Praxology in advanced geometry textbooks for distance education: A hermeneutic review of structure and knowledge representation

Background: Geometry plays a fundamental role in mathematics education by developing logical reasoning and spatial understanding. Despite its importance, geometry remains a difficult subject for university students, particularly in distance learning contexts. While several studies have analyzed geometry textbooks, few have examined their knowledge structures through a praxeological perspective. Aim: This study aims to analyze a university-level Euclidean geometry textbook by identifying how the components of praxeology, namely task (T), technique (τ), technology (θ), and theory (Θ), are organized and interconnected to support meaningful learning. Method: The research applied a hermeneutic phenomenological design. The textbook, used in a master’s geometry course at an Indonesian university, was analyzed through repeated readings and qualitative interpretation. Data were coded and categorized according to the praxeological framework and validated through researcher discussions. Result: The findings show that the textbook demonstrates a coherent praxeological structure with accurate theoretical explanations and effective technological representations. However, the analysis revealed weaknesses such as limited rationale for applying specific techniques, insufficient connection between theoretical concepts and exercises, and few examples of proofs. Conclusion: The study concludes that while the textbook reflects strong praxeological principles, improvements are needed in clarifying technique rationales, linking theory and practice, and structuring technological components. The results provide pedagogical insights for developing university geometry textbooks that enhance conceptual understanding, reflective reasoning, and learning effectiveness in both traditional and distance education settings.