Part 17

"'Name here in the class-room an object of which there are several.'--'Bench, window, wall, copy-book, pencil, slate-pencil, pupil, and so forth.'--'Name an object of which there is only one in the class-room.'--'The blackboard, stove, door, ceiling, floor, picture, teacher, and so forth.'--'If I put this cube away in my pocket, how many cubes will there be left in my hand?'--'Not one.'--'And how many must I again put into my hand, to have as many as before?'--'One.'--'What is meant by saying that Pétya fell down once? How many times did Pétya fall? Did he fall another time? Why does it say once?'--'Because we are speaking only of one case and not of another case.'--'Take your slates (or copy-books). Make on them a line of this size.' (The teacher draws on the blackboard a line two or four inches in length, or shows on the ruler that length.) 'Rub it off. How many lines are left?'--'Not one.'--'Draw several such lines.' It would be unnatural to invent any other exercises in order to acquaint the children with number one. It suffices to rouse in them that conception of unity which they, no doubt, had previous to their school instruction."

Then Mr. Bunákov speaks of exercises on the board, and so on, and Mr. Evtushévski of the number four with its decomposition. Before examining the theory itself of the transmission of ideas, the question involuntarily arises whether that theory is not mistaken in its very problem. Has the condition of the pedagogical material with which it has to do been correctly defined? The first thing that startles us is the strange relation to some imaginary children, to such as I, at least, have never seen in the Russian Empire. The conversations, and the information which they impart, refer to children of less than two years of age, because two-year-old children know all that is contained in them, but as to the questions which have to be asked, they have reference to parrots. Any pupil of six, seven, eight, or nine years will not understand a thing in these questions, because he knows all about that, and cannot make out what it all means. The demands for such conversations evince either complete ignorance, or a desire to ignore that degree of development on which the pupils stand.

Maybe the children of Hottentots and negroes, or some German children, do not know what is imparted to them in such conversations, but Russian children, except demented ones, all those who come to a school, not only know what is up and what down, what is a bench and what a table, what is two and what one, and so forth, but, in my experience, the peasant children who are sent to school by their parents can every one of them express their thoughts well and correctly, can understand another person's thought (if it is expressed in Russian), and can count to twenty and more; playing with knuckle-bones they count in pairs and sixes, and they know how many points and pairs there are in a six. Frequently the pupils who came to my school brought with them the problem with the geese, and explained it to me. But even if we admit that children possess no such conceptions as those the pedagogues want to impart to them by means of conversations, I do not find the method chosen by them to be correct.

Thus, for example, Mr. Bunákov has written a reader. This book is to be used in conjunction with the conversations to teach the children language. I have run through the book and have found it to be a series of bad language blunders, wherever extracts from other books are not quoted. The same complete ignorance of language I have found in Mr. Evtushévski's problems. Mr. Evtushévski wants to give ideas by means of problems. First of all he ought to have seen to it that the tool for the transmission of ideas, that is, the language, was correct.

What has been mentioned here refers to the form in which the development is imparted. Let us look at the contents themselves. Mr. Bunákov proposes the following questions to be put to the children: "Where can you see cats? where a magpie? where sand? where a wasp and a suslik? what are a suslik and a magpie and a cat covered with, and what are the parts of their bodies?" (The suslik is a favourite animal of pedagogy, no doubt because not one peasant child in the centre of Russia knows that word.)

"Naturally the teacher does not always put these questions straight to the children, as forming the predetermined programme of the lesson; more frequently the small and undeveloped children have to be led up to the solution of the question of the programme by a series of suggestive questions, by directing their attention to the side of the subject which is more correct at the given moment, or by inciting them to recall something from their previous observations. Thus the teacher need not put the question directly: 'Where can a wasp be seen?' but, turning to this or that pupil, he may ask him whether he has seen a wasp, where he has seen it, and then only, combining the replies of several pupils, compose an answer to the first question of his programme. In answering the teacher's questions, the children will often connect several remarks that have no direct relation to the matter; for example, when the question is about what the parts of a magpie are, one may say irrelevantly that a magpie jumps, another that it chatters funnily, a third that it steals things,--let them add and give utterance to everything that arises in their memory or imagination,--it is the teacher's business to concentrate their attention in accordance with the programme, and these remarks and additions of the children he should take notice of for the purpose of elaborating the other parts of the programme. In viewing a new subject, the children at every convenient opportunity return to the subjects which have already been under consideration. Since they have observed that a magpie is covered with feathers, the teacher asks: 'Is the suslik also covered with feathers? What is it covered with? And what is a chicken covered with? and a horse? and a lizard?' When they have observed that a magpie has two legs, the teacher asks: 'How many legs has a dog? and a fox? and a chicken? and a wasp? What other animals do you know with two legs? with four? with six?'"

