Designing a realistic mathematics learning trajectory to promote fraction concept construction in elementary school

Source abstract

Purpose: This study evaluates the effectiveness of a Hypothetical Learning Trajectory grounded in Realistic Mathematics Education to resolve primary students' persistent conceptual bottlenecks in fraction equivalency, operations, and word problem solving. Method: Utilizing a two-cycle classroom action research model, the study investigated a primary school student cohort. Data were collected using validated diagnostic assessments, classroom observation protocols, student work artifact analysis, and semi-structured interview transcripts. Findings: Quantitative assessments demonstrated progressive gains across evaluation phases, with average test scores and classical learning mastery showing substantial improvement and successfully exceeding the target success threshold. Qualitative artifact and interview analyses confirmed a pronounced cognitive shift, as students transitioned from misapplying mechanical algorithms to demonstrating model-based partitioning, visual representation, and verbal justifications. Practical implications: The validated learning trajectory provides elementary educators with an empirically supported pedagogical framework, featuring actionable task sequences, strategic linguistic scaffolding tools, and problem-posing activities that bridge informal situational reasoning with formal symbolic mathematics. Originality/value: This research advances local instruction theory by demonstrating how student-led problem posing and strategic scaffolding within a realistic mathematics environment systematically facilitate both horizontal and vertical mathematization.