Mathematical Problem-Solving Processes across Self-Efficacy Levels in Fifth-Grade Students
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Abstract
Solving least common multiple (LCM) and greatest common factor (GCF) word problems requires conceptual reasoning and systematic verification, yet how fifth-grade students’ problem-solving processes vary across mathematics self-efficacy levels remains insufficiently described. This study aims to examine these processes through Polya’s four problem-solving stages. The study employed a qualitative descriptive design involving 39 fifth-grade students at Dabasah 3 Public Elementary School, Bondowoso, Indonesia, who completed a 16-item self-efficacy questionnaire and an eight-item constructed-response LCM/GCF assessment. Five students with contrasting self-efficacy and performance profiles were purposively selected for interviews and analysis of written solutions, supported by a teacher interview and documentation. Descriptive results indicated moderate self-efficacy among 21 students (53.8%) and moderate problem-solving performance among 32 (82.1%). Cross-case findings showed that the high-self-efficacy student selected a suitable strategy but failed to detect errors when checking. Students with moderate self-efficacy demonstrated divergent performance, including one high-performing case, whereas the low-self-efficacy student hesitated and incompletely monitored solutions. Across cases, recording given information and verifying answers posed recurring difficulties. This study contributes case-based evidence that self-efficacy and demonstrated performance did not consistently align, with implications for combining confidence-building support with conceptual explanation, procedural accuracy, and explicit checking routines.
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References
Adetia, R., & Adirakasiwi, A. G. (2022). Kemampuan pemecahan masalah matematis ditinjau dari self-efficacy siswa. Journal Educatio FKIP UNMA, 8(2), 526–536. https://doi.org/10.31949/educatio.v8i2.2036
Amaliyah, A., Damayanti, D., Erika, S. A., & Latifah, U. (2022). Analisis kemampuan memecahkan masalah matematika siswa pada materi FPB dan KPK di SDN Cikokol 3 Tangerang. FONDATIA, 6(2), 162–173. https://doi.org/10.36088/fondatia.v6i2.1785
Aprilia, R., Destiniar, D., & Septiati, E. (2022). Analisis kemampuan pemecahan masalah matematis ditinjau dari self-efficacy siswa. Suska Journal of Mathematics Education, 8(2), 87–94. https://doi.org/10.24014/sjme.v8i2.18568
Bandura, A. (1997). Self-efficacy: The exercise of control. W. H. Freeman.
Bjerke, A. H. (2026). Sources of mathematics self-efficacy in primary and secondary students: A systematic review of qualitative research. Education Sciences, 16(2), Article 182. https://doi.org/10.3390/educsci16020182
Bjerke, A. H., Hungnes, T., Bachmann, K. E., Hatlevik, O. E., & Ødemark, I. L. (2026). Sources of mathematics and science self-efficacy in primary and secondary education: A systematic literature review. Educational Research Review, 50, Article 100760. https://doi.org/10.1016/j.edurev.2025.100760
Campbell, S., Greenwood, M., Prior, S., Shearer, T., Walkem, K., Young, S., Bywaters, D., & Walker, K. (2020). Purposive sampling: Complex or simple? Research case examples. Journal of Research in Nursing, 25(8), 652–661. https://doi.org/10.1177/1744987120927206
Caviola, S., Toffalini, E., Giofrè, D., Ruiz, J. M., Szűcs, D., & Mammarella, I. C. (2022). Math performance and academic anxiety forms, from sociodemographic to cognitive aspects: A meta-analysis on 906,311 participants. Educational Psychology Review, 34(1), 363–399. https://doi.org/10.1007/s10648-021-09618-5
Chytrý, V., Medová, J., Říčan, J., & Škoda, J. (2020). Relation between pupils' mathematical self-efficacy and mathematical problem solving in the context of the teachers' preferred pedagogies. Sustainability, 12(23), Article 10215. https://doi.org/10.3390/su122310215
Creswell, J. W., & Poth, C. N. (2018). Qualitative inquiry and research design: Choosing among five approaches (4th ed.). SAGE Publications.
DeVellis, R. F., & Thorpe, C. T. (2022). Scale development: Theory and applications (5th ed.). SAGE Publications.
