The effects of e-problem-based learning on students’ geometry problem-solving performance across Polya’s stages
DOI:
https://doi.org/10.29408/jel.v12i2.33540Keywords:
e-problem-based learning, geometry learning, mathematical problem solving, multimodal representations, Polya's heuristic stagesAbstract
This study addresses persistent difficulties in students’ geometry problem-solving, particularly in coordinating representations and applying structured reasoning. Prior research has shown the potential of problem-based learning (PBL) and digital tools; however, limited evidence exists regarding how technology-enhanced PBL supports students’ engagement across Polya’s problem-solving stages. To examine this issue, a quasi-experimental pretest–posttest control group design was employed involving two intact undergraduate geometry classes. The experimental group was taught using e-Problem-Based Learning (e-PBL), while the control group received conventional instruction. Students’ performance was measured using a Polya-based problem-solving test. Data were analyzed using descriptive statistics, assumption testing, and an independent samples t-test. The results showed that the experimental group outperformed the control group (M = 70.74 vs. 65.07), with a statistically significant difference (p < .001) and a large effect size (d = 1.16). Performance gains were observed across all four stages of Polya’s framework, particularly in the planning and reflection stages. These findings suggest that e-PBL is associated with improved mathematical problem-solving performance by supporting structured reasoning and reflective thinking. The research emphasizes the necessity of integrating digital scaffolding and collaborative inquiry in geometry instruction.
References
Acuña, A. M. (2014). Polya and GeoGebra: A dynamic approach to problem solving. European Journal of Science and Mathematics Education, 2(2A), 231–235. https://doi.org/10.30935/scimath/9649
Adelabu, F. M., Makgato, M., & Ramaligela, M. S. (2019). The Importance of Dynamic Geometry Computer Software on Learners' Performance in Geometry. Electronic Journal of e-Learning, 17(1), 52–63. https://files.eric.ed.gov/fulltext/EJ1216699.pdf
Almanasreh, E., Moles, R., & Chen, T. F. (2019). Evaluation of methods used for estimating content validity. Research in Social and Administrative Pharmacy, 15(2), 214–221. https://doi.org/10.1016/j.sapharm.2018.03.066
Amalia, S. R., Purwaningsih, D., Widodo, A. N. A., & Fasha, E. F. (2020). Model Problem Based Learning Berbantuan GeoGebra dan Model Realistic Mathematics Education terhadap Representasi Matematis Siswa ditinjau dari Gaya Kognitif. Jurnal Elemen, 6(2), 157–166. https://doi.org/10.29408/jel.v6i2.1692
Amiruddin, M. H., Sumarwati, S., & Amat, K. (2021). The Impact of Problem-Based Learning (PBL) on Student Achievement in Engineering Subject Material at Vocational College Kuantan, Pahang. Online Journal for Tvet Practitioners, 6(1), 1–6. https://doi.org/10.30880/ojtp.2021.06.01.001
Baker, A. R., Lin, T.-J., Chen, J., Paul, N., Anderson, R. C., & Nguyen-Jahiel, K. (2017). Effects of teacher framing on student engagement during collaborative reasoning discussions. Contemporary Educational Psychology, 51, 253–266. https://doi.org/10.1016/j.cedpsych.2017.08.007
Barrows, H. S. (1996). Problem‐based learning in medicine and beyond: A brief overview. New Directions for Teaching and Learning, 1996(68), 3–12. https://doi.org/10.1002/tl.37219966804
