Developing Algebraic Thinking: using problem-solving to build from number and geometry in the primary school to the ideas that underpin algebra in high school and beyond

AbstractAlgebraic thinking addresses general mathematical relationships, expressing them in increasingly sophisticated ways as activities move from seeing patterns in number, geometry and measurement to determining solutions to more and more complex problems. This paper reports on an ongoing research project investigating how working on, representing and solving structurally related problems in a variety of ways prepares students to think algebraically as they articulate and generalise their solution processes. Examples of problems and their solutions by students in a Year 7 primary classroom will be presented and analysed to highlight how a deeper investigation of mathematical problems can instigate student discourse that encourages general ways of thinking underpinning algebraic reasoning rather than simply using particular strategies or procedures for classes of problems. The results obtained so far suggest that students are able to build general ways of thinking that will lead them to an algebraic perspective of mathematics beyond the mechanics and procedures often associated with algebra. Not only will this build confidence in ways of operating that are their own, such a development also parallels the historical development of algebra itself