Fables for Children, Stories for Children, Natural Science Stories Part 41

So this is what the method of instruction is to be based upon. I will remark, not for contradiction, but for the sake of simplicity and clearness, that the last two statements are quite superfluous, because without the union of a.n.a.lysis and synthesis there can be not only no instruction, but also no other activity of the mind, and every instruction, except that of the deaf and dumb, is based on the sense of hearing. These two conditions are put down only for beauty's sake and for the obscuration of the style, so common in pedagogical treatises, and so have no meaning whatever. The first three at first sight appear quite true as a programme. Everybody, of course, would like to know how the method is secured that will "develop," that will "introduce into the instruction the pupil's personal interest," and that will "represent the process of self-instruction."

But to the questions as to why this method combines all those qualities you will find an answer neither in the books of Messrs. Bunakov and Evtushevski, nor in any other pedagogical work of the founders of this school of pedagogy, unless they be those hazy discussions of this nature, such as that every instruction must be based on the union of a.n.a.lysis and synthesis, and by all means on the sense of hearing, and so forth; or you will find, as in Mr. Evtushevski's book, expositions about how in man are formed impressions, sensations, representations, and concepts, and you will find the rule that "it is necessary to start from the object and lead the pupil up to the idea, and not start with the idea, which has no point of contact in his consciousness," and so forth.

After such discussions there always follows the conclusion that therefore the method advocated by the pedagogue gives that exclusive real development which it was necessary to find.

After the above-cited definition of what a good method ought to be, Mr.

Bunakov explains how children ought to be educated, and, having given an exposition of all the methods, which in my opinion and experience lead to results which are diametrically opposite to development, he says frankly and definitely:

"From the standpoint of the above-mentioned fundamental principles for estimating the value of the satisfactoriness of the methods of rudimentary instruction, the method which we have just elucidated in its general features presents the following plastic qualities and peculiarities: (1) As a sound method it wholly preserves the characteristic peculiarities of all sound method,--it starts from the impressions of hearing, at once establis.h.i.+ng the regular relation to language, and only later adds to them the impressions of sight, thus clearly distinguis.h.i.+ng sound, matter, and the letter, its representation. (2) As a method which unites reading with writing it begins with decomposition and pa.s.ses over to composition, combining a.n.a.lysis with synthesis. (3) As a method which pa.s.ses over to the study of words and sounds from the study of objects it proceeds along a natural path, cooperates with the regular formation of concepts and ideas, and acts in a developing way on all the sides of the child's nature: it incites the children to be observant, to group their observations, to render them orally; it develops the external senses, mind, imagination, memory, the gift of speech, concentration, self-activity, the habit of work, the respect for order. (4) As a method which provides ample work to all the mental powers of the child, it introduces into instruction the personal interest, rousing in children willingness and love of work, and transforming it into a process of self-instruction."

This is precisely what Mr. Evtushevski does; but why it is all so remains inexplicable to him who is looking for actual reasons and does not become entangled in such words as psychology, didactics, methodics, heuristics. I advise all those who have no inclination for philosophy and therefore have no desire to verify all those deductions of the pedagogues not to be embarra.s.sed by these words and to be a.s.sured that a thing which is not clear cannot be the basis of anything, least of all of such an important and simple thing as popular education.

All the pedagogues of this school, especially the Germans, the founders of the school, start with the false idea that those philosophical questions which have remained as questions for all the philosophers from Plato to Kant, have been definitely settled by them. They are settled so definitely that the process of the acquisition by man of impressions, sensations, concepts, ratiocinations, has been a.n.a.lyzed by them down to its minutest details, and the component parts of what we call the soul or the essence of man have been dissected and divided into parts by them, and that, too, in such a thorough manner that on this firm basis can go up the faultless structure of the science of pedagogy. This fancy is so strange that I do not regard it as necessary to contradict it, more especially as I have done so in my former pedagogical essays. All I will say is that those philosophical considerations which the pedagogues of this school put at the basis of their theory not only fail to be absolutely correct, not only have nothing in common with real philosophy, but even lack a clear, definite expression with which the majority of the pedagogues might agree.

But, perchance, the theory of the pedagogues of the new school, in spite of its unsuccessful references to philosophy, has some value in itself.

And so we will examine it, to see what it consists in. Mr. Bunakov says:

"To these little savages (that is, the pupils) must be imparted the main order of school instruction, and into their consciousness must be introduced such initial concepts as they will have to come in contact with from the start, during the first lessons of drawing, reading, writing, and every elementary instruction, such as: the right side and the left, to the right--to the left, up--down, near by--around, in front--in back, close by--in the distance, before--behind, above--below, fast--slow, softly--aloud, and so forth. No matter how simple these concepts may be, I know from practice that even city children, from well-to-do families, are frequently, when they come to the elementary schools, unable to distinguish the right side from the left. I a.s.sume that there is no need of expatiating on the necessity of explaining such concepts to village children, for any one who has had to deal with village schools knows this as well as I do."

