The development of the concept of multiplication - Park, J; Nunes, T (2001)
Two alternative hypotheses have been offered to explain the origin of the concept of multiplication in children's reasoning. The first suggests that the concept of multiplication is grounded on the understanding of repeated addition, and the second proposes that repeated addition is only a calculation procedure and that the understanding of multiplication has its roots in the schema of correspondence. This study assessed the two hypotheses through an intervention method. It was hypothesised that an intervention based on the origin of the concept of multiplication would be more effective than the one that did not offer the learners a conceptual basis for learning. Pupils (mean age 6 years 7 months) from two primary schools in England, who had not been taught about multiplication in school, were pretested in additive and multiplicative reasoning problems. They were then randomly assigned to one of two treatment conditions: teaching of multiplication through repeated addition or teaching through correspondence. Both groups made significant progress from pre- to posttest. The group taught by correspondence made significantly more progress in multiplicative reasoning than in additive reasoning problems. The group taught by repeated addition made similar progress in both types of problems. At posttest, the correspondence group performed significantly better than the repeated addition group in multiplicative reasoning problems even after controlling for level of performance at pretest. Thus, this study supports the hypothesis that the origin of the concept of multiplication is in the schema of correspondence rather than in the idea of repeated addition. © 2001 Elsevier Science Inc.