Involuntarily the question arises: Do the children know, or do they not know, what is so well explained to them in these conversations? If the pupils know it all, then, upon occasion, in the street or at home, where they do not need to raise their left hands, they will certainly be able to tell it in more beautiful and more correct Russian than they are ordered to do. They will certainly not say that a horse is "covered" with wool; if so, why are they compelled to repeat these questions just as the teacher has put them? But if they do not know them (which is not to be admitted except as regards the suslik), the question arises: by what will the teacher be guided in what is with so much unction called the programme of questions,--by the science of zoology, or by logic? or by the science of eloquence? But if by none of the sciences, and merely by the desire to talk about what is visible in the objects, there are so many visible things in objects, and they are so diversified, that a guiding thread is needed to show what to talk upon, whereas in objective instruction there is no such thread, and there can be none.

All human knowledge is subdivided for the purpose that it may more conveniently be gathered, united, and transmitted, and these subdivisions are called sciences. But outside their scientific classifications you may talk about objects anything you please, and you may say all the nonsense imaginable, as we actually see. In any case, the result of the conversation will be that the children are either made to learn by heart the teacher's words about the suslik, or to change their own words, place them in a certain order (not always a correct order), and to memorize and repeat them. For this reason all the manuals of this kind, in general all the exercises of development, suffer on the one hand from absolute arbitrariness, and on the other from superfluity. For example, in Mr. Bunákov's book the only story which, it seems, is not copied from another author, is the following:

"A peasant complained to a hunter about his trouble: a fox had carried off several of his chickens and one duck; the fox was not in the least afraid of watch-dog Dandy, who was chained up and kept barking all night long; in the morning he had placed a trap with a piece of roast meat in the fresh tracks on the snow,--evidently the red-haired sneak was disporting near the house, but he did not go into the trap. The hunter listened to what the peasant had to say to him, and said: 'Very well; now we will see who will be shrewder!' The hunter walked all day with his gun and with his dog, over the tracks of the fox, to discover how he found his way into the yard. In the daytime the sneak sleeps in his lair, and knows nothing of what is going on, so that had to be considered: on its path the hunter dug a hole and covered it with boards, dirt, and snow; a few steps from it he put down a piece of horseflesh. In the evening he seated himself with a loaded gun in his ambush, fixed things in such a way that he could see everything and shoot comfortably, and there he waited. It grew dark. The moon swam out. Cautiously, looking around and listening, the fox crept out of his lair, raised his nose, and sniffed. He at once smelled the odour of horseflesh, and ran at a slow trot to the place, and suddenly stopped and pricked his ears: the shrewd one saw that there was a mound there which had not been in that spot the previous evening. This mound apparently vexed him, and made him think; he took a large circle around it, and sniffed and listened, and sat down, and for a long time looked at the meat from a distance, so that the hunter could not shoot him,--it was too far. The fox thought and thought, and suddenly ran at full speed between the meat and the mound. Our hunter was careful, and did not shoot. He knew that the sneak was merely trying to find out whether anybody was sitting behind that mound; if he had shot at the running fox, he would certainly have missed him, and then he would not have seen the sneak, any more than he could see his own ears. Now the fox quieted down,--the mound no longer disturbed him: he walked briskly up to the meat, and ate it with great delight. Then the hunter aimed carefully, without haste, so that he might not miss him. Bang! The fox jumped up from pain and fell down dead."

Everything is arbitrary here: it is an arbitrary invention to say that a fox could carry off a peasant's duck in winter, that peasants trap foxes, that a fox sleeps in the daytime in his lair (for he sleeps only at night); arbitrary is that hole which is uselessly dug in winter and covered with boards without being made use of; arbitrary is the statement that the fox eats horseflesh, which he never does; arbitrary is the supposed cunning of the fox, who runs past the hunter; arbitrary are the mound and the hunter, who does not shoot for fear of missing, that is, everything, from beginning to end, is bosh, for which any peasant boy might arraign the author of the story, if he could talk without raising his hand.

Then a whole series of so-called exercises in Mr. Bunákov's lessons is composed of such questions as: "Who bakes? Who chops? Who shoots?" to which the pupil is supposed to answer: "The baker, the wood-chopper, and the marksmen," whereas he might just as correctly answer that the woman bakes, the axe chops, and the teacher shoots, if he has a gun. Another arbitrary statement in that book is that the throat is a part of the mouth, and so on.

