Effects of van Hiele-Based Instruction on Pre-Service Teachers’ Geometric Thinking Across the School–University Transition

This study investigates how pre-service primary education teachers (PSTs) develop geometric thinking when exposed to an instructional approach based on van Hiele’s theory. Ninety undergraduate students were divided into experimental and control groups and were assessed before and after a semester of Euclidean geometry instruction. Using mixed-methods analysis, the study examined participants’ initial levels of geometric thinking, their progression over time, and the comparative impact of traditional and van Hiele-based instruction. Both groups began with similarly limited geometric understanding and showed improvement, yet only the experimental group achieved statistically significant gains. These findings demonstrate the effectiveness of van Hiele-based instruction in strengthening conceptual understanding and supporting PSTs’ transition from procedural school mathematics to the deductive structure of university geometry. By structuring learning through van Hiele’s levels of thinking and five phases of learning, the instructional approach provided accessible entry points, systematic scaffolding, and opportunities for building coherent conceptual networks. The results suggest that integrating van Hiele-informed approaches into tertiary mathematics courses can support the development of robust geometric thinking and better prepare PSTs for future teaching of geometry.