Chapter III: Instruction (2)

He will be discouraged, and will be ready to set the pail down. Say to him, on the other hand, "I had better dismount myself. I don't think you can hold the pail up. It is very heavy;" and his eye will brighten up at once. "Oh no, sir," he will reply, "I can hold it very easily." Hence, even if the work you are assigning to a class _is_ easy, do not tell them so unless you wish to destroy all their spirit and interest in doing it; and if you wish to excite their spirit and interest, make your work difficult, and let them see that you know it is so; not so difficult as to tax their powers too heavily, but enough so to require a vigorous and persevering effort. Let them distinctly understand, too, that you know it is difficult, that you mean to make it so, but that they have your sympathy and encouragement in the efforts which it calls them to make.

You may satisfy yourself that human nature is, in this respect, what I have described by some such experiment as the following. Select two classes not very familiar with elementary arithmetic, and offer to each of them the following example in addition:

1 2 3 4 5 6 7 8 9
2 3 4 5 6 7 8 9 1
3 4 5 6 7 8 9 1 2
etc., etc.

The numbers may be continued, according to the obvious law regulating the above, until each one of the nine digits has commenced the line. Or, if you choose Multiplication, let the example be this:

Multiply 123456789
by 123456789
---------

Now, when you bring the example to one of the classes, address the pupils as follows:

"I have contrived for you a very difficult sum. It is the most difficult one that can be made with the number of figures contained in it, and I do not think that any of you can do it, but you may try. I shall not be surprised if every answer should contain mistakes."

To the other class say as follows:

"I have prepared an example for you, which I wish you to be very careful to perform correctly. It is a little longer than those you have had heretofore, but it is to be performed upon the same principles, and you can all do it correctly, if you really try."

Now under such circumstances the first class will go to their seats with ardor and alacrity, determined to show you that they can do work, even if it is difficult; and if they succeed, they come to the class the next day with pride and pleasure. They have accomplished something which you admit it was not easy to accomplish. On the other hand, the second class will go to their seats with murmuring looks and words, and with a hearty dislike of the task you have assigned them. They know that they have something to do, which, however easy it may be to the teacher, is really difficult for them; and they have to be perplexed and wearied with the work, without having, at last, even the little satisfaction of knowing that the teacher appreciates the difficulties with which they had to contend.

2. We now come to consider the subject of rendering assistance to the pupil, which is one of the most important and delicate parts of a teacher's work. The great difference which exists among teachers in regard to the skill they possess in this part of their duty, is so striking that it is very often noticed by others; and perhaps skill here is of more avail in deciding the question of success or failure than any thing besides. The first great principle is, however, simple and effectual.

_(1.) Divide and subdivide a difficult process, until your steps are so short that the pupil can easily take them._

Most teachers forget the difference between the pupil's capacity and their own, and they pass rapidly forward, through a difficult train of thought, in their own ordinary gait, their unfortunate followers vainly trying to keep up with them. The case is precisely analogous to that of the father, who walks with the step of a man, while his little son is by his side, wearying and exhausting himself with fruitless efforts to reach his feet as far, and to move them as rapidly as a full-grown man.

But to show what I mean by subdividing a difficult process so as to make each step simple, I will take a case which may serve as an example. I will suppose that the teacher of a common school undertakes to show his boys, who, we will suppose, are acquainted with nothing but elementary arithmetic, how longitude is determined by means of the eclipses of Jupiter's satellites; not a very simple question, but still one which, like all others, may be, merely by the power of the subdivision alluded to, easily explained. I will suppose that the subject has come up at a general exercise; perhaps the question was asked in writing by one of the older boys. I will present the explanation chiefly in the form of question and answer, that it may be seen that the steps are so short that the boys may take them themselves.

"Which way," asks the teacher, "are the Rocky Mountains from us?"

"West," answer two or three of the boys.

In such cases as this, it is very desirable that the answers should be general, so that throughout the school there should be a spirited interest in the questions and replies. This will never be the case if a small number of the boys only take part in the answers, and many teachers complain that when they try this experiment they can seldom induce many of the pupils to take a part.

