EXPLORING PROBLEM-SOLVING SKILLS PROFILES OF PRE-SERVICE MATHEMATICS TEACHERS THROUGH POLYA’S FOUR STAGES
Riau, Indonesia
DOI:
https://doi.org/10.36085/mathumbedu.v13i1.9075Abstract
Mathematical problem-solving skills are an essential competence for pre-service mathematics teachers, as they are expected to cultivate these skills in their future students. This study aims to describe the problem-solving profiles of pre-service mathematics teachers using Polya’s four stages as an analytical lens. A qualitative case study approach was employed to examine the cognitive processes demonstrated by pre-service teachers while solving mathematical problems. The findings reveal diverse problem-solving profiles, including conceptual understanding shaped by prior experience, logical reasoning used to interpret problem conditions, and the ability to represent problems through mathematical models. These profiles underscore the need for dedicated coursework that enhances mathematical problem-solving skills within mathematics education programs. The study provides insights into the variation of problem-solving profiles and offers implications for curriculum development in the mathematics education department.
Keywords: Mathematical problem-solving skills, pre-service mathematics teachers, Polya’s profile, qualitative research
References
Abuhasanein, Y., Rejeb, A., & Jemai, K. (2025). Challenges to learning mathematical concepts among sixth-grade students in primary education: A teachers’ perspective. International Electronic Journal of Mathematics Education, 20(2). https://doi.org/10.29333/iejme/15918
Ajani, O. A. (2024). Enhancing problem-solving skills among pre-service teachers in higher education: A systematic literature review. Journal of Pedagogical Sociology and Psychology, 6(2). https://doi.org/10.33902/jpsp.202424002
Berenger, A. (2018). Pre-Service Tea chers ’ Difficulties with Problem Solving. Proceedings of the 41st Annual Conference of the Mathematics Education Research Group of Australasia, 162–169.
Christina, E. N., & Adirakasiwi, A. G. (2021). Analisis Kemampuan Pemecahan Masalah Tahapan Polya Dalam Menyelesaikan Persamaan Dan Pertidaksamaan Linear Satu Variabel. JPMI: Jurnal Pembelajaran Matematika Inovatif, 4(2), 405–424. https://doi.org/10.22460/jpmi.v4i2.405-424
Creswell, J. W. (2014). Research Design: qualitative, quantitative, and mixed methods approaches (4th ed.). SAGE Publications, Inc.
Faradina, A., & Mukhlis, M. (2020). Analisis Berpikir Logis Siswa Dalam Menyelesaikan Matematika Realistik Ditinjau Dari Kecerdasan Interpersonal. Alifmatika: Jurnal Pendidikan Dan Pembelajaran Matematika, 2(2), 129–151. https://doi.org/10.35316/alifmatika.2020.v2i2.129-151
Fatmala, R. R., Sariningsih, R., & Zanthy, L. S. (2020). Analisis Kemampuan Pemecahan Masalah Matematis Siswa Smp Kelas VII Pada Materi Aritmetika Sosial. Jurnal Cendekia : Jurnal Pendidikan Matematika, 4(1), 227–236. https://doi.org/10.31004/cendekia.v4i1.192
Foster, C. (2023). Problem Solving in the Mathematics Curriculum: From Domain-general Strategies to Domain-specific Tactics. The Curriculum Journal, 34(4), 594–612. https://doi.org/10.1002/curj.213
Hartono, Y. (2020). Mathematical Modelling in Problem Solving. IOP Conf. Series: Journal of Physics: Conf. Series, 1480. https://doi.org/10.1088/1742-6596/1480/1/012001
Hiebert, J., Carpenter, T. P., Fennema, E., Fuson, K., Human, P., Murray, H., Olivier, A., & Wearne, D. (1996). Problem Solving as a Basis for Reform in Curriculum and Instruction: The Case of Mathematics. Educational Researcher, 25(4), 12–21. https://doi.org/10.2307/1176776
Jupri, A., Usdiyana, D., & Gozali, S. M. (2024). Exploring pre-service mathematics teachers ’ thinking for solving linear programming word problems. Journal of Honai Math, 7(3), 525–536.
Kania, N., & Fitriyani, D. (2022). Implementasi Teori Pemecahan Masalah Polya dalam Pembelajaran Matematika. Progressive of Cognitive and Ability, 1(1), 42–49. https://doi.org/10.56855/jpr.v1i1.5
Özlem, K., & Arzu, P. (2008). Enhancing problem-solving skills of pre-service elementary school teachers through problem-based learning. Asia-Pacific Forum on Science Learning and Teaching, 9(2), 1.
Polya, G. (1985). How to Solve It: A New Aspect of Mathematical Method. Princeton University Press.
