The Importance of Expliciting the One-to-many Correspondence in Solving Problems of Multiplicative Structure

Abstract

The way in which children solve multiplicative problems is influenced by several aspects, such as the numerical characteristics of the tasks and the representation support that is available during the solution procedure. The present study investigates the role played by another aspect of multiplicative reasoning: the one-to-many correspondence. This correspondence may be implicitly or explicitly mentioned in the wording of the problem. This study examined whether the degree of explicitness of the one-to-many relationship is an important factor in the solution of multiplicative problems, and whether the more explicit this correspondence is, the better the child’s performance. With that in mind, 3rd and 5th grades elementary school students were asked to solve multiplication and division problems. In the wording of the problems, the one-to-many correspondence was presented in different degrees of explicitness. It was found that performance was better in problems in which the one-to-many correspondence was explicitly mentioned than in those in which this relationship was implicit, a factobserved in both school grades. Results show the facilitating role played by the explicitness of the one-to-many correspondence in the solution of problems of multiplicative structure. Theoretical and educational implications are discussed.

Keywords:
Problem solving; Multiplicative structure; Correspondence one-to-many; Children