Characteristics Of Students’ Mathematical Problem-Solving Strategies In Problem-Based Learning Through Polya’s Stages

Ulfa Yuliana; Stepan  Tudu; Nursupiamin Nursupiamin; I Wayan Sudarsana

doi:10.24239/koordinat.v7i1.219

Ulfa Yuliana Universitas Terbuka
Stepan Tudu Universitas Terbuka
Nursupiamin Nursupiamin UIN Datokarama Palu https://orcid.org/0000-0002-1452-1961
I Wayan Sudarsana Universitas Tadulako https://orcid.org/0000-0002-9198-3414

DOI: https://doi.org/10.24239/koordinat.v7i1.219

Keywords: Mathematical Problem-Solving Strategies, Polya’s Problem-Solving Stages, Problem-Based Learning, Reflective Thinking

Abstract

This study aimed to explore the characteristics of students’ mathematical problem-solving strategies in Problem-Based Learning through Polya’s stages in solving compound interest problems. This study employed a qualitative descriptive case study. The participants consisted of 35 Grade XI students at SMA Negeri 2 Tolitoli, Central Sulawesi. Data were collected through problem-solving tests, interviews, observations, and documentation. Three representative students from high-, moderate-, and low-level problem-solving characteristic profiles were selected purposively for in-depth analysis. Data were analyzed using Miles and Huberman’s interactive model. The findings showed that students demonstrated different strategy characteristics across Polya’s stages. At the understanding stage, students demonstrated complete identification, partial understanding, and misunderstanding strategies. During the planning stage, conceptual, procedural, and trial-and-error strategies emerged. At the implementation stage, students demonstrated systematic solution, procedural error, and inconsistent-step strategies, while at the reflective stage, students showed solution evaluation, partial verification, and no verification strategies. Students with high-level profiles tended to demonstrate coherent and interconnected strategy patterns, whereas students with low-level profiles demonstrated fragmented and inconsistent processes. The findings further indicated that students’ strategies developed as interconnected processes in which difficulties emerging at earlier stages influenced subsequent stages. Reflective activities were identified as the weakest component of students’ mathematical problem-solving processes. The findings contribute theoretically to understanding how students’ mathematical problem-solving strategies emerge and develop across Polya’s stages within Problem-Based Learning environments. Practically, the findings highlight the importance of strengthening reflective activities and supporting interconnected strategic thinking in mathematics learning

References

Auliya, R., Tahir, Chairuddin, & Erfina. (2025). Analisis Kemampuan Problem Solving Siswa pada Materi Eksponen Melalui PBL Berbasis Polya. SQUARE: Journal of Mathematics and Mathematics Education, 7(2), 65–76. https://doi.org/10.21580/square.2025.7.2.28527

Cavalcante, A., Savard, A., & Polotskaia, E. (2024). Mathematical Structures of Simple and Compound Interest: An Analysis of Secondary Teachers’ Relational Thinking. Educational Studies in Mathematics, 116, 215–235. https://doi.org/10.1007/s10649-024-10308-6

Creswell, J. W. (2014). Research Design: Qualitative, Quantitative, and Mixed Methods Approaches (3rd ed.). Sage.

Ekol, G., & Greenop, S. (2023). Teacher Interventions Using Guided Discovery and Mathematical Modelling in Grade 10 Financial Mathematics. The European Educational Researcher, 6(2), 35–53. https://doi.org/10.31757/euer.623

Fathurrohman, Suparlan, Nurohmah, L., & Nurhayati. (2024). The Implementation of Problem-Based Learning (PBL) Model to Improve Critical Thinking Ability of Class IV Students in Civics Subjects at School. Jurnal Prima Edukasia, 13(2), 225–233. https://doi.org/10.21831/jpe.v13i2.84394

Fitriani, F., Hayati, R., Sugeng, S., Srimuliati, S., & Herman, T. (2022). Students’ Ability to Solve Mathematical Problems Through Polya Steps. Journal of Engineering Science and Technology, ICMScE2022, 25–32.

Hidayah, R. N., & Murti, R. C. (2025). Evaluating Mathematical Problem-Solving Skills in Primary School Students: Challenges and Insights from Polya’s Framework. Al-Ishlah: Jurnal Pendidikan, 17(3), 4984–4993. https://doi.org/10.35445/alishlah.v17i3.6534

Hmelo-Silver, C. E. (2004). Problem-Based Learning: What and How Do Students Learn? Educational Psychology Review, 16(3), 235–266. https://doi.org/10.1023/B:EDPR.0000034022.16470.f3

Jaenudin, S., Aminah, M., & Yusuf, Y. (2025). Analysis of Students’ Mathematical Problem-Solving Abilities. Jurnal Cendekia: Jurnal Pendidikan Matematika, 09(01), 195–202. https://doi.org/10.31004/cendekia.v9i1.3743

Jonassen, D. H. (2011). Learning to Solve Problems: A Handbook for Designing Problem-Solving Learning Environments. Routledge Taylor & Francis Group.

Lestari, Y., As’ari, A. R., & Muksar, M. (2021). Analysis of Students’ Mathematical Literacy Skills in Solving PISA Mathematical Problems. MaPan : Jurnal Matematika Dan Pembelajaran, 9(1), 102–118. https://doi.org/10.24252/mapan.2021v9n1a7

Lester, F., & Cai, J. (2015). Can Mathematical Problem Solving Be Taught? Preliminary Answers from Thirty Years of Research. In P. Felmer, J. Kilpatrick, & E. Pehkonen (Eds.), Posing and solving mathematical problems: Advances and new perspectives. Springer.

