Understanding and strategies for comparing fractions among pre-service teachers: Between procedural rigidity and conceptual flexibility

This study explores the cognitive structures of pre-service primary teachers regarding fraction comparison, using Vinner’s concept-image framework to analyze how these pre-service teachers mobilize their knowledge to compare fractions. The mixed-methods approach, combining both quantitative and qualitative analyses (including a questionnaire), highlights significant cognitive challenges related to fraction comparison. The study, conducted with 160 participants, reveals a marked reliance on rigid procedures, with the systematic application of a single comparison procedure, regardless of contextual variations or task-specific demands. The observed errors appear to stem from limited procedural flexibility and underdeveloped pre-service teachers’ concept-images on fractions. Furthermore, a significant number of participants do not recognize fraction comparison as a valid mathematical model in problem-solving contexts, which limits their ability to teach this concept effectively. These findings underscore the need to reform teacher education by integrating targeted interventions aimed at increasing procedural diversity and enriching the conceptual understanding of fractions. Such initiatives would enable teachers to perceive fractions not only as static mathematical objects, but as dynamic, interconnected, and evolving entities. This study thus contributes to the enhancement of teacher preparation, particularly in managing foundational arithmetic concepts, to promote a more flexible and conceptually rich approach to teaching fractions in primary education.