeed it may be said that the end determines the begin- ning. The principle of the Zielangabe demands that the pupil shall know the end, at least in the sense of the aim or purpose. But the teacher must know the end also in the sense of the termination. He must know what his process is going to accomplish, and he must also know how his process is to terminate. He must know the end from the beginning, and further, he must correlate the beginning to the end. It is true that much may happen of a very unexpected character between the beginning and the end. It is in this inter- mediate period between the beginning and the end that the teacher^s individuality has most scope; but in order that he may make the best use of his opportunities, it is essential that at the preparation stage he should determine his beginning and ending. BEGINNINGS IN EXPOSITION 185 There is nothing to prevent the teacher making the beginning that he fixes upon as best. The plan that he resolves upon in his study he can at once proceed to carry out in the class room. With the ending it is different. Too frequently the actual ending has little resemblance to the ending that had been projected. Sometimes in the course of a lesson the teacher dis- covers that he has made a mistake in his private review before the lesson. Occasionally it is a mistake in the subject-matter that he did not notice in his preparation, and that is only brought out in the process of teaching. More usually the trouble arises from the discovery that his pupils know less or more of the subject than he had given them credit for. In such cases it is essential that the predetermined end should be modified. But in all other cases it is highly desirable that the selected end should be reached. The teacher must be very elastic in his arrangements for meeting unexpected develop- ments in the course of the lesson, but he should be tenacious in his efforts to reach the predetermined stopping-place. Unforeseen difficulties may arise to disturb the prearranged distribution of time, and the teacher may thus not get within reasonable distance of the point at which he had resolved to close. This con- tingency should be provided for by selecting beforehand a series of possible endings throughout the course of the lesson, — the attainment of each Zwischenziel should be a possible ending, — and by cultivating a very tender conscience with regard to using them. The teacher should feel that every time he has to adopt one of those alternative endings he has made a blunder in his calculations. On the other hand, to persist doggedly in getting to a prearranged end, whether 186 EXPOSITION AND ILLUSTRATION IN TEACHING the pupils are able to follow or not, is worse than a blunder. In any case the point at which the lesson actually stops should be recognised by both teacher and pupil as a natural end. It must not be a mere cessation of a process, as in the case of a street organ that stops opera- tions in the middle of an air. Nor must the teacher merely allow himself to run down like a clock that grad- ually ticks more and more feebly till at last it stops. Nor must the end be reached by mechanical stages that the onlooker can anticipate. The mannerisms by which some teachers let it be understood that the end is approaching, frequently indicate rather the termina- tion of the hour than the end of the lesson. The true ending is felt to be an ending as soon as it is reached. At the end of a discourse it used to be the custom in France for the speaker to add the words, J^ai dit. At the end of an address arranged in the admirable form for which French speakers are noted, the words came as the inevitable conclusion. They were felt to be the only words that would not have been irrelevant at the point at which they were introduced. In every case the ending should find a natural place in the rhythm of interest. The predominant feeling at the ending points should be one of satisfied interest; but this satisfaction should be unstable. The interest in the particular section should be exhausted, but the interest in the wider whole of which the section is a part should be maintained. The interest to be carried forward should belong to the section that is to come, not to that with which the lesson finished. CHAPTER VIII Order of Presentation It is one thing to acquire knowledge for oneself; it is quite another to communicate that knowledge. When we say we have mastered a subject, we mean that we have not only amassed all the available matter, but have rearranged that matter so as to have it in an organised form, in which each element occupies its true relation to all the others. Teachers are apt to rest satisfied when they have reduced their mental content to this logical order, and to think that they have nothing further to do than to present the matter in the order to which they have reduced it. Many teachers will admit having had something like the following experience. When preparing for the first time a scheme for a sys- tematic course in a certain subject, the thought forces itself into the mind: ^'Why wasn't I taught this sub- ject in this logical way ? When I was a pupil, the matter always appeared to me as a thing of shreds and patches : I shall take care that my pupils are taught differently.'^ The cause of the trouble is that we are confusing know- ledge in its ripe and in its green state. The logical point of view necessarily implies a complete knowledge of the field to be covered. It represents the view that we may take of an experience that we have had, which is never quite the same thing as the anticipation of the experience we are going to have. The learner is feehng 187 188 EXPOSITION AND ILLUSTRATION IN TEACHING his way into a region that is already well known to the teacher, who must, therefore, modify his presentation to meet the needs of the pupil rather than to satisfy the demands of logical sequence. It is natural that we should suppose that logic ought to determine for us the order in which matter should be presented; but experience has shown teachers that they must not depend too much on logical arrangement in presenting matter to young people. Even when dealing with grown-up, educated people, it is necessary to be on our guard against a too rigid adherence to logical pres- entation. In describing to teachers how the struc- ture of animals should be taught, Sir Archibald Geikie interrupts himself to remark : — 'Tor the sake of logical sequence, I have placed the consideration of form before that of function. But in actual practice it will not be always possible, even were it desirable, to separate these two subjects sharply from each other. " ^ It may be logical to complete an account of the struc- ture of an animal before saying a word about the functions of the various parts, but it is certainly not the best mode of exposition. The head of a London training college, in dealing with grammar, tells us : — " Obviously the psychological order (and that is the order to be followed in school-teaching) is (1) the acquirement of the use of language ; (2) the analytical investigation of language — that is, grammar. But, it might be argued, grammar deals with the presuppositions of language, and therefore the logical order is (1) grammar ; (2) the acquirement of language. Teachers have^ how- ever, discovered as the result of much unproductive labour that it is impossible to adopt the logical order in teaching children. When, indeed, the pupil has reached a certain stage in the acquirement of * The Teaching of Geography, p. 109. ORDER OF PRESENTATION 189 the use of language, then grammar may be a means of helping him to increase his mastery; but it is impossible to begin that way.'' ^ Still, it must not be supposed that even in dealing with young people there is something objectionable in logical sequence in itself. On the contrary, the logical sequence represents the ideal order which must be followed as far as that is possible. Every deviation is a concession to human weakness. For the teacher, the logical sequence of the facts to be dealt with is the beginning of the process of Exposition : for the pupil, it is the end. In his essay on the Philosophy of Style, Herbert Spencer seeks for a general principle underlying all the recog- nised rules for verbal expression, and finds it in ^Hhe importance of economising the reader's or hearer's attention.'' ^ Every time we use the wrong word or the wrong order of words, we cause certain wrong combina- tions to be formed in the mind of the pupil, and the necessary correction of these errors is sheer waste of time and energy. Spencer does not go into the mot propre theory that for a given place in a given sentence there is one word, and one word only, that will perfectly meet the case; but he comes near to maintaining an equally rigid principle for the order of words in a sen- tence: '^We have a priori reasons for believing that in every sentence there is some one order of words more effective than any other." ^ Even when a sentence is grammatically correct and is ultimately intelligible, it may have its parts so badly arranged that an altogether disproportionate amount ^ L. Brackenbury : The Teaching of Grammar, p. 7. 2 Essays, Stereotyped Edition, Vol. II, p. 11. 3 75^-^^^ p, 16, 190 EXPOSITION AND ILLUSTRATION IN TEACHING of time and effort must be expended over it. Both of the following sentences by English authoresses of some distinction exemplify bad order of presentation : — " I am sure, too, the reputed Hibernian has afforded much inno- cent amusement who, on making his first journey, asks why, if it be true that the last carriage is, as he has been told, dangerous to travel in, it is not taken off.'' "The crowd of faces congregated round her, and from its midst emerged the one she shunned supremely ; his whose, while her will remained, she must with the last remnant of it, shut away." It is probable that Spencer carries his theory into too great detail. For example, he prefers the English order ''black horse '^ to the French '' cheval noir.''^ In all probability in both cases the two words are simulta- neously received by the mind, and the figure of the animal occurs as accurately to the Frenchman as to the Englishman. For it has to be noted that Spencer in his essay takes it for granted that all thinking is figurative. His view is that if we mention the horse first we at once make a picture of it, and since we are not guided as to its colour we are more likely to make it brown than black, because there are more brown horses than black ones. When the word black occurs, we have to recolour our mental horse, and in this way lose time and waste energy. Spencer should have gone farther with his contrast between the black horse and the cheval noir, for the French have certain very definite customs in the matter of the order of their adjectives. The underlying prin- ciple appears to be that if the quality is inherent in the substantive, the adjective should precede; while if it is an accidental quality, as colour or nationality, it should follow. " Voire aimable fille " is a compliment ORDER OF PRESENTATION 191 not only to your daughter but to you and her sisters. ^'Votrefille aimahW^ is still a compliment to this par- ticular daughter, but at the expense of her sisters and of yourself — it is no longer taken for granted that ami- ability is innate in your family. The French have thus a means denied to us of conveying a distinction, and it is not likely to be maintained that French thinking is retarded in consequence. Whatever may be true about the possibility of simul- taneously grasping the meaning of a substantive and its adjectives, there can be no doubt that when we come to larger divisions of thought process, great differences occur according to the order in which elements are presented. The total effect of a presentation is not necessarily the same in two exactly similar cases be- cause precisely the same elements have been used in each. The order in which the elements have been presented counts for something, frequently for a great deal. An excellent example is to be found in the loss of cumulative effect when a series of elements is pre- sented without regard to their degree of stimulating power. A passage may exemplify the rhetorical figure of climax, or may convey merely an unpleasant effect of mental jolting, according as the elements are arranged in regular order of stimulus or '^just as they come.'' It may be suggested that the effect here is rather aesthetic than intellectual, and it may be asked: Is it not possible that the same intellectual effect may be secured by quite different orders of presentation? As a matter of fact, it may be urged, we have practically all of us gained our present knowledge and opinions by different lines of study and experience. No two of us have had our mental content presented to us in 192 EXPOSITION AND ILLUSTRATION IN TEACHING quite the same order. This has to be admitted. But on the other hand, it will hardly be denied that, however our knowledge has been acquired, no two among us have quite the same mental content, and even if it were possible that two of us should turn out to have the same mental content so far as matter goes, the arrange- ment of that matter would be almost certainly different. Mathematicians are usually quite willing to spare a little time to show the excessively remote chances of mental coincidences of this kind. We are what we are, not merely because we know what we know, but because we possess our knowledge in a particular way. It is true that even if we have been badly taught we may have corrected the errors into which we have fallen, and have now reached the same stage as others who have been better taught, and have therefore reached their present stage with less difficulty. But it is at least arguable that in the process of being badly taught the pupil has received permanent injury, as well as suffered loss of time and energy. It may be that our present state of knowledge in any subject may bear definite traces of the process by which that knowledge has been acquired. In one of his Essays, Grant Allen tells us that at every moment we are shutting out one- half of the possibilities of life, that every choice we make is a dichotomy. The accompanying diagram may re- present Grant Allen's view. Starting from A we may reach K by Si series of four dichotomies. We may ob- viously pass from A to i^ in various ways. We may take the upper passage ABGHK, or the lower ACFEK; or we may take a zigzag course ABDHK or ABDEK. The important point for us to consider is whether the result when K is reached is the same in all cases, nor ORDER OF PRESENTATION 193 matter what the route has been. The conclusion seems inevitable that the route does modify the result. Take the German possess! ves ihr = her, and sein = his. To a pupil who approaches this matter from the standpoint of English there need never be any confusion between ihr and sein; the gender of the substantive possessed only affects the words to the extent of modifying the termination. To an English-speaking pupil, however, who approaches the subject through French there is frequently a long period of struggle with the confusion that results from the fact that in French sa may mean Msj and son may mean her. Experience shows that in book-learned German this confusion persists long after a clear statement of the facts has been thoroughly understood by the pupil. He has an intellectual per- ception of the facts of the case quite as clear as that of his fellow who has made the English approach, but he does not know them in quite the same way. 194 EXPOSITION AND ILLUSTRATION IN TEACHING The very adjective used above, ^'book-learned/' in itself either begs the question or proves that a fact learned from a book is not quite the same thing as the same fact learned in some other way. The balance certainly appears to incline towards the difference of the result according to the means of obtaining it. Pupils who have suffered from bad exposition, nearly always retain a certain lack of confidence in the use of matter that has been thus presented to them.^ They are apt to bring in as part of the completed whole certain com- binations that occurred where they had no right to occur in the original process of presentation. They were explained away, no doubt, at a later stage, but they have left their traces. Even in simple narrative the order of presentation is important to a proper understanding of the point to be brought out. Here the mere time order in which the events occurred is usually sufficient to determine the order of presentation. When the careless story-teller breaks in upon his narrative with the apologetic: ''Oh, by the by, I forgot to tell you — " it means that he has bungled his presentation. It does not as a rule mean that he has forgotten some unimportant detail, but that he has suddenly found that he has omitted an important section without which the whole is meaningless. He has accordingly to break the current of interest, and generally succeeds in confusing the impression on the listener's mind. This does not mean that the listener does not catch the point of the story, but that the point * The ihr and sein difficulty may entirely disappear under the in- fluence of constant use of German, but let a discussion arise about a particular case and the old doubt will sap the confidence of the victim of confused presentation. ORDER OF PRESENTATION 195 has been blunted. In order to illustrate the fact that illiterate people may form a just estimate of the ^'values" of a picture, a lecturer told the story of the English lady who was accompanied by her maid while visiting a certain Italian church in which there was a very fine picture of the Flight into Egypt. Talking down to the intelligence of her maid, the lady asked if she did not greatly admire the oleanders in the picture. The reply contained an unintentional reproof: ^'I wasn't thinkin' o' the oleanders, but o' the 'oly family." Unfortunately in using the illustration the lecturer began the maid's reply, '^I wasn't thinking o' the 'oly family, but — " Though he caught himself up at once and reversed the order, the point was ruined. No amount of emphatic explanation could produce the clear-cut effect the illustration had produced on previous occasions. The audience understood the point all right, but its effect was gone. The general line of presentation is practically deter- mined by the beginning, since this in its turn is deter- mined by the purpose of the exposition, as was shown in the last chapter. We are assumed, therefore, to know (1) the purpose we have in view, (2) the part of the pupil's mental content that is relevant, and (3) the new material we propose to use. The question now arises : In what order is the presentation to be made ? It may be objected that it is hopeless to discuss such a question apart from the nature of the particular matter, as this would seem to court error by omitting the most important element. But while the details of presentation must always be determined by the needs of each particular case, there is a certain body of general principles that are applicable to all cases, and give us 196 EXPOSITION AND ILLUSTRATION IN TEACHING some guidance in dealing with each new set of circum- stances. It is true that these principles are of a some- what general nature, and indeed they are sometimes so vague as to amount to little more than pious aspirations, '' Instruct so that the matter given shall be learned" does not seem to carry us very far; nor does it greatly improve matters to add — '' and so that its culture content may exercise its due influence." ^ But certain principles that bear directly on the order of presentation have recommended themselves to teachers generally, and have obtained very wide rec- ognition, perhaps because of their very obviousness. The same interest in presentation that led Herbert Spencer to seek for the underlying principle of literary expression induced him to set forth in his little book on Education ^ those fundamental principles. It is not suggested that he originated them, and it is not our present business to trace each of them to its source. We are mainly interested in the possibility of their application in our work, and it is convenient to have them in the clear way in which they are presented by Spencer. There are six of these principles in all, but only the first three and the fifth concern us here. They run: In Education we should proceed (1) from the simple to the complex, (2) from the definite to the indefinite, (3) from the concrete to the abstract. (4) '^ The educa- tion of the child must accord, both in mode and arrange- ment, with the education of mankind considered histori- cally." This is clearly not germane to our present purpose; but from it is drawn a principle that is im- ^ Otto Wilmann : Didaktik als Bildungslehre, Band II, p. 64. ' Intellectual Education, Chap. II. ORDER OF PRESENTATION 197 portant to us. As a special case of this fourth principle comes the fifth. (5) We must proceed from the empiri- cal to the rational. (6) '^Self-development should be encouraged to the uttermost " is now very generally accepted, but like principle number four it has no direct bearing upon our subject. In the very severe criticism to which Spencer's book on Education has been subjected, it is interesting to find that these general principles have met with the least opposition. They have not indeed escaped altogether, but most of the objections raised are concerned with the meaning attached to certain terms, and the critics, after they have made their protest, practically restate what Spencer wanted to say,^ though his mode of ex- pression did not quite meet with their approval. For example, we are left a little in doubt whether he meant his principles to be principles of education, or merely principles of teaching. As a matter of fact he lets us understand that he is dealing with the order of develop- ment of the mind, and since Exposition ought to follow that order, the two positions, the educational and the expository, ought in his opinion to coincide. It will be generally admitted that we ought to pro- ^ The same is true about the general criticism of the principles themselves, apart altogether from their connection with Spencer, Their blatant obviousness seems to urge critics to find fault with them. This is what Tusikon Ziller has to say in his Allgemeine Pddagogik : p. 262, "... und so falsch der Grundsatz war, das im Unterrichte vom Einfachen zum Zusammengesetzen fortzuschreiten sei, ebenso falsch ist der andere vulgare Grundsatz, dass vom Bekannten zum Unbekannten fortgeschritten werden miisse." Then he proceeds, as one expects, to explain that he does not quite mean what he says. He does not seek to reverse the principle, but merely to bring out what it really means. We advance not from the known to the unknown, but to the presently unknown " mit Hiilfe des Alten und Bekannten." 198 EXPOSITION AND ILLUSTRATION IN TEACHING ceed from the simple to the complex, though disputes naturally arise regarding what is simple and what com- plex. Spencer's meaning is made plain in his own words : ^' Not only that we should proceed from the simple to the combined in the teaching of each branch of knowledge; but that we should do the like with knowledge as a whole/' ^ Thus stated, the principle would preclude the exposition of a complex by means of analysis; we would seem to be limited to synthesis in our teaching. But it may readily happen that the pupil knows a com- plex quite well, and yet is ignorant of the elements of which it is composed. A man may know what prose is and be able to use it effectively, without knowing the elements of which it is composed and the laws of their combination. No doubt in acquiring the mastery of the use of prose the man followed the general principle, but in Exposition it is surely legitimate to reverse the process. A pupil may know the rule for dividing vulgar fractions, and may be able to apply it with great effect. He follows his instructions to ^ invert the di- visor and proceed as in multipHcation," and gets the desired result. He knows the rule as a complex,^ but he may not be aware of the elements out of which the rule is built. In such a case the expositor may well proceed from the complex to the simple. There is sometimes a little confusion between the simple in itself, and the simple to understand. Spencer is aware of this danger, and warns ^ Education, Chap. II, p. 65 (cheap edition). 