Exploring student’s mathematical representation ability in deep learning-integrated problem-based learning on circle equations

Authors

  • Indhiadma Parnata Universitas Islam Malang
  • Khikmatus Shahrin Maghfiroh Universitas Islam Malang
  • Alifiani Alifiani Universitas Islam Malang
  • Lailatul Badriyah SMA Negeri 4 Malang

DOI:

https://doi.org/10.22460/jpmi.v9i4.32043

Keywords:

mathematical representation, Deep Learning, problem based learning, circle equations, descriptive qualitative

Abstract

Mathematical representation ability is a fundamental competency for senior high school students. This study aims to describe students' mathematical representation abilities in deep learning integrated with the Problem-Based Learning model. A descriptive qualitative approach was employed, involving 36 Grade XI students at SMAN 4 Malang. Data were collected through written tests based on mathematical representation ability indicators and analyzed across representation: verbal, pictorial, and symbolic. The results reveal uneven abilities across representation types: symbolic representation was most consistently fulfilled, though with varied strategies; pictorial representation was spatially constructed but incomplete in metric annotation; verbal representation exhibited the greatest variation, with only high-ability students capable of articulating contextual geometric conclusions. These findings confirm that symbolic proficiency does not guarantee comprehensive representational competence. This study contributes an empirical profile of students' mathematical representation in a PBL context, serving as a reference for teachers in designing balanced instruction across representation types.

References

Abidin, M., & Retnawati, H. (2019). A diagnosis of difficulties in answering questions of circle material on junior high school students. Jurnal Penelitian dan Evaluasi Pendidikan, 23(2), 144–155. https://doi.org/10.21831/pep.v23i2.16454

Abreh, M. K., Owusu, K. A., & Amedahe, F. K. (2018). Trends in performance of WASSCE candidates in the science and mathematics in ghana: perceived contributing factors and the way forward. Journal of Education, 198(1), 113–121. https://doi.org/journals.sagepub.com/doi/10.1177/0022057418800950

Ali, C. A. (2022). The didactical phenomenology in learning the circle equation. International Electronic Journal of Mathematics Education, 17(4), 1–11. https://doi.org/10.29333/iejme/12472

Bariroh, A. (2025). Pengaruh pendekatan deep learning melalui model problem based learning terhadap pemahaman konsep dan kemampuan pemecahan masalah dalam pembelajaran matematika. Amaliyatu Tadris (AMYTA), 3(2), 133–156. https://ejournal.uluwiyah.ac.id/index.php/amyta/article/view/339

Creswell, J. W. (2014). Research design: Qualitative, quantitative, and mixed methods approaches (4th ed.). SAGE Publications, Inc. https://dosen.ikipsiliwangi.ac.id/wp-content/uploads/sites/6/2019/07/Creswell_J._Research_design_Qualitative_Quantb-ok.xyz-FOURTH-ED.pdf

Denzin, N. K. (2009). The research act: A theoretical introduction to sociological methods (1st ed.). https://doi.org/10.4324/9781315134543

Dewi, I., Saragih, S., & Khairani, D. (2017). Analisis peningkatan kemampuan representasi matematis siswa SMA ditinjau dari perbedaan gender. Jurnal Didaktik Matematika, 4(2), 115–124. https://doi.org/10.24815/jdm.v4i2.8863

Dolmans, D. H. J. M., Loyens, S. M. M., Marcq, H., & Gijbels, D. (2016). Deep and surface learning in problem-based learning: A Review of The Literature. Advances in Health Sciences Education, 21(5), 1087–1112. https://doi.org/10.1007/s10459-015-9645-6

Feriyanto, F., & Anjariyah, D. (2024). Deep learning approach through meaningful, mindful, and joyful learning: A Library Research. Electronic Journal of Education, Social Economics and Technology, 5(2), 208–212. https://doi.org/10.33122/ejeset.v5i2.321

Fitriyah, I. M., Putro, N. H. P. S., & Apino, E. (2022). Meta Analysis Study: Effectiveness of problem based learning on indonesian students’ mathematical reasoning ability. Jurnal Riset Pendidikan Matematika, 9(1), 36–45. https://doi.org/10.21831/jrpm.v9i1.46447

Handayani, Y., & Aini, I. N. (2019). Analisis Kemampuan Pemahaman Konsep Matematis Siswa pada Materi Peluang. Prosiding Sesiomadika, 2(1b), 575–581. https://journal.unsika.ac.id/index.php/sesiomadika/article/view/2826

Hertanti, R., Azizah, K. R., Sari, P. P., & Melissa, M. M. (2023). Guided Discovery Learning to Improve Students’ Mathematics Representation and Collaboration at SMA 6 Yogyakarta. Kontinu: Jurnal Penelitian Didaktik Matematika, 7(2), 19-35. https://doi.org/10.30659/kontinu.7.2.19-35

Hidayat, M. Q., & Fitrini, R. (2025). Systematic Overview: Problem Based Learning (PBL) in Mathematics Learning. LOGIKA: Jurnal Pendidikan Matematika, 1(2), 6–10. https://doi.org/10.71094/logika.v2i1

