Primary students’ relational thinking and computation strategies with concrete-to-symbolic representations of subtraction as difference

Abstract

Children are highly inclined to attend to the properties of numbers, operations and equality when given helpful tools for doing so. Our aim was to investigate early algebraic thinking with the compensation property of equality for subtraction. We provided 22 (9–11-year-old) students with physical blocks for building vertical towers and conducted individual interviews with them as they completed a sequence of 15 tasks involving subtraction as difference using concrete, numeric, and symbolic representations. Relational thinking was evidenced across a range of subtraction calculation skill levels. Those students who could use both indirect addition and take-away strategies flexibly, depending on the size of the numbers involved, were more likely to evidence attention to generality with symbolic equations. The shift to symbolic equations elicited some students’ productive attempts to connect subtraction as difference and subtraction as take way but seemed to hinder others by provoking a return to take away calculations rather than relational thinking strategies.