2 Of course it may be quite reasonably objected that a well -taught boy ought not to have this complex; but granted that the pupil has been badly taught, the expositor's best plan is to work from the re- sults already attained, however bad they may be. ORDER OF PRESENTATION 199 teachers that ''a generalisation is simple only in com- parison with the whole mass of particular truths it com- prehends — that it is more complex than any one of these truths taken singly/' ^ and thus he feels the necessity of laying down the " concrete to abstract principle." With this rule the teacher need have no quarrel, since it will he found to be impossible to break it. It is true that attempts have been made to teach in the reverse order, and to pass from the abstract to the concrete. Indeed, for centuries teachers believed that they were teaching from the abstract to the concrete. They taught Latin by laying down rules and then setting their pupils to apply these rules. The pupils learnt Latin, no doubt, but not because of the rules they learnt. They did not understand Latin because of the rules, but the rules because of the Latin. The teachers did not really teach at all. What they did was to provide means by which Latin might be learned, and then to place their pupils in circumstances in which it was unpleasant not to know Latin. The master thought he was teaching from the abstract to the concrete, but the pupils actu- ally learned from the concrete to the abstract. It is impossible to learn in any other way. The abstract is necessarily unintelligible unless it has been reached by means of the concrete from which it has been derived. With an entirely new abstraction in relation to an entirely new bit of the concrete the mind can work in only one way. The concrete must precede. But in ordinary experience cases of pure abstraction are rare. We nearly always know something about the materials from which abstraction has been made, and the mind passes from what it knows of the concrete to deal with ^ Education, Chap. II, p. 67. 200 EXPOSITION AND ILLUSTRATION IN TEACHING the abstraction that is presented to it. From the ab- stract statement ^'Things that are equal to the same thing are equal to one another" the pupil may be made to pass to the concrete case that if Tom is the same height as James, and William is the same height as James, then Tom is the same height as WilUam. But the abstract statement, so far from making clear the equahty in the height of Tom and William, would not be even intelligible to the pupil but for many similar measurements that have been made in his experience before the abstract statement was heard of. Indeed, is it not a contradiction in terms to maintain that one can understand an abstraction without first knowing the something from which the abstraction has been made ? The truth is that in ordinary life there is a constant alternation between the abstract and the concrete in the process of acquiring knowledge. By careful examina- tion of the concrete we reach a certain abstraction; but we at once proceed to apply this abstraction by making a new connection with the concrete. As the result of abstraction from many concrete cases Mill enunciates his canons. Forthwith he exemplifies them by means first of letters, and then by still more material examples. He appears to be teaching from the ab- stract to the concrete, but in so far as his abstractions are understood at the first presentation, they are under- stood in terms of the concrete experience of the pupil. Logical presentation is possible with pupils who have a wide though ill-arranged knowledge of the subject. Grammar, for example, may be taught in logical order to a person who has a really good working acquaintance with the language in connection with which it is to be ORDER OF PRESENTATION 201 taught. The very limitation here involved is sugges- tive. The language assumed to be known forms the necessary concrete. In many cases the facts to be presented are of coordi- nate rank and may be brought forward in almost any order. Take the different kinds of subordinate clauses as these are dealt with in the analysis of sentences. It does not matter much whether we begin with the Noun Clause, the Adjective Clause, or the Adverb Clause, on the understanding that the pupils have already mastered the Parts of Speech and are familiar with their functions. On the other hand, if gram- matical construction is being approached by means of the Analysis of Sentences instead of by Parsing, then it might be desirable to begin with the Noun Clause rather than with either of the others. Indeed, when the teacher comes to the point of choosing the order of presentation, he will almost always find that there is some one order that for some reason or other ought to be preferred. Further, this order is not a permanent one. Next time he has to deal with the same matter, but with a different class, he may find that a different order is preferable. The different clauses of Magna Charta are to a certain extent coordinate. They form part of the one great document. But their order of presentation would be different under different circum- stances. For example, if we are considering the docu- ment merely as a document, — as a specimen in the science known as Diplomatic, — the clauses would be dealt with in the order in which they occur on the parchment. In general constitutional history the clauses would be presented in their order of importance to the constitutional history of the country. We might either 202 EXPOSITION AND ILLUSTRATION IN TEACHING begin with the least important and work up to the most important, or we might reverse that order. On the other hand, if our main purpose is to illustrate some special point — say the position of the artisan class in the Thirteenth Century — our presentation might centre round one point, say the term Contenement} If our interests are mainly in commercial matters, the clauses dealing with weights and measures and personal freedom of movement from place to place might come in the first rank. It not infrequently happens that in expounding a particular subject there are two or three terms to be explained, and the whole subject cannot be properly understood until these subordinate terms are made clear. Sometimes lengthy expositions of these sub- ordinate terms are given, while the whole process of understanding the main subject is suspended. Occa- sionally this is inevitable. But we must regard it as a danger signal when we have to introduce some such statement as: '' Before we can proceed to the considera- tion of the subject at issue it is necessary, et cetera, et cetera.'' Every time we interpolate explanatory matter we must satisfy ourselves that there is no more suitable place for it ; and when we see no way of avoiding the interpolation, we must do all we can to prevent its materially interfering with the flow of the main line of thought. ^ " A freeman shall not be amerced for a small fault, but after the manner of his fault; and for a great crime according to the heinous- ness of it, saving to him his contenement ; and after the same manner a merchant, saving to him his merchandise." Then the explanation is in place : Contenement signifies the chattels necessary to each man's station, as the arms of a gentleman, the merchandise of a trader, the ploughs and waggons of a peasant. ORDER OF PRESENTATION 203 We must always try to keep our subordinate ex- planations closely connected with our main subject, and with each other. In order to explain A, of which the pupils know a little, we may have to explain X and Y, of which they know less. We must guard ourselves against leaving A and Y quite isolated while we plunge into long explanations of X. We must adopt at least a working explanation of Y while we are elaborating X, else the bearing of X upon A will probably be obscured. This will be better understood by an example; the writer quoted is expounding the nature of Narrative: — ^^A narrative is a representation of a series of events. This is a very simple definition; and only two words of it can possibly demand elucidation. These words are series and event. The word event will be explained fully in a later section of this chapter : mean- while it may be understood loosely as synonymous with happening. Let us first examine the exact meaning of the word series. The word series implies much more than the word succession: it implies a relation not merely chronological but also logical ; and the logical relation it implies is that of cause and effect. . . ." ^ Then the writer goes on for seven pages elaborating the meaning of this term series, before he begins to treat of the parallel term. But thanks to his thoughtfulness in supplying us with a working definition of event, we are able all the time we are considering series to make use of both this term and the term event to help us in under- standing what the expositor is telling us about nar- rative. This anticipatory treatment in which we refer to cer- tain aspects of a subject before we actually deal with them in detail is applicable on a large scale. In plan- ning out a book, for example, the same principles obtain ^ Clayton Hamilton : Materials and Methods of Fiction, p. 44. 204 EXPOSITION AND ILLUSTRATION IN TEACHING as in planning out a chapter. We are working with a different size of unit, but the principle is the same. This may be illustrated by reference to the idea of unit itself as treated in this book. In Chapter II we have a general reference to the idea of the unit of Exposition, in which it is treated in connection with the need for destructive process in preparation for constructive. Then again in Chapter IV we have the unit regarded as a part of a background, where we have to deal with it at the stage of complexity at which we find it. Finally in Chapter XII we have a new view of the unit. In that chapter it is used for purposes of comparison. Instead of being something to be analysed out, or to be used as a brick to build up with, it is to be used as a standard by which quantities of all kinds may be measured. It may naturally be objected that it is bad presentation to separate thus the different aspects of the same sub- ject. Why, it may be asked, does not the writer say all he has to say about the unit in one place, and have done with it? But it is all a matter of emphasis. If in planning the book the writer had determined to lay great stress on the notion of the unit as such, then he would have devoted a chapter to this subject, and in that case the contents of some of the other chapters would have had to be distributed throughout the book, as the unit has been under the present arrangement. But even when a special chapter has been set apart for a certain subject, it sometimes happens that an aspect of that subject is better treated in some other connection. Thus though there is a chapter (XIV) on the Picture, this is limited to the use of the picture as illustration. In Chapter IV some pages are devoted to the treatment of the picture, but here it is the mental picture that is ORDER OF PRESENTATION 205 under discussion, the picture the pupil forms for him- self as the result of verbal description. In Chapter XIV we are dealing with the picture as something ob- jective, in Chapter IV as something subjective. The index of any book one takes up supplies many illustrations of the distribution throughout the text of the treatment of certain subjects that the reader might prefer to have had grouped together in one place. But apart from the fact that we cannot have a book ar- ranged according to the desires of each reader, it has to be remembered that there is a certain compensating advantage in treating the same matter at different stages, and in different connections. There is an ad- vantage in familiarising the mind of the reader with a given fact before that fact is brought forward for more or less exhaustive treatment. Novelists frequently introduce a fact two or three times in a very incidental way at the early part of the story in order that it may be the more effectively treated when its turn comes. This principle of casual introduction of matter to be afterwards elaborated may be used by the teacher in two ways. He may imitate the novelist and use this order of presentation in order to build up interest. Several illustrations will be found further on in this chapter, and in the next there occurs a deferred illustra- tion of a generalisation from Herbert Spencer quoted in Chapter III. It will probably be felt that this illus- tration is not only useful where it is, but that it has an increased force in relation to its original generalisation because of the delay. [This paragraph, within brackets, is deliberately in- troduced in order to explain its own vices in relation to the principles of Presentation. It is thrust in, you will 206 EXPOSITION AND ILLUSTRATION IN TEACHING observe, between two sections. The teacher uses a novelist's device in two ways: one of them has been dealt with, the other is yet to come, and this paragraph is thrust in between them. This is bad, and is only justifiable because it emphasises a defect by calling attention to it at the very moment when it is producing its irritating results. The paragraph originates really in the desire to call immediate attention to a blunder in presentation that has just been made. While it is excellent to refer to something that has already occurred in a book, it is generally a mistake to refer specifically to what has not yet been reached. In the preceding paragraph the reader is practically invited to turn to the next chapter and read a particular passage, which he is then to compare with a passage in Chapter III. This not only seriously interferes with the reader's line of thought in this chapter, but spoils the effect of the passage he is invited to read. That passage occurs in a certain connection, where it is assumed it ought to occur. To read it in the first instance apart from this connection is obviously to do it injustice. It is quite different in cases where we are referring back to passages that have been read in their proper order and are now considered in a new connection. The same objection does not lie against the reference in the previous para- graph to Chapter XIV. There is in that case no call to turn to Chapter XIV at all. Its very title conveys all the information necessary to understand the reference in the text. After reading in typoscript the above de- plorable divagation, my colleague. Dr. T. Percy Nunn,* ^ This does seem a most inopportune place, but in the absence of a preface I have no other; — I want to express mj'^ indebtedness to Dr. Nunn for his kindness in reading through, in the very limited time ORDER OF PRESENTATION 207 SO far from helping me to return to the straight path, led me into temptation by sending me his copy of a work by that Master of Exposition, Sir Oliver Lodge. I looked into the book ^ and was lost. Sir Oliver's words in the Preface form an admirable commentary on what I have already written : — ''Since the book is intended to be useful to the higher class of students, it seemed very permissable to adopt a method which I al- ways use in teaching ; viz. to begin by giving some ideas at first, and to gradually polish them up later, rather than by attempting a too highly finished statement ab initio to overburden and depress, and possibly to confuse, a student. Because of this progressive arrangement, I may be permitted to urge students to read the book through before proceeding to dip into it by help of the index, and before taking notice of references forward which subsequently it is hoped will prove useful.""^ (Italics mine, to emphasise the applica- tion to the present book.) Naturally the same principles may be applied in oral Exposition, but with a greater sense of responsibility, as the pupil is entirely in the expositor's hands.] ^ The second use the teacher may make of the inciden- just before going to press, the typescript of this book, and for the really valuable criticism and help he gave. ^ Modern Views of Electricity. 2 Those who are interested in the presentation of this subject will find in Modern Views of Electricity examples of "anticipations " and "references forward" on pages 16, 17, 28, 42, 90, 94, 96, 98, 99, 105, 128, 144, etc., of the first edition, 1889. For an interesting illustration of the preparation for a subject by incidental reference to it in order gradually to build up an interest in it, see Sir Oliver's treatment of the topic "Does electricity possess inertia?" in sections (not pages) 7, 42-48, 88, 89, 98, 105. 2 On re-reading the above paragraph illustrating defective arrange- ment it strikes me that I have rather overdone it. We could hardly have a worse case of congestion : but I let it stand, as the reader's irritation will only emphasise the lesson meant to be conveyed. 208 EXPOSITION AND ILLUSTRATION IN TEACHING tal introduction of some matter before it is really wanted is exactly the opposite of the novelist's. He may seek to exhaust the intrinsic interest of matter that is to be afterwards used as illustration. By introducing the attractive matter in unimportant places, he allows the pupil to enjoy its interest for its own sake, and when this has been repeated two or three times, the pupil is ready to take a new point of view from the teacher, and get up a secondary interest at the proper place.^ Sometimes the order of presentation is determined by very practical considerations. In preparing hydrogen it makes some difference whether the pupil is told to pour in the water before he is told to pour in the sulphuric acid. In that form of practical presentation commonly known as ^'directions," when supplied along with machines, implements, or commodities, the order of presentation is of vital importance. I have seen the pointer of a typewriting machine broken because the direction, ''Be careful to lower the pointer when re- placing the carriage" occurred after the instructions, " How to replace the carriage." At the head of every set of practical directions should appear the caution: Please read the directions right through before beginning to , etc. This naturally raises the question of the help that one part of a presentation gives to another. It may happen that what is obscure when only two elements have been presented becomes quite clear so soon as a third element is brought forward. This involves the problem of suspended understanding during a process of presentation. Is it justifiable to present at a given time certain matters that cannot possibly be under- ^ This is further dealt with in Chap. XVI, p. 391, ORDER OF PRESENTATION 209 stood by the pupils till at a later stage additional matter is supplied ? If it is a case of presenting matter that cannot be understood at all at a particular stage, but must be got up by memory for use later on, it will probably be agreed that the presentation should not be made. It is different, however, when the presented matter cannot be fully understood at the time of pre- sentation, but will be fully understood when additional matter is presented at a later stage. Almost all our presentations are open to the objection that the matter brought forward cannot at the moment be fully under- stood. All that we can hope for is that it may not be misunderstood. From the material supplied, the pupils may make premature conceptions that must after- wards be painfully destroyed in order to make way for the correct construction. It is not uncommon to hear post-graduate students who are being trained to teach the elementary subjects confess that they never under- stood the true meaning of what is called simple sub- traction till they saw the subject taught in the demon- stration school. They often find that they have to break down and reconstruct all their idea combinations on the subject. So with pupils who have been taught scansion or music on purely mathematical lines: there comes a period of necessary reconstruction when they reach the stage of artistic appreciation. Pupils who have had drawing presented to them as a system of fine- line copying from the flat have to fight very hard indeed before they can break up the false combinations and by reconstruction attain the freedom to use drawing as a means of expression. Doubtless the reader's own edu- cation furnishes him with more than one illustration of this need for reconstruction. There are cases, as we 210 EXPOSITION AND ILLUSTRATION IN TEACHING shall see later in the chapter, in which this formation of premature conceptions and their correction may be turned to good account, as a means of strengthening a desired aesthetic or moral effect. But on the cognitive side we must do all we can to secure the correct (not necessarily the complete) conception at the very start. Taking it for granted that certain orders of presenta- tion are more economical of the pupil's time and energy than are others, it may be objected that the teacher's business is not to save the pupil's time and energy, but rather to make him expend both. There are those who maintain that the best progress is made by the process of trial and error. The argument is that you know a thing better if you have made your blunders, and found out the truth for yourself. The result is more your own than if it had been pumped into you by a watchful teacher who stood by all the time to prevent the possi- bility of your going wrong. In all arguments of this kind there is a slight confu- sion of thought between the different parts of a teacher's work. The formation of character is one thing, the ex- position of a subject another. A man may often be a better, because a stronger, man on account of the diffi- culties he experienced in acquiring the knowledge he needed. But it does not follow that he knows his subject better because he had to study it under bad conditions. The argument of those who underesti- mate the value of careful teaching is that the pupils become emasculated, and unfit for any serious study. But surely it is idle to complain that we are doing too much for our pupils. There is a Hmit beyond which it is impossible to help them at all. Beyond that limit our help becomes a hindrance. To pass that ORDER OF PRESENTATION 211 limit is clearly bad Exposition, but up to that limit the more we can help the pupil the better. There always will remain the irreducible surd of individual effort that cannot be eliminated by any amount of external help. On the other hand, there is the danger that some teachers may regard the giving of trouble as in itself a laudable thing. The implied argument is surely easily disposed of by a reductio ad ahsurdum. If the increasing of the difficulties of our pupils is an advantage, it would naturally follow that the worse our exposition the better for our pupils. The teacher who provided the worst text-books and made his pupils work under the worst conditions would do them most good. Some teachers actually adopt this attitude, and oppose the in- troduction of the metric system on the ground that their pupils would lose the enormous advantage of having to cope with those curious vestigial items 5| and 30j that adorn our present arithmetical tables. In the course of a recent examination in Education as one of the subjects for a university degree, I set the follow- ing question : — " Speaking of the limited educational curriculum in the best days of Greece, Professor Bosanquet asks : ' How was so much made out of so little ? ' What answer would you suggest ? " A large percentage of the candidates took occasion to point out that the curriculum was not nearly so inade- quate as it appeared. The subjects studied had the advantage of several difficulties that are no longer available in our modern schools. For example, the Greek characters were not only made by the hand and therefore rather clumsy, but they were arranged with 212 EXPOSITION AND ILLUSTRATION IN TEACHING no spaces between the words, and to separate out the