Addressing misconceptions in ratio and proportion: A constructivist approach for enhancing grade 9 learners' understanding

Backgorund: Proportionality, deeply rooted in the fundamental principles of ratio and proportion, is a core component of mathematics education that supports cognitive processes such as problem-solving and reasoning. Despite its inclusion in global curricula, empirical research suggests that students often face significant challenges in applying ratio and proportion in problem-solving scenarios. These challenges are largely attributed to the use of flawed cognitive strategies, resulting in persistent misconceptions.Aim: This study examines the misconceptions regarding ratio and proportion among Grade 9 learners in the Lebowakgomo District, Limpopo Province, and aims to explore how these learners conceptualize and solve related mathematical problems through the lens of constructivist learning theory.Method: Employing a qualitative case study approach, this research utilized tests and semi-structured interviews to gather data from 30 Grade 9 learners. A representative subset was selected for qualitative analysis, with five learners chosen for follow-up interviews to ensure diverse perspectives.Results: The study revealed that learners struggled primarily with problems requiring proportional reasoning, resorting to incorrect strategies such as intuitive thinking, additive methods, incomplete problem-solving approaches, and erroneous use of cross-multiplication.Conclusion: These misconceptions are primarily due to a lack of foundational mathematical skills and conceptual understanding, which impede learners' ability to engage in proportional reasoning. Based on these findings, the study advocates for enhancing teachers' pedagogical content knowledge in ratio and proportion to improve the instructional support provided to learners.