The epistemic path toward early algebraic knowledge: A didactical reconstruction
DOI:
https://doi.org/10.29408/jel.v12i3.34441Keywords:
anthropological theory of the didactic, didactic transposition, didactical design research, early algebra, epistemological obstacles, linear equation in one variable, praxeologyAbstract
Epistemological obstacles in acquiring variables and linear equations in one variable (LEOV) remain a systemic and unresolved issue in Indonesian mathematics education. Prior research has identified their symptoms but not their origins. This study reconstructs the epistemic path towards early algebraic knowledge by integrating the Anthropological Theory of the Didactic (ATD) and Didactical Design Research (DDR). Using a qualitative hermeneutic-phenomenological approach, ATD-based praxeological analysis was applied to the responses of 120 students in Grades VII to X in West Java, Indonesia, and to their teaching modules and lesson plans, followed by the design and implementation of a didactic sequence. Four obstacles were identified: ambiguity in the meaning of variables, difficulties with algebraic operations, procedural dependency without justification, and conceptual collapse when variables appear on both sides of an equation. Each was traced to the systematic absence of the logos block in didactical transposition. After implementation, full relational justification rose from 9.4% to 65.6%. The findings affirm that this epistemic path can be traversed only through designs that deliberately construct praxeological completeness, from practical technique to logical justification, with implications for curriculum and teacher professional development.
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