individual words involved a great exercise of attention and ingenuity; while the fact that the Greek numerals were so awkward to deal with provided still further opportunities for strenuous training. The truth is that all this pother about the dangers of a soft pedagogy is based upon the assumption that it is possible to make teaching so perfect that nothing is left for the pupils to do. But all that the most skilful presentation can do is to prevent the pupils from having to waste their time in unprofitable ways of expending their energy; as, for example, in manipulating antique tables and separating words that should never have been united. The better the exposition the more rapid the progress of the pupils; the only limit to their progress under these conditions being, in fact, the neces- sary limits imposed by the need of time for consoli- dation. For it has to be remembered that a pupil cannot go on indefinitely piling up knowledge, no matter how skil- fully it may be presented. However brilliant the natu- ral parts of the pupil, and however skilful the expositor may be, there is a limit to the speed at which a pupil can master a subject. Even the plain practical man admits this, though with obvious regret. It is with reluctance that he acknowledges that we cannot put old heads on young shoulders. There are no doubt sound psycho-physical reasons why even an Isaac Newton requires a certain minimum of years before he can deal with certain mathematical problems. For our present purpose it is more important to observe that all mental processes involve a certain expenditure of time. Natural processes may be greatly accelerated in ORDER OF PRESENTATION 213 a forcing house, but even in a forcing house a minimum time Hmit is imposed. Stupid pupils demand a long time/ but even the cleverest, when treated under the most favourable conditions, must have a minimum time to consolidate their gains. There is no fear of excessive speed through excellent exposition. The figure of the forcing house brings forward an- other aspect of the objection that deserves treatment, since there is a basis of truth underlying it. Some writers want to know whether, by this very carefully prepared exposition, we may not weaken the power of initiative of our pupils and make them incapable of learning anything for themselves. It is pointed out that certain schools that have specially laid themselves out to prepare pupils for examinations, have reduced the art of Exposition to such a state of formal perfection that nothing is left for the pupils to do. But cramming and Exposition are different things. The crammer's aim is to get his pupil to reproduce under unhealthy conditions a certain amount of information. He is not concerned how the matter is retained, so long as it is there when called for; nor whether it is understood or not, so long as it can be put down on paper without betraying any lack of comprehension. The aim of the expositor, on the other hand, is frustrated if the pupil does not understand the matter presented. But surely the more easily the pupil can be made to understand the ^ Experienced coaches have great faith in the efficacy of time in removing difficulties. Dr. David Rennet, the distinguished mathe- matical coach at the University of Aberdeen, whose success in pre- paring for examinations is phenomenal, is sometimes encouraging to dull but earnest pupils when they are worsted by a problem even after it has been explained. His remark is :" Aweel, than. Ye must juist wait till it sipes [soaks] in." 214 EXPOSITION AND ILLUSTRATION IN TEACHING better. It does not follow that the most direct recti- lineal exposition is the easiest in the long run. Every- thing has to be judged by the kind of understanding attained. But assuming that our aim is the highest form of understanding, then it may be taken for granted that the easiest way to attain that form is the best. To deny this is to assert that labour and trouble are in themselves desirable. If there is any suggestion about " their value as training, '' etc., it is a sufficient reply that all this is already discounted when we have accepted as our aim the highest form of result. It is for this reason that the expositor is entitled to use con- trast, and even contradiction, if he can show that these are better means of expounding his subject than straightforward presentation of facts that are easily assimilated. Under certain conditions it may be desir- able to go against the principle of economy on which Spencer lays so much stress. But in all such cases it will be found that we are keeping to the spirit of Spen- cer's principle, though we reject the letter. It is well to follow the line of least resistance, but naturally every- thing depends upon where one wishes to go. The means are relative to the end : it is another case of the longest way round being sometimes the shortest way home. When Nathan led the unsuspecting David to con- demn himself in the person of the robber of the one ewe lamb, he was supplying us with an excellent ex- ample of a ^'premature conception '' that had to be destroyed and reconstructed before the prophet's ex- position was successful. But obviously the result was worth the expenditure of time and energy. Indeed, it may fairly be said that to attain the result the prophet ORDER OF PRESENTATION 215 had in view the roundabout way was the line of least resistance. An intellectual understanding of the case could no doubt have been secured in David's mind without this troublesome reconstruction, but the prophet wanted something more than mere intellectual consent. In Nathan's case the matter was so skilfully pre- sented that there was no room for error. The recon- struction was not called for till the very moment it was needed, and the first construction did not in itself in any way conflict with the effect of the second. But the greatest care is necessary to prevent the first construc- tion from making the second impossible. An amiable old gentleman was called upon to propose a vote of thanks to the chairman and governors of a great school at the distribution of prizes. Tired of the con- ventional way of doing what was expected of him, he thought he would introduce an agreeable variety by emphasising the brighter side of a governor's office. Accordingly he pointed out that though the duties of a governor were very exacting, and involved a great expenditure of time and energy, the governors were very well paid for it. He had intended to round off his speech with a glowing account of the joys of being kept young by constant contact with the fresh young life that he saw before him, and of being cheered by the glow of good work well done, and a number of other compensating satisfactions that come by way of re- ward to the conscientious governor. But at the mere words ^^well paid for it" there arose such a murmur of protest among the assembled governors that the re- mainder of the amiable gentleman's speech consisted of a hurried explanation that '^that is not what I meant." 216 EXPOSITION AND ILLUSTRATION IN TEACHING This unhappy gentleman applied unskilfully an arti- fice that is quite legitimate in Exposition. He sought to create a vacuum for a fact that he proposed to pre- sent. He knew that his remark would excite a certain amount of surprise which would in its turn lead to a curiosity that he would then proceed to satisfy. He had not calculated on surprise passing over into indigna- tion instead of into curiosity. With the less personal issues raised in instructing in school it is often desir- able to apply this principle of the vacuum. If the teacher can create the desire for a particular bit of knowledge, he is on the way to the best possible pres- entation of that knowledge. The following example from actual teaching illustrates what is meant. It is taken from the essay of one of my students at the University of London: — " I was teaching a class to scan the hexameter line in Latin, and after teaching the division of the line into six feet, two beats in each foot made by either dactyl or spondee, and the invariable na- ture of the fifth and sixth feet, I put up some fines on the board for us to work out together. The pupils got on swimmingly for the first fine, as the lengths of the syUables were well known to them. But the second fine was : — * Mutat terra vices, et decrescentia ripas.' Working backwards, they arrived at all the feet except the first, and there they stopped in difficulty. Only two syllables were left for this foot, and they had been carefully taught that the third person singular present indicative of the four conjugations was short. Was the foot a trochee \j ? That was the time for the explanation of 'vowels long by position,' which would have been imperfectly comprehended if given before the children had found the difficulty for themselves." Leaving to specialists the decision of the question whether scansion should ever be taught in this way, ORDER OF PRESENTATION 217 whether in direct or in inverted order, it is necessary to point out, what the student herself discovered after sending in the essay, that the appHcation of the vacuum here involved the fallacy of assuming that the pupils would make et long by position in order to get into difficulties at the end so as to be led to enquire into the very rule that they had already applied. The student's reply was that her plan worked: she desired to get the pupils into this difficulty, and she succeeded. Obviously the excellence of the plan is not diminished by the fact that a more suitable verse ^ was not chosen. The principle of the vacuum may be usefully applied in the introduction of new technical terms. If at the beginning of teaching geometry we speak a great deal about ^Hhe line joining the opposite angles of a square,'' the pupils will get tired of the cumbrous phrase, and when the term diagonal is introduced, will welcome it as a relief from the wearisome description. In science teaching, the principle may be applied by giving half a dozen applications of a certain rule, e.g, different phe- nomena resulting from the pressure of the atmosphere, without enunciating the rule till the last application is made. By this time the pupils want to know what is the cause of the peculiar phenomena they have seen, and are glad to have such an economical arrangement as one principle (whether given by the teacher, or, better, discovered by themselves) to explain half a dozen re- ^ The verse — " Scindit se nubes, et in sethera purgat apertum " would have led to the desired result, and would have had the addi- tional advantage of including a third person singular (purgat) that follows the usual rule, and therefore emphasises the difference in scindit. 218 EXPOSITION AND ILLUSTRATION IN TEACHING markable things that at first appear altogether different from each other. Sometimes the principle is more deliberately applied. A certain problem is stated, and various more or less plausible solutions are offered one after the other, and each dismissed in turn as unsatisfactory. But all through the discussion there is constant reference to the true theory. Phrases like the following are scattered throughout: '^as we shall see presently"; ''when we come to what we hold to be the true theory'^; ''as will be evident in the light of the theory about to be pre- sented; '^ "a natural mistake in a writer who has not the information that is about to be laid before you.'' For example, the lesson may be on those curious medal- lions that the antiquarians of the seventeenth and eighteenth centuries called contorniates. The un- skilled would naturally regard them as coins. People who know more are aware that this is not so, and various theories as to their nature have been held, such as (1) amulets to bring success to competitors at the games; (2) tickets to reserved seats at the games; (3) lots to determine the starting order in the chariot races; (4) medals indicating success in the games. Now the teacher starting with the view that the true use of contorniates was to serve as "men" in certain table games resembling our "draughts," keeps this in view all the time he is discussing the other theories, and takes every opportunity of shadowing it forth without actu- ally stating it. While pointing out all the difficulties of the other theories, he refers to " the better-supported " theory, "the clue is to be found in M. Froehener's brilliant suggestion," ^ "before what we believe to be ^ Annuaire de Numismatique, 1894, p. 88 : quoted by K, A. Mac- dowall, in the Numismatic Chronicle, Fourth Series, Vol. VI. ORDER OF PRESENTATION 219 the true solution was offered/^ By the time the Froe- hener theory is actually presented, a real need for it has been created. The pupil is tired of indirect suggestions, and welcomes the positive statement of the final theory. There is one limitation to the application of the prin- ciple of the vacuum in Exposition. The pupil should not be taught anything that is actually false. In using contrast and in preparing a vacuum, error is introduced, no doubt, but in the first place it is not taught as truth, and in the second place, the error is only relative. It must be associated with a certain amount of truth before it can have any value in a process that seeks to pass from apparent truth to a nearer approach to ulti- mate truth. There has to be reconstruction, perhaps, but the original construction is usually correct for some other set of circumstances, though unsuitable for the present. There can be no justification in presenting matter that is, so far as we know, false under all cir- cumstances. We want the pupil to get at the truth as it is known to us, and though we may find it desir- able to contrast his view of truth with ours, we need never present actual falsehood to him. We must distinguish between falsity and mere in- completeness in presentation. ''An instrument for telling the time^' is an incomplete, but not a false, definition of a watch. Many teachers are willing to al- low an incomplete presentation of ordinary terms, but draw the line when technical words are in question. Dr. T. Percy Nunn is frequently challenged by his students of the London Day Training College for giving ''wrong" meanings to scientific terms. For example, he deliberately calls a mass of peroxide of lead, whatever its size, a "molecule," and when, under heat, it gives up 220 EXPOSITION AND ILLUSTRATION IN TEACHING just the amount of oxygen to enable it to become lith- arge, he says it has given off one atom of oxygen, and is now a molecule of litharge, made up of one atom of oxygen and one atom of lead. This scandalises his young men, who have been brought up in the belief that size (or rather lack of size) is of the essence of mole- cules, and particularly of atoms. My colleague defends himself by maintaining that his meanings are not wrong, but merely incomplete. He believes that the qualitative approach gives the students a much better chance of getting the true meaning than does the quanti- tative. In the ordinary presentation the pupil is thrust into the middle of a theory before he realises the facts of the case. In very many instances he is so busy whip- ping up his imagination in the pursuit of the incon- ceivably small that he has no energy or interest left to attend to what, after all, are the essentials of the laws of chemical combination. It is always wise to begin with the proper point of view where it is possible, and in this case it is not only possible but actually easier than what may not unfairly be called the metaphysical approach. We should teach by good example rather than by bad, by showing what should be rather than by showing what should not be. Positive teaching is always better than negative. The ^^ awful example," as it is called, is bad exposition unless under conditions in which there is no doubt as to the right and the wrong. To write the word feild on the blackboard and enlarge on the heinousness of spelling it in that way only strengthens the chances of that form of the word reappearing in the pupils' exercise books. There is no self-interpreting standard compared with which feild will stand out as ORDER OF PRESENTATION 221 inherently bad. In certain forms of symmetrical free- hand drawing, on the other hand, common errors made by the pupils may be with safety placed upon the black- board, since their very juxtaposition to the model will at once condemn them. There is here an objective stand- ard to which appeal may be made with no fear of misunderstanding. So with the objectionable para- graph on pages 205-207 of this chapter. It carries its own condemnation with it. In dealing with grammatical errors the type should be: '^The correct form is 'Charles and his cavaliers were defeated.' '' The emphasis on the were calls atten- tion to the fact that this is correct, without recalling the incorrect was of the exercise book. Even in a case of greater difficulty, where there might be room for a little argument, it is well to stick to the positive form. ' ' Charles with his cavaliers was defeated. ' ' If the pupils themselves raise objections, a little argument may be permitted, but even then the repetition should always be of the correct form, and not of the alternative were, as suggested by the pupils. Reiteration of the right should be the expositor's principle rather than condemnation of the wrong. Some teachers set what they call mistake-traps, in order to illustrate certain forms of error. The condi- tions here should be the same as in the case of the awful example. Traps should never be set unless there is an objective standard to which the wrong answer may be referred. These traps are legitimate only in those cases in which matters can be so arranged that not only shall the expected mistake occur, but it shall bring its own condemnation with it by confronting itself with some irreconcilable ideas that make investigation and 222 EXPOSITION AND ILLUSTRATION IN TEACHING consequent reconstruction inevitable. It may be con- ceded that so long as a mistake-trap leads the mis- take maker to perceive and rectify his mistake, no harm is done. But it is at the best a dangerous form of exer- cise, and when used should always be followed by a series of exercises leading to normal results, so that the final impression left on the pupiFs mind is the correct one. It is a favourite charge against the average teacher that he is too fond of rules. But, after all, in his mind the rule occupies only the second place. His real first love is the exception. All his professional activities seem to centre round exceptions. His pupils, indeed, acquire from the teacher's bias a distorted view of the relative values of rule and exception. The following dialogue from real life is full of instruction : — Teacher (going over examination paper of pupil — subject, French Accidence). I see you have given generals as the plural of general. Don't you know that nouns in -al form their plural in -aux'i Pupil. Yes, sir, but I thought it was an exception. Teacher. But what made you think it was an exception ? Pupil. Because it was set in the examination, sir. To the same effect is the advice given by the Scotch Dominie to the promising pupil whom he is sending up to the Scholarship Competition at Edinburgh Uni- versity: — ''When in doubt mind [remember] that practically everything in an examination governs the subjunc- tive.'^ ' No doubt the demands of examinations have had a great deal to do with the unhealthy prominence given to exceptions. Examiners who are more anxious to ^ Ian Hay : The Right Stuff, p. 6. ORDER OF PRESENTATION 223 show what a candidate does not know than to find out what he does, have naturally a warm side to exceptions. But the teacher, too, is not without guilt. His besetting virtue is accuracy, and he cannot bear that even for a time his pupil should be told something that will not bear the fullest investigation. No sooner has he enun- ciated a general principle than some wretched excep- tion occurs to his mind, and he proceeds with indecent haste to modify his original statement by indicating in what respect it comes short of absolute truth as known to him. Before the rule has time to be established, its authority is undermined. The old Latin grammars were grossly disloyal to their rules. In a couple of lines they describe the behaviour of nine-tenths of the words under a particular category, and then having eased their conscience and having got rid of the herd of common- place words, they proceed to the real business of life and wallow in exceptions. The exceptions have, of course, a place in teaching. Fine scholarship is determined, no doubt, just by the accuracy with which the excep- tion is treated. But in a procession, mere precedence does not determine the importance of the people. In some processions the important persons come first, in others last, in the majority the important place is some- where in the middle. It does not, therefore, degrade the exception to say that its place is at the tail of the pro- cession. The rule must be thoroughly well established before the exception can come into being. We may in certain forms of teaching pass from the example to the rule. But we cannot pass from the exception to the rule. For if we try to do so, what happens is that we for the time being erect the exception into a rule, and then bring in the rule as an exception. 