Understanding students’ transition in mathematical thinking in algebra: The three worlds of mathematics

Abstract

This study uses three worlds of mathematics framework proposed by [3], which explains the progression of human mathematical thinking from embodied, symbolic and formal worlds of mathematics. To understand the mathematical thinking of the first year undergraduate students learning algebra, this study focuses on embodied and symbolic thinking aspects of the three worlds framework, and explains transitional mathematical thinking. Written tasks and online surveys are used to understand the development of mathematical thinking in algebra. Transitions in student mathematical thinking from the embodied to the symbolic world and symbolic to the embodied are explained analyzing the written tasks. Results suggest that students’ mathematical thinking is at more ease with transition from embodied to symbolic compared to the transition from symbolic to the embodied.