The reason ordinarily is that they say that _any_ of the boys may answer instead of that _all_ of them may. The boys do not get the idea that it is wished that a universal reply should come from all parts of the room, in which every one's voice should be heard. If the answers were feeble in the instance we are supposing, the teacher would perhaps say,

"I only heard one or two answers; do not more of you know where the Rocky Mountains are? Will you all think and answer together? Which way are they from us?"

"West," answer a large number of boys.

"You do not answer fully enough yet; I do not think more than forty answered, and there are about sixty here. I should like to have _every one in the room_ answer, and all precisely together."

He then repeats the question, and obtains a full response. A similar effort will always succeed.

"Now does the sun, in going round the earth, pass over the Rocky Mountains, or over us, first?"

To this question the teacher hears a confused answer. Some do not reply; some say, "Over the Rocky Mountains;" others, "Over us;" and others still, "The sun does not move at all."

"It is true that the sun, strictly speaking, does not move; the earth turns round, presenting the various countries in succession to the sun, but the effect is precisely the same as it would be if the sun moved, and, accordingly, I use that language. Now how long does it take the sun to pass round the earth?"

"Twenty-four hours."

"Does he go toward the west or toward the east from us?"

"Toward the west."

But it is not necessary to give the replies; the questions alone will be sufficient. The reader will observe that they inevitably lead the pupil, by short and simple steps, to a clear understanding of the point to be explained.

"Will the sun go toward or from the Rocky Mountains after leaving us?"

"How long did you say it takes the sun to go round the globe and come to us again?"

"How long to go half round?" "Quarter round?"

"How long will it take him to go to the Rocky Mountains?"

No answer.

"You can not tell. It would depend upon the distance. Suppose, then, the Rocky Mountains were half round the globe, how long would it take the sun to go to them?" "Suppose they were quarter round?"

"The whole distance is divided into portions called degrees--360 in all. How many will the sun pass in going half round?" "In going quarter round?"

"Ninety degrees, then, make one quarter of the circumference of the globe. This, you have already said, will take six hours. In one hour, then, how many degrees will the sun pass over?"

Perhaps no answer. If so, the teacher will subdivide the question on the principle we are explaining, so as to make the steps such that the pupils _can_ take them.

"How many degrees will the sun pass over in three hours?"

"Forty-five."

"How large a part of that, then, will he pass in one hour?"

"One third of it."

"And what is one third of forty-five?"

The boys would readily answer fifteen, and the teacher would then dwell for a moment on the general truth thus deduced, that the sun, in passing round the earth, passes over fifteen degrees every hour.

"Suppose, then, it takes the sun one hour to go from us to the River Mississippi, how many degrees west of us would the river be?"

Having thus familiarized the pupils to the fact that the motion of the sun is a proper measure of the difference of longitude between two places, the teacher must dismiss the subject for a day, and when the next opportunity of bringing it forward occurs, he would, perhaps, take up the subject of the sun's motion as a measure _of time._

"Is the sun ever exactly over our heads?"

"Is he ever exactly south of us?"

"When he is exactly south of us, or, in other words, exactly opposite to us in his course round the earth, he is said to be in our meridian; for the word meridian means a line drawn exactly north or south from any place."

There is no limit to the simplicity which may be imparted, even to the most difficult subjects, by subdividing the steps. This point, for instance, the meaning of meridian, may be the subject, if it were necessary, of many questions, which would render it simple to the youngest child. The teacher may point to the various articles in the room, or buildings, or other objects without, and ask if they are or are not in his meridian. But to proceed:

"When the sun is exactly opposite to us, in the south, at the highest point to which he rises, what o'clock is it?"

"When the sun is exactly opposite to us, can he be opposite to the Rocky Mountains?"

"Does he get opposite to the Rocky Mountains before or after he is opposite to us?"

"When he is opposite to the Rocky Mountains, what o'clock is it there?"

"Is it twelve o'clock here, then, before or after it is twelve o'clock there?"

"Suppose the River Mississippi is fifteen degrees from us, how long is it twelve o'clock here before it is twelve o'clock there?"

"When it is twelve o'clock here, then, what time will it be there?"

Some will probably answer "one," and some "eleven." If so, the step is too long, and may be subdivided thus:

"When it is noon here, is the sun going toward the Mississippi, or has he passed it?"

