Didactic Transposition Analysis on Circle Material in High School

Circle material is a fundamental topic in geometry that often causes misconceptions in high school students due to the difference between scientific knowledge and knowledge taught in school. This study aims to analyze the external didactic transposition of circle material by comparing the conceptual structure of scientific knowledge (scholarly knowledge) to the knowledge to be taught in high school mathematics textbooks. This study uses a qualitative descriptive approach with a document analysis method, comparing university-level geometry textbooks as a representation of scholarly knowledge with high school mathematics textbooks as a representation of knowledge to be taught. The results of the study show that external didactic transposition occurs in almost all circle concepts, characterized by simplification of language, adjustment of abstraction levels, reduction of concept classification, and addition of pedagogical and visualization contexts. The simplification and addition of pedagogical context can affect students’ conceptual understanding, especially in the relationships among elements of circles, such as arcs, central angles, circumferential angles, and tangents. These findings open up further research opportunities into internal didactic transposition and other mathematics topics and can serve as a reference for teachers and book developers to improve the quality of coherent, conceptual mathematics learning.