Constraints to a justification of commutativity of multiplication

Abstract

In this paper we investigate a pre-service teacher’s whole-class discussion at Grade 6, where she attempts to justify the general claim that multiplication is commutative in ℕ. Our analysis points at two conditions that constrain the discussion in class: The first is that the diagram used to represent a multiplicative situation—and the way the diagram is used—is inadequate because it does not illustrate the meaning of multiplication. The second is that the diagram enables the students to respond “adequately”, even if they may not have understood why multiplication is commutative. The latter is a constraint because it deprives the pre-service teacher of the opportunity to get feedback that might have let her understand that she would need to revise her intervention.