Students’ mathematical problem-solving based on geometric thinking skills in circle topic: a mixed-method research

Abstract

Despite the central role of geometry in the senior high school curriculum, students continue to struggle with abstract concepts in circle topics, often relying on rote memorization rather than conceptual understanding. This study employed a mixed-methods sequential explanatory design involving 69 senior high school students selected through purposive sampling. Data were collected using the Van Hiele geometry test to measure geometric thinking skills and a circle problem-solving test based on Polya’s stages. Quantitative data were analyzed using Pearson product–moment correlation, while qualitative data were examined through document analysis of students’ written responses. The results revealed a statistically significant but weak positive correlation between geometric thinking skills and mathematical problem-solving abilities (r = 0.277, p = 0.21), with geometric thinking contributing only 7.7% to the variance (R² = 0.077). Qualitative findings showed notable discrepancies: some students with low geometric thinking achieved high problem-solving scores through procedural approaches, while others with high geometric thinking performed poorly due to difficulties in execution and representation. These findings imply that improving geometric thinking alone is insufficient to enhance problem-solving performance. Mathematics instruction should move beyond rote memorization by integrating visualization activities and explicit heuristic training to better connect conceptual understanding with effective problem-solving strategies.