We examine whether the array representation can support children's understanding and reasoning in multiplication. To begin, we define what we mean by understanding and reasoning. We adopt a "representational-reasoning" model of understanding, where understanding is seen as connections being made between mental representations of concepts, with…

Although equal sharing problems appear to support the development of fractions as multiplicative structures, very little work has examined how children's informal solutions reflect this possibility. The primary goal of this study was to analyze children's coordination of two quantities (number of people sharing and number of things being shared)…

Children use acquired knowledge as they learn basic multiplication facts. If informal thinking strategies are stressed, the border between "figuring out" and "knowing by heart" gradually disappears. Children will acquire a flexible mental structure of multiplication facts instead of a collection of rules. (MNS)

This study, written in French, presents the hierarchy of strategies used by children in solving multiplication and division problems, as they acquire the linear function concept. It is based on analysis of the different classes of problems, of specific tasks, and of strategies actually used in solutions. (MP)