Internal Transposition on Constructing Quadratic Functions Based on Praxeological Theory
The sub-topic of constructing quadratic functions requires students to integrate various concepts. However, students still encounter various learning obstacles, one of which relates to the structure of knowledge in textbooks and teachers’ lesson plans. This study aims to analyze the praxeological structure in textbooks and teachers’ lesson plans, identify forms of internal transposition, and examine the didactic implications for potential obstacles to student learning in the sub-topic of constructing quadratic functions. This research employs a qualitative approach with a case study design. The participants in this research consist of one mathematics teacher and tenth-grade students at a private school in Bandung, selected by convenience sampling. Data were collected through document analysis, classroom observation, and semi-structured interviews. Analysis was conducted using praxeological-didactical analysis, as well as triangulation techniques, member checking, and audit trails to ensure the trustworthiness of the data. The results indicate that the praxeological structure in the textbooks is dominated by evaluative tasks (83.33%) with techniques that are not conceptually integrated, alongside a lack of explicit technology and theory. In the teacher's lesson plans, task types are reorganized. However, flexibility occurs in technical aspects without conceptual reinforcement. The internal transposition observed is adaptively limited, merely modifying tasks and techniques without developing conceptual aspects. The didactic implications of these conditions are reflected in the potential learning obstacles identified in the observed instructional context. The study concludes that modifying textbook tasks into open-ended, multi-representational activities is crucial for overcoming students’ learning obstacles, with practical implications: the lesson plan must be reconstructed based on predictions of student responses to enhance teachers’ adaptive instructional readiness.
Keywords: mathematics textbooks, quadratic functions, praxeology, teachers’ lesson plans, potential learning obstacles.
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