"Then has noon gone by at that river, or has it not yet come?"

"Then will it be one hour before or one hour after noon?"

"Then will it be eleven or one?"

Such minuteness and simplicity would, in ordinary cases, not be necessary. I go into it here merely to show how, by simply subdividing the steps, a subject ordinarily perplexing may be made plain. The reader will observe that in the above there are no explanations by the teacher--there are not even leading questions; that is, there are no questions the form of which suggests the answers desired. The pupil goes on from step to step simply because he has but one short step to take at a time.

"Can it be noon, then," continues the teacher, "here and at a place fifteen degrees west of us at the same time?"

"Can it be noon here and at a place ten miles west of us at the same time?"

It is unnecessary to continue the illustration, for it will be very evident to every reader that, by going forward in this way, the whole subject may be laid out before the pupils so that they shall perfectly understand it. They can, by a series of questions like the above, be led to see, by their own reasoning, that time, as denoted by the clock, must differ in every two places not upon the same meridian, and that the difference must be exactly proportional to the difference of longitude. So that a watch which is right in one place can not, strictly speaking, be right in any other place east or west of the first; and that, if the time of day at two places can be compared, either by taking a chronometer from one to another, or by observing some celestial phenomenon, like the eclipses of Jupiter's satellites, and ascertaining precisely the time of their occurrence, according to the reckoning at both, the distance east or west by degrees may be determined. The reader will observe, too, that the method by which this explanation is made is strictly in accordance with the principle I am illustrating, which is by simply _dividing the process into short steps._ There is no ingenious reasoning on the part of the teacher, no happy illustrations, no apparatus, no diagrams. It is a pure process of mathematical reasoning, made clear and easy by _simple analysis._

In applying this method, however, the teacher should be very careful not to subdivide too much. It is best that the pupils should walk as fast as they can. The object of the teacher should be to smooth the path not much more than barely enough to enable the pupil to go on. He should not endeavor to make it very easy.

(2.) Truths must not only be taught to the pupils, but they must _fixed_, and _made familiar._ This is a point which seems to be very generally overlooked.

"Can you say the Multiplication Table?" said a teacher to a boy who was standing before him in his class.

"Yes, sir."

"Well, I should like to have you say the line beginning nine times one."

The boy repeated it slowly, but correctly.

"Now I should like to have you try again, and I will, at the same time, say another line, to see if I can put you out."

The boy looked surprised. The idea of his teacher's trying to perplex and embarrass him was entirely new.

"You must not be afraid," said the teacher. "You will undoubtedly not succeed in getting through, but you will not be to blame for the failure. I only try it as a sort of intellectual experiment."

The boy accordingly began again, but was soon completely confused by the teacher's accompaniment. He stopped in the middle of his line, saying,

"I could say it, only you put me out."

"Well, now try to say the Alphabet, and let me see if I can put you out there."

As might have been expected, the teacher failed. The boy went regularly onward to the end.

"You see, now," said the teacher to the class who had witnessed the experiment, "that this boy knows his Alphabet in a different sense from that in which he knows his Multiplication Table. In the latter, his knowledge is only imperfectly his own; he can make use of it only under favorable circumstances. In the former it is entirely his own; circumstances have no control over him."

A child has a lesson in Latin Grammar to recite. She hesitates and stammers, miscalls the cases, and then corrects herself, and, if she gets through at last, she considers herself as having recited well, and very many teachers would consider it well too. If she hesitates a little longer than usual in trying to summon to her recollection a particular word, she says, perhaps, "Don't tell me," and if she happens at last to guess right, she takes her book with a countenance beaming with satisfaction.

"Suppose you had the care of an infant school," might the instructor say to such a scholar, "and were endeavoring to teach a little child to count, and she should recite her lesson to you in this way, 'One, two, four--no, three--one, two, three----stop, don't tell me--five--no, four--four--five--------I shall think in a minute--six--is that right? five, six,' &c. Should you call that reciting well?"

Nothing is more common than for pupils to say, when they fail of reciting their lesson, that they could say it at their seats, but that they can not now say it before the class. When such a thing is said for the first time it should not be severely reproved, because nine children in ten honestly think that if the lesson were learned so that it could be recited any where, their duty is discharged. But it should be kindly, though distinctly explained to them, that in the business of life they must have their knowledge so much at command that they can use it at all times and in all circumstances, or it will do them little good.

