Generalizing Fractional Structures: A Critical Precursor to Algebraic Thinking

Abstract

Our research focuses on how students find an unknown whole, when given a known fractional part of the whole, and its equivalent quantity. This chapter will show how Year 5 and Year 6 students, who have yet to meet formal algebraic notation, create algebraic meaning and syntax through their solutions of these fraction problems. Some students rely on diagrammatic representations using different mixes of multiplicative and additive strategies. Other students use fully multiplicative approaches to find the whole. Some students’ solutions show how they use “best available” symbols to move beyond arithmetic calculation and show evidence of algebraic thinking, especially when students are able to t..