Problem-Based Learning within UbD Framework to Enhance Mathematical Conceptual Understanding of Circle Equation

Khikmatus Shahrin Maghfiroh(1*), Indhiadma Parnata(2), Alifiani Alifiani(3),

(1) Universitas Islam Malang
(2) Universitas Islam Malang
(3) Universitas Islam Malang
(*) Corresponding Author

Abstract


This study aims to explore and describe the implementation of PBL within the Understanding by Design (UbD) framework to enhance students' mathematical conceptual understanding of the circle equation. This research employed a mixed-methods approach with a sequential explanatory design. The subjects were 30 eleventh-grade students at SMAN 4 Malang. Quantitative data were collected through pre-test and post-test, while qualitative data were gathered through questionnaires, observations, interviews, and documentation. The results showed a significant improvement in students' conceptual understanding, with the mean score increasing from 6.06 (pre-test) to 8.21 (post-test). The paired sample t-test revealed a statistically significant difference with a large effect size (Cohen's d = 1.131). Questionnaire results indicated that students responded positively to the implementation, particularly appreciating the clarity of learning objectives, the alignment between assessments and instruction, the use of contextual problems, and the support of visual media and collaborative activities. This study contributes a validated instructional design that mathematics teachers can adopt to improve the quality of mathematics instruction at the senior high school level.

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References


Arends, R. I. (2012). Learning to teach (9th ed.). Library of Congress Cataloging.

Aristanti, A. P., & Fatayan, A. (2024). The Effect of the UbD-Based Problem-Based Learning Model on the Critical Thinking Skills of Grade IV Students in IPAS Subject at Elementary. Mimbar Sekolah Dasar, 11(2), 268–280. https://doi.org/10.53400/mimbar-sd.v11i2.71794

Berhanu, K. Z. (2025). Academic social loafing among Summer Debre students , Ethiopia : Effect of intervention. Perspectives in Education, 43(1), 267–281. https://doi.org/https://doi.org/10.38140/pie.v43i1.7135

Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences (2th ed.). Lawrence Erlbaum Associates.

Creswell, J. W., & Poth, C. N. (2007). Qualitative inquiry and research design: Choosing among five approaches. Sage.

Field, A. (2018). Discovering Statistics Using IBM SPSS Statistics (5th ed.). SAGE.

Gürbüz, Ö., & Yap?c?, N. (2026). Understanding by Design (UbD) model in mathematics teaching and its impact on students. International Electronic Journal of Elementary Education, 18(3), 361–376.

Hidayat, M. Q., & Fitrini, R. (2025). Systematic Overview : Problem Based Learning ( PBL ) in Mathematics Learning. LOGIKA: Jurnal Pendidikan Matematika, 1(2), 6–10.

Kalita, K., & Nath, M. (2025). A Comparative Analysis of Different Teaching Methods on Student Achievement in Mathematics. International Scientific Refereed Research Journal Available (Shodhshauryam), 8(4), 100–117.

Kpotosu, C. K., Amegbor, S., Mifetu, B., & Ezah, R. B. K. E. (2024). Senior High School Students ’ difficulties with Geometry Topics Senior High School Students ’ Difficulties with. Preprints. https://doi.org/10.20944/preprints202405.0126.v1

Kuntari, F. R., Rondonuwu, F. S., & Sudjito, D. N. (2019). Understanding by Design (UbD) for the Physics Learning about Parabolic Motion. Jurnal Penelitian Fisika Dan Aplikasinya, 09(01), 32–43. https://doi.org/10.26740/jpfa.v9n1.p32-43

Laurentino, T. G., Scheller, M., Glover, G., Proulx, M. J., & Sousa, A. A. De. (2024). Thinking on your feet: potentially enhancing phylogenetic tree learning accessibility through a kinaesthetic approach. Evolution: Education and Outreach, 17(1), 1–8. https://doi.org/https://doi.org/10.1186/s12052-024-00215-y

Lee, J., & Paul, N. (2023). A Review of Pedagogical Approaches for Improved Engagement and Learning Outcomes in Mathematics. Journal of Student Research, 12(3), 1–9.

