A constructivist analysis of Grade 8 learners’ errors and misconceptions in simplifying mathematical algebraic expressions

Abstract

Algebra is an important branch of mathematics which applies to many fields related to mathematics. However, many studies show algebra as posing problems even to the most gifted students. This phenomenon, therefore, necessitates more studies to be conducted in this area. As such, the study explored the types of errors that Grade 8 learners committed in simplifying algebraic expressions and the misconceptions that might have given rise to such errors. Ninety-five Grade 8 learners were selected as the subjects of the study at one high school in Lesotho. Within the framework of the Qualitative case study design, the study used tasks and interviews for data collection. The thematic approach to data analysis within the framework of the constructivist theory was adopted. The study identified most errors committed by the learners as persistent. Overgeneralizing the rules of prior knowledge to new knowledge, particularly in different contexts, was the most frequent cause of the errors. In addition to this was the misunderstanding and misinterpretation of correct meanings in the given context.  Some of the identified errors overlapped with those in the reviewed literature while others did not.