One of the most common cases of difficulty in pursuing mathematical studies, or studies of any kind where the succeeding lessons depend upon those which precede, is the fact that the pupil, though he may understand what precedes, is not _familiar_ with it. This is very strikingly the case with Geometry. The class study the definitions, and the teacher supposes they fully understand them; in fact, they do _understand_ them, but the name and the thing are so feebly connected in their minds that a direct effort and a short pause are necessary to recall the idea when they hear or see the word. When they come on, therefore, to the demonstrations, which in themselves would be difficult enough, they have double duty to perform. The words used do not readily suggest the idea, and the connection of the ideas requires careful study. Under this double burden many a young geometrician sinks discouraged.

A class should go on slowly, and dwell on details so long as to fix firmly and make perfectly familiar whatever they undertake to learn. In this manner the knowledge they acquire will become their own. It will be incorporated, as it were, into their very minds, and they can not afterward be deprived of it.

The exercises which have for their object this rendering familiar what has been learned may be so varied as to interest the pupil very much, instead of being tiresome, as it might at first be supposed.

Suppose, for instance, a teacher has explained to a large class in grammar the difference between an adjective and an adverb; if he leave it here, in a fortnight one half of the pupils would have forgotten the distinction, but by dwelling upon it a few lessons he may fix it forever. The first lesson might be to require the pupils to write twenty short sentences containing only adjectives. The second to write twenty containing only adverbs. The third to write sentences in two forms, one containing the adjective, and the other expressing the same idea by means of the adverb, arranging them in two columns, thus:

He writes well. | His writing is good.

Again, they may make out a list of adjectives, with the adverbs derived from each in another column. Then they may classify adverbs on the principle of their meaning, or according to their termination. The exercise may be infinitely varied, and yet the object of the whole may be to make _perfectly familiar_, and to fix forever in the mind the distinction explained.

These two points seem to me to be fundamental, so far as assisting pupils through the difficulties which lie in their way is concerned. Diminish the difficulties as far as is necessary by shortening and simplifying the steps, and make thorough work as you go on. These principles, carried steadily into practice, will be effectual in leading any mind through any difficulties which may occur. And though they can not, perhaps, be fully applied to every mind in a large school, yet they can be so far acted upon in reference to the whole mass as to accomplish the object for a very large majority.

3. _General cautions_. A few miscellaneous suggestions, which we shall include under this head, will conclude this chapter.

(1.) Never do any thing _for_ a scholar, but teach him to do it for himself. How many cases occur in the schools of our country where the boy brings his slate to the teacher, saying he can not do a certain sum. The teacher takes the slate and pencil, performs the work in silence, brings the result, and returns the slate to the hands of his pupil, who walks off to his seat, and goes to work on the next example, perfectly satisfied with the manner in which he is passing on. A man who has not done this a hundred times himself will hardly believe it possible that such a practice can prevail, it is so evidently a mere waste of time both for master and scholar.

(2.) Never get out of patience with dullness. Perhaps I ought to say, never get out of patience with any thing. That would, perhaps, be the wisest rule. But, above all things, remember that dullness and stupidity--and you will certainly find them in every school--are the very last things to get out of patience with. If the Creator has so formed the mind of a boy that he must go through life slowly and with difficulty, impeded by obstructions which others do not feel, and depressed by discouragements which others never know, his lot is surely hard enough without having you to add to it the trials and suffering which sarcasm and reproach from you can heap upon him. Look over your school-room, therefore, and wherever you find one whom you perceive the Creator to have endued with less intellectual power than others, fix your eye upon him with an expression of kindness and sympathy. Such a boy will have suffering enough from the selfish tyranny of his companions; he ought to find in you a protector and friend. One of the greatest enjoyments which a teacher's life affords is the interest of seeking out such a one, bowed down with burdens of depression and discouragement, unaccustomed to sympathy and kindness, and expecting nothing for the future but a weary continuation of the cheerless toils which have imbittered the past; and the pleasure of taking off the burden, of surprising the timid, disheartened sufferer by kind words and cheering looks, and of seeing in his countenance the expression of ease and even of happiness gradually returning.

