A design study for investigating and improving competencies in teaching proof

This design study aims to develop and implement a program to equip preservice teachers with the knowledge and skills necessary to prepare them to teach proof. The educational policies that guide mathematics education, teacher preparation, and professional development opportunities were examined to shape the designed program. Eight experts in mathematics and mathematics education were interviewed. Preservice teachers' proof knowledge and beliefs on proof were obtained through developed data collection tools. The program, consisting of two modules on content and pedagogical content knowledge, was implemented for eight weeks for two groups of preservice teachers in two cycles. The implementations in the second cycle followed the first cycle one week later. The learning processes of the participants in the program were evaluated by observations of their performances and through quizzes and exams. At the end of the program, the participants designed proof-based activities for geometry objectives and taught geometry proofs to a student. Semi-structured interviews with ten participants provided feedback on the effectiveness of the program and the learning processes. At the end of the program, it was observed that preservice teachers' knowledge about proof and teaching proof improved. Preservice teachers' beliefs about constructing proof and students' proof skills developed positively.