Breda, A., Pino-Fan, L. R., & Font, V. (2017). Meta Didactic-Mathematical Knowledge of Teachers: Criteria for The Reflection and Assessment on Teaching Practice. EURASIA Journal of Mathematics, Science and Technology Education, 13(6). 1893–1918. https://doi.org/10.12973/eurasia.2017.01207a
Budakoğlu, I. İ., Coşkun, Ö., & Özeke, V. (2023). e-PBL with multimedia animations: A design-based research. BMC Medical Education, 23(1), 338–348. https://doi.org/10.1186/s12909-023-04298-x
Campbell, D. T., & Stanley, J. C. (2015). Experimental and quasi-experimental designs for research. Ravenio Books. https://www.sfu.ca/~palys/Campbell&Stanley-1959-Exptl&QuasiExptlDesignsForResearch.pdf
Castro, M. D. B., & Tumibay, G. M. (2021). A literature review: Efficacy of online learning courses for higher education institution using meta-analysis. Education and Information Technologies, 26(2), 1367–1385. https://doi.org/10.1007/s10639-019-10027-z
Chen, G. D., Chang, C. K., & Wang, C. Y. (2008). Ubiquitous learning website: Scaffold learners by mobile devices with information-aware techniques. Computers & Education, 50(1), 77–90. https://doi.org/10.1016/j.compedu.2006.03.004
Choi, Y.-R., Lee, Y.-N., Kim, D., Park, W. H., Kwon, D. Y., & Chang, S. O. (2022). An e-Problem-Based Learning Program for Infection Control in Nursing Homes: A Quasi-Experimental Study. International Journal of Environmental Research and Public Health, 19(20), 13371. https://doi.org/10.3390/ijerph192013371
Creswell, J. W., & Creswell, J. D. (2017). Research design: Qualitative, quantitative, and mixed methods approaches. Sage publications. https://edge.sagepub.com/creswellrd5e
Daulay, K. R., & Ruhaimah, I. (2019). Polya theory to improve problem-solving skills. Journal of Physics: Conference Series, 1188, 012070. https://doi.org/10.1088/1742-6596/1188/1/012070
Doo, M. Y., Bonk, C., & Heo, H. (2020). A Meta-Analysis of Scaffolding Effects in Online Learning in Higher Education. The International Review of Research in Open and Distributed Learning, 21(3). 60–80. https://doi.org/10.19173/irrodl.v21i3.4638
Eilouti, B. (2018). A Hybrid Framework of Computer-aided Instruction and Problem-based Learning for Metamorphic Design Pedagogy. The International Journal of Design Education, 13(2), 29–46. https://doi.org/10.18848/2325-128X/CGP/v13i02/29-46
Fuchs, L. S., Gilbert, J. K., Powell, S. R., Cirino, P. T., Fuchs, D., Hamlett, C. L., Seethaler, P. M., & Tolar, T. D. (2016). The role of cognitive processes, foundational math skill, and calculation accuracy and fluency in word-problem solving versus prealgebraic knowledge. Developmental Psychology, 52(12), 2085–2098. https://doi.org/10.1037/dev0000227
Hendriyanto, A., Suryadi, D., Juandi, D., Dahlan, J. A., Hidayat, R., Wardat, Y., Sahara, S., & Muhaimin, L. H. (2024). The didactic phenomenon: Deciphering students’ learning obstacles in set theory. Journal on Mathematics Education, 15(2), 517–544. https://doi.org/10.22342/jme.v15i2.pp517-544
Hu, L. L., & Tseng, S. S. (2016). Applying an e-PBL Platform to Develop a Storytelling-Based Arithmetic Card Game. MATEC Web of Conferences, 44, 01013. https://doi.org/10.1051/matecconf/20164401013
Hung, W. (2011). Theory to reality: A few issues in implementing problem-based learning. Educational Technology Research and Development, 59(4), 529–552. https://doi.org/10.1007/s11423-011-9198-1
Jian, P., Guo, F., Wang, Y., & Li, Y. (2023). Solving Geometry Problems via Feature Learning and Contrastive Learning of Multimodal Data. Computer Modeling in Engineering & Sciences, 136(2), 1707–1728. https://doi.org/10.32604/cmes.2023.023243