All the other exercises, such as "The ducks fly, and the dogs?" or "The linden and birch are trees, and the horse?" are quite superfluous. Besides, it must be observed that if such conversations are really carried on with the pupils (which never happens) that is, if the pupils are permitted to speak and ask questions, the teacher, choosing simple subjects (they are most difficult), is at each step perplexed, partly through ignorance, and partly because _ein Narr kann mehr fragen, als zehn Weise antworten_.

Exactly the same takes place in the instruction of arithmetic, which is based on the same pedagogical principle. Either the pupils are informed in the same way of what they already know, or they are quite arbitrarily informed of combinations of a certain character that are not based on anything. The lesson mentioned above and all the other lessons up to ten are merely information about what the children already know. If they frequently do not answer questions of that kind, this is due to the fact that the question is either wrongly expressed in itself, or wrongly expressed as regards the children. The difficulty which the children encounter in answering a question of that character is due to the same cause which makes it impossible for the average boy to answer the question: Three sons were to Noah,[1]--Shem, Ham, and Japheth,--who was their father? The difficulty is not mathematical, but syntactical, which is due to the fact that in the statement of the problem and in the question there is not one and the same subject; but when to the syntactical difficulty there is added the awkwardness of the proposer of the problems in expressing himself in Russian, the matter becomes of greater difficulty still to the pupil; but the trouble is no longer mathematical.

[Footnote 1: The Russian way of saying "Noah had three sons."]

Let anybody understand at once Mr. Evtushévski's problem: "A certain boy had four nuts, another had five. The second boy gave all his nuts to the first, and this one gave three nuts to a third, and the rest he distributed equally to three other friends. How many nuts did each of the last get?" Express the problem as follows: "A boy had four nuts. He was given five more. He gave away three nuts, and the rest he wants to give to three friends. How many can he give to each?" and a child of five years of age will solve it. There is no problem here at all, but the difficulty may arise only from a wrong statement of the problem, or from a weak memory. And it is this syntactical difficulty, which the children overcome by long and difficult exercises, that gives the teacher cause to think that, teaching the children what they know already, he is teaching them anything at all. Just as arbitrarily are the children taught combinations in arithmetic and the decomposition of numbers according to a certain method and order, which have their foundation only in the fancy of the teacher. Mr. Evtushévski says:

"Four. (1) The formation of the number. On the upper border of the board the teacher places three cubes together--I I I. How many cubes are there here? Then a fourth cube is added. And how many are there now? I I I I. How are four cubes formed from three and one? We have to add one cube to the three.

"(2) Decomposition into component parts. How can four cubes be formed? or, How can four cubes be broken up? Four cubes may be broken up into two and two: II + II. Four cubes may be formed from one, and one, and one, and one more, or by taking four times one cube: I + I + I + I. Four cubes may be broken up into three and one: III + I. It may be formed from one, and one, and two: I + I + II. Can four cubes be put together in any other way? The pupils convince themselves that there can be no other decomposition, distinct from those already given. If the pupils begin to break the four cubes in this way: one, two, and one, or, two, one and one; or, one and three, the teacher will easily point out to them that these decompositions are only repetitions of what has been got before, only in a different order.

"Every time, whenever the pupils indicate a new method of decomposition, the teacher places the cubes on a ledge of the blackboard in the manner here indicated. Thus there will be four cubes on the upper ledge; two and two in a second place; in a third place the four cubes will be separated at some distance from each other; in a fourth place, three and one, and in a fifth one, one, and two.

"(3) Decomposition in order. It may easily happen that the children will at once point out the decomposition of the number into component parts in order; even then the third exercise cannot be regarded as superfluous: Here we have formed four cubes of twos, of separate cubes, and of threes,--in what order had we best place the cubes on the board? With what shall the decomposition of the four cubes begin? With the decomposition into separate cubes. How are four cubes to be formed from separate cubes? We must take four times one cube. How are four cubes to be formed from twos, from a pair? We must take two twos,--twice two cubes, two pairs of cubes. How shall we afterward break up the four cubes? They can be formed of threes: for this purpose we take three and one, or one and three. The teacher explains to the pupils that the last decomposition, that is, 1 1 2, does not come under the accepted order, and is a modification of one of the first three."