Iffa, D. S., Subarinah, S., Baidowi, B., & Sripatmi, S. (2022). Kemampuan Representasi Matematis Siswa dalam Memecahkan Masalah Relasi dan Fungsi Kelas VIII SMP. Jurnal Riset Pendidikan Matematika Jakarta, 4(1), 1–11. https://doi.org/10.21009/jrpmj.v4i1.23021

Inayah, C. F., & Dasari, D. (2023). Kemampuan Representasi Matematis pada Siswa Indonesia Berdasarkan Karakteristik Cara Berpikir: Sistematik Literatur Review. Symmetry: Pasundan Journal of Research in Mathematics Learning and Education, 8(2), 230–242. https://doi.org/10.23969/symmetry.v8i2.11009

Kemendikdasmen. (2025). Naskah Akademik Pembelajaran Mendalam Menuju Pendidikan Bermutu Untuk Semua. Kementerian Pendidikan Dasar dan Menengah Republik Indonesia. https://guru.kemendikdasmen.go.id/dokumen/kGn0z42DeN

Kho, R., Solihati, T., & Lumbantobing, H. (2024). The Impact of Problem-Based Learning on Motivation and Mathematics Outcome For Sixth-Grade Students. Journal of Honai Math, 7(3), 363–378. https://doi.org/10.30862/jhm.v7i3.693

Khoerunnisa, R., & Maryati, I. (2022). Kemampuan Representasi Matematis Siswa SMP terhadap Materi Segiempat. Plusminus: Jurnal Pendidikan Matematika, 2(1), 165–176. https://doi.org/10.31980/plusminus.v2i1.1089

Kholid, I., Basyari, M. M. A., Saman, Nurhadi, & Mulhat. (2025). Menumbuhkan Pemahaman Konseptual Matematika melalui Deep Learning: Sebuah Kajian Sistematik Literatur. Pedagogy: Jurnal Pendidikan Matematika, 10(4), 1494–1506. https://doi.org/10.30605/pedagogy.v10i4.7108

Lutfi, J. S., & Juandi, D. (2023). Mathematical Representation Ability: A Systematic Literature Review. Union: Jurnal Ilmiah Pendidikan Matematika, 11(1), 124–135. https://doi.org/10.30738/union.v11i1.14048

Lutfi, J. S., & Khusna, H. (2021). Analisis Kemampuan Representasi Matematis Siswa Berdasarkan Tingkat Motivasi Belajar Pada Pandemi Covid-19. Jurnal Cendekia : Jurnal Pendidikan Matematika, 5(3), 2185–2197. https://doi.org/10.31004/cendekia.v5i3.728

Mainali, B. (2020). Representation in Teaching and Learning Mathematics. International Journal of Education in Mathematics, Science and Technology, 9(1), 1–21. https://doi.org/10.46328/ijemst.1111

Marliani, S., & Puspitasari, N. (2022). Kemampuan Representasi Matematis Siswa pada Materi Kesebangunan dan Kekongruenan di Kampung Sukawening. Jurnal Inovasi Pembelajaran Matematika: PowerMathEdu (PME), 1(2), 113–124. https://doi.org/10.31980/powermathedu.v1i2.2224

Maryati, I., & Monica, V. (2021). Pembelajaran Berbasis Masalah dan Inkuiri dalam Kemampuan Representasi Matematis. Mosharafa: Jurnal Pendidikan Matematika, 10(2), 333–344. https://doi.org/10.31980/mosharafa.v10i2.666

Miles, M. B., Huberman, A. M., & Saldaña, J. (2014). Qualitative Data Analysis: A Methods Sourcebook (3rd ed.). https://www.metodos.work/wp-content/uploads/2024/01/Qualitative-Data-Analysis.pdf

Mutmainnah, N., Adrias, A., & Zulkarnaini, A. P. (2025). Implementasi Pendekatan Deep Learning terhadap Pembelajaran Matematika di Sekolah Dasar. Pendas: Jurnal Ilmiah Pendidikan Dasar, 10(1), 858–871. https://journal.unpas.ac.id/index.php/pendas/article/view/23781/11686

Nurrahmawati, N., Sa’dijah, C., Sudirman, S., & Muksar, M. (2021). Assessing Students’ Errors in Mathematical Translation: From Symbolic to Verbal and Graphic Representations. International Journal of Evaluation and Research in Education (IJERE), 10(1), 115. https://doi.org/10.11591/ijere.v10i1.20819

OECD. (2023). PISA 2022 Results: Factsheets Indonesia. OECD Publishing. https://www.oecd.org/content/dam/oecd/en/publications/reports/2023/11/pisa-2022-results-volume-i-and-ii-country-notes_2fca04b9/indonesia_0e09c072/c2e1ae0e-en.pdf