224 EXPOSITION AND ILLUSTRATION IN TEACHING The true order of presentation is first of all to enun- ciate the rule, then to support it. The rule may be either given, as in deductive teaching, or worked for, as in inductive. In either case it must be buttressed up with many examples, and not weakened by any exceptions. In the case of inductive teaching the rule is really built up on examples. In deductive teaching it is justified by the examples adduced. The rule should be appUed in many ways, all involving normal examples of its working. By and by the pupil acquires confi- dence in his rule, and treats it as a part of the nature of things. Then the teacher may either introduce an exception, or merely permit his vigilance in editing examples to relax, and allow an exception to occur in the ordinary course of study. Whether the exception occurs by accident or is deliberately introduced by the teacher, the detection of the exception should be left to the pupil. Unless the pupil is struck by the exception, as an exception, the rule has not been properly assimi- lated. When the pupil comes to complain about the rule failing in a particular case, he is in a position to be told of the nature and number of the exceptions for which he must be prepared. It will be noted that the pupil's complaint in the first instance will not be against the rule, but against the exception. His first attitude is and ought to be to regard the exception as a blunder on the part of some one or other. Obviously there are cases, especially in dealing with older pupils, when it may be permissible to introduce rule and exception together. This is especially true when the rule has been reached by an examination of a great series of examples, and when the number of excep- tions is limited. Suppose the pupil has, after much ORDER OF PRESENTATION 225 turning up of the dictionary, come to the conclusion that most German substantives that are dissyllabic and that end in e are feminine, it is desirable to add on the spot the limitation ^^not denoting members of the male sex,'^ and to give the exceptions das Auge, das EndCy and das Erbe. On the other hand, the ten German substantives now ending in e but etymologi- cally ending in n should be left to be discovered, as exceptions to this rule, and as examples of a rule of their own. So far we have been dealing with Exposition as it affects the individual mind. The problem is to some extent complicated when we treat of exposition to a class. The same principles of presentation must, of course, hold in both cases, but they may have to be differently applied. To begin with, when there are from twenty to sixty minds to be considered (and in the case of public exposition often many hundreds), it is clear that there is greater difficulty in getting at the common segment of mental content. In the case of a class doing ordinary school work there is usually much less difficulty on this score than one might expect. The ground has already been prepared. The pupils are of approximately the same age, they have gone through a similar course, they come from homes that are at least in a general way similar. The difficulty in finding common ground is mainly in connection with outside matters, and is felt chiefly in introducing more or less concrete illustrations. With a really large audi- ence the expositor must adopt the purely human atti- tude. He must assume in his hearers only the most universal qualities of human nature, and whatever de- gree of knowledge his acquaintance with the circum- 226 EXPOSITION AND ILLUSTRATION IN TEACHING stances of his audience may warrant him in assuming as a minimum. In dealing with a particular mind, we may approach it on one particular side because we know that to be the most accessible. The visual and the audile, for example, would be approached in a different way; but with a class we have to make an appeal that will meet all needs. We may have to approach a subject from several differ- ent points in turn, in order that one or other of our approaches may appeal to the different members of the class. We may, for instance, present the matter from five different points of view. It is probable that some of the really capable pupils will appreciate all the five presentations. Others may appreciate only four or three or two or one. It may chance that after all there may be one or two in the class who have been im- pervious to all five modes of approach. These zeros may be safely regarded as unfit for class instruction, and as they require individual treatment maybe neg- lected in our present consideration. With regard to the others there is the serious problem of interest. Especially if the subject is not in itself difficult, it becomes very tiresome to a clever boy to have it explained in four different ways, after he has mastered it at the first exposition. The same holds of the other pupils for all the explanations given after they have mastered the point at issue. The expositor to a class must therefore lay his account with this danger, and do what he can to introduce a second line of inter- est that may compensate the quicker pupils for their enforced retreading of the old ground. It has to be remembered that interest does not arise merely in the new or merely in the old, but in the new in an old setting ORDER OF PRESENTATION 227 or the old in a new setting. By the conditions of the case the five presentations are made from different points of view, and therefore fulfil to some extent at least the conditions on which interest depends. But in the actual process of teaching it is possible to introduce different lines of interest. The quicker pupils may be taken into the teacher's confidence in the recapitula- tory presentations. Questions that the duller pupils cannot answer because they have not yet caught the essential point may be answered by the quicker pupils to their own satisfaction and to the edification of the duller pupils. What is a line of investigation and discovery for the duller pupils may well be a course of practical applications for those who have mastered the principles at the first or at any rate at one of the earlier stages. CHAPTER IX Exemplification and Analogy Natueally Illustration must observe the fundamen- tal principle of proceeding from the known to the unknown. We must approach the little known by means of the better known, and this principle must over- ride all others. Probably the most fundamental mode of Illustration is exemplification, and this is commonly understood to mean the illustration of the rule by the presentation of examples. It would seem to be implied that this form of illustration always proceeds deduc- tively. But while in Exposition we may be said to pass from the rule to the example, in Illustration it would seem that we are really passing from the example to the rule. Of the two the example is supposed to be better known than the rule, on which as a matter of fact it casts light. When we say, '^ Will in the first person promises or threatens, and in the second and third persons simply foretells: as, / will go in spite of all he says. He will come to supper to-night, " we take it for granted that the person we are speaking to knows the shades of meaning of will in the two ex- amples as a mere matter of experience of the language, though we do not assume that he knows anything about the grammatical statement of the fact. But in practice the example may be just as well illus- trated by the rule as the rule by the example. Every- 228 EXEMPLIFICATION AND ANALOGY 229 thing depends upon which is better known to the per- son we are dealing with. It is commoner, no doubt, in ordinary teaching to set forth a general rule and then follow with more or less copious examples. But it is quite as useful to explain a puzzling instance by refer- ring it to the class to which it belongs, in other words by referring it to the rule of which it is an example. When a boy on the classical side cannot understand the mean- ing of the word profaner in the line, "Where no profaner eye may look," the master may make matters quite clear by merely uttering the words ^^ Latin comparative.'' What he has done is to refer this troublesome example to a rule that he knows is familiar to the pupil. When a less experienced doctor calls in a more experienced one to diagnose a difficult case, the mere mention of the dis- ease by the older practitioner settles the matter by referring the case to the rule of which it is an example. Every time that the teacher suggests the particular geometrical proposition that will solve a ''rider," he is really illustrating the example by the rule. When we are told in the dictionary that Illustration means explaining or exemplifying as by means of figures, comparisons, and examples, it would seem that we have a twofold classification of the materials of Illustration. On the one hand there are comparisons implying like- ness and unlikeness, and on the other there are mere examples that owe their power as illustrations to the fact that they show some rule in operation. But after all, the very fact that the different examples illus- trate the same rule proves that they have something in common, and that therefore the idea of resemblance 230 EXPOSITION AND ILLUSTRATION IN TEACHING is present in them also. Aristotle distinguishes be- tween them, calling reasoning by example paradigm and reasoning by resemblance analogy. In paradigm we reason from one example to another; but in analogy we reason from a more clearly stated resemblance. With Aristotle analogy is treated as equivalent to mathematical proportion, which involves the equality of ratios. Our whole experience is intelligible only on the as- sumption that the operations of mind and matter are regulated according to certain laws that act uniformly. The law remains the same though the cases of its appli- cation vary as to what may be called content. When therefore we find a particular law acting in connection with one content we assume that the same law will hold under similar conditions in connection with another content. The selection of the common element from two disparate cases is ^ naturally very difficult. For pur- poses of illustration, therefore, it is well to adopt the Aristotelian view of analogy as limited to the equality of ratios. This enables us to express all illustrative analogies in mathematical terms, as thus, a :h : :c : d. Now if a has the same relation to h that c has to SOUTH AMERICA 1 H I > S m 33 EUROPE I > > m c AUSTRALIA Fig. 8. * John Macturk: Elementary Physical Geography, p. 317. 2 Reproduced by kind permission of Messrs. William Collins, Sons and Co., London and Glasgow. THE DIAGRAM 363 worst when Asia was the standard; the best results followed when either North or South America formed the starting-point. Classes that had studied mensura- tion did better than those that had not. I was able to eliminate the difference in age, for I managed to get four classes of boys of the same age, two of which had studied mensuration and two had not. A further pecu- liarity was that when the diagram was put in the form of a series of six squares standing outside of each other, and arranged in order of size, the results were better than when the squares were so placed as to have one angle common. The explanation is probably that when the squares were superimposed there was greater '^ interfer- ence '^ in the sense that term bears when used in physics. Conspicuously better results were obtained when two of the six areas were given, the best results of all being obtained when Europe and Africa were the continents selected as standards, though Asia and Australia made a combination that had results very little inferior. In point of fact, however, the following table that accompanies the diagram in Mr. Macturk^s book gives a more useful presentation than does the diagram: — Size of THE Continents (including Islands)* Greatest Greatest Area in Sq. Comparative Length Breadth Miles Size Europe . . . 3400 m. 2450 m. 3,700,000 1 Asia .... 6700 m. 5400 m. 16,400,000 ^ Africa .... 5000 m. 4600 m. 11,100,000 3 N. America . . 5600 m. 3120 m. 7,600,000 2 S. America . . 4500 m. 3000 m. 6,800,000 H Australia . . . 1900 m. 2400 m. 3,000,000 ■ 1 ^ Take Europe as the standard of comparison. 364 EXPOSITION AND ILLUSTRATION IN TEACHING In the table the areas are given in sufficiently round numbers to admit of easy comparison with each other, a comparison that is further aided by the ^'compara- tive size" column. It would be well, however, as a matter of presentation that the continents should be arranged in the table in regular ascending or descending order of size to match the diagram. Taken along with the table, the diagram may be said to be helpful; but if the teacher has to choose between the comparative size column and the diagram, he will be well advised to give up the diagram. The illustrandum being the column of ''area in square miles,'' the comparative size column will certainly be a better illustration than is the diagram. When a class is confronted with the squares in figure 8 without any indication that they represent continents, the pupils are found to be inca- cable of estimating the relative areas of the squares. Given the area of the Europe square as 100, only two out of a class of 75 postgraduate students esti- mated with reasonable correctness the areas of the re- maining five. Eighteen of them estimated the largest square as between 700 and 800. The general impres- sion produced by the students' estimates was that the diagram by itself confused rather than helped. Still less hopeful is the accompanying diagram, figure 9. The wider circle has an area one hundred times as great as has the small black circle in the centre. As the total area of the United States, including Alaska, is 3,617,384 square miles, and the area of Indiana is 36,350 square miles, the diagram might be used to illus- trate the relation between the area of this state and the area of the whole republic. The diagram is supposed to make the ratio clearer than does the mere statement THE DIAGRAM 365 of the figures. As a matter of fact, the statement that the one area is almost exactly a hundred times the other conveys a much clearer idea than does the presentation of the diagram. Pupils are unable to estimate the ratio between the two circles. I have made this the Fig. 9. subject of experiment by placing a large copy of the diagram drawn to scale before about thirty classes of pupils between 12 and 15 years of age (representing altogether 1245 individual pupils) without giving any hint about what it represented geographically. The only question asked was: How many times is the big circle bigger than the little one? I made the same test with various classes of undergraduate students (453 in- 366 EXPOSITION AND ILLUSTRATION IN TEACHING dividual students in all) of ages 19 to 22. The follow- ing is the percentage results of the estimates formed by the various pupils : — Group I Group II - Pupils 12-15 Pupils 19-22 Under 100 Exactly 100 Over 100 56.2 15.7 28.1 30.1 29.0 40.9 100.0 100.0 Naturally the older pupils made fewer wild guesses than the juniors. In Group 1, 17.2 per cent estimated the area as under 20 times; in Group II, only 2.3 per cent made this low estimate. But strangely enough, while of Group I only 8.0 per cent estimated over 300 times, 9.3 per cent of Group II made this exaggerated estimate. One striking difference between the two groups is that there is much more ^^ round number" work among the first Group. The second Group quite obviously deals with squares of numbers, while the first Group have exactly 50.7 per cent of even number guesses — i,e, 20, 30, 40, . . . 200, 300, 400, etc., up to 1000. In Group I 2.5 per cent estimate exactly 1000. Only one student in Group II makes this loose guess. In the first Group one pupil guesses 5000, and one actually goes the length of 10,000. The great majority of the guesses are, in fact, quite wild. About a dozen pupils in Group I give such inexplicable answers as ^^They are as big as each other.'' But a good many must have thought what one pupil had the courage to write: THE DIAGRAM 367 '^One cannot tell how much bigger, as the small one can go into it almost as many times as one likes/' In the case of Group II it appears likely that 29 per cent represents the real proportion of those who esti- mated 100 correctly. The same can hardly be said for Group I. The tendency to select round numbers is so marked that we must make allowance for the in- clination to be specially attracted to 100 because it is so preeminently a round number. Thus, while 15.7 per cent guessed 100 exactly, no fewer than 12.04 per cent guessed 50 exactly, while 5.5 per cent guessed 200 exactly. The important result of the experiments from the point of view of Illustration is that the diagram gives no real help in estimating the relative sizes of two geo- graphical areas. Can it be maintained that the illus- tration works the other way? If the pupils are unable to estimate that the big circle is a hundred times bigger than the little one, are they at all likely to be clearer about the ratio of 1 to 100 by looking at the diagram after being told what the ratio is? If not, can the dia- gram be said to serve any useful purpose? The answer would appear to be that, taken in connection with the actual figures, there may be a certain aesthetic satis- faction in seeing the diagram. It may therefore help in fixing an impression that is made by other means, but its effect must be recognised to be aesthetic, not didactic. Geometricians discriminate between what they call diagrams of illustration and metrical diagrams. The first kind " are intended to help the reader to follow the mathematical rea- soning. The construction of the figure is defined in words so 368 EXPOSITION AND ILLUSTRATION IN TEACHING that even if no figure were drawn the reader could draw one for himself." ' The second kind are "employed in an entirely different way — namely, for purposes of measurement. The plans and designs drawn by architects and engineers are used to determine the value of certain real magni- tudes by measuring certain distances on the diagram. "^ The diagrams we have just been dealing with must be regarded as more or less illegitimate examples of the metrical kind. No doubt they are used to illustrate certain relations, and these relations are of a purely quantitative nature. On the other hand, they are not set out so that measurements may be taken from them. No doubt we could calculate from them the relations they illustrate, but this is certainly not the function they were introduced to perform. Rather are they called upon to illustrate calculations that have already been made. They are, in fact, a hybrid between the two classes. In spite of the literal meaning, — ''marked out by lines," — the term diagram may be applied to drawings in which colour plays an essential part. The areas in the drawing may indicate one set of facts, while the colours that are washed in over the areas may indicate another. The areas may, for example, indicate quantitative re- lations, the colours qualitative. In a geological map the extent of the various strata is indicated by the area set apart for each, while the nature of the strata is ^ How far this is true of the ordinary reader may be tested by asking some one to read the Meno, 82-85, from a text without a dia- gram, and then make an illustrative diagram to suit. Few indeed will be able to supply what is wanted. 2 J. Clark Maxwell, in the Ency. Brit., ninth ed. Vol. VII, p. 149. THE DIAGRAM 369 indicated by the colours : hlack may indicate coal; yellow, chalk; red, volcanic rocks; and so on. It is to be noted that here we have another example of the immanence of the picture in the diagram. There is a natural con- nection between black and coal, and between red and the rocks that are produced by fire. The same feeling after the pictorial is seen in the maps illustrating the various levels of the different parts of the earth's surface. It is a natural convention to represent the low-lying lands by different shades of green according to their height, the higher mountainous levels by various shades of brown (points above the snow-line being left white), and the sea by varying shades of blue. But colours may be used in a completely abstract way, as in the case in which exports and imports are repre- sented by different colours. Sometimes colours and areas are combined for illus- trative purposes. When this is done, there should be the greatest care in maintaining consistency in the use of the colours. In a diagram lying before me as I write, there are two circles, each divided up into sectors representing the amounts of the imports and exports of Great Britain from and to various countries. Here each country should retain the same colour in both cir- cles. But I find that France is green in the imports and salmon-coloured in the exports ; Holland is salmon- coloured in the imports and blue in the exports ; Russia is yellow in the exports and blue in the imports. It may be thought that change in the colours is a trifling matter; but somehow colour has a great attraction for all of us, and particularly for young people. Nothing can be called trifling that draws attention in the wrong place and suggests difference where none exists. 2b 370 EXPOSITION AND ILLUSTRATION IN TEACHING A favourite method of representing statistical facts is by means of columns of varying height. The method is excellent, but it must be used with certain restrictions. First, the element of area must be eliminated. The columns must be of uniform width, so that the real measurement is made in height. In several diagrams I have examined I have found that when very large numbers have to be used along with small numbers, the columns representing the bigger numbers are so tall that it is impossible to include them in the page. Accord- ingly they are broken up into strips and placed side by side. No objection need be taken to this so long as the strips are of uniform length. Six such strips would naturally make a biggish rectangle, and would there- fore represent a very large number, but the largeness of the number would be estimated by the number of strips, not by the area of the rectangle. Sometimes the mis- take is made of representing a quantity that is just too big for a single strip by two equal strips, each a little bigger than half a standard strip. This is a blunder, for in this case we are driven to deal with area and not merely with length. The quantity should be repre- sented by a complete standard strip and a little bit of an additional strip. Each column is, in fact, treated as a line, and the complex diagram is really made up of a series of lineal measurements. We judge by the heights of the various columns, and thus get a good general idea of the comparative importance of the different quantities. When it comes to accurate details, we must fall back upon the actual figures, which are usually available. As a rule it is not wise to use illustrations of this kind as metrical diagrams. Psychologically, it is not quite accurate to say that THE DIAGRAM 371 columns may be treated merely as lines. Our estimate of the width of columns is affected by the relative heights of the columns compared. A low column appears wider in proportion to a high column of the same real width. But this peculiarity need not interfere with the use of columns as illustrations of statistical relations in one denomination. So long as we have a standard height and a uniform width, we can treat them merely as thicker lines than usual. A particularly useful form of colum- nar diagrams is that in which squared paper is used as the groundwork, and squares are blackened so as to form columns of various heights. Each column is in this case so many squares high, and the ^^ permanent sug- gestion'^ of the squareness of the unit prevents the question of breadth arising; though it must be ad- mitted that in the case of a fraction of a square being filled up at the top of a column there is danger of a trifling disturbance through the breadth bias. While it is true that quantities are better represented by straight lines ^ than by areas, there is the limitation that when there is a great disparity between the two quantities compared, the mind may be unable to make the comparison. If, instead of the squares in figure 7, we draw a line one inch long to represent the area of Delaware, and another twenty-five inches long to represent North Carolina, it will be discovered that pupils find it impossible to make an accurate estimate ^ In connection with the view that the straight line is the funda- mental form of quantitative illustration, my friend, Dr. William Gar- nett, the eminent physicist, refers to the fact that in physics all meas- urements are ultimately reduced divisions of a line. The galva- nometer, the thermometer, the barometer all exemplify this. Even in the balance the line remains the standard, though in this case it is reduced to zero. 372 EXPOSITION AND ILLUSTRATION IN TEACHING of the relation between the two areas. In such cases the Hne must be broken up in some way, so that the ratio may be made manifest. One writer who wishes to represent by means of straight hues the ratio between the trade of the British Isles and the trade of the vari- ous British colonies, represents the British trade by a line so long in proportion to the others that he has to fold it into what may be described as a spiral rectangle that has rather more than two and a half whorls. Then this rectangle is filled with other lines variously folded. The perverted ingenuity of the plan may be gathered from its application in figure 10 to the areas of various states of the Union. The plain statement of the facts is : — Rhode Island 1,250 square miles. Maryland 12,210 square miles. Kentucky 40,400 square miles. New York 49,220 square miles. Illinois 56,650 square miles. Texas 265,780 square miles. This is contorted into TEXAS RHODE ISLAWD Fig. 10. THE DIAGRAM 373 Two principles should be kept in view when we are dividing up a line so as to use it effectively in quantita- tive illustration. The first is that we should always work in multiples of the smallest line to be included. Thus, in the area-of-North-Carolina illustration (figure 7, page 361), we should divide the twenty-five line into five lines, each five times the length of the line represent- ing the area of Delaware. Had we been dealing with the state of New York, which is almost exactly twenty- four times the area of Delaware, we would divide the longer line into four parts, each six times the Delaware length. Naturally, if there is not a convenient multiple to include all that we want without leaving anything over, than we must adopt the nearest multiple and represent the remainder by a proportionately smaller length. If the bigger state were represented by the number twenty-six (Arkansas, with 53,850 square miles, fits in here almost exactly), we might either take nine as the multiple and give two full lines and eight-ninths of another, or take five, as before, and add a fifth of