Solving subtractions adaptively by means of indirect addition: influence of task, subject, and instructional factors

This article reports on two studies dealing with a relation between addition and subtraction that, to date, has received little research attention, namely the extent to which people are able to solve adaptively direct subtraction problems of the type a-b = __ using indirect addition ("how much do I have to add to b to get a?"). In the first study, we compared the strategic performance on a paper-and-pencil test, comprising four types of subtractions, of secondto fourth-graders with low, aboveaverage, and high mathematical achievement from regular classes with that of children from a school wherein the use of indirect addition got special instructional attention. Although the children from the latter school generated somewhat more indirect addition strategies, the number of indirect additions remained extremely low. To test the possibility that these unexpected results were due to the data-gathering method used, we did a follow-up study wherein the children from the regular classes received the same problems during an individual interview. Although the frequency of indirect addition increased somewhat, it remained low. We consider some theoretical, methodological, and instructional implications of both studies.