Exploring quantitative relationship through area conservation activity

Abstract

Algebra as a study of quantitative relationship is one of four conceptions of school algebra which serves as a foundation for the concept of function. However, there is still a lack of attention to this particular relationship, especially in early algebraic reasoning. This study aims to investigate how the aspect of quantitative relationship in early algebra can be explored through area conservation activities. Understanding area conservation is said to be fundamental in developing the concept of area measurement. In this study, a ten-year old pupil was observed during her involvement while comparing area of two polygons that can be decomposed into equivalent triangles. Data for this study include the pupil’s written artefacts, and video recordings of the activities and interviews. Findings from this study show that the area conservation activity has the potential to build the notion of quantitative relationships in early algebra. The quantitative relationship between the unit of measurement and the result of measurement of a shape can also be explored, that is, the smaller the unit of measurement, the larger the result of measurement. Hence, this study can provide a groundwork for further studies in the relation between quantitative relationship in algebra and area conservation in geometry at the elementary school level.