George
- Author:
Donald L. McDonough, M.A.,
Graduate Student, University of Pennsylvania.
George, a boy of eleven, of Lithuanian parentage, was suffering from an affliction common to school children, particularly to those children whom Providence, or whatever else you may call it, has not picked out to do the mental work of the world. George was suffering from mathematics. The social worker who brought George to the clinic reported that he was doing excellent work in everything except arithmetic, in spite of the fact that he refused to follow school schedule when it pleased him to do otherwise. George is the second of three children. He walked at eighteen months of age and talked at three years. He is now in the seventh grade of a parochial school. His brother Charles, who is now fourteen, and in a special class, did not talk until he was five years of age. Their father is troubled with rheumatism. The mother’s health is reported as good. George was brought to the clinic because of what was considered irrational behavior in school. The social worker reported that he annoyed the other boys in class and wrote compositions while the rest of the class was working arithmetic. Probably this could not be considered very irrational, considering that he did not like arithmetic and that he was evidently getting away with what he was doing.
George did the Witmer formboard in 26, 25 and 18 seconds respectively, and the Witmer cylinder test in 1 minute 30 seconds, 1 minute 4 seconds, and 47 seconds respectively in three successive trials. He showed an auditory memory span of 7. The examiner found him poor in analytical discrimination but diagnosed him as normal and made the following note on his record: “One of the difficulties in handling George is that he jumps to conclusions and is not much worried whether they be right or wrong. His desire to be the center of attraction may lead him to do things considered irrational when viewed from other angles. If he is in the upper 10 per cent of his class at school, it might be well to advance him to the next grade, provided he is sufficiently interested to show that he is capable of doing the work. If convenient, the teacher should somehow leave the impression with him that she is dependent on him for assistance in running the school.”
George was turned over to me for clinical teaching in arithmetic with the idea of finding out what he could do, and, if possible, to arouse an interest in him in arithmetic. He was a boy of fair size for his age and rather inclined to be plump. The first thing that impressed one about him was his initiative. He was ready to do anything, and it turned out as the examiner had said, he was not much concerned as to whether he did it correctly or not. His initiative deceived one at first and left the impression that he was more capable than a careful analysis of the situation showed him to be. There is not much doubt in my mind that right here lies the secret of George’s apparent success in some of the subjects in which the measure of success is not so accurate as it is in mathematics. I learned later that he was also having trouble with grammar, another subject in which the measure of accomplishment is rather obvious. In other words, it looks to me as though through his initiative he had succeeded in bluffing his way through some of his subjects. In history, for instance, I do not doubt but that George would tell some sort of a story regardless of what he knew.
That George was deficient in arithmetic proficiency was evident. The thing to decide was whether his deficiency was due to his attitude towards the subject (likes and dislikes); whether he lacked the ability to do the work, or whether his trouble was due to the method used in teaching him. The method of teaching does not make much difference in dealing with children of ability. They will get it in spite of the methods. But the less ability the pupil may have along the line in question, the more real teaching is necessary to put it across. When George first came for clinical teaching he had a vague smattering of the various types of problems commonly taught in elementary schools, but he could not perform simple divisions correctly. When the conditions of the problems were carefully explained to him, he could do simple problems applying addition, subtraction and multiplication, but as soon as division was involved he “went up into the air” and resorted to wild guessing. He showed lack of confidence in himself. After almost every figure he set down he would look to the teacher for approval, and tried to find out from the teacher’s expression whether he was right or wrong. In this respect George showed improvement in the course of the clinical teaching. However, at the close of the clinical work with him this lack of confidence was still in evidence. To throw him on his own resources I would give him a problem and then leave the room. His lack of confidence is, no doubt, closely connected with his lack of ability and of proficiency. His improvement in this respect was, no doubt, due to improvement in proficiency.
That George is deficient in understanding was shown throughout the weeks during which I worked with him. He could not be brought to see that division is the reverse process of multiplication. Although he learned to divide, he could not apply it. If in a given problem he were told that he had to divide he could perform the operation, but if left to himself he would either do something ridiculous or would arrive at his result by trial and error through multiplication. That is, he would multiply the number which should be his divisor by some number, and continue this process until he arrived at the answer. If the numbers in question were too large for this, he might add, subtract or do almost anything else. One day he told me that they were working “ratio and proportion” problems in school. I attempted to teach him “ratio and proportion.” After several days of this work he not only was unable to set down the proportion from the given conditions, but even failed utterly to grasp the mechanical process of arriving at the result after the problem was put into type form. After four hours were spent on different days in an attempt to teach George the areas and perimeters of simple figures, such as the square and rectangle, he seemed to be utterly unable to grasp the difference between the area and the perimeter. At the end, just as in the beginning, he would guess as to whether he should mult iply one side of the square by four or whether he should multiply the side by itself to get the area. Drawing the small squares within the large one did not seem to help him to make this distinction. His retention as well as his understanding seemed to be at fault. On three different days George learned that the area of a triangle is one-half the base multiplied by the altitude, and forgot it as often.
Before I undertook to teach George arithmetic the examiner thought that probably it was merely a matter of arousing his interest in the subject. To a certain extent this was true. George lacked interest in arithmetic. But, no doubt, his lack of interest, as is frequently the case, was due to a lack of ability. The individual delights in exercising those functions for which nature has endowed him with a strong mechanism. However, George’s interest in arithmetic seemed to increase. He asked that he be given work to do at home. His teacher also reported that he was showing more interest and doing better work. This interest may not have been interest in arithmetic for arithmetic’s sake. First, George came to me at 10.30 a. m. and left at 11.30 a. m. This, together with the time it took him to get there and back again gave him practically a half-holiday from school. In the second place, George, I discovered, was getting graft out of the situation. He was clever enough to do that but not clever enough to prevent being caught. I furnished him with car fare both ways from the start. During the first three weeks I had him come on three mornings. He then made the remark that his parents desired that he should not come oftener than twice a week. His father was not working and they could not afford the car fare. When I called his attention to the fact that I had been furnishing his car fare he became very much confused. There must have been some suspicion, too, that he was pretending to come to the University more frequently than he actually was coming, for during the last two weeks he brought a card from the principal of the school which he attended, requesting that I write on it the time he was to come again. Another reason why George may have desired to continue to come to the clinic was the fact that it afforded him an opportunity to have his morning smoke. He would come out about half an hour earlier than necessary and walk around the neighborhood of the University smoking.
There is another item in George’s behavior which seems to me to be the key to the whole situation. On some days George would keep right down to work and do pretty well; on other days he seemed to be absolutely wanting in such a thing as persistent concentration of attention. His mind seemed to be a mass of confusion. He could not concentrate his attention on anything long enough to do it correctly. He was unable to perform the simplest operations of arithmetic correctly. On these days he would guess wildly at the operations necessary to solve a particular problem. Having been told what to do, he could not do it correctly. As time went on these off days came less frequently. The presence of someone else in the room was always very distracting to him. One day the examiner came into the room to see how he was getting along. While he was there George was unable to multiply 88 by 4. He fumbled around and hesitated. He seemed to be utterly confused.
George’s trouble seems to be in the field of motivation. From his lack of confidence, which displays itself in spite of his initiative, and from his periods of mental confusion it would seem to me that his trouble is of a hysterical nature. George did learn to do with reasonable efficiency such rote performances as are involved in the various operations with fractions; he can do simple problems involving the application of addition, multiplication. He learned, also, to divide but could not apply it. Whether or not George’s apparent high standing in some of his subjects is warranted, I do not know. I doubt that he will ever acquire and be able to use more mathematics than is necessary for ordinary use in everyday life.
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