Pradnyana, P., & Amanda, S. (2023). Analisis Peran Dan Upaya Guru Dalam Mengatasi PermasalahanBelajar Siswa Kelas Ii Sdn 1 Sulahan Tahun 2023. Dharmas Education Journal, 4(2), 961–971. http://ejournal.undhari.ac.id/index.php/de_journal
Putri, R. I. I., Zulkardi, & Riskanita, A. D. (2022). Students’ problem-solving ability in solving algebra tasks using the context of Palembang. Journal on Mathematics Education, 13(3), 549–564. https://doi.org/10.22342/jme.v13i3.pp549-564
Qohar, M. A. (2023). Analisis Mendalam Kemampuan Pemecahan Masalah Matematis Siswa: Pendekatan, Tantangan dan Manfaatnya. MAXIMA : Jurnal Pendidikan Matematika, 1(1), 23–31. https://ejournal.iaida.ac.id/index.php/maxima/
Rizqiani, A. S., Sridana, N., Junaidi, & Kurniati, N. (2023). Analisis Kemampuan Pemecahan Masalah Matematis dalam Menyelesaikan Soal Cerita Ditinjau dari Kemampuan Berpikir Kritis Siswa. Jurnal Ilmiah Profesi Pendidikan, 8(1), 232–239. https://doi.org/10.30605/27458326-60
Santos-Trigo, M. (2024). Problem solving in mathematics education: tracing its foundations and current research-practice trends. ZDM - Mathematics Education, 56(2), 211–222. https://doi.org/10.1007/s11858-024-01578-8
Schoenfeld, A. H. (2016). Learning to Think Mathematically: Problem Solving, Metacognition, and Sense Making in Mathematics. Journal of Education, 196(2), 1–38. https://doi.org/10.1177/002205741619600202
Shiddiq, N. F., & Herman, T. (2023). Concept Image Siswa Kelas VII SMP pada Materi Bentuk Aljabar. Jurnal Cendekia : Jurnal Pendidikan Matematika, 7(2), 1404–1415. https://doi.org/10.31004/cendekia.v7i2.2238
Steiner, G. (2001). Transfer of Learning, Cognitive Psychology of. International Encyclopedia of the Social & Behavioral Sciences, 21, 15845–15851. https://doi.org/10.1016/b0-08-043076-7/01481-9
Sugiyono. (2014). Memahami Penelitian Kualitatif. CV Alfabeta.
Sumarni, S., Darhim, D., & Fatimah, S. (2021). Kemampuan Pemecahan Masalah Mahasiswa Calon Guru Matematika Sekolah Menengah Berdasarkan Tahapan Polya. AKSIOMA: Jurnal Program Studi Pendidikan Matematika, 10(3), 1396. https://doi.org/10.24127/ajpm.v10i3.3717
Tractenberg, R., Lee, A., & Decoste, R. (2024). A Mathematical Problem-Solving Pipeline (MPSP) to strengthen scaffolding in higher education STEM courses. MathArXiv, 2024, 1–31.
Umi, F., Syarifuddin, H., & Fitria, Y. (2024). The Development of Realistic Mathematics Education ( RME ) Based Mathematics Learning Tools to Improve Problem Solving Ability in Elementary School. Al-Ishlah: Jurnal Pendidikan, 16(3), 3310–3321. https://doi.org/10.35445/alishlah.v16i3.4293
Usdiyana, D., Purniati, T., Yulianti, K., & Harningsih, E. (2009). Meningkatkan Kemampuan Berpikir Logis Siswa SMP Melalui Pembelajaran Matematika Realistik. Jurnal Pengajaran MIPA, 13(1), 1–14.
Wahyuni, R., Suwanto, F. R., Sthephani, A., & Ahyan, S. (2025). Students’ o bstacles in solving algebra problems in viewed from mathematical problem-solving ability. Infinity Journal, 14(3), 587–606. https://doi.org/https://doi.org/10.22460/infinity.v14i3.p587-606
Widjajanti, D. B. (2009). Kemampuan Pemecahan Masalah Matematis Mahasiswa Calon Guru Matematika. Seminar Nasional Matemaitika Dan Pendidikan Matematika, 402–413.
Widodo, S. A., Sari, Y. N., Chiphambo, S. M., Fitriani, N., Sulistyowati, F., Murtafiah, W., & Pratama, D. F. (2025). The effect of teaching props on the mathematical problem-solving skills: A meta-analysis study. Infinity Journal, 14(1), 235–258. https://doi.org/10.22460/infinity.v14i1.p235-258
Yayuk, E., & Husamah, H. (2020). The difficulties of prospective elementary school teachers in item problem solving for mathematics: Polya’s steps. Journal for the Education of Gifted Young Scientists, 8(1), 361–378. https://doi.org/10.17478/jegys.665833