Oranga, J., & Matere, A. (2023). Qualitative Research: Types, Essence and Advantages. International Journal of Social Science, Educational, Economics, Agriculture Research and Technology (IJSET), 2(11), 1072–1078. https://doi.org/10.4236/oalib.1111001

Orhani, S. (2024). Deep Learning in Math Education. International Journal of Research and Innovation in Social Science, 8(4), 270–278. https://dx.doi.org/10.47772/IJRISS.2024.804022

Paloloang, M. F. B., Juandi, D., Tamur, M., Paloloang, B., & Adem, A. M. G. (2020). Meta Analisis: Pengaruh Problem-Based Learning Terhadap Kemampuan Literasi Matematis Siswa di Indonesia Tujuh Tahun Terakhir. AKSIOMA: Jurnal Program Studi Pendidikan Matematika, 9(4), 851–864. https://doi.org/10.24127/ajpm.v9i4.3049

Panduwinata, B., Tuzzahra, R., Berlinda, K., & Widada, W. (2019). Analisis Kesulitan Representasi Matematika Siswa Kelas VII Sekolah Menengah Pertama pada Materi Sistem Persamaan Linier Satu Variabel. Jurnal Pendidikan Matematika Raflesia, 04(02), 202–210. https://ejournal.unib.ac.id/index.php/jpmr/article/view/9819/4855

Patmaniar, Ilyas, M., Ma’rufi, Syamsu Alam, Taufiq, Nisraeni, & A, F. (2025). Deep Learning dalam Pembelajaran Matematika. Abdimas Langkanae, 5(1), 63–71. https://doi.org/10.53769/jpm.v5i1.405

Patton, M. Q. (2002). Qualitative Research and Evaluation Methods (3rd ed.). SAGE Publications, Inc. https://doi.org/10.1177/1035719X0300300213

Ramadhan, M. I., & Aini, I. N. (2021). Analisis Kemampuan Representasi Matematis Siswa Kelas VIII dalam Menyelesaikan Soal Matematika pada Materi Bangun Ruang. JPMI: Jurnal Pembelajaran Matematika Inovatif, 4(4), 975–984. https://doi.org/10.22460/jpmi.v4i4.975-984

Ruslin, Mashuri, S., Rasak, M. S. A., Alhabsyi, F., & Syam, H. (2022). Semi-structured Interview: A Methodological Reflection on the Development of a Qualitative Research Instrument in Educational Studies. IOSR Journal of Research & Method in Education (IOSR-JRME), 12(1), 22–29. https://doi.org/10.9790%2F7388-1201052229

Sanjaya, I. I., Maharani, H. R., & Basir, M. A. (2018). Kemampuan Representasi Matematis Siswa pada Materi Lingkaran Berdasar Gaya Belajar Honey Mumfrod. Kontinu: Jurnal Penelitian Didaktik Matematika, 2(1), 72. https://doi.org/10.30659/kontinu.2.1.72-87

Sari, M. C. P., Mahmudi, M., Kristinawati, K., & Mampouw, H. L. (2023). Peningkatan Kemampuan Representasi Matematis melalui Model Problem Based Learning. PTK: Jurnal Tindakan Kelas, 4(1), 1–17. https://doi.org/10.53624/ptk.v4i1.242

Sofa, E. L., Saptanigrum, E., Khoiri, N., Kurniawan, A. F., & Ristanto, S. (2025). Effectiveness of Integrating Deep Learning into Problem-Based Learning with PhET Simulations to Enhance Students’ Problem-Solving Skills. Jurnal Pendidikan Fisika, 13(3), 416–428. https://doi.org/10.26618/ttrea958

Suparman, S., Yohannes, Y., & Arifin, N. (2021). Enhancing Mathematical Problem-Solving Skills of Indonesian Junior High School Students through Problem-Based Learning: A Systematic Review and Meta-Analysis. Al-Jabar : Jurnal Pendidikan Matematika, 12(1), 1–16. https://doi.org/10.24042/ajpm.v12i1.8036

Suwanti, & Maryati, I. (2021). Kemampuan Representasi Matematis Siswa melalui Model Problem Based Learning dan Probing Prompting Learning. Plusminus: Jurnal Pendidikan Matematika, 1(2), 303–314. https://doi.org/https://doi.org/10.31980/plusminus.v1i2.903

Villegas, J. L., Castro, E., & Gutiérrez, J. (2009). Representations in Problem Solving: A Case Study with Optimization Problems. Electronic Journal of Research in Educational Psychology, 7(1), 279–308. https://repositorio.ual.es/bitstream/handle/10835/713/Art_17_297_eng.pdf

Downloads

Published

2026-07-29

Issue

Vol. 9 No. 4 (2026): JPMI

Section

Articles

License

Creative Commons License

This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

The author is responsible for acquiring the permission(s) to reproduce any copyrighted figures, tables, data, or text that are being used in the submitted paper. Authors should note that text quotations of more than 250 words from a published or copyrighted work will require grant of permission from the original publisher to reprint. The written permission letter(s) must be submitted together with the manuscript.

Article Metrics

Abstract view : 0 times
PDF - 382 times