Polya–Van Hiele Integration Hierarchical Model in Students' Geometric Thinking Processes
DOI:
https://doi.org/10.51454/jet.v7i3.944Keywords:
Geometric thinking process, Polya problem-solving, Van Hiele theory, Hierarchical model, Plane geometryAbstract
This research aims to develop the Polya–Van Hiele Integrated Hierarchical Model to describe students' geometric thinking processes in solving geometry problems. This study uses a qualitative approach with a case study design. The research subjects were selected based on the level of geometric thinking ability in the students. Data was collected through geometric thinking tests and in-depth interviews, then analyzed using qualitative descriptive methods. The results of the study show that students' geometric thinking processes develop progressively and are in harmony with the stages of Polya problem-solving, namely understanding problems, making plans, executing plans, and looking back. At the planning stage, students demonstrate skills at the level of visualization and analysis. Furthermore, at the stage of planning implementation, geometric thinking develops towards the level of informal deduction, formal deduction, and precision. At the level of rigor, students are able to provide valid mathematical justifications, compare, and generalize geometric concepts. This research resulted in the Polya-Van Hiele Integrated Hierarchical Model, which shows that the development of geometric thinking is embedded in the process of solving mathematical problems.
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Copyright (c) 2026 Venissa Dian Mawarsari, Martyana Prihaswati, Eko Andy Purnomo, YL Sukestiyarno, Scolastika Mariani, Iwan Junaedi
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