Arithmetic Without Fear
- Author:
ROGERS, M.A.
Lecturer in Mathematics, Hockerill Training College It has been said by those who have experience in welfare clinics, and whose kindly labours are directed to the betterment of the lives of children, that one cause of distress among those children is the terror that sometimes seems to be inseparable from their ” sums the sense of dread that the mere thought of Arithmetic brings to them.
Now why should such things be ? How can we make the rough places plain and the crooked straight, so that all children may enter into their rightful heritage, that fairyland which the realm of number was to Lewis Carroll or A. A. Milne ? The extent of the Arithmetic phobia is not so widespread as it is usually supposed to be. I have repeatedly found that the majority of small children really do enjoy ” doing their sums “, but this majority often dwindles as the children go up the school until in Standard VI and VII there may be only a minority who really delight in Arithmetic, a majority who are indifferent, and a few who honestly detest it. A questionnaire addressed to a class of Training College students at the end of their first year produced the result that 13-3 per cent, hated Arithmetic, 21-7 per cent, were indifferent, and 65 per cent, liked it. The minority who dislike Arithmetic is always there, and the fact that it is a minority makes us feel that it is possible as well as imperative to rescue it.
The causes of the phobia are many. If one asks children why they hate Arithmetic one is met with the pathetic reiterated plaint ” Because I cannot do it * Abridged.
They hate it when they ” can never get it right Students who are asked why they or their pupils hate Arithmetic answer as follows:
” Because I was badly taught; Arithmetic seemed a dead thing to me, when I am sure it need not have been.” ” I had a bad teacher who frightened me by grumbling when I couldn’t do the sums.”
” Because I had so many teachers with different methods of teaching, so that I got thoroughly muddled.”
‘’ I was moved up too quickly and never made up what was lost.” ” Because children get behindhand through absence and never can catch up.” It has been suggested that dislike of Arithmetic is traditional and in some cases a pose.
Turning next to the far more numerous cases in which students or their children like Arithmetic, the answers again are of various types.
” I have always been lucky enough to have teachers who were sufficiently interested themselves to arouse interest in the children.” ” My teacher always made it real, not a jumble of unrelated figures.” ” I had everything explained clearly.”
” I found it fascinating, and the fact that something was absolutely right, and not just ‘fair ‘, made the subject worth any effort.” (This delight in attainable perfection recurs constantly.)
” I like puzzling out harder problems.” (This also recurs constantly, and the popularity of cross-word puzzles and detective fiction surely indicates that such a taste is by no means uncommon.)
There is no room for doubt that Arithmetic can be a delight. Nevertheless, there are always in a class three or four who cannot do it and so hate it. And this hatred is bitter, intense, and very real, sometimes producing such terror that a child go to all sorts of lengths simply to get out of the dreaded Arithmetic lesson. Our concern at the moment is with these hapless ones; for surely we should be able to stop this needless suffering, which undoubtedly exists. And this brings us to the m?st important part of this discussion, namely, the search for remedies. Two may be suggested for the present state of affairs :
(1) Diagnostic treatment, which discovers and cures specific difficulties, thereby obviating much remediable distress. (See Diagnosis of Individual Difficulties in Arithmetic. F. J. Schonell; published by Oliver & Boyd.) (2) Agreement as to method. (See Mathematical Gazette, May 1940. “The Multiplication of Decimals.”)
These, however, do not touch the root of the matter, which is the necessity for drastic reform in the subject matter of school Arithmetic, especially in the upper standards. The questionnaire above produced many such statements as ” I used to sums for pleasure.” “One boy did 30 sums instead of 8 for homework.”
When some children were given sums to do as a punishment, others tried to get Punished too.” All this?because essential Arithmetic is both easy and pleasant; difficulties, fear and disgust, are almost always caused by the conglomeration of utterly useless stuff which has grown up round it, apparently with the sole object of passing examinations. Text-books are improving, but there is still too often the wrong approach, in which a situation is invented to illustrate a rule, thereby producing a sham reality which is only boring to the unerring judgment of the child. Instead we should look out for the situations, and then find the necessary Arithmetic. I have discussed this matter at some length in Arithmetic is Easy, and offered sugges- tions as to how the rubbish might be cleared away, and something better substituted, since one tragic result of the hours wasted in futile calculations is the inability to perform necessary ones. When the work can be shown to be real, it comes to life at once, and the actual calculation becomes interesting, necessary, and worth while. For instance, if boys, and girls, too, in this present time, are set to make an actual bus-conductors’ way-bill, in the form in which the local bus company demand it, they immediately become keen, alert, and eager to produce a perfect sheet. Instances might be multiplied indefinitely.
There are a few Arithmetic books which do such things, and where they are used intelligently the anti-arithmetic complex diminishes visibly. But there remains one major difficulty. Ask teachers why they have to spend hours on the useless type of example. ” Because of the scholarship examination.” Why do they force their classes to do harder Arithmetic than the average child can grasp ? ” Because of the scholarship examination.” Why do text-books still abound in fictitious examples on the ” compound rules ” ? ” Because of the scholarship examination.” Why have we no time for individual remedial treatment of Arithmetical weaknesses ? ” Because of the scholarship examination.” At present we are bound in a vicious circle: the examinations set the kind of examples that are in the text-books, the text-books print the kind of examples that are set in examinations. Nobody really wants them, everybody agrees as to the futility of certain types, and the urgent necessity for better work in the essentials. In the present world-upheaval, very much that is good in our educational system has had to go. Some little good might come out of the evil if we made it the opportunity to get rid of the dead matter of our Arithmetic, making sure that what remains is well done, clearing the way for fresh fields of knowledge. I asked an intelligent student what would happen if we did something of this kind. Her answer was ” It would save much misery “. Surely now is the time to do so.
There is a certain type of ” nervous ” anxiety prone child whose emotional difficulties whether arising from within or in relation to its environment centre round its school work. The subjects most often involved in this are (1) Arithmetic, (2) Reading, (3) French, in this order of frequency. For such cases to permit the child to become discouraged and distressed is damaging to the development of its whole personality and may well lead to the establishment of neuroses or to regression or retardation which will hamper it for many years or even for life. The remedy here lies (i) in referring the child to a child guidance clinic, if possible, or, if not, talking its problems out with it and trying to give it comfort and reassurance, (ii) in special teaching in the subject to get over the specific difficulty which is holding it back. Educational psychologists are trained for this work, but a wise teacher can do much if she has the time. v
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