Kirabo, E., Batiibwe, M. S. K., Mbulankende, J. S., & Lie, J. (2024). Technology-supported problem-based learning in mathematics education for pre-service teachers: A systematic literature review. SN Social Sciences, 4(10), 173. https://doi.org/10.1007/s43545-024-00973-y
Kotsis, K. T. (2025). Inquiry-Based Learning in Science: Mathematical Reasoning’s Support of Critical Thinking. Journal of Research in Mathematics, Science, and Technology Education, 2(1), 60–72. https://doi.org/10.70232/jrmste.v2i1.35
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), a659. https://doi.org/10.4102/pythagoras.v43i1.659
Mao, X., Dai, Y., Liu, Y., Jiang, Y., & Zhang, Y. (2025). Optimizing Cognitive Load in Digital Mathematics Textbooks: A Mixed-Methods Study on Content Organization and Application Models. Journal of Educational Technology and Innovation, 7(3). 44–59 https://doi.org/10.61414/pxn87q66
Maulana, A., Murtafiah, W., Handhika, J., & Alvares, J. I. (2025). Integrating augmented reality with the e-IM3 structured thinking model to enhance problem-solving skills and learning interest in elementary spatial geometry. Jurnal Elemen, 11(4), 1030–1049. https://doi.org/10.29408/jel.v11i4.32139
Moreno, R., & Mayer, R. (2007). Interactive Multimodal Learning Environments: Special Issue on Interactive Learning Environments: Contemporary Issues and Trends. Educational Psychology Review, 19(3), 309–326. https://doi.org/10.1007/s10648-007-9047-2
Munawaroh, M., Setyani, N. S., & Susilowati, L. (2022). The Development of Electronic Problem Based Learning (E-Pbl) Method in Entrepreneurship Course. https://doi.org/10.2991/978-2-494069-15-2_15
Ng, O.-L., & Sinclair, N. (2015). Young children reasoning about symmetry in a dynamic geometry environment. ZDM, 47(3), 421–434. https://doi.org/10.1007/s11858-014-0660-5
Phumeechanya, N., & Wannapiroon, P. (2014). Design of Problem-based with Scaffolding Learning Activities in Ubiquitous Learning Environment to Develop Problem-solving Skills. Procedia - Social and Behavioral Sciences, 116, 4803–4808. https://doi.org/10.1016/j.sbspro.2014.01.1028
Quarder, J., Greefrath, G., Gerber, S., & Siller, H.-S. (2025). Pedagogical content knowledge for simulations and mathematical modelling with digital tools: A quasi-experimental study with pre-service mathematics teachers. ZDM – Mathematics Education, 57(2–3), 395–409. https://doi.org/10.1007/s11858-025-01673-4
Rahmat, A. R., Saidi, S. B., & Mohd Nasir, N. S. (2024). Content Validity of Digital Knowledge using CVI Method. Environment-Behaviour Proceedings Journal, 9(SI20), 21–28. https://doi.org/10.21834/e-bpj.v9iSI20.6092
Saat, N. A., Alias, A. F., & Saat, M. Z. (2024). Digital Technology Approach in Mathematics Education: A Systematic Review. International Journal of Academic Research in Progressive Education and Development, 13(4), 173-184. https://doi.org/10.6007/IJARPED/v13-i4/22956
Sachan, M., Dubey, A., Hovy, E. H., Mitchell, T. M., Roth, D., & Xing, E. P. (2020). Discourse in Multimedia: A Case Study in Extracting Geometry Knowledge from Textbooks. Computational Linguistics, 45(4), 627–665. https://doi.org/10.1162/coli_a_00360
Sengupta-Irving, T., & Enyedy, N. (2015). Why Engaging in Mathematical Practices May Explain Stronger Outcomes in Affect and Engagement: Comparing Student-Driven With Highly Guided Inquiry. Journal of the Learning Sciences, 24(4), 550–592. https://doi.org/10.1080/10508406.2014.928214
Siegler, R. S., & Braithwaite, D. W. (2017). Numerical Development. Annual Review of Psychology, 68(1), 187–213. https://doi.org/10.1146/annurev-psych-010416-044101