Faozan, D., & Kusno, K. (2023). Systematic literature review: Pengaruh self-efficacy matematis terhadap kemampuan pemecahan masalah matematika. Indonesian Journal of Intellectual Publication, 4(1), 11–16. https://doi.org/10.51577/ijipublication.v4i1.454
Fitriani, A., Dewi, M. S. A., & Dharma, I. M. A. (2024). Analisis miskonsepsi siswa sekolah dasar dalam materi KPK dan FPB. Jurnal Ilmiah Pendidikan Citra Bakti, 11(1), 25–35. https://doi.org/10.38048/jipcb.v11i1.2146
Fitriani, E. (2025). The effectiveness of Polya's problem-solving strategy in enhancing mathematical word problem comprehension among fifth-grade students. Jurnal Penelitian Ilmu Pendidikan, 18(2), 181–192. https://doi.org/10.21831/jpip.v18i2.93790
Govender, R., Adendorff, S. A., & Rawoot, S. (2024). Preferred problem-solving methods employed by Grade 4 learners for measurement word problems. South African Journal of Childhood Education, 14(1), Article a1571. https://doi.org/10.4102/sajce.v14i1.1571
Kusaka, S., & Ndihokubwayo, K. (2022). Metacognitive strategies in solving mathematical word problems: A case of Rwandan primary school learners. SN Social Sciences, 2(9), Article 186. https://doi.org/10.1007/s43545-022-00495-5
Liu, J., & Jacobson, E. (2022). Examining US elementary students' strategies for comparing fractions after the adoption of the common core state standards for mathematics. The Journal of Mathematical Behavior, 67, Article 100985. https://doi.org/10.1016/j.jmathb.2022.100985
Mahmud, M. R., Turmudi, T., Sopandi, W., Rohimah, S. M., & Pratiwi, I. M. (2023). Learning obstacles analysis of lowest common multiple and greatest common factor in primary school. Jurnal Elemen, 9(2), 440–449. https://doi.org/10.29408/jel.v9i2.12359
Miles, M. B., Huberman, A. M., & Saldaña, J. (2020). Qualitative data analysis: A methods sourcebook (4th ed.). SAGE Publications.
Mustofa, R. D., & Danuri, D. (2025). Self-efficacy dan strategi pemecahan masalah matematika siswa sekolah dasar: Studi kasus di kelas IV. Pedagogik Journal of Islamic Elementary School, 8(3), 1279–1294. https://doi.org/10.24256/pijies.v8i3.8710
Nurhalisha, E., Zaenuri, Z., Wijayanti, K., Mariani, S., & Rosyida, I. (2025). Meta-synthesis: Mathematical problem-solving ability reviewed from students' self-efficacy. Mathema: Jurnal Pendidikan Matematika, 7(2), 367–378. https://doi.org/10.33365/jm.v7i2.82
Nurhasanah, A., Raharjo, T. J., Sumartiningsih, S., & Isdaryanti, B. (2026). Diversity in elementary students' mathematical problem-solving based on Polya's theory. Journal of Mathematics Instruction, Social Research and Opinion, 5(2), 1649–1660. https://doi.org/10.58421/misro.v5i2.1661
Nurmajumitasari. (2023). Kesulitan siswa dalam menyelesaikan soal cerita pada materi FPB dan KPK di sekolah dasar. Plusminus: Jurnal Pendidikan Matematika, 3(2), 299–306. https://doi.org/10.31980/plusminus.v3i2.1345
Orosco, M. J., & Reed, D. K. (2024). Supplemental intervention for third-grade English learners with significant problem-solving challenges. Learning Disabilities Research & Practice, 39(2), 60–69. https://doi.org/10.1177/09388982241229407
Oudman, S., van de Pol, J., & van Gog, T. (2022). Effects of self-scoring their math problem solutions on primary school students' monitoring and regulation. Metacognition and Learning, 17(1), 213–239. https://doi.org/10.1007/s11409-021-09281-9
Oudman, S., van de Pol, J., Janssen, E., & van Gog, T. (2024). Primary school students' awareness of their monitoring and regulation judgment accuracy. Learning and Instruction, 92, Article 101907. https://doi.org/10.1016/j.learninstruc.2024.101907
Polya, G. (1945). How to solve it: A new aspect of mathematical method. Princeton University Press.
