Exploring misconceptions and errors that manifest when grade 10 learners simplify tasks involving algebraic fractions: a case of selected high school in Mopani West District, Limpopo Province

Abstract

Poor mathematics performance is a global issue, including in South Africa, with a reported decline in skills worldwide Berisha et al. (2024). Learners struggle with understanding algebraic fractions, which are essential in mathematics. Inadequate algebraic knowledge can impact learners' confidence and success in Further Education and Training, limiting their career prospects in Science and Engineering. The purpose of this study was therefore to explore the misconceptions and errors that manifest when Grade 10 learners simplify tasks involving algebraic fractions. Thirty-six (36) learners from Mopani West District in Limpopo studying mathematics were purposively sampled to participate in the study. The qualitative case study method used included data collection techniques such as a written test and semi-structured interviews. This dissertation draws upon Newman’s theory to provide a framework for understanding and explaining the phenomenon. Findings reveal that learners manipulate rules they learned in whole numbers and inappropriately apply them in algebraic fractions. This misapplication is evident in errors related to comprehension, procedural skills, transformation, and encoding. Based on the findings, the study recommends that learners should work on problems that foster connections in mathematics. A further recommendation is that learners need to have a deep understanding of the underlying principles governing the operations with fractions. Further research is necessary to explore alternative learner-centered strategies, such as inquiry-based learning and active notetaking, to assess their potential impact on enhancing learner performance in algebraic fractions. Investigating the efficacy of these approaches will provide valuable insights into their effectiveness in fostering deeper understanding and improving learner performance in mathematics education.