Exploring the challenges of learning quadratic equations and reflecting upon curriculum structure and implementation

Abstract

An important topic of study in secondary mathematics is non-linear functions, including quadratic equations. In this study, findings from 25 Year 11 students indicated that difficulties with critical prerequisite concepts such as algebraic conventions impeded students’ success in understanding and working with quadratics. Analysis of student errors identified misconceptions associated with the null factor law, and the nature of quadratic equations. This paper proposes that these findings are a result of limited timeframes nominated for learning quadratic topics outlined in the enacted curriculum. The implication of this is that the enactment of the Australian Curriculum: Mathematics F-10 did not support the development of conceptual understanding or procedural fluency with key mathematical concepts for these students. Without purposeful attention to prerequisite knowledge, and suitable time allocated to develop understanding and fluency, students’ proficiency with topics such as quadratics is negatively influenced. A mastery approach to the hierarchically organised curriculum is supported by findings of this study.