Connecting the threads: the role of multiplicative thinking in algebraic, geometrical, and statistical reasoning

Making connections within and between different aspects of mathematics is recognised as fundamental to learning mathematics with understanding. However, exactly what these connections are and how they serve the goal of learning mathematics is rarely made explicit in curriculum documents with the result that mathematics tends to be presented as a set of discrete, disconnected topics. Interest in establishing a more coherent approach to the teaching and learning of school mathematics has led to a focus on big ideas. That is, networks of related concepts, skills and ways of thinking that facilitate learning mathematics with understanding. Research on learning progressions has helped identify what these big ideas are and how they serve to build connections within and between different aspects of mathematics. This paper draws on research that provides an evidenced-based learning progression for multiplicative reasoning to illustrate the connective role of multiplicative thinking in the development of algebraic, geometrical, and statistical reasoning.