Designing a hypothetical learning trajectory for mathematical reasoning through situation-based learning and semantic mediation

Abstract

Mathematical reasoning constitutes a fundamental component of mathematics learning; nonetheless, many students encounter persistent challenges in developing this competence beyond procedural problem solving. This challenge reflects a persistent discrepancy between the expectations of higher-order thinking emphasized in curricula and the instructional practices typically enacted in classrooms. Addressing this issue requires learning designs that guide students not only in executing procedures but also in constructing, interpreting, and justifying the mathematical meaning underlying given situations. One promising direction involves integrating Situation-Based Learning (SBL) with semantic analysis within the framework of a Hypothetical Learning Trajectory (HLT). Despite such potential, systematic incorporation of semantic elements into SBL-oriented learning trajectories remains underexplored in prior research. Accordingly, this study sought to design an HLT that fosters students’ mathematical reasoning by embedding semantic scaffolds within situation-based learning tasks. The research employed the preliminary stage of design research, concentrating on the theoretical formulation and development of the learning trajectory, subsequently followed by a small-scale pilot implementation. The design process encompassed theoretical analysis, task development, expert validation, and a pilot involving 20 junior secondary school students. Students’ written responses were analyzed through a mathematical reasoning framework encompassing interpretative, symbolic, and justificatory reasoning. Expert evaluation produced an average score of 3.84 on a four-point scale, indicating both conceptual soundness and practical feasibility. Findings from the pilot implementation suggest that semantic scaffolding effectively supports students in progressing from contextual interpretation toward symbolic representation and justification of mathematical solutions. Finally, the findings provide preliminary evidence that a semantically oriented learning trajectory can enhance the development of students’ mathematical reasoning.