TRANSFORMATION OF MATHEMATICAL KNOWLEDGE FOR TEACHING NON-EUCLIDEAN GEOMETRY CONCEPT THROUGH E-LEARNING BASED ON THE THEORY OF DIDACTIC SITUATIONS USING A MULTIPHASE MIXED METHOD

The understanding of non-Euclidean geometry is essential for mathematics teachers as it can broaden the spatial perspective and enhance logical and abstract thinking. However, many teachers face challenges in teaching this concept because it conflicts with the long-established intuitive understanding of Euclidean geometry. An innovative technology-based method is then required to make non-Euclidean geometry learning more effective. Therefore, this research aimed to explore how mathematical knowledge related to non-Euclidean geometry could be transformed and enhanced through e-learning based on the Theory of Didactic Situations (TDS). A multiphase mixed method (MMM) was used to achieve this objective. Approximately 20 mathematics teachers, including 6 males and 14 females, were selected as the participants. Data were collected using content development guidelines, observation sheets, interviews, and tests, as well as analyzed qualitatively and quantitatively. The results showed that e-learning based on TDS effectively improved teachers' understanding of non-Euclidean geometry. In addition, this method enhanced teachers' engagement and encouraged independent exploration during the learning process. There were still challenges in understanding hyperbolic, spherical, and elliptic geometry due to a limited understanding of non-Euclidean axiomatic systems. Conceptual and procedural errors were commonly traced back to the limitations of visualizing non-Euclidean spaces. To address such issues, a more interactive method, combining visual simulation and problem-based learning, was recommended to improve non-Euclidean geometry literacy among teachers and students.