Linda, L., & Asyura, I. (2021). Students’ Mathematical Reasoning Ability in Solving Post-COVID-19 PISA Model Mathematics Problems. Jurnal Riset Pendidikan Matematika, 8(2), 140–152. https://doi.org/10.21831/ jrpm.v8i2.44739

Lutfiani, S., Liliawati, W., Samsudin, A., & Aviyanti, L. (2026). Analysis of The Thermodynamics Problem-solving Process Based on Polya’s Stages in High School Students. Jurnal Pendidikan Matematika Dan Sains, 14(1), 1–10. https://doi.org/10.21831/jpms.v14i1.90339

Malik, M. A., & Mas’ud, B. (2025). Analysis of Students ’ Mathematical Literacy Ability in Solving Contextual Problems in Linear Equations. Journal of Educational Analytics, 4(3), 647–662. https://doi.org/10.55927/jeda.v4i3.364

Miles, M. B., Huberman, A. M., & Saldaña, J. (2014). Qualitative Data Analysis: A Methods Sourcebook (Third). SAGE Publications, Inc.

Mustamin, K., Wahdah, Intiardy, D., Jumrah, A. M., & Pattiasina, P. J. (2024). The Impact of Project-Based Learning on Students’ Collaboration Skills in Secondary Schools. International Journal of Educational Research Excellence (IJERE), 03(02), 992–998. https://doi.org/10.55299/ijere.v3i2.740

NCTM. (2000). Principles and Standards for School Mathematics. The National Council of Teachers of Mathematics, Inc.

Ncube, M., & Luneta, K. (2025). Concept-Based Instruction: Improving Learner Performance in Mathematics Through Conceptual Understanding. Pythagoras, 46(1), a815. https://doi.org/10.4102/ pythagoras.v46i1.815

OECD. (2023). PISA 2022 Assessment and Analytical Framework. PISA, OECD Publishing. https://doi.org/10.1787/dfe0bf9c-en

Polya, G. (1973). How To Solve It: A New Aspect of Mathematical Method (2nd ed.). Princeton University Press.

Putri, N. M., Kristiantari, M. G. R., & Marisa, R. (2026). The Effect of the Deep Learning-Based Problem-Based Learning (PBL) Model on the Critical Thinking Skills and Mathematical Disposition of Elementary School Students. Jurnal Pamator, 19(1), 17–27. https://doi.org/10.21107/pamator.v19i1.33994

Samosir, C. M., Herman, T., Prabawanto, S., Melani, R., & Mefiana, S. A. (2024). Students’ Difficulty in Understanding Problems in the Contextual Problem-Solving Process. Prisma, 13(1), 20–29. https://doi.org/10.35194/jp.v13i1.3726

Sarmila, Tahir, & Hidayati, U. (2025). Profile of Students’ Problem-Solving Ability Based on Mathematical Literacy in PISA Context. Journal of Mathematics Education, 10(2), 250–266. https://doi.org/10.31327/jme.v10i2.2536

Schoenfeld, A. H. (2016). Learning to Think Mathematically: Problem Solving, Metacognition, and Sense Making in Mathematics. Journal of Education and Educational Development, 196(2), 1–38. https://doi.org/10.1177/002205741619600202

Sugiharti, A., Rahmawati, D., & Anwar, R. B. (2026). Trends in Mathematical Problem-Solving Skills in Mathematics Learning. International Journal of Studies in Education and Science, 7(2), 188–201. https://doi.org/10.46328/ijses.6725

Syaputra, H., Armiati, & Harisman, Y. (2025). The Interaction between Mathematical Problem-Solving Skills and Mathematical Communication Skills of Junior High School Students : A Qualitative Approach. EDUMATIKA: Jurnal Riset Pendidikan Matematika, 8(2), 129–144.

Tañola, M. D., & Lomibao, L. S. (2024). Understanding How Students Learn Mathematics: A Systematic Literature Review of Contemporary Learning Strategies in Mathematics Education Post-2020. Journal of Innovations in Teaching and Learning, 4(1), 66–75. https://doi.org/10.12691/jitl-4-1-11

Uliyandari, M., Candrawati, E., Herawati, A. A., & Latipah, N. (2021). Problem-Based Learning To Improve Concept Understanding and Critical Thinking Ability of Science Education Undergraduate Students. IJORER : International Journal of Recent Educational Research, 2(1), 65–72. https://doi.org/10.46245/ijorer.v2i1.56

Umayrah, A., Herman, T., Jupri, A., & Salsabila, S. (2025). Elementary School Students’ Problem-Solving Strategies in Adding and Subtracting Whole Numbers through Open-Ended Problems. Journal of Educational Research, 28(3), 492–502. https://doi.org/10.20961/Paedagogia.v28i3.103035

Usman, U., Juniati, D., & Khabibah, S. (2026). Analysis of Students’ Mathematical Reasoning Ability in Junior High School. Journal of Innovative Mathematics Learning, 9(1), 138–148. https://doi.org/10.22460/jiml.v9i1.p30533

Widiastuti, I. A. M. S., Mantra, I. B. N., Utami, I. G. A. L. P., Sukanadi, N. L., & Susrawan, I. N. A. (2023). Implementing Problem-based Learning to Develop Students’ Critical and Creative Thinking Skills. Jurnal Pendidikan Indonesia, 12(4), 658–667. https://doi.org/10.23887/jpiundiksha.v12i4.63588

Yuwono, T., Verawati, P., & Wahyuni, T. (2025). Implementing Polya’s Problem-Solving Framework to Improve Word Problem Solving in Secondary School Mathematics. Tirtamath: Journal of Mathematics Research and Teaching, 7(1), 120–130.