Developing Conceptual Understanding of Algebraic Fractions in Grade 9 Learners

Many Grade 9 learners in South Africa encounter considerable challenges with algebraic fractions, frequently relying on memorized procedures instead of developing the profound conceptual understanding essential for success in higher-level mathematics. This descriptive qualitative case study explores how learners develop meaning from algebraic fractions and evaluates the efficacy of targeted instructional strategies in redirecting learners’ attention from procedural fluency to conceptual comprehension. Anchored in a constructivist framework that incorporates theories of conceptual change and cognitive conflict, the study investigates how error analysis, reflective discussion, and guided exploration facilitate the reorganization of learners’ prior knowledge. The study was conducted in a South African high school with thirty-six Grade 9 learners and one mathematics teacher as participants. Data were collected through field notes, observations, learner tasks, and semi-structured interviews. The intervention had an emphasis on connecting symbolic manipulation with visual representations and verbal reasoning to enhance learners’ understanding of algebraic fractions within real-world problem contexts. The findings indicate that learners initially depended on superficial strategies like cross-multiplication; however, organized opportunities for contextualized problem-solving, error analysis, and collaborative discourse allowed most of them to develop more substantial conceptualizations of equivalence, the role of the denominator, and factorization. This research provides evidence of integrated instructional strategies based on conceptual change, constructivism, and metacognition. The study offers evidence-based recommendations for developing instruction that connects foundational fraction knowledge with algebraic reasoning, thereby supporting diverse learners’ critical thinking, engagement, and mathematical agency.