Problem-Solving Errors in Highest Common Factors and Lowest Common Multiples: An Analysis of Pre-Service Teachers’ Misconceptions

Source abstract

<p>This study examined the conceptual understanding of South African pre-service teachers regarding the Highest Common Factor (HCF) and Lowest Common Multiple (LCM), with a focus on errors and misconceptions that affect problem-solving. There is a paucity of research that specifically analyses how pre-service teachers’ misconceptions about HCF and LCM contribute to problem-solving errors in foundational mathematics. This study is grounded in two complementary theoretical perspectives: the Mathematical Knowledge for Teaching (MKT) framework and the Conceptual–Procedural Knowledge Theory. A sequential explanatory mixed-methods design was employed. Quantitative data were analysed using one-sample t-tests and Pearson’s correlation, and qualitative data were supported by error analysis. The three hypotheses were tested. Results showed a significant difference in understanding (t = 25.685, p < 0.001), leading to the rejection of the first hypothesis. A moderate negative correlation (r = -0.48, p < 0.001) between misconceptions and accuracy led to the rejection of the second hypothesis. The third hypothesis was not rejected, as no strong correlation was found between strategy use and conceptual errors (r = -0.12, p = 0.425). Findings highlight gaps in conceptual understanding and emphasise the need for conceptually focused instruction, diagnostic assessments, and real-life applications in teacher education programmes.</p>