Children Have the Capacity to Think Multiplicatively, as long as …

Abstract

Multiplicative thinking has been widely accepted as a critically important ‘big idea’ of mathematics and one which underpins much mathematical understanding beyond the primary years of schooling. It is therefore of importance to consider the capacity of children to think multiplicatively but also to consider the capacity of their teachers to teach multiplicative thinking in a conceptual manner. This article focusses specifically on the conceptual links between the multiplicative array, the notion of numbers of equal groups in the multiplicative situation, factors and multiples, the commutative property of multiplication, and the inverse relationship between multiplication and division. A study involving a large sample of primary school students found that whilst most students demonstrated an understanding of some of the aforementioned elements, hardly any of the students were able to connect the ideas or to explain them in terms of each other. As a consequence of the findings, the impact of teacher knowledge on children’s capacity to think multiplicatively was considered.