Long Division versus Short Division

Abstract

To what extent do pupils use short division in examples with single digit divisors? What are some of the factors which influence the selec tion of the method used? W^hich method is selected by brighter pupils? Is long division used with greater accuracy than short division? The customary order of procedure in teaching division of numbers to elementary school pupils is to teach a child first to know a specific number of simple division combinations; secondly, to work examples with single-digit divisors and with varying numbers of digits in the dividend by a short division method; and, thirdly, to divide numbers containing divisors with two or more digits by a long division process. In short division the pupil mentally carries out the steps in the process, writing only the answer; in long division the child places each step of his calculations on paper. Several writers have contended, and some evidence has been produced to prove/ that long division should precede short division and that the latter should be taught as a short-cut to the former. The evidence and arguments center largely in the problem of the order of introducing the two processes. Few individuals seem to have considered the question whether we should continue our present insistence on pupils' using the short division method with single-digit divisors. If we knew to what extent pupils throughout the different grades regularly use the short method under the condition prescribed and also the comparative accu racy with which the short and long processes are employed, we might even see reasons for contending that our present stress on short division is not worthwhile. By thus abandoning our insistence on short division, we could eliminate a field of considerable worry for the elementary school teacher. With the purpose in mind, therefore, of determining the extent to which and also the accuracy with which pupils throughout the grades use the short division method with single-digit divisors, the present study was undertaken.