Operationalizing didactical situation-based online learning to support eighth-grade students’ mathematical reasoning and understanding in geometry: Participatory design research

Mathematics education continues to encounter enduring challenges in fostering students’ mathematical reasoning and conceptual understanding, particularly in geometry, where learning frequently remains procedural and empirically driven. This study reports a participatory design research (PDR) project that operationalized a Didactical Situation–Based Online Learning (DS-OL) approach to enhance eighth-grade students’ mathematical reasoning (MR) and understanding (MU) in the topic of lines and angles. The research involved 120 students and 16 mathematics teachers, implemented through four iterative PDR phases: co-exploration, co-design, iterative implementation, and collaborative analysis. Diagnostic findings from the co-exploration phase indicated a predominance of instrumental understanding and empirically or authority-based reasoning, informing critical design decisions. During the co-design phase, principles from the Theory of Didactical Situations were transformed into online learning components structured around action, formulation, validation, and institutionalization, and were iteratively refined across two implementation cycles. Across these cycles, significant improvements were observed in students’ MR and MU, including marked pre–post gains (mean scores increasing from 65.00 to 83.79; Cohen’s d = 2.60) and shifts toward more deductive reasoning and relational understanding. Framed within a design-based epistemology, these findings are interpreted as design-supported enhancements rather than evidence of causal effectiveness. The study contributes to design-based knowledge by articulating empirically grounded principles for operationalizing didactical situations within online geometry learning environments.