Why does Mr. Evtushévski not admit this last decomposition? Why must there be the order indicated by him? All that is a matter of mere arbitrariness and fancy. In reality, it is apparent to every thinking man that there is only one foundation for any composition and decomposition, and for the whole of mathematics. Here is the foundation: 1 + 1 = 2, 2 + 1 = 3, 3 + 1 = 4, and so forth,--precisely what the children learn at home, and what in common parlance is called counting to ten, to twenty, and so forth. This process is known to every pupil, and no matter what decomposition Mr. Evtushévski may make, it is to be explained from this one. A boy that can count to four, considers four as a whole, and so also three, and two, and one. Consequently, he knows that four was produced from the consecutive addition of one. Similarly he knows that four is produced by adding twice one to two, just as he knows twice one is two. What, then, are the children taught here? That which they know, or that process of counting which they must learn according to the teacher's fancy.

The other day I happened to witness a lesson in mathematics according to Grube's method. The pupil was asked: "How much is 8 and 7?" He hastened to answer and said 16. His neighbour, too, was in a hurry and, without raising his left hand, said: "8 and 8 is 16, and one less is 15." The teacher sternly stopped him, and compelled the first boy to add one after one to 8, until he came to 15, though the boy knew long ago that he had made a blunder. In that school they had reached the number 15, but 16 was supposed to be unknown yet.

I am afraid that many people, reading all these long refutals of the methods of object instruction and counting according to Grube, which I am making, will say: "What is there here to talk about? Is it not evident that it is all mere nonsense which it is not worth while to criticize? Why pick out the errors and blunders of a Bunákov and Evtushévski, and criticize what is beneath all criticism?"

That was the way I myself thought before I was led to see what was going on in the pedagogical world, when I convinced myself that Messrs. Bunákov and Evtushévski were not mere individuals, but authorities in our pedagogics, and that what they prescribe is actually carried out in our schools. In the backwoods we may find teachers, especially women, who spread Evtushévski's and Bunákov's manuals out before them and ask according to their prescription how much one feather and one feather is, and what a hen is covered with. All that would be funny if it were only an invention of the theorist, and not a guide in practical work, a guide that some follow already, and if it did not concern one of the most important affairs of life,--the education of the children. I was amused at it when I read it as theoretical fancies; but when I learned and saw that that was being practised on children, I felt pity for them and ashamed.

From a theoretical standpoint, not to mention the fact that they faultily define the aim of education, the pedagogues of this school make this essential error, that they depart from the conditions of all instruction, whether this instruction be on the highest or lowest stage of the science, in a university or in a popular school. The essential conditions of all instruction consist in selecting the homogeneous phenomena from an endless number of heterogeneous phenomena, and in imparting the laws of these phenomena to the students. Thus, in the study of language, the pupils are taught the laws of the word, and in mathematics, the laws of the numbers. The study of language consists in imparting the laws of the decomposition and of the reverse composition of sentences, words, syllables, sounds,--and these laws form the subject of instruction. The instruction of mathematics consists in imparting the laws of the composition and decomposition of the numbers (but I beg to observe,--not in the process of the composition and the decomposition of the numbers, but in imparting the laws of that composition and decomposition). Thus, the first law consists in the ability of regarding a collection of units as a unit of a higher order, precisely what a child does when he says: "2 and 1 = 3." He regards 2 as a kind of unit. On this law are based the consequent laws of numeration, then of addition, and of the whole of mathematics. But arbitrary conversations about the wasp, and so forth, or problems within the limit of 10,--its decomposition in every manner possible,--cannot form a subject of instruction, because, in the first place, they transcend the subject and, in the second place, because they do not treat of its laws.

That is the way the matter presents itself to me from its theoretical side; but theoretical criticism may frequently err, and so I will try to verify my deductions by means of practical data. G---- P---- has given us a sample of the practical results of both object instruction and of mathematics according to Grube's method. One of the older boys was told: "Put your hand under your book!" in order to prove that he had been taught the conceptions of "over" and "under," and the intelligent boy, who, I am sure, knew what "over" and "under" was, when he was three years old, put his hand on the book when he was told to put it under it. I have all the time observed such examples, and they prove more clearly than anything else how useless, strange, and disgraceful, I feel like saying, this object instruction is for Russian children. A Russian child cannot and will not believe (he has too much respect for the teacher and for himself) that the teacher is in earnest when he asks him whether the ceiling is above or below, or how many legs he has. In arithmetic, too, we have seen that pupils who did not even know how to write the numbers and during the whole time of the instruction were exercised only in mental calculations up to 10, for half an hour did not stop blundering in every imaginable way in response to questions which the teacher put to them within the limit of 10. Evidently the instruction of mental calculation brought no results, and the syntactical difficulty, which consists in unravelling a question that is improperly put, has remained the same as ever. And thus, the practical results of the examination which took place did not confirm the usefulness of the development.