Purnomo, Y. W., Prananto, I. W., Fitriya, Y., & Kaur, A. (2024). The role of self-regulation in the relationship between adaptability and engagement: A case of online mathematics learning for elementary school students. Online Learning, 28(1). https://doi.org/10.24059/olj.v28i1.3849
Putri, A. A., & Juandi, D. (2022). Kemampuan pemecahan masalah matematis ditinjau dari self efficacy: Systematic literature review (SLR) di Indonesia. Symmetry: Pasundan Journal of Research in Mathematics Learning and Education, 7(2), 135–147. https://doi.org/10.23969/symmetry.v7i2.6493
Rahman, A. A., Mushlihuddin, R., 'Afifah, N., Refugio, C. N., & Zulnaidi, H. (2024). Problem-based learning innovation through realism and culture: Impact on mathematical problem solving and self-efficacy in primary school students. Al-Jabar: Jurnal Pendidikan Matematika, 15(1), 251–264. https://doi.org/10.24042/ajpm.v15i1.21932
Ramlan, A. M., Ramlan, S. M., Farman, F., & Ramdani, F. (2026). Self-efficacy in Indonesian mathematics pedagogy: A systematic literature review. Journal of Research in Science and Mathematics Education, 5(1), 15–28. https://doi.org/10.56855/jrsme.v5i1.1947
Samsuddin, A. F., & Retnawati, H. (2022). Self-efficacy siswa dalam pembelajaran matematika. Buana Matematika: Jurnal Ilmiah Matematika dan Pendidikan Matematika, 12(1), 17–26. https://doi.org/10.36456/buanamatematika.v12i1.5521
Soetjipto, H. P., Putra, M. D. K., Widhiarso, W., & Khakim, Z. (2023). Assessment of the psychometric properties of the Indonesian version of the General Self-Efficacy Scale-12 (GSES-12) in a sample of Indonesian high school students. Psikohumaniora: Jurnal Penelitian Psikologi, 8(2), 259–274. https://doi.org/10.21580/pjpp.v8i2.18024
Street, K. E. S., Malmberg, L.-E., & Schukajlow, S. (2024). Students' mathematics self-efficacy: A scoping review. ZDM – Mathematics Education, 56(2), 265–280. https://doi.org/10.1007/s11858-024-01548-0
Vessonen, T. S. M., Hellstrand, H., Kurkela, M., Aunio, P., & Laine, A. (2025). The effectiveness of mathematical word problem-solving interventions among elementary schoolers: A systematic review and meta-analysis. International Journal of Educational Research, 132, Article 102642. https://doi.org/10.1016/j.ijer.2025.102642
Wang, C., Xu, Q., & Fei, W. (2024). The effect of student-perceived teacher support on math anxiety: Chain mediation of teacher–student relationship and math self-efficacy. Frontiers in Psychology, 15, Article 1333012. https://doi.org/10.3389/fpsyg.2024.1333012
Wiguna, M. B., Sutisnawati, A., & Uswatun, D. A. (2022). Analisis self-efficacy dalam pembelajaran matematika pada siswa kelas 5 sekolah dasar. Jurnal Cendekia: Jurnal Pendidikan Matematika, 6(3), 2489–2497. https://doi.org/10.31004/cendekia.v6i3.1603
Yang Hansen, K., Thorsen, C., Radišić, J., Peixoto, F., Laine, A., & Liu, X. (2024). When competence and confidence are at odds: A cross-country examination of the Dunning–Kruger effect. European Journal of Psychology of Education, 39, 1537–1559. https://doi.org/10.1007/s10212-024-00804-x
Yulianti, D., Siroj, R. A., Rizta, A., & Na'imah, U. (2023). Kesalahan siswa SD dalam menyelesaikan soal pemecahan masalah materi FPB dan KPK berdasarkan tahapan Polya. Differential: Journal on Mathematics Education, 1(2), 171–184. https://doi.org/10.32502/differential.v1i2.111
Zakariya, Y. F. (2022). Improving students' mathematics self-efficacy: A systematic review of intervention studies. Frontiers in Psychology, 13, Article 986622. https://doi.org/10.3389/fpsyg.2022.986622
Živković, M., Pellizzoni, S., Doz, E., Cuder, A., Mammarella, I., & Passolunghi, M. C. (2023). Math self-efficacy or anxiety? The role of emotional and motivational contribution in math performance. Social Psychology of Education, 26(3), 579–601. https://doi.org/10.1007/s11218-023-09760-8