An analysis of task design for pre-service teachers on the circumcenter of a triangle: Focusing on the process of justification

This study aims to examine how pre-service teachers design tasks that justify the circumcenter of a triangle based on given original tasks. Tasks designed by 28 secondary pre-service teachers were analyzed according to justification types derived from prior research. The findings revealed that pre-service teachers, while distinguishing between the justification of the existence and uniqueness of the circumcenter or modifying the order of defining the circumcenter, focused on ensuring that students could recognize and understand the argument for justification. This study suggests specific focal points that need to be emphasized in pre-service teacher education for both empirical and deductive justification of the circumcenter of a triangle.