Treffer: An Examination of Pre-Service Teachers' Van Hiele Levels of Geometric Thinking and Proof Perception Types in Terms of Thinking Processes

The primary goal of advanced mathematics courses is to equip students with proof skills. That is why the competence of pre-service mathematics teachers in proof is considered an assessment of their performance. Despite the emphasis on mathematical proof in undergraduate education, students studying higher mathematics at university often face difficulties with proofs. Therefore, it is essential to examine students' perceptions and thinking processes regarding proof. Accordingly, this study aims to explore the types of proof perceptions and thinking processes of pre-service elementary mathematics teachers based on their Van Hiele geometric thinking levels. The study utilized the case study design, one of the qualitative research designs. The study group comprised 67 fourth-grade pre-service elementary mathematics teachers studying at a medium-sized education faculty in western Turkey. The study group was determined using the convenience sampling technique, one of the non-probability-based sampling methods. Van Hiele's geometric thinking level test, proof selection scale, and scale for determining proof thinking processes were employed as data collection tools. The data were analyzed descriptively. Consequently, it was found that pre-service teachers were predominantly at the fourth geometric thinking level and exhibited the B-proof perception type. Only a few students were observed to reach the level of proof in their thinking processes. According to the results obtained from the study, the geometric thinking levels and proof perception types of pre-service teachers significantly affect their thinking processes.

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