Examining Learners’ Understandings of Algebraic Variables: Evidence from Modelling in the Classroom

Abstract

In response to difficulties in learning algebra, researchers claim that the modelling approach is a powerful tool to build a foundation for learning mathematics at the middle school level. This article explores the conceptual difficulties and understandings of variables that Grade 8 learners have when they work in a modelling activity after these concepts have been learned from Grades 5–8. To this end, 25 Grade 8 learners in one school (in one classroom) in North Wollo district were conveniently sampled to participate in this qualitative methods study. In this study, data were collected using audio recordings of communicative events and analysed using learners’ conversational statements during their discussion to solve the modelling activity. The findings in this study indicate that participating learners’ understandings of algebraic concepts (variables, constructs and sub-constructs) after these concepts were taught using the traditional method of teaching from Grades 5–8 did not equip them with the necessary skills to understand variables as unknown quantities involved in real-life problem situations. This study provides an insight for teachers to incorporate modelling in their classrooms by exploring the strategies in the textbook to explain concepts in mathematics through the lens of Action, Process, Object, Schema theory. It could also serve as a catalyst for further investigation on the effectiveness of the teaching treatment implemented in this study in other domains of mathematics with the aim of helping learners develop a sound conceptual understanding.