an- other. The second principle is that we should arrange our rows of multiple lines horizontally rather than vertically, as it is found that the eye works more easily from side to side than up and down. It is probable that it is this difficulty in dealing in terms of straight lines with widely different quantities that has led to the introduction of illustrations by areas. These give a wider range, without the need of trouble- some foldings or duplications. Rectangular areas seem to lend themselves more readily to subdivision than do circular areas. But this does not prevent the enter- prising illustrator from using the circle. Indeed, this 374 EXPOSITION AND ILLUSTRATION IN TEACHING form of illustration is at present rather in favour. A circle is taken to represent some total, and is divided up into various sectors, each representing a specific part of this total. But here, again, it is very difficult to estimate the areas of the sectors. The usual way is to make an estimate of the relative areas of the various sectors by comparing the parts of the circumference cut off by the including radii. Considerable skill in estimat- ing angular measurement may be acquired by a study of the face of the clock and the different positions of the hands. Limiting himself to the positions of the twelve hours, the student assumes the unit of the hour as equivalent to 30°, and by estimating the position of the radii in relation to the fixed points of the hours, he can make a fair guess at the number of degrees included, and therefore of the proportion of the area of the circle included in a given sector. The two following diagrams were published in an official document to illustrate certain quantitative relations. One would have thought that the percent- THE DIAGRAM 375 ages required no help, but somehow the drawings were assumed to make the matter clearer, till one of the offi- cials, who had trained his eye on the clock-face standard, chanced to see them, and declared after a moment's inspection that both were incorrect (a) to the extent of two-thirds of an hour {i.e. 10°) and (6) to the extent of one-third of an hour {i.e. 5°). On measurement, the reader will find that the estimate is almost exactly right, so skilful is it possible to become at estimating angular measurement by reference to a fixed standard. It is true that this is not quite an estimate of areas, but rather of positions on a circle. The estimate of the included area is really an inference from the angular measurement. This last fact has probably something to do with the popularity of the circular form of quantitative illustration. Sometimes the circular diagram is used in a way that depends still less on the area-sense. The state of a particular business of some complexity, or of some government department, in a given year is represented by an inner circle. Each succeeding year is represented by an outer concentric circle, and the increase or dimi- nution in certain elements (sales, cases, prosecutions, deaths, or what not) is indicated by the protrusion of larger or smaller extensions of uniform shape, but vary- ing size, from the original circle. If the concentric circles increase by a uniform lengthening of radius each year, the protrusions from the original circle may be compared with each other on the same standard, so long as their shape does not depend on the diameter of the circles. Oblong protrusions of uniform width may press into any number of concentric circles without being affected by the increasing diameters. We are, in 376 EXPOSITION AND ILLUSTRATION IN TEACHING fact, enabled to treat the oblong prolongations as mere lines. Ingenious people, of course, can introduce all manner of more or less useful complications/ It may very reasonably be questioned whether the general weakness that we have observed in estimating areas is an essential part of human nature. It may well be that this is merely a department of experience that has not received its proper share of attention. Ed- ucation has certainly done little towards training this particular mode of dealing with the materials presented by the outside world. Experiments have been made, it is true, but seldom on a large scale, or continued for a long time. Several years ago an enthusiast in educa- tion in the east of Scotland produced a scheme for the training of all our sense perceptions. On the analogy of Athletics, he called his system ^^Mentics.'^ It was not widely taken up, but in one or two cases it was applied with great thoroughness and success. An es- sential part of the scheme was a training in the estimat- ing of areas, and in one case, at least, in which it was applied the pupils developed quite a striking skill in estimating areas that happened to fall into the geo- metrical forms that had been used in their training. That is to say, the pupils could readily arrange in order of area a number of cardboard hexagons, triangles, squares, and other regular figures. They were less happy in arranging in order figures that had not occurred in their regular exercises, but they did much better work even with irregular figures than any class of equally intelligent but untrained pupils. On the ^ For a very interesting example of this form of circular illustration, see the Report of the Minister of Public Instruction of New South Wales, 1908. (Physical Condition of Children.) THE DIAGRAM 377 other hand, when the ^^mentically'^ trained pupils were taken into the country, they showed no unusual skill in estimating in acres the fields through which they passed; though looking at clearly marked fields from a height at some distance, they were able to compare with fair accuracy the areas of the different fields. There can be no doubt but that under the rapidly approaching development of handwork in all its branches in schools the area-sense will be much more highly cultivated than in the past, and even the bulk- sense will receive a certain amount of training. In the meantime, it is very difficult to get an ordinary pupil to understand how a fifty-cent microscope can be said, without actual lying, to magnify ^^ nearly 30,000 times,'' while a fifty-dollar instrument claims no more for itself than four or five hundred times, or seven hundred at the most. We may point out to the pupil that the first is estimated in cubical content and the second in diameters. But after we have explained that the cheaper microscope probably magnifies 30 diameters, or 900 {i.e, 30 x 30) area units, or 27,000 {i.e. 30 x 30 X 30) cubic units, the pupil still finds a difficulty in taking in our meaning. To be fair to the good micro- scope, we must claim that it magnifies 343,000,000 times (700 X 700 X 700) . But this seems to prove too much. The pupil clearly thinks he is being imposed on. This enormous figure, he thinks, must be a mere ^^way of talking" — and he is right. As a matter of fact, ex- cept on the smallest scale, we cannot perceive cubical content ; we must deal with it as a matter of inference. We are all familiar with the very common confusion between eight feet square and eight square feet. But confusion is much more general when we deal with 378 EXPOSITION AND ILLUSTRATION IN TEACHING cubic content. Most people who are preparing for their first ocean voyage make a very serious error in their interpretation of the 'Hwenty cubic feet/' or the ''sixty cubic feet" allowed for baggage. Their minds are dazzled by a spaciousness in which an additional trunk or two are matters of no moment. Some people never acquire the volumetric sense, but have through- out life to take the shipping people's word for the surcharge. Others are amenable to the teachings of experience, and come to form a fair idea of what the phrase ''sixty cubic feet" means when expressed in crates and trunks. But while this form of inference may be trained, the process is a part of substantive teaching, and ought to precede the use of the area- or volumetric-sense as an aid in illustrating something else. Diagrammatic illustration offers a capital field for the sense when cultivated, but is not the field in which the cultivation should take place. Pending the further development of the area-sense, it will be wise to limit the range of the diagrammatic. Since the great value of the diagram is its abstractness, it does not seem desirable to carry it into a region where extraneous elements have to be taken into account. If we can represent all we want by means of straight lines, why should we seek for a more complicated medium ? When we know that Indiana is only one- hundredth part of the area of the whole of the states, why should we seek for illustrations that only' hamper our freedom in dealing with this fact? After all, it is a quantitative fact, and should not be confounded with a qualitative one. It is true that after we have mastered this mere numerical ratio, we have a very great deal to learn before we can apply this knowledge intelligently. THE DIAGRAM 379 Mere area is not everything. But the necessary amplification of our knowledge is to be brought about by other forms of illustration. We shall understand the meaning of Indiana and the United States a little, but not much, better because we have learnt that a certain white circle is one hundred times as big as a certain black one. What is wanted after that is an application of the principle of elaboration. So far as mere quantity is concerned, we have enough when we have the bald statement of the ratio. One of the best illustrations of the application of the Jacototian principle, '^ Learn one thing thoroughly and refer everything else to it,'' is to be found in a diagram (figure 12) that occurred in the geography book ^ on which I exhausted my boyish enthusiasm. Unfortu- nately, my teacher did not attend to the Note at the foot. The diagram was always taken for granted, so that a large number of my classmates never quite knew what was meant by the remarks that headed the various countries dealt with in the text. For example, under Peru, one read ^^ Latitude in the middle the same as the south of Lower Guinea"; and under Arabia, ^^Same latitude as from the middle of Morocco to the middle of Senegambia." In schools, however, where the book is properly used (for it has still a wide sale), there is continual reference to the diagram, with the result that the pupils learn to know exceedingly well the relative positions of the different countries on the face of the globe. Naturally, this is not the final stage in teaching relative position on the earth's surface. It represents the pictorial stage, or perhaps, better, the pictorial aspect. There is not only room, but necessity, ^ Modern Geography for the Use of Schools, by Robert Anderson. 380 EXPOSITION AND ILLUSTRATION IN TEACHING Note. — Teachers are requested to see that their pupils thoroughly master this brief lesson. The position of these eleven countries, which occupy the western shores of the Old Wojrld, is used to indicatcihe latitude of all. other countries of_the globe. Fig. 12.1 * Reproduced by kind permission of Messrs. Thomas Nelson and Sons, London and New York. THE DIAGRAM 381 for the freer indication of position on the surface of the globe as indicated by latitude and longitude. But the diagram follows the laws of good teaching in beginning with the matter and ending with the form. A similar diagram of the Eastern states might be used with very great advantage in teaching the relative positions of the various parts of the Union. When we are given the latitude and longitude of Georgia and Oregon, we can, by referring to a common standard reason out their rela- tive positions. But in facts that are so close to our everyday life it is well to get, wherever possible, at immediate connections. If we fni the position of a given state, by reference to a certain state on the Eastern coast, we are working up our complex of the states as a whole. Speaking generally, a diagrammatic illustration should be reduced to its lowest possible terms. Caran d'Ache, Phil May, and other artists who dazzle us by the fewness of their lines, seek quite a different effect from that proper to the diagram.^ Their aim is to reach the maxi- mum of suggestiveness with the minimum of representa- tion. They invite the spectator to supply as full details as he can, and their success is measured by the con- trast between the exiguous presentation and the ex- ^ We are told that such artists make their first drawings in the ordinary way, filling in all the details so as to get a broad general eff"ect. Then they proceed to discover which lines are essential, and by a grad- ual process of elimination they reach the effective skeleton that is finally reproduced. The same thing is true of writing. Mr. H. G. Wells, for example, tells us that he first writes down things as they come into his mind, so as to "get some idea of the shape of" his subject. This first writing he calls "slush," and it is ruthlessly cut down as the book approaches completion. The "slush" may amount to over 100,000 words, the completed book to 55,000. (Interview in To-day, Sept. 11, 1897). 382 EXPOSITION AND ILLUSTRATION IN TEACHING uberant mental picture. The diagram, on the other hand, seeks to confine the attention to one particular direction. It seeks to illustrate one relation. Caran d'Ache invites to an exercise in elaboration, the dia- gram to an exercise in elimination. A curious illustra- tion of this invitation to elaboration was supplied some 189^ 1890 Fig. 13. years ago when there was a passing fashion in what was called ^'match-drawing.'^ This consisted in represent- ing human beings by means of straight lines only, as a child might do by placing matches on a table, so as to represent the trunk, legs, and arms. The interesting point for us is the skill with which the draughtsmen could suggest characteristic attitudes with this very limited means of expression. Fencers, boxers, walkers, runners, were all reproduced in the penny illustrated magazines in such a way that the spectator had to fill in the details whether he would or no. Sometimes match-drawing is used for real illustration. Thus, in a journal called Cycling, on July 22, 1894, there ap- peared the preceding drawing, figure 13, to illustrate the difference of the attitude in riding the bicycle in the year 1890 and in the year 1894. It appears that be- THE DIAGRAM 383 tween these two dates a lamentable degeneration had taken place, owing to the scorching habit. It is to be hoped that the accompanying sketches represent an exaggeration: what we are certain of is that they viv- idly represent the views of the magazine writer. The reader's attention is not distracted by the personal appearance of the riders, or the qualities of the machines. Only the essentials appear. There is a certain amount of complication involved here, since suggestion will naturally invite to poten- tial elaboration. One may read as much anatomy and physiology and fashion into the figures as one's know- ledge admits. But there is not a line in the illustration that can be fairly called non-essential. We have here practically reached the limits of suggestion by resem- blance in a diagram. There remains that kind of diagram that represents certain truths without indicating any sort of resem- blance between the lines and forms used and the con- tent of the complex that forms the illustrandum. All the newer graphic methods used in the teaching of mathematics belong to this class, and all the various schemes of plotting out results in charts. The ac- companying diagram, figure 14, for example, has no re- semblance to either work or fatigue, yet it represents in a very efficient way the relation between fatigue effect and practice effect in determining the amount of intellectual work done in a given time. The abscissa, OM, represents the length of time the test lasted, in this case two hours. The ordinate, OL, represents the amount of work done. The work begins at A, and for a little time, through distraction and the effort to concentrate, there is a slight diminution of efficiency in 384 EXPOSITION AND ILLUSTRATION IN TEACHING work. At B the practice effect begins to tell, and the line gradually rises to C. At this point the practice effect is counterbalanced by the fatigue effect that goes o length of time the test lasted: in this case two hours m Fig. 14.1 on increasing, while the practice effect cannot increase further. The result is that there is a gradual falling off in the effectiveness of the work till we reach D. Here the prospect of a speedy release from effort, along with a quickening of the conscience, in view of the approach- ing end of further opportunity, gives a little fillip to the student, and his effectiveness rises somewhat till the two hours end at E.^ The value of such diagrams is that we can envisage at one glance a large number of facts that would baffle any mind to deal with when presented seriatim. What Professor Karl Pearson calls an ''observation frequency polygon," ^ and Mr. Graham Wallas (from a * Reproduced by kind permission of Messrs. Schleicher Fr^res, Paris. 2 A. Binet and V. Henri : La Fatigue Intellectuelle, p. 239. ^ For illustrations, see the periodical Biometrika, passim, or Karl Pearson's Chances of Death. THE DIAGRAM 385 vague memory of its shape) calls a '^ cocked hat/' ^ is one of the best examples of this graphic aid to think- ing. Mr. Wallas quotes from Professor Marshall ^ in support of the statement that qualitative reasoning in economics is passing away and quantitative reasoning is beginning to take its place.^ Among my postgraduate (science) students, many of whom have studied under Professor Karl Pearson, and most of whom have been influenced by him, I note an increasing tendency to think in diagrams. I come across this line-thinking in all manner of unexpected places. An essay on the Shakespeare-Bacon controversy was full of ^^ cocked hats," and in an essay handed in the other day on the interactions between pupil and teacher, I found the whole positions set out in a sort of diagram of forces. The now common school plan of recording such matters as lengths of shadows, temperatures, baro- metric pressures, school attendances, have rendered the chart form of illustration familiar even to young children. It is true that these records are treated as processes of instruction rather than of illustration, and in the preparation of the curves there is training of a very valuable kind. Children are, in fact, being taught to think quantitatively. For our present pur- pose the important point is that pupils are now pre- pared by their substantive school work to understand all manner of chart illustrations. We have seen already the value of the straight line ^ Human Nature in Politics, 1908, p. 133. 2 Journal of Economics, March, 1907, pp. 7 and 8. 3 Human Nature in Politics, p. 143. Here Mr. Wallas gives a very amusing and enlightening illustration of quantitative thinking on the subject of the best size for a debating hall of given shape. 2c 386 EXPOSITION AND ILLUSTRATION IN TEACHING as the best way of indicating a comparison in one single element, as area, or length, or cost, or weight. But there is another way in which the straight line has a special illustrative value. In dealing with mental activity we find that sense of direction is character- istic of mental functioning. ^^When this ^direction' is determined for me," says Dr. James Ward, '^I am said to be passive; when it is determined by me, I am said to be active.''^ There appears to be something more than mere metaphor in this psychological use of the word direction. Here is what Professor S. Alexander has to say on the subject: — "Now that I know what my brain is, I feel my thought occurring there, or, if not there, in some other part of my body. It is only as thus understood in connection with the bodily organism that I can say my mental activity is a movement with direction. But in this sense it is a movement that does occur in time and space. In other words, my mental activity is always qualified by what, on the analogy of local signs, I must call signs of direction.'' ^ Without laying too much stress on the psychological basis thus suggested, it may fairly be said that the straight line in certain diagrams performs the functions of those signs of direction. In a genealogical table the lines really do direct the mind, which in following this direction shows itself to be in this case passive. It is a matter of common experience that the mind is dominated by arrows and other indications of direction as they appear in graphic form. That such indications are a saving of thought effort is proved by their use in the graphic humour of the Sunday papers, in which it is now customary to indicate the direction of a projectile ^ Proceedings of the Aristotelian Society, 1908, p. 226. 2 Ihid., p. 220. THE DIAGRAM 387 by dotted lines, so that the indolent spectator may be saved even the trifling trouble of discovering from which direction the projectile came on its fun-making errand. The plain man's desire ^Ho see a thing in black and white" is better met by a linear diagram than in any other way. Even when the letterpress is perfectly THE TEACHER'S USE OF LANGUAGE. THE BRIDGE ( BUT J SOMETIMES J NOT V I FAMILIAR UNDEBSTOOO EXAMPLE. HAVE TW KINDS I. OF MEA NINGS EXAMPLBr ^*— *~->^ " DOG SUGGESTS X X /^ X DOoTl'irrFVs'Ta 1. FOUR-LEGGEDNE83, / \ f \ i rftb?^vfJ ■II HAIRINESS ) /cONNOTATIOnX / DENOTATION \ ( , " ^^YernaRO /^T^'i-^E^E^D^N^SS A QUALITIES J TH?n"gS { <" FOX-tSeR 'Y:STEDNElf -^V J \ / V-P00DL°."'''^'° etc.; etc. \,__,^ \^____^/ ^- poodle Fig. 15. simple, the reader frequently likes to have a diagram- matic representation. In 1903 I published a little Primer on Teaching meant specially for Sunday-school people. Naturally I wished to make the text as simple as possible, and thought that I had made it so plain that no one could need any help to understand its meaning. Some time after its publication I received from a clever engineer ^ in New York a set of eleven diagrams that give a graphic representation of the main points in the various chapters. The engineer was the superintendent of a Sunday-school, and told me ^ Mr. John Calder. 388 EXPOSITION AND ILLUSTRATION IN TEACHING that he found his teachers understood the book in a much more practical way after he had given them his diagrams. Figure 15 reproduces one of these diagrams. On looking at it, one would think that the matter could have been equally well expressed in plain verbal exposition. But on putting the matter to several fairly well-educated Sunday-school teachers, I found that they, on the whole, preferred to have the diagram, but were good enough to admit that it must come after the text. We need be the less surprised, then, to find diagrams in such abstract books as Mr. W. MacdougalFs Social Psychology. In introducing an admirably clear exposi- tion of the neural bases of the sentiments of hate and love he says: ^^It is, I think, helpful, at least to those who make use of visual imagery, to attempt to picture a sentiment as a nervous disposition and to schematise it crudely by the aid of a diagram/' ^ As a matter of fact, the diagram consists of a row of seven small circles, each representing one of the primary emotional dis- positions. The rest consists merely of certain lines and arrows indicating direction. These lines have a com- pelling power, and cause the mind to follow them al- most in spite of itself. They are more useful in help- ing the student to understand than in helping him to recall details. It has to be noted that the mere presence of the lines helps to fix the attention. This is the justification of the habit some capable teachers have of making what seem quite unnecessary lines on the blackboard. They will put down this sort of thing on the blackboard and accompany it by something like the following: ^ Social Psychology, p. 124. THE DIAGRAM 389 ''Let A represent Walpole, B Queen Caroline, and C George the Third. The natural way of communicat- ing with the king would have been for the minister to speak directly to him; but as a matter of fact, impor- tant communications usually took the route indicated by the arrows.