Pre-service middle school mathematics teachers' perceptions and competencies regarding proof

This study examined the perceptions and competencies of middle school mathematics preservice teachers regarding proof, focusing on their views, proof-construction skills, and approaches to evaluating proofs. Understanding these dimensions provides insights into how future teachers might approach teaching proofs while also revealing any gaps in knowledge or misunderstandings that might influence their teaching practices. A nested multiple case study design was used to capture both individual and conceptual perspectives. The study group consisted of 24 preservice middle school mathematics teachers purposively selected from four grade levels (six preservice teachers per grade level) at a state university in Türkiye during the 2022-2023 academic year. Data were collected through semi-structured interviews guided by a three-stage protocol: (1) questions regarding perceptions of proof, (2) tasks assessing proof-construction skills, and (3) evaluation of sample arguments. Data were analyzed using content analysis and open coding within the framework of Grounded Theory. Findings indicated that preservice teachers unanimously emphasized the importance of proof but indicated that it was not sufficiently included in secondary mathematics education, often attributing this to teachers' limited awareness of proof. Consistent with current research trends, many preservice teachers relied on example-based approaches to constructing proofs. Although they expressed multifaceted understandings of proof, these understandings were not consistently reflected in their proof production or evaluation. Development across grade levels did not demonstrate the expected progression, and preservice teachers' proposed solutions to teaching challenges remained limited and superficial. The study highlights both strengths and weaknesses in preservice teachers' proof-related competencies and highlights the need for targeted support in teacher education programs. Future research is recommended to examine the development of proof perceptions and competencies over time, while also considering contextual influences such as institutional culture, curriculum, and teaching practice experiences. Keywords: Mathematical proof; Proof perceptions; Proof competencies; Proof-construction and evaluation; Pre-service mathematics teachers