MR. VON OSTEN'S METHOD OF INSTRUCTION

[By C. Stumpf]

The following is a report of the account, which Mr. von Osten gave Professor Schumann and me, of the method which he had used in the instruction of the horse, and which was illustrated by actual demonstrations. I cannot testify, of course, that Mr. von Osten really did adhere to this method throughout the four years in which he tutored the horse, but I will say that I have several good reasons for believing that it was impossible for him to have trumped up this make-believe scheme afterward, merely to mislead us. Among the reasons are the following: He was always ready to give a detailed explanation of any question which we might interpose; the written statements of Major von Keller, who has known Mr. von Osten for a period of fifteen years; the testimony of General Zobel, who became acquainted with the whole process fully a year before any public exhibitions were given; the accounts given by the tenants in Mr. von Osten's house, who for years saw the process of instruction going on in the courtyard of the apartment building,—according to their account his intercourse with the horse was like that with a child at school,—he made much use of the apparatus and never did they notice anything like an habituation to respond to certain signals; and finally the appearance of the apparatus itself—some of which could not be bought at second hand—was most convincing.

The apparatus used for the work in arithmetic consisted mainly of a set of large wooden pins, a set of smaller ones (such as are to be had in toy-shops), a counting-machine, such as is commonly used in the schools, a chart upon which were pasted the numbers from 1 to 100, and finally the digits, cut large and in brass and suspended from a string. For the work in reading Mr. von Osten used the chart shown in the frontispiece of this book. Here we have the letters of the alphabet in small German script with numbers written below which serve to indicate the row, and what place in that row, the letters occupy. For tones, a small, child's organ was used with the diatonic scale C^1 to C^2, and for instruction in colors, a number of colored cloths were used.

The work in arithmetic began by placing a single wooden pin in front of Hans and then commanding him: "Raise the foot!—One!" Here we must assume that the horse had learned to respond to the command to raise the foot during the preceding period, when tapping in general had been taught. In order to get the horse to learn that he was to give only one tap, Mr. von Osten tried to control the tapping by means of holding the animal's foot, just as a teacher tries to aid a pupil in learning to write by guiding his hand. He repeated this exercise so often that finally the single tap was made. And always the right foot was insisted upon. Bread and carrots were the constant rewards.

Two of the pins were now set up and the command given: "Raise the foot!—One, two!" Mr. von Osten again aided the establishment of the proper association by using his hand as before. At the same time the two pins were pointed out, and the order was always without exception from left to right. Gradually it became unnecessary to touch the foot or to point to the pins, and instead the question was introduced: "How many are there?", in order that the horse should become accustomed to these words as an invitation to give the taps when he saw the wooden pins before him.

Then three pins were taken and the words "one, two, three" were spoken, and so on. In naming a number the preceding ones were always named along with it, in order that the normal order might thus be learned at the same time. Later the number alone, without the preceding ones, sufficed to elicit the proper number of taps. The last word of the series thus becomes characteristic of the series as a whole. It differs from all the others, and thus becomes the sign for the whole series of numbers thus named, each of which arises as a memory image at the proper place in the series and is accompanied by a tap of the foot. Thus, Mr. von Osten at any rate had accounted to himself for his success.

But Hans was not to acquire merely this relatively mechanical process of counting (hardly to be called counting), but he was to acquire also some meaning content for the number terms. For this purpose everything depended upon the concept "and". Only he who can grasp its meaning will be able to understand a number. 2 is 1 and 1, 3 is 2 and 1. Mr. von Osten had someone hold a large cloth before the horse, where the wooden pins usually were placed. He then had the cloth taken up and he would pronounce emphatically the word "and". After this had been done a number of times, he put up two of the pins and obscured them by the cloth. The cloth was again raised and the word "and" pronounced. Then Hans, as a result of his previous instruction (so Mr. von Osten thought) would give two taps at sight of the pins. The thing was repeated with three pins, then with one, and so on, and the horse would always execute the proper number of taps.

Now, five pins were set up, the three to the right being covered by the cloth. The horse tapped twice and Mr. von Osten said "two". Then the cloth was raised, Hans gave three further taps, and Mr. von Osten said "and three" with emphasis.

In this simple manner he tried to get the horse to understand that the three belongs to the two, and that both together make five. The image of the five pins as it was known from previous experience, was to be associated with the combined groups of two and three, and conversely, it was to be reproduced when these groups were presented. Later the cloth and pins were omitted and the question was asked: "How much is two and three?". The horse tapped five times. It had learned how to add. Still this could be regarded only as a mechanical process, if the horse were able to add only those numbers which had been presented together one or more times in the manner just described. And so long as we remained within the first decade, we could get twenty-five binary combinations whose sum does not exceed 10 (counting inverted orders we would have forty-five binary permutations),—all of which might have been practised separately. But as a matter of fact, Mr. von Osten did not take this course, for as he himself says, he allowed Hans to discover a great deal for himself. "Hans had to develop the multiplication table for himself."—With larger numbers and more addends, the number of combinations becomes so great that there can be no doubt they were not practised separately.