^' All that this triangular method im- A B plies has, of course, to be brought out by the teacher, but he feels that he has had a greater grip on the pupil's attention because of the apparently unnecessary figure. When I suggested to the teacher that it might have been better to use significant letters, W, C, and G, he main- tained — influenced, no doubt, by his memories of math- ematics — that the more conventional the symbols the better. To put the actual names Walpole, Caro- line, and George would, he maintained, have spoiled everything. Here he differed from the originator^ of this illustration — strangely enough the teacher to whom I spoke seemed to re- gard the illustration as his own — who uses the signi- ficant initials W, K, and Q. The view that significant letters are objectionable is evidently adopted by the writers of the Public School Latin Primer, in which the *R. Somervell in P. A. Barnett's Teaching and Organisation, p. 171. Fig. 16. 390 EXPOSITION AND ILLUSTRATION IN TEACHING solitary little diagram in the book, figure 16, illustrates case by means of letters without significance : — — " Case {casus, from cado) is, literally, a falling. Grammarians rep- resented that form which a Noun takes when it is the Subject of a sentence by an upright line, as AB, and likened the other forms to lines falling away from the perpendicular at various angles, as, AC, AD, AE, AF, etc. These they called Cases; and their series, the declension, declining, or sloping down of the word. Afterwards, the Nominative or Subject case was called (with evident impropriety) Casus Rectus, the Upright Case, and the others (except the Voca- tive), Casus Obliqui, Oblique Cases; whereas the Stem {or Crude form) of the word is more properly the upright Hne, and the several cases, including the Nominative and Vocative, are branches deflecting from it. So, from the Stem nuc- (walnut-tree), the Cases are : N. V., nuc-s (-ux). Ace, nuc-em, G., nuc-is, D., nuc-i, Ab., nuc-e.'' ^ Probably the influence of custom on the schoolmaster in making ^'Diagrams of Illustration'^ in Euclid had a good deal to do with the selection in this case of the first letters of the alphabet. At any rate, in actual exposition to a class, experience shows that it is better to adopt significant letters. is substituted for A, and S for B; thus, OS represents the stem; then Ace. would represent the accusative, OG the genitive, and so on. It would seem that the pupil can hardly understand the meaning of case much better from seeing his teacher draw seven lines from a given point; but in practice it is said that the drawing does actually help. Probably some, at least, of the advantage comes from the draining off of a certain amount of nervous energy on the part of both teacher and pupil, an energy that might other- wise interfere with the learning process, just as in think- ing out riders in Euclid the pupil works more steadily when he has a pencil in his hand, even if he makes no use of it in the way of either drawing or writing. ' P. 154. CHAPTER XVI Dangers of Illustration As an ending to a question the words '^Give exam- ples/' are very dear to the heart of the examiner. With those who are called upon to write answers to ex- amination questions, the words are not quite so popular. The complaint of the examiners is that the examples given are stereotyped. If an example is given in a text-book, it reappears with cloying persistency in the answers. Out of nine hundred answers to a question in a Board of Education school management paper asking for an example of one word being run into an- other in reading aloud, over six hundred gave ^Hhis shrub" the actual phrase used in a then popular text- book. Very few candidates had the originality even to change the letters while retaining the actual example, as in ^Hhis stable." Experience shows that there is a strong tendency to fall into ruts in illustrating any particular point. Ask a class for examples of sentences. If the first pupil says ^^Cows eat grass," the chances are that his fel- lows will go on mentioning what other animals eat. If we wish to provide reasonably varied examples for class work, we must consider beforehand which illus- trations we shall use in a given lesson. It is the com- monest thing in the world to find a teacher depending for his illustrations on the spur of the moment. If he 391 392 EXPOSITION AND ILLUSTRATION IN TEACHING has a mind particularly well stored with matter on the subject he is dealing with, he may escape from the seri- ous defect of supplying tiresome strings of more or less similar and eminently commonplace examples of the rules he is expounding. It is easy enough to supply almost unlimited quantities of examples of particular kinds of nouns and verbs, or of natural orders in botany, or of islands in geography. In writing on the black- board sums to be worked out, the teacher finds that the numbers come without the least difficulty. In all these cases the connection between the rule and the example is so clear that no mistake is possible except through such culpable ignorance as is seldom to be found among teachers. Here one example does almost as well as another. The content of the individual example does not affect the general rule to be illustrated. So far, what may be called the hand-to-mouth method of illustration is innocuous, and is even advantageous, since it saves unnecessary labour. So soon as the con- tent of the illustration becomes of importance, the method will be found to be full of danger. The teacher who carelessly dictates at random half a dozen English sentences to be translated into Latin to illustrate the construction of cum with the subjunctive, may lead to all manner of confusion among his pupils, because they find in the sentences other difficulties than those con- nected with cunij difficulties that have not been pre- pared for by any previous instruction. A teacher's brilliant scholarship is no safeguard against error here. All such illustrative sentences must be carefully edited by the teacher in the light of what he knows of the previ- ous training of his pupils. No doubt there comes at a later stage of instruction in Latin prose a time when the DANGERS OF ILLUSTRATION 393 pupils must be prepared to deal with unedited English passages for translation into Latin; for at that stage they have a sufficiently wide knowledge of Latin con- struction to allow them to exercise a certain freedom. But even at this stage the master must not select his English passage entirely at random. Certain passages cannot be translated into Latin, since they contain words and ideas that the classical writers have not had the forethought to anticipate. Some teachers escape the dangers of the hand-to- mouth illustration by more or less unconsciously ac- quiring a stock of illustrations that they stereotype, and keep in hand so as to produce them on appropriate occasions. Great weariness often results for the pupils who have to submit to the same illustration without explanatory comments that might make it intelligible. As soon as the question of transitive or intransitive came up, a certain teacher might be relied upon to make the following remark, and no other: ^^The cat cannot sit the mat, therefore sit is intransitive. '^ Years afterwards that teacher's pupils spoke with bitterness of that intransitive cat. The reproach of the stereo- typed illustration is removed when it can be shown that it is a real touchstone of truth that may be applied to all cases within its sphere. For instance, there is a peren- nial difficulty among young students of French about which of the verbs take etre and which avoir in conju- gating their past tenses. Some text-books deliberately give lists of verbs that are conjugated with avoir, and no attempt is made to lay down the principle that may explain this peculiarity. This principle seems to be that where the action of the verb is followed by a corre- sponding state, the verb Ure is to be used ; in all other 394 EXPOSITION AND ILLUSTRATION IN TEACHING cases, the verb avoir. The stereotyped test is in the form of the question : ^' If the subject has done so-and-so, is it so-and-so?'^ This is obviously obscure, so a parti- cular case is taken. ^'If the subject has come, is it comef^^ If the answer is yes, then etre is the verb; if no, then avoir. It may be simpler to adopt the form of the second person: '^If you have done so-and-so, are you so-and-so?'^ ^'If you have eaten, are you eaten?'' No; then use avoir. But whatever the form, it must enable us to discriminate between those cases in which a verb sometimes has etre and sometimes avoir. Take the verb descendre, with the subject le chef. '^If le chef has descended, is he descended?" Yes; therefore etre. "If le chef has descended the dinner, is he descended?" No ; therefore avoir. Le chef a descendu le diner. So with the simpler case of quotation marks in writ- ing a dialogue. The pupil may be given the stereo- typed question: Did the speaker open his mouth and let out the very words in question? If the answer is yes, then quotation marks must be used. With duller pupils some teachers adopt the grosser device of making the pupils ask themselves whether the doubtful words could be represented within the bladders of words that are drawn as coming out of the mouths of persons in in- ferior comic cartoons. The method may be objection- able because of its associations with trashy literature, but so far as being stereotyped is concerned, no harm is done, since the illustration is of universal application. In almost every subject the hand-to-mouth illustra- tor gets into trouble by demanding from his pupils knowledge that is not yet due in the course of their study. It is probably unnecessary to labour this point here, for the reader who has taken the trouble to DANGERS OF ILLUSTRATION 395 follow this book so far has given proof that he has enough interest in the subject of method to prevent his making the discreditable bungles that not infrequently mark the teaching of brilliant scholars who rely upon their mere knowledge of the subject to carry them through, without taking the trouble necessary to make their teaching efficient. The reader^s danger may in- deed be quite the opposite. Because of his interest in the theoretical aspect of his work, he may be inclined to over-elaborate his illustrations, and may thus fall into certain errors that are likely to interfere with the suc- cess of his teaching. To begin with, there is the danger of over-illustration. Some teachers seem to regard it as an established prin- ciple that every point that arises must be illustrated, whether it offer any difficulty or not. What is per- fectly clear already needs no illustration as a matter of Exposition. A straightforward statement of fact deal- ing with elements that come well within the pupiFs range should not be illustrated, so long as the teacher's purpose at the time is only to get the pupil to under- stand. Indeed, it is possible that by illustrating what requires no illustration the teacher may cause needless difficulty to arise, especially in the minds of the more eager and attentive pupils. Accustomed to attach a meaning to all the teacher says, such pupils are apt to think that since he makes so much of the point he is labouring, there must be something in it which they do not yet perceive, and they may grope about for a meaning that is not there. By the commonplace teacher the temptation to over- illustration is easily resisted. His danger lies in quite a different direction. But there is a very real risk in the 396 EXPOSITION AND ILLUSTRATION IN TEACHING case of the zealous expositor. No limit can be set to the possibilities of illustration, once the lust of the collector is joined to the enthusiasm of the teacher. Every keen expositor is a potential grangerite. "In our time the term 'grangerite ' has come to be applied to the commentator who summons illustration to his aid in dealing with a book already printed. That, however, does not cover his art, which includes everything bearing on the elucidation of the text. I use the word 'grangerising,' then, as a term for the general art of what may be called the methodised scrap-book — for in its very method it differs widely from the oUa-podrida usually known by that name." ^ The art, named after the Rev. James Granger, who began life in Dorset, England, in 1723, is full of attrac- tion, not to say temptation, for the industrious and in- genious teacher. When he is taking a class through one of Shakespeare's plays, and as a help in his preparation cuts up two cheap copies of the text and pastes the sepa- rate leaves each in the middle of one of the pages of a large manuscript book, so that he may fill the abundant margin thus supplied with notes of all kinds on the text, he may not know that he has set out on a grangerising expedition. He cuts out some critical remarks from newspapers or magazines and pastes them in his book. If he can get pictures, he naturally includes them in his collection. By and by it is clear that even the huge manuscript page is insufficient, and a new book is neces- sary. He is not likely to go to the excess that drove Lefevre to grangerise Voltaire into ninety volumes, but he may very easily be carried away beyond the bounds of prudence. Kept within modest hmits, a grangerised copy of a classic to be studied or a text- 1 J. M. Bullock : The Art of Extra- Illustration (1903) p. 10. DANGERS OF ILLUSTRATION 397 book to be taught is a valuable possession, both for the information it actually contains and for the mastery of the subject that its compilation helps to secure. But there is always the danger of the collecting interest getting the upper hand, and the book becoming an end in itself. Instead of illustrating the original text, it dwarfs that text, swamps it, drowns it. The teacher must never forget that as teacher his interest lies in ex- pounding the text or other subject. His illustrations are to be illustrations of the original subject. The grangeriser very rapidly gets off the main line and goes on illustrating illustrations, till the real subject is left far behind. What the teacher must avoid is well exemplified in Hill Burton's caricature of the granger- ite's methods of illustrating the familiar lines: — How doth the little busy bee Improve each shining hour, And gather honey all the day From every opening flower. "He pictured him starting with the poet, Isaac Watts. This would suggest all manner of bees, — Attic and other, — and all sorts of beehives would be appropriate, to be followed by portraits of Huber and other bee-collectors, and views of Mount Hybla and other honey districts. Burton poured good-humoured contempt on the process by drawing out the agony of subjects to be illustrated; but in the forty years that have elapsed since he penned the Book Hunter, the subject of the bee has been extended to a point more elaborate than Burton ever contemplated. To-day the exhaustive (and exhausting) grangerite would have to include, for example, a portrait of Maeterlinck, who has told us the story of the bee in terms of the most charming philosophy, to say nothing of Lord Avebury's many works, and the scientific construction of the bee- hive. Burton then went on to say that the grangerite would have to remember that there was once a periodical called the Bee, edited by Dr. Anderson, who was the grandfather of Sir James Outram, 398 EXPOSITION AND ILLUSTRATION IN TEACHING whose career might be included. Finally, he genially suggested that, when the illustrator came to the last hne, * which invites him to add to what he has already collected a representative of every opening flower, it is easy indeed to see that he had a rich garden of delights before him. '" ^ A French psychologist, writing on the theory of laughter, admits that he used to read the examples of fallacious reasoning in his text-book on logic, as a sort of legitimate jest-book. George Eliot gives us a delight- fully true account of the seductive charms of the matter supplied in the illustrative examples in the Latin grammar. Maggie TuUiver : — "presently made up her mind to skip the rules in the Syntax — the examples became so absorbing. These mysterious sentences snatched from an unknown context — like strange horns of beasts, and leaves of unknown plants, brought from some far-off region — gave boundless scope for her imagination — the fortunate gentle- man whom every one congratulated because he had a son 'en- dowed with such a disposition ' afforded her a great deal of pleasant conjecture; and she was quite lost in the 'thick grove penetrable by no star.'"'' We have here a force with which every teacher has to reckon, the examples always have been and always will be so absorbing. As a rule they are not in them- selves dangerously interesting: they usually obtain their power by contrast with the still less entertaining matter of the text. Even the pubhsher's advertise- ments at the end of the book are not without their attractions as a relief from what the book itself con- tains. Making all allowance for this unearned incre- ment of interest that attaches to examples, we find that 1 J. M. Bullock; T/ie Art of Extra Illustration, p. 19 (published 1903). The original passage will be found in The Book Hunter, Part I, "Class- ification." 2 ]\j;j^ii Q^ if^Q Floss, Book II, Chap. I. DANGERS OF ILLUSTRATION 399 the legitimate attraction of the examples is a dangerous rival to the teacher. The way to meet the difficulty is not to make all the examples of the most uninteresting character, but to select them, as far as possible, from matter that has already exhausted its interest in other parts of school work. Let the teacher consider the wiles of the clever advertising tailor and learn of him. In a certain shop in Holborn, London, there appeared a little while ago a new set of wax heads to surmount the dummies that displayed the ready-made suits in the window. The new heads were exceedingly well made and formed a very agreeable change from the wooden knobs that had formerly finished off the dummies. The passers-by were greatly interested, and gave un- stinted admiration to the type of head adopted. There was, however, one fatal defect from the point of view of the critical public. The whole thirteen heads were of exactly the same pattern; in fact, they were the same head, cast in the same mould, coloured with the same pigments and by the same process, supplied with the same glass eyes and the same curly brown hair. On being remonstrated with, the tailor admitted that his aim was not entirely disinterested. The heads were specially good in order to attract attention to his window. They were made exactly alike so as to ex- haust very rapidly the interest of the onlooker, who, disappointed at the similarity, sought for and obtained the necessary variety by examining the different kinds of suits of clothes. In the case of teachers who use as examples matter that has already exhausted its interest in other depart- ments of school work, there is a double end served — old matter is revised, and a new interest is created in it, 400 EXPOSITION AND ILLUSTRATION IN TEACHING which new interest is of exactly the kind the teacher desires to arouse, for it is connected with the work actually in hand. The pupil is interested to know what the teacher is going to do with this familiar old fact that is being presented. The whole question of corre- lation is involved here. Teachers are now aware of the dangers of weariness that are implicit in the overzeal- ous use of correlation. But our present consideration recognises the loss of interest in certain parts 9f school work, and proposes to take advantage of this loss. Certain matter is selected because it has lost its in- trinsic interest, and if, in the process of teaching, a cer- tain amount of mediate interest is developed, that is all to the good. One of the chief dangers of the use of illustration is connected with this problem of the incidence of atten- tion. There is always the risk that the illustration will prove more attractive than the illustrandum. The attraction to which Maggie Tulliver yielded is not confined to examples. An illustration fails when it derails the interest of the pupils from the main lines of the lesson. In the case of certain material illustrations, such as models or pictures, the derailing of interest is so obvious that it at once attracts the teacher's attention, and he takes means to recall it to the main subject. This is comparatively easily done if he has the sense to allow the illustration to exhaust most of its primitive interest before he proceeds to use it as a mere illustra- tion. It used to be a matter of professional pride with a class teacher not to let a particularly interesting ob- ject be seen till the moment came at which it had to be produced for illustration. No great harm resulted if, when it was introduced, the teacher allowed a reason- DANGERS OF ILLUSTRATION 401 able time for the pupils to gloat over it before he began to demand their attention to its purely illustrative aspect. The skilful lecturer, on presenting an attrac- tive slide on the screen, follows the plan recommended in Chapter VIII,^ and allows a reasonable time for the subsidence of that gasp of appreciation with its suc- ceeding murmur of whispers that welcomes every strik- ing picture. When he does begin to talk, he takes care to deal with comparatively unimportant matters till the edge of the intrinsic interest of the slide is blunted. If the slide is really important as an illustration, he may introduce it at an early stage in his lecture mainly to rub off its intrinsic attraction. At its first appear- ance he merely calls attention to facts that are in any case attracting the attention of his audience; when, at a later stage, it reappears, he is able to direct the attention of his hearers in the way he desires, for they are now able to concentrate on the line of secondary interest as brought out in the illustrative process. Too frequently the derailing of interest is not antici- pated by the teacher, because he has failed to consider the immediately preceding content of the minds of the pupils. Any reference to certain of the more urgent interests of the pupils may be an excellent way of getting up a secondary interest in some part of school work. Mensuration may be connected with the football field or the cricket pitch, hydrostatics with boating, dynam- ics with the proceedings in the gymnasium. But in all such cases there is great danger of derailing the in- terest from the school subject. No doubt it may be won back again, but in a case of class instruction it is probable that the temporary aberration has caused at 'p. 208. 2d 402 EXPOSITION AND ILLUSTRATION IN TEACHING least a few pupils to lose some important link that they may not be able to catch up during the course of the lesson. The teacher has to remember that every illustration he uses must run the gantlet of divergent association in the mind of every one in his class. He can never be quite sure that the most innocent illustration may not derail the interest of some of his pupils, even though he takes all possible precautions. But he ought at least to minimise the danger by doing all he can to remove temptations. For example, he must avoid the arith- metical challenge^ of which we have already had one or two examples.