Exploring high school students’ 3D geometry problem-solving: Role of cognitive style and mathematical ability

Purpose: This research investigates how high school students approach three-dimensional geometry problems by considering differences in cognitive styles (impulsive and reflective) and levels of mathematical ability. The aim is to understand the variations in problem-solving strategies based on Polya’s stages, which include understanding the problem, planning, executing, and reviewing the solution. Method: A descriptive qualitative method was used with a comparative case study design. Four students were selected through purposive sampling, each representing a unique combination of cognitive style and mathematical ability. Data collection involved problem-solving tests and semi-structured interviews. The analysis focused on tracing the students’ reasoning and decision-making processes throughout each stage of problem solving. Findings: The results show that students with a reflective cognitive style tend to be more thorough when planning and reviewing their work. Impulsive students, on the other hand, often rush through the process, resulting in errors, although those with high mathematical ability can still demonstrate effective strategies and occasionally correct their mistakes. Students with stronger mathematical ability generally show better visualization, abstraction, and accuracy in applying geometric concepts. Significance: These findings suggest the need for instructional strategies that are sensitive to students’ cognitive profiles. Teaching approaches that emphasize structured reflection and scaffolding may enhance geometry learning outcomes, especially for students who tend to act impulsively.