Students’ mathematical problem-solving based on geometric thinking skills in circle topic: a mixed-method research
DOI:
https://doi.org/10.29408/jel.v12i3.34070Keywords:
circle geometry, geometric thinking, mathematical problem-solving, mixed-methods, Polya’s stages, senior high school, Van Hiele levelsAbstract
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.
References
Abidin, M., & Retnawati, H. (2019). A diagnosis of difficulties in answering questions of circle material on junior high school students. Jurnal Penelitian dan Evaluasi Pendidikan, 23(2), 144–155. https://doi.org/10.21831/pep.v23i2.16454
Ambarita, J., Purnamasari, U., & Siahaya, A. (2025). Deep learning as a pathway to pedagogical transformation in Indonesia. Jurnal Penelitian Kebijakan Pendidikan, 18(1). https://doi.org/10.24832/jpkp.v18i1.1229
Andira, A., Darwis M, M., & Syam, H. (2022). Exploring of students’ ability to solve geometry problems based on Van Hiele’s level of thinking. ETDC: Indonesian Journal of Research and Educational Review, 1(2). https://doi.org/10.51574/ijrer.v1i2.181
Celik, H. S., & Yilmaz, G. K. (2022). Analysis of Van Hiele geometric thinking levels studies in Turkey: A meta-synthesis study. International Journal of Curriculum and Instruction, 14(1). https://ijci.net/index.php/IJCI/article/view/845
Hermiati, K., Suprihatiningsih, S., & Annurwanda, P. (2021). Visual thinking ability of mathematics education students on geometry transformation learning material. AlphaMath: Journal of Mathematics Education, 7(2), 84. https://doi.org/10.30595/alphamath.v7i2.12034
Ishak, M., Oderinde, I., & Ahmad, S. (2025). The role of metacognitive strategies in enhancing learning outcomes and educational efficiency: A systematic review of quantitative, qualitative and mixed-method studies. International Journal of Academic Research in Business and Social Sciences, 15(4). https://doi.org/10.6007/ijarbss/v15-i4/24964
Klau, K. Y., Siahaan, M. M. L., & Simarmata, J. E. (2020). An identification of conceptual and procedural understanding: Study on preservice secondary mathematics teacher. Al-Jabar: Jurnal Pendidikan Matematika, 11(2), 339–350. https://doi.org/10.24042/ajpm.v11i2.7310
Krawitz, J., Schukajlow, S., Yang, X., & Geiger, V. (2025). A systematic review of international perspectives on mathematical modelling: Modelling goals and task characteristics. ZDM – Mathematics Education, 57(2–3), 193–212. https://doi.org/10.1007/s11858-025-01683-2
Lachenbruch, P. A., & Cohen, J. (1989). Statistical power analysis for the behavioral sciences (2nd ed.). Journal of the American Statistical Association, 84(408). https://doi.org/10.2307/2290095
Mahlaba, S. C., & Mudaly, V. (2022). Exploring the relationship between commognition and the Van Hiele theory for studying problem-solving discourse in Euclidean geometry education. Pythagoras, 43(1). https://doi.org/10.4102/pythagoras.v43i1.659
Mifetu, R. K. (2023). Using activity method to address students’ problem-solving difficulties in circle geometry. Contemporary Mathematics and Science Education, 4(1). https://doi.org/10.30935/conmaths/13079
Miles, M. B., Huberman, A. M., & Saldaña, J. (2016). Qualitative data analysis: A methods sourcebook (3rd ed.). In Educacao e Sociedade (Vol. 1, Number 1). Safe Publications. https://www.metodos.work/wp-content/uploads/2024/01/Qualitative-Data-Analysis.pdf
Mirna, Fauzan, A., Yarman, Arnawa, I. M., & Lufri. (2026). Geometric thinking skills of prospective mathematics teachers in the transformation geometry course: Effects and obstacles. Mathematics Education Journal, 20(1), 225–240. https://doi.org/10.22342/mej.v20i1.pp225-240
Mirna, M., Dwina, F., & Khairani, K. (2020). Students’ characteristics, learning outcomes and needs of geometry media tools in junior high school at Padang. Journal of Physics: Conference Series, 1554(1). https://doi.org/10.1088/1742-6596/1554/1/012051
Naufal, M. A., Abdullah, A. H., Zainal, Z., Ihsan, H., Zaki, A., & Alshaye, I. A. (2024). The trend of geometric thinking studies: A systematic review. ITM Web of Conferences, 58, 03010. https://doi.org/10.1051/itmconf/20245803010
OECD. (2023). PISA 2022 results (volume I). OECD Publishing. https://doi.org/10.1787/53f23881-en
