Praxeological analysis of junior secondary students’ epistemological obstacles in algebraic operations

Abstract

This study investigates junior secondary students’ epistemological obstacles to learning algebraic operations through a praxeological framework grounded in the Anthropological Theory of the Didactic (ATD), with Didactical Design Research (DDR) as the conceptual orientation. Diagnostic algebra tasks and semi-structured interviews were administered to six seventh-grade students in Indonesia to examine their algebraic techniques and justifications. Students’ written and verbal responses were analysed by reconstructing tasks (T), techniques (τ), technologies (θ), and theories (Θ). The findings reveal that students generally exhibit procedural fluency in routine tasks, such as simplification and distributive expansion. However, substantial epistemological obstacles arise in tasks that require justification, relational interpretations of equality, variable generalisation, and contextual transfer. These obstacles are characterised by a misalignment between students’ correct techniques and weak or absent justificatory discourse, indicating that procedural correctness does not consistently reflect conceptual understanding. This study contributes to mathematics education by offering a fine-grained praxeological analysis that makes epistemological obstacles often overlooked in error-based analyses visible. By distinguishing students’ actions from their justifications, the study clarifies the structural nature of algebraic difficulties and identifies instructional directions that emphasise relational equality, explicit justification, and stable conceptions of variables to support deeper structural and theoretical understanding of algebra.