(3.) The teacher should be interested in _all_ his scholars, and aim equally to secure the progress of all. Let there be no neglected ones in the school-room. We should always remember that, however unpleasant in countenance and manners that bashful boy in the corner may be, or however repulsive in appearance, or unhappy in disposition, that girl, seeming to be interested in nobody, and nobody appearing interested in her, they still have, each of them, a mother, who loves her own child, and takes a deep and constant interest in its history. Those mothers have a right, too, that their children should receive their full share of attention in a school which has been established for the common and equal benefit of all.

(4.) Do not hope or attempt to make all your pupils alike. Providence has determined that human minds should differ from each other for the very purpose of giving variety and interest to this busy scene of life. Now if it were possible for a teacher so to plan his operations as to send his pupils forth upon the community formed on the same model, as if they were made by machinery, he would do so much toward spoiling one of the wisest of the plans which the Almighty has formed for making this world a happy scene. Let it be the teacher's aim to co-operate with, not vainly to attempt to thwart, the designs of Providence. We should bring out those powers with which the Creator has endued the minds placed under our control. We must open our garden to such influences as shall bring forward all the plants, each in a way corresponding to its own nature. It is impossible if it were wise, and it would be foolish if it were possible, to stimulate, by artificial means, the rose, in hope of its reaching the size and magnitude of the apple-tree, or to try to cultivate the fig and the orange where wheat only will grow. No; it should be the teacher's main design to shelter his pupils from every deleterious influence, and to bring every thing to bear upon the community of minds before him which will encourage in each one the development of its own native powers. For the rest, he must remember that his province is to cultivate, not to create.

Error on this point is very common. Many teachers, even among those who have taken high rank through the success with which they have labored in the field, have wasted much time in attempting to do what never can be done, to form the character of those brought under their influence after a certain uniform model, which they have conceived as the standard of excellence. Their pupils must write just such a hand, they must compose in just such a style, they must be similar in sentiment and feeling, and their manners must be formed according to a fixed and uniform model; and when, in such a case, a pupil comes under their charge whom Providence has designed to be entirely different from the beau ideal adopted as the standard, more time, and pains, and anxious solicitude is wasted in vain attempts to produce the desired conformity than half the school require beside.

(5.) Do not allow the faults or obliquities of character, or the intellectual or moral wants of any individual of your pupils to engross a disproportionate share of your time. I have already said that those who are peculiarly in need of sympathy or help should receive the special attention they seem to require; what I mean to say now is, do not carry this to an extreme. When a parent sends you a pupil who, in consequence of neglect or mismanagement at home, has become wild and ungovernable, and full of all sorts of wickedness, he has no right to expect that you shall turn your attention away from the wide field which, in your whole school-room, lies before you, to spend your time, and exhaust your spirits and strength in endeavoring to repair the injuries which his own neglect has occasioned. When you open a school, you do not engage, either openly or tacitly, to make every pupil who may be sent to you a learned or a virtuous man. You do engage to give them all faithful instruction, and to bestow upon each such a degree of attention as is consistent with the claims of the rest. But it is both unwise and unjust to neglect the many trees in your nursery which, by ordinary attention, may be made to grow straight and tall, and to bear good fruit, that you may waste your labor upon a crooked stick, from which all your toil can secure very little beauty or fruitfulness.

Let no one now understand me to say that such cases are to be neglected. I admit the propriety, and, in fact, have urged the duty, of paying to them a little more than their due share of attention. What I now condemn is the practice, of which all teachers are in danger, of devoting such a disproportionate and unreasonable degree of attention to them as to encroach upon their duties to others. The school, the whole school, is your field, the elevation _of the mass_ in knowledge and virtue, and no individual instance, either of dullness or precocity, should draw you away from its steady pursuit.

