Epistemic alignment in students’ understanding of rational inequalities: a didactical design research beyond the cognition perspective

Abstract

This study investigates students’ understanding of rational inequalities from a beyond-cognition perspective by examining how epistemic alignment develops as structural complexity increases. Moving beyond traditional cognitive and error-analysis approaches, this research conceptualizes learning as an epistemic process shaped by the interaction between students’ reasoning, task design, and institutional mathematical norms. The study employed a Didactical Design Research (DDR) approach within a qualitative interpretative framework, involving Grade 10 students in a public senior high school in Indonesia. Data were collected through diagnostic tasks, classroom observations, semi-structured interviews, and document analysis, and analyzed using an epistemic lens grounded in concept image theory and institutionalization. The findings reveal a systematic redistribution of students’ responses across three increasingly complex tasks. Integrated understanding decreased significantly, while procedural and fragmented responses increased. This pattern indicates that students’ understanding is not stable but dynamically reorganized in response to structural demands. Three levels of epistemic alignment were identified: integrated (coherent and transferable reasoning), procedural (compensatory reasoning without conceptual grounding), and fragmented (structural misalignment and breakdown of coordination). The study contributes to the literature by reconceptualizing students’ errors as indicators of epistemic misalignment rather than cognitive deficiencies, and by proposing a data-driven model of epistemic alignment. These findings highlight the importance of designing instructional tasks that support conceptual–procedural integration and suggest that meaningful mathematical understanding emerges through the coordination of multiple epistemic dimensions.