Developing algebraic reasoning in primary school using a hanging mobile as a learning supportive tool = El desarrollo del razonamiento algebraico en educación primaria utilizando una balanza como herramienta de apoyo

Abstract

In this study, we investigated the development of algebraic reasoning in 65 fifth-grade students who never had algebra instruction before. In the six-lesson teaching sequence on solving linear equations, a hanging mobile, a physical balance model, played the central role. We expected students’ perceptual-motor experiences with this hanging mobile to be beneficial for the development of their reasoning related to linear equation solving. To investigate how students’ reasoning developed, we analysed videos of classroom interactions, students’ written work during the lessons and students’ responses to lesson-specific assessment tasks. Our results reveal that students showed progress in their level of algebraic reasoning and in their writing down of strategies. While working with the hanging mobile, students applied algebraic strategies such as restructuring, isolation and substitution. They later used these algebraic strategies for solving linear equations in new contexts. This suggests that the experiences students gained in the embodied learning environment provided a basis for algebraic reasoning, which appeared to support them when solving systems of symbolically presented linear equations.