(6.) The teacher should guard against unnecessarily imbibing those faulty mental habits to which his station and employment expose him. Accustomed to command, and to hold intercourse with minds which are immature and feeble compared with our own, we gradually acquire habits that the rough collisions and the friction of active life prevent from gathering around other men. Narrow-minded prejudices and prepossessions are imbibed through the facility with which, in our own little community, we adopt and maintain opinions. A too strong confidence in our own views on every subject almost inevitably comes from never hearing our opinions contradicted or called in question, and we express those opinions in a tone of authority, and even sometimes of arrogance, which we acquire in the school-room, for there, when we speak, nobody can reply.

These peculiarities show themselves first, and, in fact, most commonly, in the school-room; and the opinions thus formed very often relate to the studies and management of the school. One has a peculiar mode of teaching spelling, which is successful almost entirely through the magic influence of his interest in it, and he thinks no other mode of teaching this branch is even tolerable. Another must have all his pupils write on the angular system, or the anti-angular system, and he enters with all the zeal into a controversy on the subject, as if the destiny of the whole rising generation depended upon its decision. Tell him that all that is of any consequence in any handwriting is that it should be legible, rapid, and uniform, and that, for the rest, it would be better that every human being should write a different hand, and he looks upon you with astonishment, wondering that you can not see the vital importance of the question whether the vertex of an _o_ should, be pointed or round. So in every thing. He has _his way_ in every minute particular--a way from which he can not deviate, and to which he wishes every one else to conform.

This set, formal mannerism is entirely inconsistent with that commanding intellectual influence which the teacher should exert in the administration of his school. He should work with what an artist calls boldness and freedom of touch. Activity and enterprise of mind should characterize all his measures if he wishes to make bold, original, and efficient men.

(7.) Assume no false appearances in your school either as to knowledge or character. Perhaps it may justly be said to be the common practice of teachers in this country to affect a dignity of deportment in the presence of their pupils which in other cases is laid aside, and to pretend to superiority in knowledge and an infallibility of judgment which no sensible man would claim before other sensible men, but which an absurd fashion seems to require of the teacher. It can, however, scarcely be said to be a fashion, for the temptation is almost exclusively confined to the young and the ignorant, who think they must make up by appearance what they want in reality. Very few of the older, and more experienced, and successful instructors in our country fall into it at all; but some young beginner, whose knowledge is very limited, and who, in manner and habits, has only just ceased to be a boy, walks into his school-room with a countenance of forced gravity, and with a dignified and solemn step, which is ludicrous even to himself. I describe accurately, for I describe from recollection. This unnatural, and forced, and ludicrous dignity cleaves to him like a disease through the whole period of his duty. In the presence of his scholars he is always under restraint, assuming a stiff and formal dignity which is as ridiculous as it is unnatural. He is also obliged to resort to arts which are certainly not very honorable to conceal his ignorance.

A scholar, for example, brings him a sum in arithmetic which he does not know how to perform. This may be the case with a most excellent teacher, and one well qualified for his business. In order to be successful as a teacher, it is not necessary to understand every thing. Instead, however, of saying frankly, "I do not understand that example; I will examine it," he looks at it embarrassed and perplexed, not knowing how he shall escape the exposure of his ignorance. His first thought is to give some general directions to the pupil, and send him to his seat to make a new experiment, hoping that in some way or other, he scarcely knows how, he will get through; and, at any rate, if he should not, the teacher thinks that he himself at least gains time by the manoeuvre, and he is glad to postpone his trouble, though he knows it must soon return.

All efforts to conceal ignorance, and all affectation of knowledge not possessed, are as unwise as they are dishonest. If a scholar asks a question which you can not answer, or brings you a difficulty which you can not solve, say frankly, "I do not know." It is the only way to avoid continual anxiety and irritation, and the surest means of securing real respect. Let the scholars understand that the superiority of the teacher does not consist in his infallibility, or in his universal acquisitions, but in a well-balanced mind, where the boundary between knowledge and ignorance is distinctly marked; in a strong desire to go forward in mental improvement, and in fixed principles of action and systematic habits. You may even take up in school a study entirely new to you, and have it understood at the outset that you know no more of it than the class commencing, but that you can be their guide on account of the superior maturity and discipline of your powers, and the comparative ease with which you can meet and overcome difficulties. This is the understanding which ought always to exist between master and scholars. The fact that the teacher does not know every thing can not long be concealed if he tries to conceal it, and in this, as in every other case, HONESTY IS THE BEST POLICY.