Improving algebraic understanding using history of mathematics: the case of structural reasoning in cubic equations

Abstract

Teaching algebra at the senior high school level often privileges procedural fluency at the expense of deeper conceptual understanding, which has left students unable to reason about the underlying structures of algebraic objects. This study investigates the potential of integrating the history of mathematics (HoM) as a pedagogy to foster students' structural reasoning in cubic equations. Grounded in the structural reasoning framework of Harel and Soto, the study employed a quasi-experimental non-equivalent control group design involving 128 senior high school students from two schools in Ghana. The experimental group received history-integrated lessons on cubic equations, drawing on historical developments such as the classification of cubic forms, transformations to depressed cubics, and early solution methods, while the control group received standard curriculum-based lessons. Quantitative data were collected using structural reasoning test and analysed using Quade's non-parametric ANCOVA to control for pre-existing differences. Results revealed statistically significant and practically meaningful difference in structural reasoning between groups. Qualitative data collected using semi-structured interviews further illuminated how historical contexts enhanced students' recognition of algebraic structure, deepened conceptual understanding, and shifted problem-solving approaches from procedures execution to structural analysis. The findings provide empirical evidence that the HoM can function as more than an enrichment tool; it can serve as a powerful instructional resource for promoting advanced algebraic thinking. This study contributes to research in history-and-pedagogy-of-mathematics by demonstrating how historically informed lessons can support structural reasoning in higher-order polynomial contexts and offers a theoretically grounded model for integrating HoM into secondary algebra teaching.