Arithmetic Problems Formulation and Working Memory Load

Abstract

First, third, and fifth graders (French children in American-numbered grades) were asked to solve arithmetic problems in which an initial state was modified by two successive transformations. Three independent variables were manipulated systematically. First, the unknown state was either the final state (Sl) or the initial state (S2). Second, either the known state (01) or the transformations (02) appeared in the first place in the problem wording. Third, the question was either located at the end (Ql) or at the beginning (42) of the problem text. As anticipated, these modifications strongly affected the performances at every age: S1 appears clearly easier than S2; 0 1 leads to a better performance than 02; and Q1 is better than 42. The third graders participated in a second experiment in which they had to solve the same problems but with easier numbers. As in the first experiment, we found strong effects related to the problem types (S1 vs. S2) and to the place of the transformations in the problem. However, modifying the place of the question did not show any reliable effect. The theoretical implications of these results are discussed in terms of span of working memory.