Palinkas, L. A., Mendon, S. J., & Hamilton, A. B. (2019). Innovations in mixed methods evaluations. In Annual Review of Public Health (Vol. 40). https://doi.org/10.1146/annurev-publhealth-040218-044215
Pebrianti, A., & Suhendra, S. (2023). Ways of thinking senior high school student to solve geometri Van Hiele problem use reversible thinking ability. Al-Jabar: Jurnal Pendidikan Matematika, 14(2). https://doi.org/10.24042/ajpm.v14i2.18116
Polya, G. (1973). How to solve it: A new aspect of mathematical method. NJ: Princeton University Press. https://www.hlevkin.com/hlevkin/90MathPhysBioBooks/Math/Polya/George_Polya_How_To_Solve_It_.pdf
Pujawan, I. G. N., Suryawan, I. P. P., & Prabawati, D. A. A. (2020). The effect of Van Hiele learning model on students’ spatial abilities. International Journal of Instruction, 13(3). https://doi.org/10.29333/iji.2020.13332a
Saputra, F. A. D. W. P., Yayuk, E., & Tinus, A. (2025). Challenges and success factors in digital classroom implementation. Academia Open, 10(1). https://doi.org/10.21070/acopen.10.2025.11144
Schoenfeld, A. H. (2016). Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics (reprint). Journal of Education, 196(2). https://doi.org/10.1177/002205741619600202
Sfard, A. (2007). When the rules of discourse change, but nobody tells you: Making sense of mathematics learning from a commognitive standpoint. Journal of the Learning Sciences, 16(4). https://doi.org/10.1080/10508400701525253
Sihlangu, S., Maphutha, K., & Mokwana, L. (2025). A commognitive analysis of learners’ mathematical thinking on mathematics vocabulary used during classroom discourse. Journal on Mathematics Education, 16(4). https://doi.org/10.22342/jme.v16i4.pp1389-1406
Siregar, T., Fauzan, A., Yerizon, Y., & Syafriandi, S. (2025). Designing mathematics teaching through deep learning pedagogy: toward meaningful, mindful, and joyful learning. Journal of Deep Learning, 188–202. https://doi.org/10.23917/jdl.v1i2.11969
Sulistiowati, D. L., Herman, T., & Jupri, A. (2019). Student difficulties in solving geometry problem based on Van Hiele thinking level. Journal of Physics: Conference Series, 1157, 042118. https://doi.org/10.1088/1742-6596/1157/4/042118
Tambychik, T., & Meerah, T. S. M. (2010). Students’ difficulties in mathematics problem-solving: What do they say? Procedia - Social and Behavioral Sciences, 8. https://doi.org/10.1016/j.sbspro.2010.12.020
Tiwari, S., Obradovic, D., Rathour, L., Narayan Mishra, L., & Mishra, V. N. (2021). Visualization in mathematics teaching. Journal of Advances in Mathematics, 20, 431–439. https://doi.org/10.24297/jam.v20i.9136
Usiskin, Z. (1982). Van Hiele levels and achievement in secondary school geometry [University of Chicago]. https://eric.ed.gov/?id=ED220288
Van Hiele, P. M. (1986). Structure and insight: A theory of mathematics education. FL: Academic Press. https://archive.org/details/structureinsight0000hiel
Verina, I., & Juandi, D. (2022). Indonesian students’ conceptual understanding in mathematics based on learning style: Systematic literature review (SLR). Symmetry: Pasundan Journal of Research in Mathematics Learning and Education, 7(2), 160–170. https://doi.org/10.23969/symmetry.v7i2.6409
Wijaya, T. T., Hidayat, W., Hermita, N., Alim, J. A., & Talib, C. A. (2024). Exploring contributing factors to PISA 2022 mathematics achievement: Insights from Indonesian teachers. Infinity Journal, 13(1), 139–156. https://doi.org/10.22460/infinity.v13i1.p139-156
Yi, M., Flores, R., & Wang, J. (2020). Examining the influence of Van Hiele theory-based instructional activities on elementary preservice teachers’ geometry knowledge for teaching 2-D shapes. Teaching and Teacher Education, 91, 103038. https://doi.org/10.1016/j.tate.2020.103038
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2026 Mirna Mirna, Hamdani Syaputra, Dewi Murni, Nur 'Aini, Ainil Mardhiah
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Authors who publish with the Jurnal Elemen agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under Creative Commons Attribution-ShareAlike 4.0 International License (CC BY-SA 4.0).
- Authors are able to enter into separate, additional contractual arrangements for the distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.
Jurnal Elemen is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License
