An analysis of learners’ ways of solving linear equations: The case of grade 10 learners in the Western Cape, South Africa

Abstract

While there are several factors for poor performance (Mamba,2013), there is a tendency amongst learners to struggle to transform linear equations from other types of equations and thereafter follow a suitable solution-seeking path. This study presents a conceptual framework that gives a comprehensive idea of the research that was done in this field as well as formulating an analysis framework from it. The theoretical underpinning is further strengthened by the constructivist learning approach. The objective of this study is to understand the types of errors and misconceptions learners make in their ways of working with Mathematics in an examination context. These errors are observable in the learners written responses in their answer-seeking pursuance when solving linear equations in the grade 10 school-based final examination. The study sought to find errors that will show learners' conceptual and procedural understanding of Mathematics when engaging with linear equations in Algebra. The study seeks to give feedback, which will contribute to the teaching and learning of linear equations and how they may be derived from other types of equations or Mathematics problems. From this, the researcher noted that learners' learning difficulties are usually presented in the form of errors they show (Mamba,2013). Additionally, Mamba notes that some errors in procedures can be caused by faulty algorithms or “buggy algorithms”. Other errors can have a conceptual basis and hence can be termed “misconceptions”.