ARITHMETIC In arithmetic the guiding idea of the reform was contact with reality. Except for mensuration which had to some extent pre served contact with reality, arithmetic before the reform was chiefly mechanical computation, the pupil being told which process he was to use. The reform substituted problems from every day life and left the pupil to decide on the process. The change is well illustrated by one of the early reform questions. The question being "Mr. Gladstone was born in 1809 and died in 1898; how many years did he live?", one candidate replied "I do not know whether this is multiplication or division," while another used multiplication and gave the answer as This laudable striving after making arithmetic entirely con crete and practical has led however in some instances to a form of pseudo-realism which though clothed ostensibly in a concrete form, postulates (say) the mowing of an impossible number of acres by a certain number of men in a fixed time, to cite only one instance, taken from a paper set in a recent public examination. Again the attempt to base the early teaching of arithmetic pre dominantly on logic is being challenged to-day, mainly in America, by psychologists. It is asserted that many children, especially young children, like to perform numerical manipulations without the conscious need to understand their rationale and that rote and even the recitation of the multiplication table are a pleasure to such minds, the reward in such cases coming from the sense of rhythm and of enhanced skill and dexterity, together with the im mediate satisfaction of getting the sum right. There is probably
a good deal to be said for such types of mind that are content with the "how" and ignore the "why," practical types of mind that instinctively prefer doing to thinking how a thing is done ; their motto seems to be Primo agere deinde philosophari (first act, then analyse), if we may slightly alter Bergson's favourite phrase. Possibly between these two extreme views, one that builds on conscious logic, the other on the formation of accurate automatisms (sub-conscious logic), the real deciding factor is the "mental age" of the child. With very young children the automatic process should be at its maximum, as in the older ones the rational should be predominant, though neither should be absent at any period. Both elements, mastery of technique and mind-training are indispensable ; the problem lies in the particular weight and importance to be attached to each at different stages of the course.