And Mr. Evtushevski says:

"Without entering into the broad field of the debatable question about the innate ability of man, we only see that the child can have no innate concepts and ideas about real things,--they have to be formed, and on the skill with which they are formed by the educator and teacher depends both their regularity and their permanency. In watching the development of the child's soul one has to be much more cautious than in attending to his body. If the food for the body and the various bodily exercises are carefully chosen both as regards their quant.i.ty and their quality, in conformity with the man's growth, so much more cautious have we to be in the choice of food and exercises for the mind. A badly placed foundation will precariously support what is fastened to it."

Mr. Bunakov advises that ideas be imparted as follows:

"The teacher may begin a conversation such as he deems fit: one will ask every pupil for his name; another about what is going on outside; a third about where each comes from, where he lives, what is going on at home,--and then he may pa.s.s over to the main subject. 'Where are you sitting now? Why did you come here? What are we going to do in this room? Yes, we are going to study in this room,--so let us call it a cla.s.s-room. See what there is under your feet, below you. Look, but do not say anything. The one I will tell to speak shall answer. Tell me, what do you see under your feet? Repeat everything we have found out and have said about this room: in what room are we sitting? What are the parts of the room? What is there on the walls? What is standing on the floor?'

"The teacher from the start establishes the order which is necessary for the success of his work: each pupil is to answer only when asked to do so; all the others are to listen and should be able to repeat the words of the teacher and of their companions; the desire to answer, when the teacher directs a question to everybody, is to be expressed by raising the left hand; the words are to be p.r.o.nounced neither in a hurry, nor by drawing them out, but loudly, distinctly, and correctly. To obtain this latter result the teacher gives them a living example by his loud, correct, distinct enunciation, showing them in practice the difference between soft and loud, distinct and correct, slow and fast. The teacher should see to it that all the children take part in the work, by having somebody's question answered or repeated, now by one, now by another, and now by the whole cla.s.s at once, but especially by rousing the indifferent, inattentive, and playful children: the first he must enliven by frequent questions, the second he must cause to concentrate themselves on the subject of the common work, and the third he must curb. During the first period the children ought to answer in full, that is, by repeating the question: 'We are sitting in the cla.s.s-room' (and not in brief, 'In the cla.s.s-room'); 'Above, over my head, I see the ceiling;' 'On the left I see three windows,' and so forth."

Mr. Evtushevski advises that in this way be begun all the lessons on numbers from 1 to 10, of which there are to be 120, and which are to be continued through the year.

"One. The teacher shows the pupils a cube, and asks: 'How many cubes have I?' and taking several cubes into the other hand, he asks, 'And how many are there here?'--'Many, a few.'

"'Name here in the cla.s.s-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 cla.s.s-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 Petya fell down once? How many times did Petya 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. Bunakov speaks of exercises on the board, and so on, and Mr.

Evtushevski 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. Bunakov 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.

Evtushevski's problems. Mr. Evtushevski 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. Bunakov 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 cla.s.sifications 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. Bunakov'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 p.r.i.c.ked 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. Bunakov'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 j.a.pheth,--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. Evtushevski'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. Evtushevski 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 repet.i.tions 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. Evtushevski 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. Evtushevski 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 Bunakov and Evtushevski, 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.

Bunakov and Evtushevski 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 Evtushevski's and Bunakov'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 h.o.m.ogeneous 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.

But I will be more exact and conscientious. Maybe the process of development, which at first is confined not so much to the study, as to the a.n.a.lysis of what the pupils know already, will produce results later on. Maybe the teacher, who at first takes possession of the pupils'

minds by means of the a.n.a.lysis, later guides them firmly and with ease, and from the narrow sphere of the descriptions of a table and the count of 2 and 1 leads them into the real sphere of knowledge, in which the pupils are no longer confined to learning what they know already, but also learn something new, and learn that new information in a new, more convenient, more intelligent manner. This supposition is confirmed by the fact that all the German pedagogues and their followers, among them Mr. Bunakov, say distinctly that object instruction is to serve as an introduction to "home science" and "natural science." But we should be looking in vain in Mr. Bunakov's manual to find out how this "home science" is to be taught, if by this word any real information is to be understood, and not the descriptions of a hut and a vestibule,--which the children know already. Mr. Bunakov, on page 200, after having explained that it is necessary to teach where the ceiling is and where the stove, says briefly: