Learning to measure the area of circles

Abstract

ABSTRACT The study of the area of circles is an important component of mathematics education for students of all ages; however, evidence suggests that many middle school students struggle to interpret and apply the area formula of a circle. In this article, I report the findings of a classroom design study conducted to investigate the collective establishment and justification for the area formula of a circle. An instructional sequence comprising paper-based decomposition and recomposition measurement tasks situated on a grid was implemented in a Year 8 classroom (n = 18) and the collective mathematical practices that emerged from an analysis of the argumentation of students during whole-class discussion were documented. The findings extend the existing literature by illustrating how decomposition/recomposition tasks can be leveraged in a classroom context by grounding students’ reasoning in measurement strategies and opportunities to examine alternative strategies and justifications through whole-class discussions.