Since, after all this preliminary instruction, Hans really began to give solutions of new problems, the master believed that this was proof that he had succeeded in inculcating the inner meaning of the number concepts, and not merely an external association of memory images with certain movement responses. But he always remained within the sphere of the ideas thus developed, and adhered closely to the customary vocabulary and its usage. Every new concept, each additional word was explained anew.

It would not be legitimate to condemn the whole procedure from the very beginning on the ground of the horse's lack of knowledge of language or of its use. It was Mr. von Osten's aim to convey to the horse an understanding of the language, by means of sense-presentations, adequate to give rise to the proper sense-perceptions. Helen Keller and other blind deaf-mutes have been educated to an understanding of the language without the aid of vision and hearing. They have come to it through the sense of touch alone. Everything depends upon whether or not the predisposition for it is present. And it was quite rational that Mr. von Osten should have chosen counting and arithmetical calculation as the processes by which to make his attack upon the animal mind, for as a matter of fact, nowhere else is it so easy to bridge the gap between perception and conception and nowhere else can the sign of success or failure be perceived so readily as in the handling of numbers. It is unfortunate, however, that he did not utilize these same signs for purposes of counter-testing also, as, for instance, by inquiring for the cube root of 729. But he was prevented from doing this by his close adherence to his pedagogical principle and by his unquestioning faith in the soundness of the entire procedure.

In teaching multiplication the counting machine was used. Two of the ten balls on one of the rods were pushed far to the left, thus: 00. "How many are there?" Two taps. "Very well. That is once two." Another group of two was pushed to the left, at a short interval from the first group, thus: 00 00. "How many times two balls are there?" was asked, with a decided movement of the hand toward the two groups. Two taps. "How many, therefore, are two times two?" Four taps.

The horse was supposed to learn the meaning of the word "times" by means of the spatial separation of the groups; he was to be taught to notice and to count the groups, and also the number of units in a single group. Three times two then meant three groups with two units in each group. The horse was supposedly aided by the following factors: the relative nearness of the units belonging to one group, as over against the space interval between the groups themselves; also that the groups were pointed out as wholes in connection with the emphatic enunciation of the words

Subtraction was taught in the following manner. Five pins were set up; the horse tapped five times. Mr. von Osten then removed two of them and said emphatically: "I take away,—minus.

In division four balls were first pushed to the left end of the rod, thus: 0000. "How many balls are there to the left?" Four taps. They were now divided into two pairs, thus: 00 00. Pointing to the units of one group, the teacher asks: "There are always how many in the group?" Two taps. Three groups were formed, thus: 00 00 00. "There are now how many balls to the left?" Six taps. "And there are always how many in each group?", (pointing at them). Two taps. "And how often is two contained in six?", (pointing to the groups consecutively). Three taps, etc.

The ideas of 'part', of 'whole', and of 'being contained' were illustrated by means of a chalk line which was interrupted in one or more places by erasure.

In all these operations Mr. von Osten adhered strictly to the rule, and required others to do so too, that the number upon which the operation was performed, must be mentioned first. Thus, one was not to say, "take 3 away from 7", but "from 7 take away 3." Otherwise, he believed, Hans would become easily confused. Also one was not allowed to say "to multiply", but to "take" a certain number so many "times". He, himself, never departed from this practice.

We will not go into the details of the method by which Hans was taught the meaning of the number signs, of the signs of operation, of the numbers above 10, or the significance of "digits", "tens", etc. Only this,—when in problems in addition the sum was greater than 10, the 10 was first tapped and then the remainder of the number added to the 10. Thus: "You are to add 9 and 5. How much must you add to the 9 to have 10?" One tap. "But now, you were to add not merely 1, but 5; how much have you still to add to the 10?"—Four taps. In like manner, whenever the addends were below 20 or 30 and the sum above 20 or 30, Mr. von Osten would ask for the 20 or 30 taps first. He thought that he was thus giving his pupil an ever firmer grasp upon the principle of the structure of our number system, in which all higher numbers are constituted of tens and digits. For the same reason he used at first, instead of the words 'eleven' and 'twelve' ('elf' and 'zwölf' in the German), expressions which in English might be rendered as 'one-teen' and 'two-teen' ('einzehn' and 'zweizehn' in the German); and only later, after the animal had seemingly mastered the meaning in question, did Mr. von Osten replace them by the usual forms.

All this was beautifully conceived and might perhaps form the basis for the instruction of primitive races. But it is of immediate interest for us only because it enables us to better understand the origin of the conviction under which Mr. von Osten and his followers labored.