Lin, J.-W., & Chen, H.-R. (2024). Integrating group awareness into team-based learning. Journal of Computer Assisted Learning, 40(6), 3111–3124. https://doi.org/https://doi.org/10.1111/jcal.13058

Liu, Y. (2026). Learning that lasts : developing 4C skills in college English through Understanding by Design framework. Frontiers in Education, 11(January), 1–13. https://doi.org/10.3389/feduc.2026.1678369

Maghfiroh, K. S., & Kusumasari, V. (2025). Pengembangan LKPD Berbasis Problem Based Learning Bermuatan Etnomatematika pada Materi Bangun Ruang untuk Mendukung Kemampuan Visual Spasial. Jurnal Ilmiah Pendidikan Matematika, 14(1), 21–36. https://doi.org/https://doi.org/10.25273/jipm.v14i1.22299

Mapeni, Anwar, R. B., Rahmawati, D., & Anghel, C. V. (2026). Implementation of a problem-based learning model viewed from students ’ learning styles on students ’ mathematical problem. Journal of Research Mathematics Education, 9(I), 60–75.

McQuade, R., Ventura-medina, E., Wiggins, S., Hendry, G., & Anderson, T. (2019). Students ’ strategies for managing social loafers in PBL: Interactional means of dealing with unequal participation in group work. In S. Bridges & R. Imafuku (Eds.), Interactional Research into Problem-Based Learning (Issue May, pp. 1–15). Purdue University Press (May.

Miles, M. B., Huberman, A. M., & Saldaña, J. (2020). Qualitative data analysis: A methods sourcebook. SAGE.

Niam, M. A., Sugiyanti, Prasetyowati, D., & Gunarto. (2024). Understanding by Design (UbD) pada pembelajaran berbasis Problem Based Learning (PBL) berbantuan LKPD untuk meningkatkan kemampuan koneksi matematis siswa. Prosiding Seminar Nasional Pendidikan Profesi Guru, 105–114. https://conference.upgris.ac.id/index.php/psnppg/article/view/6273

Ostinelli, G. (2024). Testing Understanding by Design. New Zealand Journal of Teachers’ Work, 21(1), 104–119.

Payadnya, I. P. A. A., Prahmana, R. C. I., Lo, J.-J., Noviyanti, P. L., & Atmaja, I. M. D. (2023). Designing area of circle learning trajectory based on “what-if” questions to support students’ higher-order thinking skills. Journal on Mathematics Education, 14(4), 757–780. https://doi.org/http://doi.org/10.22342/jme.v14i4.pp757-780

Peranginangin, A. P. (2025). The Application of Problem-Based Learning Model to Improve Students ’ Mathematical Problem -Solving Skills in Junior High School. Jurnal Info Sains: Informatika Dan Sains, 15(1), 140–150. https://doi.org/10.54209/infosains.v15i01

Putri, M. H., & Syarqawi, A. (2024). Effectiveness problem-solving techniques through group guidance sevices to reduce sosial loafing. Jurnal Pendidikan Islam Dan Multikulturalisme, 6(2), 87–99. https://doi.org/10.37680/scaffolding.v6i2.5336

Rahayu, S., & Nugroho, A. A. (2025). A Needs Analysis of Problem-Based Learning Media Using the Design Thinking Framework to Improve Critical Thinking. Jurnal Penelitian Pendidikan IPA, 11(9), 63–71. https://doi.org/10.29303/jppipa.v11i9.12415

Saputra, A. ., Minggi, I., & Djadir. (2021). The Identification of the Concept Understanding on Limit of Functions Based on Students ’ Learning Styles in Mathematics Department at FMIPA UNM. Journal of Physics: Conference Series, 1–8. https://doi.org/10.1088/1742-6596/1899/1/012130

Simanjuntak, M. P., Hutahaean, J., Marpaung, N., & Ramadhani, D. (2021). Effectiveness of Problem-Based Learning Combined with Computer Simulation on Students ’ Problem-Solving and Creative Thinking Skills. International Journal of Instruction, 14(3), 519–534.

Sugiyono. (2007). Metode Penelitian Kuantitatif Kualitatif dan R&D. Alfabeta.

Taherdoost, H., Business, H., Sdn, S., Group, C., & Lumpur, K. (2016). Validity and Reliability of the Research Instrument ; How to Test the Validation of a Questionnaire / Survey in a Research. 5(3), 28–36.

Wiggins, G., & McTighe, J. (2005). Understanding by Design: Expanded 2nd Edition. Association for Supervision and Curriculum Development (ASCD).

Yurniwati. (2018). Improving Conceptual and Procedural Knowledge of Prospective Teachers through Multisensory Approach : Experience from Indonesia. Journal of Research and Advances in Mathematics Education, 3(2), 106–117.




DOI: https://doi.org/10.31327/jme.v11i1.2787

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