^ Certain minds are so constituted that as soon as two terms of an arithmetical problem are presented, they must proceed at once to work it out. If at one part of a literature lesson the master mentions that he first read Lycidas at the age of twelve, and at a later stage that it is now a quarter of a century since he first read Lycidas, sl large number of his pupils will neglect the point he is making in speaking of the differ- ent effect of Lycidas on the boy and on the man : their attention will be taken up in calculating the exact age of the master. Young people are particularly open to the arithmetical challenge when it implies a certain amount of criticism of a statement made. Though it was an adult mathematician who made the following arithmetical criticism of Tennyson, it is quite in the schoolboy vein. In his Vision of Sin Tennyson ven- tures the statement : — ^ Pages 250, 309. An excellent example of the irritating effect of the challenge is to be found in the quotation from Mauclair on p. 337. The hourly change and the " twenty times " call for explanatory com- ment. DANGERS OF ILLUSTRATION 403 "Every moment dies a man, Every moment one is born." The man of figures at once accepted the challenge, and pointed out that if this were true, the population of the world would necessarily remain stationary, which, of course, was contrary to recognised facts. He suggested as an emendation the following: — "Every moment dies a man, And one and a sixteenth is born." * He admitted that it was not absolutely accurate, but it was at least approximately correct. It is because this perverse mathematician takes such an unreasonable view that the story forms a useful illustration. The pupil ought to be thinking in terms of poetry; if he persists in thinking in terms of number, there is serious damage done to the lesson. Even when no reference to number is involved in the exposition, certain minds are tempted to introduce calculation. One of the students of an exceptionally slow lecturer at Oxford confessed that, in the inordinate pauses during the lecture, he ac- quired a habit of calculating what each pause cost him on the basis of so much for a course of twelve lectures of one hour each. The moral for the teacher is that Satan's employment bureau does not limit itself to manual labor. Teachers should be very careful in their use of the allusive style. Any reference, for example, to a person or place without mentioning the name will often set up a disturbance that takes quite a long time to settle down. To refer to Milton in a lesson merely as '^the author of the Defensio Populi AnglicanV^ may give satisfaction ^ Quoted by Paratus in the British Weekly, June 3, 1909. 404 EXPOSITION AND ILLUSTRATION IN TEACHING to a certain number of pupils who happen to know who is meant. But to certain others the reference will prove a stumbling-block, for they will go on wondering who it can be, when they should be following the work of the class. In this particular case the average boy would probably not trouble much, for the reference is not in itself interesting to him. But let the teacher use some superlative descriptive reference, and dissipation of attention will necessarily follow. ^'The worst king who ever ruled England,^' ^Hhe author of the longest poem in the English language,'^ are references that will disturb any intelligent class. It goes without saying that it is a laudable thing to be interested in discover- ing the actual persons referred to in such statements. The trouble is that the interest is roused at the wrong time. We are so fond of rousing interest that we are apt to forget that it is as necessary to allay interest as to excite it. In order that the interest of the pupils in the main subject of the lesson may be maintained, all subordinate interests must be ruthlessly dissipated. The way to kill an interest is to satisfy it. Nothing must be left for the imagination to work upon. Every- thing must be represented with pikestaff directness, and the mind will seek interest elsewhere. While writing the above paragraph I have furnished for myself an unexpected and involuntary illustration of my theme. No sooner had I written the words, 'Hhe author of the longest poem in the English language,^' than I began to feel uncomfortable. I realised that I did not know who he was, and I began to wonder who he could possibly be. Milton wandered through my mind, and distracted my attention from the main sub- ject of the paragraph. I had an uneasy feeling that, DANGERS OF ILLUSTRATION 405 though the Paradise Lost was long, it was far from being the longest poem in the English language. I had a vague memory of having heard the phrase ^Hhe longest poem in the English language'^ applied to Drayton's Polyolbion. But there came to me the disquieting im- pression that I had somewhere read that one of the in- dustrious early settlers in New England had outstripped Drayton. Could it be Michael Wigglesworth? Next I comforted myself with the reflection that all I had to do was to turn to some standard book on the subject of lit- erature, and get the matter settled; so I was able to dis- miss temporarily the troublesome interest in favour of the general interest, which was, in any case, the stronger. Had I been a careless pupil in a class with a sporting interest in superlatives, and little interest in what was going on at the time, it is probable that I should have continued to worry about that longest poem instead of turning to the main subject.^ As a test of the truth of the view here adopted, let the reader try to remember whether his attention was not a little dissipated, and if, indeed, he was not somewhat annoyed by the unfinished sentence, ''The most op- timistic writer on Education is . . .,'' introduced^ in Chapter I to illustrate the mind's tendency to anticipate what is coming. Since the hiatus has served its pur- pose, the reader is now entitled to the tardy explana- ^ On referring to text-books, I found no help in settling the question, so I fell back upon an examination of some of the poems that might claim first rank. Paradise Lost reaches the modest total of a trifle over 10,500 lines. The Polyolbion attains to nearly 16,000. The Ring and the Book swells out to 21,133 lines. But the limit seems to be reached in Festus, a Poem, by Philip James Bailey, which, in its reorganised form (Fiftieth Anniversary Edition, 1893), reaches a total that on a rough calculation amounts to 40,800 lines. 2 See p. 15. 406 EXPOSITION AND ILLUSTRATION IN TEACHING tion that the writer referred to is Helvetius, who boldly proclaims " L'education peut tout/' Under certain conditions the allusive style may be excellent in print, but when used in lecturing or teaching, it ought to be limited to the most obvious allusions, allusions that are well within the range of the less informed of the class or audience, so that the main effect of the allusion will be to rouse that feeling of sat- isfaction that accompanies the recognition of an old friend under new circumstances. A typical example of the sort of thing that may perhaps be permitted in a book, but that must be excluded from oral teaching, is to be found in the extract from Madame de Coulevain in Chapter XI of this book/ There we find allusions to "si king," and to ^Hwo of our great newspapers, one of our best reviews." At this point Madame de Coule- vain' s reader puts his finger between the leaves and leans back, wondering who that king and what those publications can be. Unless from the point of view of piquancy, the allusions are a mistake in exposition. If there were any indication of how the missing names could be discovered by the reader for himself, there might be some justification for the mystification, since it would rouse him to take a fair share of the work. But as they stand, they only aggravate the reader by making him feel his ignorance and — it is no extenu- ating circumstance to add — Madame de Coulevain's superiority. Apart from this unprofitable disturbance of mind, the same end could be obtained by saying merely that a king could be as bourgeois as the tenant of a flat, and that some of our great newspapers and reviews are bourgeois. In a lecture or lesson the hearer 1 See p. 294. DANGERS OF ILLUSTRATION 407 would not only be irritated by the unintelligible allu- sion, he would, necessarily, from the distraction of his attention, lose a great deal of what immediately fol- lows the derailing references. If the authoress means Louis Philippe, why not say so? The names of the two great newspapers and the review would be much more illuminating than the piquant riddle she has set us. No doubt, in thus making our references specific we kill a certain amount of interest, but the interest killed is of the unhealthy, distracting kind; audit has always to be remembered that we are mainly concerned here with the didactic use of illustration. An author may feel that it is worth while to aggravate his duller readers so long as he wins the admiration of the clever, and if he is prepared to pay the price, there is nothing more to be said. The irritated reader, on his part, is free to throw aside the tantalising book. But when it comes to oral exposition, it is necessary to carry the whole of one^s audience with one. We cannot, of course, as Dr. Johnson pointed out with some asperity, supply our hearers with understanding, but we are not justified in distracting what understanding they pos- sess by leading it into blind alleys. I have had occasion already to refer to the teacher^s overgrown respect for accuracy. In certain forms of illustration this respect leads him into serious difficulties, for there practically emerge two kinds of accuracy, and these two kinds cannot be reconciled. He has to make a drawing of the earth as an ^^ oblate spheroid.'^ If he makes an accurate drawing, the pupils will be un- able to notice any difference between his drawing and an ordinary circle, but if he flattens the polar ends suffi- ciently to make the true shape apparent, he has played 408 EXPOSITION AND ILLUSTRATION IN TEACHING havoc with the other kind of accuracy, and multiphed many times the paltry six-and-twenty miles by which the equatorial diameter exceeds the polar. Sir John Herschel may speak bluntly about circles representing the orbits of the planets, but knowing that the orbits are really ellipses, the teacher is in a strait between two. If he draws them as circles, he is inaccurate qualitatively, for they are not circles; but if he draws them elliptical enough to make his class easily perceive that they are not circles, then he has to err quantitatively. For they are not so elliptical as all that. Clearly, the teacher must be allowed sufficient quantitative exaggeration to make clear his qualitative distinctions. If his pupils are at a stage at which it is important that they should know that the earth is an oblate spheroid, then he must be permitted so to represent it as to suggest that particu- lar form. It is quite a different matter when little children are sedulously taught that the earth is '^nearly, but not quite, a perfect globe. '^ This is the same lust for accuracy that has canonised the additional two feet in the height of Kinchin junga — ^Hwenty-nine thou- sand and two feet.'' Naturally, inteUigent pupils will be warned when necessary exaggerations are made. They will be told, for example, that though the earth's orbit is elliptical, its major axis is not quite so big in proportion to the minor as the drawing would make out. Another very real danger in the use of illustration is the tendency to carry over the illustration as a whole with non-essential as well as essential elements. A teacher wished his class to understand that for a particular ex- periment he was describing it was necessary to cut out an oblong piece from the middle of one end of a board. As some of the pupils had a difficulty in understanding DANGERS OF ILLUSTRATION 409 what he meant, he explained that the bit cut out was to leave a hole in the bottom of the board, so that when it was placed on end there would be an opening in it like the entrance to a dog's kennel. This seemed to satisfy the pupils, but at a later stage, when they had to make a drawing of the apparatus, several of them made the board appear as a pentagon, like the gable end of a house. They had carried the kennel comparison too far. What in this case could be tested by the sketches, would, in the case of merely verbal description, probably have escaped detection, and with young children, in particular, it is probable that many of our illustrations are carried over bodily and incorporated in connections in which certain of their elements are quite out of place.^ The teacher must be continually on his guard, and must try to anticipate and avoid possible misconceptions of this kind. Nearly always he will find that, in spite of all his endeavours, some dull, commonplace child has contrived an impossible combination that, had it been deliberately made, would be regarded as very ingenious. To meet such contingencies a certain amount of verbal pruning is necessary, but above all there ought to be a good deal of intercourse in the way of applying illustra- tions. A teacher in a city school, in giving a lesson on the Charge of the Light Brigade at Balaclava, made a sketch-plan on the blackboard, with the Russian guns on the right of the board and the formation of hussars represented by two vertical hnes on the left. The class as a whole seemed to understand the state of affairs on the field, but in the course of discussion it came out that some of the boys (the average age of the class was 12+) thought a mistake had been made in the position ^ Cf, the Castle misunderstanding, p. 112. 410 EXPOSITION AND ILLUSTRATION IN TEACHING of the hussars. As they were represented, the boys maintained, they were charging either north or south instead of eastwards, as they ought to do if they meant to get at the Russian guns. On probing, the teacher discovered that the double line had misled the boys. There was a cavalry barracks in the city, and when the troops passed through the streets, they always went two abreast because of the traffic. The boys had got it into their heads that this two-abreast mode of progression was the natural one for cavalry, and that therefore they would charge in this order. It was a revelation to them that the charge was made with such a wide front. Allied to this error of carrying over non-essentials is that of arousing altogether wrong masses of ideas through some superficial resemblance. Beginners in landscape painting are warned against the little cottage on the hillside with its two tiny windows, one on each side of the DANGERS OF ILLUSTRATION 411 door, and the little doorstep, with the resulting resem- blance to a grotesque human face. Not infrequently young people see a ludicrous aspect of some matter that to the adult mind appears to be of the most matter-of- fact character. ^' Speaking of babies," said the Sunday- school superintendent, ^^I have a baby in my eye now." He was quite serious, and did not at first understand what the youngsters found to laugh at in what he re- garded as a very commonplace statement. Occasion- ally private jokes of this kind interrupt the attention of individual pupils, but it is the business of a good teacher to anticipate and provide against any such misapplication of ordinary words, so far as such mis- applications are likely to affect a whole class. The teacher^s safety here depends upon his knowledge of the pupil's mental content. Unintentional jokes in class are always the mark either of ignorance or of bad psychology. Illustrations are often put in what the illustrator regards as a striking way, and yet are apt to mislead the pupils because of their very vividness. I have heard a teacher, in seeking to give his class an adequate idea of the size of London, make the statement that if all the houses in that city were placed end to end, they would reach right round the earth, following the equator. In dealing with the class afterwards, I found that the general impression produced was complicated by an incongru- ous picture in the pupils' minds of an interminable street, with only one side to it. Quite a number of the pupils had the literal objection that most of the houses would be flooded, as the equator was for most of the time over the ocean. On asking the teacher how he got his data for the measurement, he frankly confessed 412 EXPOSITION AND ILLUSTRATION IN TEACHING that he had no data, but 'thought it would be a very effective way of bringing home to the class the enor- mous extent of the city." He further wanted to know, ^^ morals apart/' what objection I had to the illustra- tion. The objection is indicated in the incongruity brought out above, and also in the mistaken notion that in some way or other the imagination of the pupils is aided by the picture of this straggling street. After all, the figure suggested great extent, but nothing more. It carried the pupils far past the Threshold of Stun. A companion picture to that supplied by this ingen- ious teacher is to be found in a text-book of geography that seeks to emphasise the progress of London in this way: ^' A house rises out of the ground every hour of the day; a village of more than three hundred persons is added to its population every day." ^ This has ob- viously no pictorial value. We certainly do not want to figure forth the hourly emergence of a completed house, and the very name of a village suggests some- thing antipathetic to the city spirit. The mere state- ment of a daily increase of three hundred inhabitants is sufficiently clear without the obscuring figure. So far as the figure is pictorial, it is inaccurate. The popu- lation does not increase in that good-naturedly uniform way. The figure interferes with the pupil's chance of clearly understanding the theory of averages. As a matter of fact, in actual experience I have found that quite a large percentage of those to whom I have presented this illustration have at once accepted the arithmetical challenge and multiplied 300 by 365 to get the annual increase, and have maintained that the ^ Meiklejohn : The British Empire, p. 49. DANGERS OF ILLUSTRATION 413 resulting 109,500 was much more stimulating than the daily village. There may be cases at a very low stage of intelligence when a crude illustration of a pictorial kind may enable a person to understand in a very inaccurate and in- complete wa}^ something that he cannot otherwise understand at all. To this class belongs the ingenious figure by which one Italian rustic conveyed to another, who was puzzled by the telegraph, some conception of the possibility of what a man does at one end of a wire producing an effect at the other. Starting from the well-known fact that if you pinch your dog's tail the bark issues from the other end, the expositor invited his friend to imagine that his dog grew long enough to reach from Milan to Rome, having its tail end in Milan and its head end in Rome. It then became clear that, if you pinch the tail in Milan, the bark will take place in Rome.^ In dealing with Exemplification, it is obvious that the elements found in the illustration must be cognate with those found in the illustrandum. But when we are dealing with analogical illustration, it is desirable that the material should be different in the two cases. This is manifestly true in the aesthetic use, but it also holds in didactic work. It is a mistake to use exactly the same sort of material in the illustration as is found in the illustrandum, unless the very fact of this com- munity of material is to be utilised as a part of the illus- trative process. If you turn to Chapter V, p. 133, you ^ The story ends here, but we can imagine the triumph of the dull one in pointing out the impossibility of getting through a message from Rome to Milan, and the intelligent one's satisfaction in suggesting an additional but inverted dog. 414 EXPOSITION AND ILLUSTRATION IN TEACHING will find a case in point. There I wished to illustrate the weakness of the negative not as against the positive suggestion represented by a noun or a verb. Turning my thoughts to the Latin grammar for an example of two terms often confused with each other, I found the words non and ne had arisen in my mind. They were probably suggested by the fact that I was dealing with the subject of negatives at the time. In themselves they form quite a good illustration, but as soon as I reread the passage I saw that there was a certain con- fusion likely to arise in the reader's mind. He might very naturally think that the Latin negatives as nega- tives had something to do with the general subject of the paragraph. In any other book I would at once have changed the illustration to some other two terms, — perhaps scire and cognoscere, — but an example of an actual blunder in illustration in the very act of treating of illustration was too useful to be thrown aside, so I let the blunder stand. Further, no reference was made to it in the earlier chapter, in order to give the reader an opportunity of testing at a later stage whether he could remember any slight confusion having arisen in his mind at the time. A final danger of the use of certain forms of illustra- tion is said to be the tendency it has to make the pupils dependent on illustrations for their actual thinking. They become incapable, it is said, of doing any thinking at all unless suitable illustrations are supplied. They never trouble to deal with a generalisation till it is followed by illustrations. But it is surely undesirable that pupils should be encouraged to accept generalisa- tions without examples, and sufficient cautions have been already given against allowing the pupil to adopt DANGERS OF ILLUSTRATION 415 a purely passive attitude in respect of illustrations. The active reaction of the pupil being secured, he will, of necessity, provide certain illustrations of his own. Indeed, the supplying of fresh illustrations by the pupil is one of the best ways of his securing a mastery over the illustrandum. CHAPTER XVII The Torpedo Shock In Plato we find Meno, after being treated on the aggravating Socratic method, driven to complain: — " Socrates, I used to be told before I knew you that you were always doubting yourself and making others doubt ; and now you are casting your spells over me, and I am simply getting bewitched and enchanted, and am at my wits' end. And if I may venture to make a jest upon you, you seem to me both in your appearance and in your power over others to be very like the flat torpedo fish, who torpifies those who come near him and touch him, as you have now torpified me, I think. For my soul and my tongue are really torpid, and I do not know how to answer you." ^ This is a passage that touches closely all of us who concern ourselves with the theory of method in teaching; for there is a certain danger that in setting forth more or less elaborate theories we may induce a mild form of intellectual paralysis in the teachers whom we seek to influence. After learning the numberless possibili- ties of going wrong, and the small chance of hitting upon the absolutely right way to deal with any particular case that arises, the student of method may not un- naturally become discouraged. There are not lacking people who say that to study method is to acquire know- ledge that is not only of little use, but is positively noxious. Their attitude reminds me of the indignant protest of an old college acquaintance of mine, a medical ^ Meno, 80, A. Jo watt's English. 