Representing and understanding multiplication.

In this paper, we examine the importance of representations, in particular with respect to the understanding of multiplication by primary school pupils. We first of all look at the theoretical background to representations in mathematics. In particular, we look at the use of the array representation for reasoning with and understanding multiplication. We then describe some preliminary work that we have carried out, examining Year 4 and Year 6 pupils' use of the array representation for multiplication calculations. Using a novel methodological approach of recording children's workings on a computer, we observed that the array representation can be a powerful tool for supporting work in multiplication. At the same time, we also observed pupils who were unable to access the mathematical meanings of the representation. Further work is needed to understand such difficulties when developing the use of the array as a tool for mathematical understanding