Advancing future mathematics teachers' geometric thinking through a Van Hiele-based elementary geometry course

Research in mathematics education has increasingly emphasized the importance of developing deep conceptual understanding and higher-order thinking skills in geometry learning. However, traditional approaches to teaching elementary geometry in teacher education programs often remain procedural and insufficiently foster progression through the Van Hiele levels of geometric thinking. Addressing this gap, the present study introduces and examines the method of local axiomatization as a novel instructional approach for preparing future mathematics teachers. The purpose of the study is to identify, characterize, and test practical strategies for teaching an "Elementary Geometry" course through this method, with the goal of facilitating teacher candidates’ advancement across the Van Hiele model of geometric thinking. The research highlights effective educational practices, including maintaining student motivation, inquiry-based learning, collaborative interaction, integration of technology, strategic problem-solving, and reflective error analysis. Based on these principles, a university-level course in elementary geometry was designed and implemented as research training for 56 prospective mathematics teachers. Data were collected through the Van Hiele Geometry Test (VHGT), administered before and after the intervention, and through reflective essays written by participants. Statistical analysis using the Pearson criterion demonstrated a significant increase in students’ levels of geometric thinking, while qualitative reflections indicated enrichment of geometric knowledge and more independent, yet guided, learning. The findings suggest that the method of local axiomatization, despite implementation challenges, can serve as an effective and innovative pedagogical framework in mathematics teacher education, contributing to the development of both conceptual understanding and reflective practice in geometry learning.