416 THE TORPEDO SHOCK 417 student, who had just come down in his anatomy: '^What's the sense in knowing every miserable nerve in the neck ? There's Launceston knows 'em all, and is so nervous he's afraid to put in his knife in case he severs some of 'em. I don't know 'em, so I've confi- dence. I stick in my knife, and there you are." It need hardly be said that Launceston was nervous by temperament, and not because he was the medallist in anatomy. Real, positive knowledge gives power and confidence. The man with wide and accurate know- ledge is not afraid to give an opinion and act upon it, though he has no monopoly of this courage. Neverthe- less, there is a certain danger attending the close study of method. All the positive principles mastered are of direct service in practical work, and your hurriedly trained person, with little theory and a great deal of practice, is only too willing to lay down the law and put it into immediate operation. But the thoughtful student who looks all round the subject, and notes this defect and the other, even in methods that are on the whole excellent, has not the certainty of his less critical fellow. The man of criticism is always less confident than the man of action. It is important, therefore, that critical study should be accompanied by the corrective of vigorous practice. The work of the study must be brought to fruition in the class room. But this is not quite the same thing as to say that the student is to carry his theories with him and painfully apply them by a conscious effort in front of his class. I have seen a man fishing in a pond in Buckinghamshire, with a book by his side with the alluring title ^'How to Angle." To this he referred when matters became critical — but he caught no fish. 2e 418 EXPOSITION AND ILLUSTRATION IN TEACHING In the stress and strain of the class room the teacher must be independent of the book of method. I have no doubt that a great deal may be learnt about angling in the study, but the riverside is not the place to continue the study as study. This is by no means an admission that those depressing critics are right who maintain that in education theory and practice cannot be harmo- nised. ' ' Theory is all very well in the study, but when a man gets before a class — " This sort of sentence is usually left unfinished, which is a pity. It would be pleasant to have a frank statement of the acceptance of rule of thumb. As a matter of experience there is no difficulty in combining theory and practice, but the combination cannot be made in the mechanical way that lends itself to easy registration in an educational book. The matter was put epigrammatically, but with a different kind of truth than that the epigrammatist intended in the complaint: ''So far as I can gather, students of method learn laboriously certain principles that they forget the moment they are face to face with a class." For the outside observer this is a sufficiently accurate description of what takes place; but the inner meaning of the change of attitude is apt to be overlooked by the casual person. A better description of the same phenomenon would be to say that the moment the student of method gets before a class he loses conscious- ness of the theoretical principles he has been studying. It does not follow that those principles have lost their influence. It is all a matter of the incidence of con- sciousness. Too frequently it is true that theoretical considerations do obtrude themselves on the considera- tion of the inexperienced teacher when he should be THE TORPEDO SHOCK 419 giving himself up entirely to practice. This means that he has not mastered his principles, and therefore is unable to forget them in the moment of application. A man who has been trained by a proper combination of theory and application of theory gradually acquires the right to forget all about theory when he is engaged in practice. His theory has become a part of himself, and affects his activities even when he is not at all thinking of theory. The facts of theory have become the faculty of practice. One of my students told me the other day that she did not believe she could begin a sentence with the word And, even if she were writing in her sleep, so thoroughly had this part of the teaching of the theory of compo- sition been assimilated. She remembered that the teacher had given her a great many reasons why no sentence should ever begin with the word, — reasons that many modern authors would dismiss with scant ceremony, — but these she could rather guess at than remember; the important point is that they had consoli- dated themselves into an inveterate rejection of this conjunction as the first word in a sentence. This little chapter is added mainly to reassure readers who may be disturbed by the criticisms that have been made of certain illustrations that are not in themselves very bad, but are not so good as they might be. The reader in his modesty may protest that he will be only too glad if in the rough-and-tumble of strenuous teaching he can evolve such good illustrations as are held up as warnings in these pages, and may feel a little uneasy lest in the moment of action some memory of criticism may arise and torpify him. From this point of view illustrations must be regarded as of two distinct kinds: 420 EXPOSITION AND ILLUSTRATION IN TEACHING those that are prepared for before the lesson, and those that are summoned on the spur of the moment to clear up more or less unexpected points as they arise. For confused or careless illustrations of the first class there is never any excuse; but for those of the second class there must be great allowance made. Still, the more practice the teacher has in preparing good illustrations before the lesson, the greater his power of improvising illustrations that do not break any of the principles to which he has given his assent. In teaching we must let ourselves go : the practical interests of the moment must dominate everything. But, after all, teaching is not a mechanical process. We do not need to leave our minds at the door of the class room as the Mohammedan leaves his shoes on the mat before entering the mosque. A trained rhetorician addressing a public assembly does not think of the laws of rhetoric as he makes his appeal. But he does apply them. The teacher must be able to think on his feet; must be capable of changing an illustration in the process of making it; and must all the while de- pend upon the paid-up capital of his theorising to keep him straight. No doubt he will often make mistakes, and will wonder afterwards how, knowing what he did, he could have made this blunder and that. But as the result of his studies he knows that, in the main, he is right. Every blunder he makes gives him something to consider after the lesson. But it is to be used in warn- ing him against repetitions of this error and its like and in strengthening his grip of the positive principles of his art, not in discouraging him, and sapping his confidence in himself. INDEX Abstract, place of the, in illustration, 248; interaction with concrete, 280-281. Abstraction in models, 320, 322. Accuracy, excess of, 408. Advertising, 22 note, 350, 399. ^nedd, 105, 138. Esthetic illustration, 21-22, 242, 369. Alexander, Professor S., 128, 386. Algebra, 184. Allen, Grant, 192. Allen, Professor J. W., 6. Alpha Centaur i, 306. Alphabetical index, 253, 273. Analogy, 73, 90, 91 ; mathematical, 230 ; spreading of, 232. Analysis, the lust of, 64 ; of sentences, 201. Analytic step, 147. Anderson, Robert, 310, 379. Anticipation, in listening, 15; by contraries, 16; in presentation, 207 note. Anticipatory illustration, 31, 32, 33. Apperception, 37; masses, 71, 74. Application step, 151-152. Approaches, kinds of, 226. Archimedes, 118. Areas, feebleness in estimating, 357 ff . ; of United States, 364 ; cultiva- tion of sense of, 376. Aristotle, 230, 234, 240. Arithmetic, 176, 281. Arithmetical challenge, 250, 309, 332 ; (by implication), 402, 412. Armstrong, Professor H. E., 34. Arnold, Dr., 272. Arrest, 71-74, 234. Arrows, in diagrams, 386, 388. Artists', difficulties in illustration, 345-347; carelessness, 342. Ascham, Roger, 101, 257. Association, systematic, 70, 72, 73; step, 148; divergent, 292, 402. Assumptions underlying theory of Formal Steps, 145 ff. Attendant circmnstances, 293. Attention, 119; rhythm of, 157; in- tensity of, 158; incidence of, 400; fixed by lines, 385. Audiles, 188. Author and artist, relations of, in illustration, 342 ff. Automatic, view of mind, 117-118; level, 163. Auto-suggestion, 129 ff. Awful example, 220, 254. Backgrounds: emotional, 92; har- monising of, 95; elements of, 97; kinds of: fixed, 100; unstable, 102; mobile, 103; to sermons, 103; to lectures, 104; temporary, 107; normal, 122; preferential, 123; relation to suggestion, 126. Bacon, 23, 25. Bailey, Philip James, 405 note. Bain, Professor A., 116 note. Balaclava illustration, 409. Baldwin, Professor Mark, 127. Ball, Sir Robert, 307-308. Barnett, P. A., 389. Bates, Charles Austin, 22 note. Beginning, 62, 105; degrees of, 179; problem of, 178, 179; determines order of presentation, 182; condi- tions determining, 195; thinking a, 278. Bell, Sir Charles, 140. Bennett and Bristol, 155 note. B^ranger, 137. Binet and Henri, 384 note. Biology, teaching of, 323. Bipolar processes and terms, 10. Blast-furnace temperature, 301. Bosanquet, Professor, 211. Botany, teaching of, 322. Bourgeoisisme, 294-295. 421 422 INDEX Brackenbury, L,, 189. Bradley, F. H., 39, 116 note, 230 note. Brain-action, theories of, 88-90. British Isles and British Empire, position, 327; trade and popula- tion, 369 ; 372. Browne, Sir Thomas, 150. Bruce, Robert the, 96, 97. Bullock, J. M., 396, 398. Bums, 291. Burton, J. Hill, 397. Csesar, 154, 321, 322. Calder, Mr. John, 387. Campe, 173 note, 175 note. Caran d'Ache, 381. Castellar, Maurice, 140. Catalogue elaboration, 287. Challenge, arithmetical, 253, 309, 337; (by implication), 402-403; 412. Chapman, 18. Chesterfield, 250. Chesterton, G. K., 8 note. Chromatists, 336. Circle, in diagrams, 374-376; of thought, 179. Classification, 59-60. Clearly imaged ends, 176. Collier, Hon. John, 91, 199 note. Colour, idea of, 48 ; in diagram, 368 ; of shadows, 76, 246; affected by canvas, 91. Columns in diagrams, 371. Combination, false, 209. Complex, 64, 98, 102, 198, 287; ready-made, 108. Complication, 73-74. Composition, exercises in, 299. Compromise in education, 99. Concentration beat, 159. Concept, 55 ff. Concrete, interpretation of, 245; to abstract, 280. Confrontation, 79, 80, 81. Consciousness, individual and general, 38; field of, 67-68, 84; distribu- tion of, 68; stream of, 68. Contenement, 202. Continents, area of, illustrated, 359 ff . Continuum, 69, 97. Contorniates, 218. Contradiction and reconciliation, 78. Contrariant characters, 132. Co-ordinate planes, 333. Correlation, excess of, 27; 400. Correspondence between inner and outer worlds, 54. Coteries, 95. Coulevain, Madame de, 294-295, 407. Countries of Europe, size of, illus- trated, 360-361. Cramming, 213. Cross purposes, 94. Cruikshank, 349. Cubic content, 377. Cubic mile, 311 ff. Deductive methods of teaching, 156- 157. Definition, place of, 58; concrete form of, 247 ; wider sense of, 294. De Garmo, Charles, 147 note. Delaware, area, 361. Demonstrate, meaning of, 3. De Quincey, 6, 11, 242, 243, 244. Diagram, imdrawn, 245; distin- guished from picture, 348; of the seasons, 327-328; place of, in teaching, 355; danger of pictorial element in, 355 ff . ; two kinds of, 367; colour in, 368; "of illustra- tion," 367, 390. Diagrammatic, 352. Dialectic, 12 note; Socratic, 276. Dickens, Charles, 8 note, 290-291; 350. Diesterweg, 173 note. Diffusion beat, 159. "Directions," 208. Discovery distinguished from apper- ception, 236. Docendum, 6 note, 11, 26. Doyle, Sir A. Conan, 285-286. Drayton, 405. Drummond, Professor Henry, 230. Dunnottar Castle as misleading type, 113. Dynamic view of concept and inner world, 57. East and west as permanent sugges- tion, 138. Eastern reliefs, 351. Education by deception, 132. INDEX 423 Elaboration, as school exercise, 276; pictorial, 277 ; two forms of, 285- 286; by catalogue, 287; under limitations, 295. Eliciting, 153. Eliot, George, 398. JEmile, 257. Emotional background, the, 92. Ending, 184 ff. ; as termination, 184. Eniuneration, 289-291. Estimate of cubic content, 377-378. Ethics, 268. Euclid, 333, 390. Euler's Theorem, 33, 154. Exaggerations necessary, 407. Example and precept, 268. Examples, too attractive, 398 ; stere- otyped, 393. Exceptions, 222-223. Excluded middle, 40, 86. Explanation, 5, 7, 8, 76 ; subordinate, 203. Expositandum, 11, 161. Exposition, by pupil and by teacher, 4; data of, 5; bipolar, 9; essen- tially constructive, 60, 61, 63; destructive stage of, 62; unit of, 64; relativity of, 160; starting- point of, 168; possibility of too good, 210-211; distinguished from illustration, 18, 257; to class as opposed to individuals, 225. Expound, meaning of, 2. Fable, need for details in, 270 ; truth in, 271. Fact and faculty, 63, 162, 419. Facts, explanation and interpreta- tion of, 5-6; organised, 161; of co-ordinate rank, 201. Faculties, 44 ff. Fairytales, 272. Fait accompli, 342. Fatigue diagram, 384. Faust, 257. Field of consciousness, 67, 68 ; 84. Finger-post criticism, 25, 26. Fixed backgrounds, 100. Fluid minds, 101. Focal ideas, 67, 129. Foreign suggestion, 129. Formal Steps, 145 ff.; errors in application of, 152; in notes of lessons, 154. Frankland, Dr. Edward, 170 note, 331,332. French, order of adjectives in, 190; auxiliary verbs, 393. Frith, W. P., 347. Froehener, M., 218. Fuller, Thomas, 22, 23. Fusion, 73, 74, 234. Galton, Francis, 279. Gaping Point, 163 ff., 277. Garnett, Dr. William, 120 note. Geikie, Sir Archibald, 188. Generalisation, 36, 155, 199, 262, 354; step, 148-149. Geography, 183; commercial, 182; text-book, 318. Geometry, the new, 184; descriptive, 333. German, vocabulary, 28 ; possessives, 193; rule as to gender, 225. Globes, the, 327. Glyptic formula, 331-332. Grammar, teaching of, 188. Granger, Rev. James, 396. Grangerising, 396. Greek education, 211. Growing Point, 162. Guy Fawkes, 338. Guyau, J. M., 127. Hamilton, Anthony, 180. Hamilton, Clayton, 203. Hamilton, Sir William, 40, 70. Hardewittes, 101. Harris, Dr. W. T., 142 note. Hartmann, Dr. Berthold, 98 note. Hay, Ian, 222. Hayricks, painted, 337. Hayward, Dr. F. H., 318. Helvetius, 406. Herbart, 145, 146, 147. Herschel, Sir John, 329, 330, 331, 408. Heuristic method, 32, 172, 173. Hill, Burton, 397. History, 183; imder different pow- ers, 160; text-book in, 293, 294; pictures in teaching of, 338; "true" pictures in, 339. Hobbes, 275 ; credit system, 276. Hodgson, Shadworth H., 116. 424 INDEX Hofmann, 331. Homer, 251, 288. Homonyms, 123. Howatt, Rev. J. R., 289. Hugo, Victor, 293. Hume, 48. Huxley, Professor T. H., 48, 77 notes. Hypostasis, 44, 45, 46. Iconographs, 139-140. Ideas, 40; distinguished from facul- ties, 45; as material of thought, 46; as forces, 46-47; interaction of, 47; focal and marginal, 67; realisation of, 72, 275; complica- tion and fusion of, 73; as perma- nent potentialities, 84 ; in subcon- scious state, 87-89 ; complexes of, 98; organisation of, 99; breaking up of complexes of, 169-170; re- call of, 104; ready-made com- plexes of, 99; mediate and im- mediate recall of, 119; conditions of recall of, 122; development in consciousness, 283. Idie fixe, 99, 100. Identity, principle of, 39; sense of, 69. Illustrandum, 19, 28, 30, 31, 232, 235, 241, 312, 320, 321, 327; cognate with illustration, 413; mastery over, 415. Illustrate, meaning of, 18, 19. Illustration, distinguished from ex- position, 18, 257; in a circle, 27; as a sedative, 22; anticipatory, 31, 32; twofold classification of, 229; verbal and material, 317; teacher's use of the incidental of, 207; classification of, 319; hand- to-mouth method of, 392; over-, 395; misplaced pictorial, 411; pupils dependent on, 414; dia- grams of, 367, 387. Illustrations, interstitial, 23; di- dactic use of, 242; misleading, 242; stock of, 393; carried over bodily, 408; prepared and extem- pore, 419-420. Illustrative enumeration, 290-291. Imagery, visual, 385. Images, 55; generalised, 56. Immediate recall, 119. Impressionability, threshold of, 300; zone of, 303. Impressionists, 336. Incidence of external influence in suggestion, 129. Incidental references, 205, 207. Induction, 32, 33. Inductive methods of teaching, 156, 157. Inference point, 161, 162, 277. Information, 153, 292, 319. Inhibition, 71. Instruction, 153. Inter-aims, 173. Intercourse, 51. Interest, rhythm of, 186; in relation to recapitulation, 226-227; de- railing of, 400; killing of, 404, 407. Interstitial, vision, 13; illustrations, 23. Introductions, 179. Isocrates, 244. Ivanhoe, 339, 344 note. Jacotot, 2, 3; Jacototian, 379. James, Professor William, 15, 68, 103, 232, 233. Janet, Professor Pierre, 127. Joe Millers, religious, 273. Johnson, Dr., 132, 407. Johnston, F. W., 22 note. Keatinge, M. W., 129, 132. Key, 31 note. Knowledge, reproduction of, 50 ; not yet due, 153, 394. Knox, John, 49. La Fontaine, 257, 262, 263, 270. Lamb, Charles, 237-238. Landois, 77 note. Language, teacher's use of, 387. Latin, genders, 27-28; oratio ohli- qua in, 31 ; order of teaching, 61 ; negatives, 133, 414; method of teaching, 157; from abstract to concrete in, 200; grammars and exceptions, 223; Latin Compara- tive, 229; cum with subjunctive, 392; examples in grammar, 398. Law stage, 55. Laws of Thought, 40, 75. INDEX 425 Lawson, William, 310. Lectures, lantern, 23, 26. Lecturing, 12. Lesson-lengths, 173. Leutz, Ferdinand, 174 note. Liebig, Baron, 20. Listening, analysis of, 12 ff. Liverpool, Lord, 269 note. Locke, John, 41 note, 85. Lodge, Sir Oliver, 207. Logic, 86, 269. Logical presentation, 187 ff. Lucas, E. v., 14, note. Macaulay, Lord, 284. Macdougall, W., 10 note, 126, 127, 388. Macdowall, K. A., 218. Macleod, Norman Islay, 269. Macturk, John, 363. Magna Charta, 201. Marshall, Professor, 385. "Match drawing," 382. Material, 319. Materialism, 88. Mathematics, 9, 61, 183. Mauclair, Camille, 337. Maxwell, J. Clerk, 368. Mediate recall, 119. Meiklejohn, Professor, 412. Meno, 368 note, 416. Mental activity, 116, 131. Mental content, 38, 41, 42, 61, 138, 156; analysis of, 167; overlap of, 168; organisation of, 192; com- mon segment of, 225, 277; limits of organisation of, 163, 411. Mental focus, 158; sliding scale of, 160. Mental harmony, law of, 75. Mental imagery, 280-281. Mental parallax, 113. Mental pictures, 108, 111, 277; ex- ternal standard of, 112. Metaphor, 130; as analogy, 231; conditions of, illustrative use of, 232; dangers of, 234; relation to illustrandum, 235 ff. ; cumulative effect of, 238; one-sided, 240. Method, deductive and inductive, 156-157; Socratic, 80 ff., 96, 172, 174-175; heuristic, 32, 172, 173; dangers of study of, 416 ff. Metric system, 211. Metrical diagrams, 367. Mill, J. S., 19, 200. Million, meaning of, 298, Milton, 240, 403, 405. Minds, kinds of, in respect of back- grounds, 98; rigid, 98; fluid, 101; plastic, 103; the associative, 102. Minimum suggestible, 141. Mistake-traps, 221. Mitchell, Professor W., 131. Mitchill and Carpenter, 4 note, 306. Model, the, 317; relation to real object, 319; as type, 323; three dimensions of, 324, 326, 330; im- reality of, 325; relation to senti- ments, 325; contrast with dia- gram, 328 ; made by pupils, 334. Monet, Claude, 336. Moral, place of the, 267 ; child's view of the, 270. Mot 'propre, 189. Multiplication through addition, 29. Murray, Dr. J. A. H., 249. Myers, Dr. C. S., 349. Narrative, 203. Nathan the prophet, 214, 215. Nebuchadnezzar's furnace, 300. Newton, Dr. Richard, 254, 256. Niagara, 301, 304, 311. Nicholson, Professor H. A., 59. Non-contradiction, law of, 40. Norris, Frank, 339. North, Lord, 135. North Carolina, area of, 359. Novelist's anticipatory references, 205. Nunn, Dr. T. Percy, 206, 219, 334, 335. Object lessons, 64. Objective standard in illustration, 344. Objects, 317. Observation frequency polygons, 384. Ohm, 120. Onions, Oliver, 136. Order, of substantive and objective, 190-191; of figure and illustra- tion, 241. Order of presentation, determined by beginning, 195; by practical con- siderations, 208. 426 INDEX Originality in lectures, 14. Ornithorh5nichus, 59-60. Orrery, 328. Orthographic story, 180. Osier, Dr. W., 239, 240. Paradise Lost, 405 note. Paragraph, the first, 178; illustrative of bad order, 205. Parallelism between physical and mental, 89. Passive poets, 341. Paterculus, 242, 244. Paulhan, Fr., 70, 71, 117. Pearson, Professor Karl, 384. Percentages and suggestion, 137. Perspective, 8, 345, 350. Petit, M. Edouard, 349. Pictorial, the, 306, 355; diagram, complication of, 356-357. Picture, limits imposed by, 340 ; two conditions of use of, as historical illustration, 339; as illustrating poetry, 341; infidelity of illus- trative, 341 ff. ; in text-books, 347; distinguished from diagram, 348; informative aspect of, 349- 350; in advertisement, 350; clas- sification of, in order of abstract- ness, 352; place of, in teaching, 355. Pictures, mental, 277-280. Plastic mind, 103. Plato, 250, 251, 253, 254, 416. Poe, Edgar Allan, 130, 241 note. Point of view, 1, 113. Polyolhion, 405 note. Portraits, 337. Preaching, 11. Preferred, apperception mass (or backgroimd), 120, 123, 125; sense, the, 108-109; ideas, 68. Premature conception, 214, 242. Preparation Step, 147, 167. Presentation, 145; order of, 146; falsity and incompleteness of, 219 ; logical, 187 ff., 199; preliminary conditions of, 195; bad order of, 205. Presentative activity, 66-67, 74, 120. Presented content, 65, 93. Primary colours, 169; psychological, 170. Primer on Teaching, 387. Problems, 182, 217. Prompting, 135. Pseudo-auto-suggestion, 129. "Psychic fringes," 284. Psychology, 86, 268; of listening, 12. Pupil, as technical term, 11. Purpose unit, 173. Qualitative and quantitative reason- ing, 385. Quotation marks, 394. Ramsay, Sir W., 318. Raven, Rev. J. H., 31. Reading, 14. Realising, ideas, 72, 275; figures, 291 ; sizes and nimibers, 297. Reality in models, 325. Recall, 104; conditions of, 122; mediate and immediate, 119. Reconstruction, 214. Redintegration, 134. "References forward," 207. Relative sizes of countries and conti- nents, 359-304. Relativity, in exposition, 160; in manipulating vast nimibers, 309- 311. Rennet, Dr. David, 213. Republic, the, 250. Rhythm, of attention, 157; in teach- ing, 179; of interest, 186; of ab- stract and concrete, 199. Richter, Jean Paul, 235 note; 268 note. Richter, Karl, 173 note. Rickerton Medal, 176. Riddle, 240. Right and left, confusion of, 114. Rigid minds, 98. Romanes, G. J., 349. Rothschild, Nathan, 267, 269, 270 note. Rousseau, 257 ff., 326. Rule, and exception, 222 ff. ; and example, 228. "Rules," 222, 282. Ruskin, 8, 298. Saving pupils trouble, 210. Scansion, 216. Science teaching, 217. INDEX 427 Scott, Sir W., 237, 339, 350. Self-activity, 130. Self-referent tendency, 265. Sentences, loose and periodic, 248. Shadows, colour of, 246. Shakespeare, 15, 25, 78. Shelley, 15. Sidis, Dr., 132. Silhouettes, Chinese, 140. Silvestre, M. J. B., 139. "Simple" and "easy to understand," 198. Simplon Tunnel, 182. Sirius, 309. Socrates, 80, 250-251, 416. Soft pedagogy, 212. Spencer, Herbert, 76, 169, 189-190, 196, 197, 198, 205, 214, 246, 279. Sprachgefuhl, 44. Standard, area, 315, 360; for differ- ent powers, 160; map of West of Old World, 380. Starting-point of exposition, 167. Static view of concept and inner world, 57. Stephens, Winifred, 294. Stevenson, R. L., 271. Stirling, Hutchison, 277, 278, 280. Story, three uses of, 251 ; the in- vented, 271 ; sources of, 273. Stout, Professor G. F., 42, 116, 128, 284. Straight lines in diagram, 353, 371, 378. Stun, Threshold of, 301, 302, 303, 304, 306, 307, 313, 412; raising of, 305. Style, test of, 7; tmderlying, 16; philosophy of, 189; allusive, 403, 405. Subconscious, the, 85; physical correlate of, 87-88. Subjunctive, 222, 392. Substantive, elements of thought, 43, 73, 125; meaning, 123. Sufficient reason, law of, 40. Suggestion, external, 122; Wundt's and Thomas's definitions, 128 Baldwin's and Janet's definitions, 127; auto-, 128; foreign, 129 pseudo-auto-, 129; unilateral, 133 relation to apperception, 134 permanent, 135, 159, 371 ; moral justification of, 143; as an end, 143-144; most obvious kind, 350. Superlative references, 404. Superstition, one function of, 75. Synthetic step, 147. System, stage of, 55; step, 147, 149. Tactiles, 109. Teaching, six principles of, 196-197; criticism of six principles of, 197 ff. ; by text-books, 318; deductive and inductive methods of, 156- 157; to class, 226. "Telling," 153. Temptation, 144, 256-257. Tennyson, 235, 288, 402-403. Theory and practice, 419. Therefore, use of, 165-166. "Thing stage," 44, 55. Thing-in-itself, 53. Thinking, atomistic, 15; small change type of, 277; pictorial, 278-279. Thomas, Professor P. E., 127. "Thorough," 159. Thought, laws of, 39, 75; swiftness of, 281. Threshold, 85 ; of Consciousness, 86 ; of Impressionability, 300-303; of Stun, 301-307, 412. Time-imit, 174. Transitive, elements of thoughts, 43 ; meaning, 125. Trapp, E. Ch., 171. Turbid media, 91. Type, the, as illustration, 247. Unconscious humour, 411. Unit, time and purpose, 174; size of, 204; general treatment of, 204; highest available, 315; standard, 315-316, 360. United States, area of, 364. Units, 66. Unstable backgrounds, 102. Vacuum, the, in exposition, 216 ff. Velasquez, 337. Veronese, 339. Virgil, 105. Vision, interstitial, 13; field of, 14. Visuals, 108. Vorstellung, 278, 283. 428 INDEX Wallas, Graham, 384-385. Walpole, Horace, 284. Ward, Dr. Jaraes, 386. Weariness from over-correlation, 27, 400. Webster, dictionary, 17, 249. Wells, H. G., 301, 304. Whately, 130 note. Whitman, Walt, 287, 288, 346. Whittier, 171. Wight, Isle of, 314. Wilmann, Otto, 196. Witmer, Lightner, 171, 359. Witt, Robert Clermont, 348. Wolf, Lucien, 270. Wordsworth, 99, 271. 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