Siregar, T. (2025). Literature Review: The Use of GeoGebra Software on Mathematical Comprehension Ability. Computer Science and Mathematics. https://doi.org/10.20944/preprints202510.0925.v1
Sugianto, S., Waluya, St. B., Sukestiyarno, Yl. S., & Wardono, W. (2025). Problem-Based Learning based on Electronic Module: Students’ Mathematical Communication Process in terms of Cognitive Style. Educational Process International Journal, 16(1). 1–16 https://doi.org/10.22521/edupij.2025.16.222
Tassilova, N. A., Shashayeva, G. K., Yernazarova, Z. Sh., Akhmetova, A. I., Arynov, Z. M., & Karimova, Z. K. (2025). Communication technologies in STEM education: A systematic review. Eurasia Journal of Mathematics, Science and Technology Education, 21(10), em2719. https://doi.org/10.29333/ejmste/17178
Tessema, G., Michael, K., & Areaya, S. (2024). Realist hands-on learning approach and its contributions to learners’ conceptual understanding and problem-solving skills on solid geometry. Pedagogical Research, 9(1), em0186. https://doi.org/10.29333/pr/14096
Türkoğlu, H., & Yalçınalp, S. (2024). Investigating problem-solving behaviours of university students through an eye-tracking system using GeoGebra in geometry: A case study. Education and Information Technologies, 29. 15761–15791. https://doi.org/10.1007/s10639-024-12452-1
Udil, P. A., Dasari, D., & Nurlaelah, E. (2025). Pedagogical Interventions for Enhancing Students’ Mathematical Literacy: A Systematic Literature Review. Pedagogika, 158(2), 29–59. https://doi.org/10.15823/p.2025.158.2
Vilenius‐Tuohimaa, P. M., Aunola, K., & Nurmi, J. (2008). The association between mathematical word problems and reading comprehension. Educational Psychology, 28(4), 409–426. https://doi.org/10.1080/01443410701708228
Wagino, W., Maksum, H., Purwanto, W., Simatupang, W., Lapisa, R., & Indrawan, E. (2024). Enhancing Learning Outcomes and Student Engagement: Integrating E-Learning Innovations into Problem-Based Higher Education. International Journal of Interactive Mobile Technologies (iJIM), 18(10), 106–124. https://doi.org/10.3991/ijim.v18i10.47649
Wahyuni, R., Suwanto, F. R., Sthephani, A., & Ahyan, S. (2025). Students’ obstacles in solving algebra form problems viewed from mathematical problem-solving ability. Infinity Journal, 14(3), 587–606. https://doi.org/10.22460/infinity.v14i3.p587-606
Wardi, Z., Satriawan, R., Ahyan, S., & Halqi, M. (2023). Interelasi model Problem Based learning dan Interaksi Teman Sebaya melalui Sikap Matematis terhadap Prestasi Matematika. Plusminus: Jurnal Pendidikan Matematika, 3(3), 521–538. https://doi.org/10.31980/plusminus.v3i3.1514
Yang, Y., Du, W., Mavrikis, M., & Geraniou, E. (2025). Spatial Skill Development Through Augmented Reality in Mathematics Education: A Scoping Review. Digital Experiences in Mathematics Education. https://doi.org/10.1007/s40751-025-00187-8
Yu, L., & Zin, Z. M. (2023). The critical thinking-oriented adaptations of problem-based learning models: A systematic review. Frontiers in Education, 8, 1139987. https://doi.org/10.3389/feduc.2023.1139987
Zhang, D., Wang, L., Zhang, L., Dai, B. T., & Shen, H. T. (2018). The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers (Versi 2). arXiv. https://doi.org/10.48550/ARXIV.1808.07290
Zuckerman, H. S., & Polya, G. (1966). Mathematical Discovery, On Understanding, Learning, and Teaching Problem Solving. The American Mathematical Monthly, 73(3), 323. https://doi.org/10.2307/2315372
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