A Study on Mental Models and Geometric Strategies of Prospective Mathematics Teachers: Dynamics of Triangle and Quadrilateral Representations

Abstract

This study aims to analyze the mental models and geometric strategies of prospective mathematics teachers in representing plane figures, particularly triangles and quadrilaterals. A qualitative descriptive method was employed involving 27 undergraduate students from Universitas Negeri Medan in the 2023/2024 academic year. Data were collected through a structured drawing task covering various types of triangles and quadrilaterals and were analyzed using data reduction, data display, and conclusion drawing techniques. The findings reveal that students predominantly rely on prototypical representations in drawing geometric figures, such as right, isosceles, and equilateral triangles, as well as squares and rectangles. Their partitioning strategies are also dominated by simple approaches, particularly vertical and horizontal divisions, which are considered cognitively efficient and easier to execute. These results indicate that students’ mental models are strongly influenced by prior learning experiences, visual prototypes, and cognitive load during problem-solving processes. Overall, students’ mental representations have not yet fully developed toward flexible and formal conceptual understanding in geometry.