Pedagogical investigation of secondary school mathematics teachers' proofing abilities in the field of geometry

Geometry is present in many areas of daily life and plays a significant role in the concretization and proof of mathematics. Mathematical proofs not only demonstrate the truth of a statement; they also make mathematics meaningful by revealing the reasons for this truth. Therefore, training individuals capable of performing geometric proofs is of paramount importance. This study aimed to examine the pedagogical competencies of high school mathematics teachers in performing and teaching geometric proofs. In this study, conducted using qualitative research methods, interviews were conducted with 20 mathematics teachers, most of whom work in project schools, using scenario-type proofs. The proof form, interviews, and observations served as data sources. For the purpose of the study, the data were examined in depth using content analysis. The results revealed that teachers generally viewed proofs solely as a means of proving the truth of theorems and employed rote-based methods. In addition, it has been determined that teachers have difficulties in the process of transferring proofs to students. Therefore, the dominance of a teacher-centered approach makes proofs less engaging for students. This situation leads to the neglect of the functions of proof in mathematics education, such as meaning-making, reasoning, and justification. Therefore, it is recommended that studies be conducted to contribute to the training of teachers who understand proof not merely as a result but as a process of thinking and constructing, and that proof be given greater prominence in high education curricula.