Investigation of the Mathematical Proof Ability of Prospective Teacher Students Through Cooperative Learning Approach

Authors

  • Nila Kesumawati Universitas PGRI Palembang
  • Lusiana Lusiana Universitas PGRI Palembang
  • Nyiayu Fahriza Fuadiah Universitas PGRI Palembang

DOI:

https://doi.org/10.22437/edumatica.v16i1.43191

Keywords:

ability level, cooperative learning , higher education, mathematical proof, student teacher candidates

Abstract

The research investigates pre-service teachers’ ability to create mathematical proofs through cooperative learning, as this skill becomes essential in university mathematics education. The research used a mixed-methods survey design to study 24 students who attended the Mathematics Education program at Universitas PGRI Palembang. Data was collected by a questionnaire, a mathematical proof test, and in-depth interviews. Data analysed descriptively. The results showed that most students were in the medium category of mathematical proof ability using a cooperative learning approach, with smaller proportions in the high and low categories. The investigation concluded that students with high mathematical proof ability demonstrated the ability to implement the five Mathematical Proof Indicators (IPMs) in constructing logical and systematic arguments and using mathematical representations appropriately. Students with moderate mathematical proof ability had difficulty with IPMc (third IPM) and IPMd (fourth IPM), while students with low mathematical proof ability had difficulty with almost all IPMs. The analysis of the investigation results indicates that strategies for conducting mathematical proofs require cooperative learning support to facilitate understanding of the concepts required for proofs and collaboration, and recommends its application in mathematics learning in higher education.

Downloads

Download data is not yet available.

References

Afrison, J. (2022). Penanaman Nilai-Nilai Dalam Tari Jalur Melalui Pendekatan Cooperative Learning Untuk Meningkatkan Kerjasama Siswa Kelas X Di Skm Negeri 2 Teluk Kuantan Provinsi Riau. UPI.

Ahmed, S., Shehata, M., & Hassanien, M. (2020). Emerging Faculty Needs for Enhancing Student Engagement on a Virtual Platform. MedEdPublish, 9, 75. https://doi.org/10.15694/mep.2020.000075.1

Aisyah, N., Susanti, E., Meryansumayeka, Siswono, T. Y. E., & Maat, S. M. (2023). Proving Geometry Theorems: Student Prospective Teachers’ Perseverance and Mathematical Reasoning. Infinity Journal, 12(2), 377–392. https://doi.org/10.22460/infinity.v12i2.p377-392

Alcalá, D. H., Garijo, A. H., Pérez-Pueyo, Á., & Fernández-Río, J. (2019). Cooperative Learning and Students’ Motivation, Social Interactions and Attitudes: Perspectives from Two Different Educational Stages. Sustainability (Switzerland), 11(24). https://doi.org/10.3390/su11247005

Almpani, S., & Stefaneas, P. (2023). Bridging Informal Reasoning and Formal Proving: The Role of Argumentation in Proof-Events. Foundations of Science, 30(1), 201–225. https://doi.org/10.1007/s10699-023-09926-9

Anwar, L., Goedhart, M. J., & Mali, A. (2023). Learning trajectory of geometry proof construction Learning trajectory of geometry proof construction : Studying the emerging understanding of the structure of Euclidean proof. 7–11. https://doi.org/10.29333/ejmste/13160

Aziz, T. A. (2021). Eksplorasi Justifikasi dan Rasionalisasi Mahasiswa dalam Konsep Teori Graf. Jurnal Pendidikan Matematika Raflesia, 06(02), 40–54.

Baugerud, G. A., Johnson, M. S., Dianiska, R., Røed, R. K., Powell, M. B., Lamb, M. E., Hassan, S. Z., Sabet, S. S., Hicks, S., Salehi, P., Riegler, M. A., Halvorsen, P., & Quas, J. (2025). Using an AI-based avatar for interviewer training at Children’s Advocacy Centres: Proof of Concept. Child Maltreatment, 30(2), 242–252. https://doi.org/10.1177/10775595241263017

Carl, M., Cramer, M., Fisseni, B., Sarikaya, D., & Schröder, B. (2021). How to Frame Understanding in Mathematics: A Case Study Using Extremal Proofs. Axiomathes, 31(5), 649–676. https://doi.org/10.1007/s10516-021-09552-9

Eslit, E. R. (2023). Effects of Cooperative Learning on Student Achievement: A Meta-Analysis of Randomized Controlled Trials. April.

Firmasari, S., Herman, T., Firdaus, E. F., Swadaya, U., Djati, G., Indonesia, U. P., & Peradaban, U. (2022). K r e a n o. 13(2), 246–256. https://doi.org/https://doi.org/10.15294/kreano.v13i2

Flaherty, H. B. (2022). Using Collaborative Group Learning Principles to Foster Community in Online Classrooms. Journal of Teaching in Social Work, 42(1), 31–44. https://doi.org/10.1080/08841233.2021.2013390

Hamami, Y., & Morris, R. L. (2024). Understanding in mathematics: The case of mathematical proofs. Nous, 58(4), 1073–1106. https://doi.org/10.1111/nous.12489

Hartono, S. (2025). Evolving trends in mathematical proof research in Indonesian mathematics education: A systematic review from design to data analysis. Multidisciplinary Reviews, 10(| Accepted Articles), 70–88. https://malque.pub/ojs/index.php/mr/article/view/8409

Himmah, W. I. (2022). The Ability of Proof Using Mathematics Induction Through Cooperative Learning Type Team Assisted Individualization. 6(2), 19–27.

Imjai, N., Aujirapongpan, S., & Yaacob, Z. (2024). Impact of logical thinking skills and digital literacy on Thailand’s generation Z accounting students’ internship effectiveness: Role of self-learning capability. International Journal of Educational Research Open, 6(January), 100329. https://doi.org/10.1016/j.ijedro.2024.100329

Ko, Y.-Y. & Rose, M. K. (2022). Considering Proofs: Pre-Service Secondary Mathematics Teachers’ Criteria for Self-Constructed and Student-Generated Arguments. The Journal of Mathematical Behaviour, 68. https://doi.org/https://doi.org/10.1016/j.jmathb.2022.100999

Lusiana, & Kesumawati, N. (2023). Mathematical proving as a way to improve understanding the concepts of integral calculus application in digital era. AIP Conference Proceedings, 2811(1). https://doi.org/10.1063/5.0142759

Mendo-Lázaro, S., León-del-Barco, B., Polo-del-Río, M. I., & López-Ramos, V. M. (2022). The Impact of Cooperative Learning on University Students’ Academic Goals. Frontiers in Psychology, 12(January), 1–7. https://doi.org/10.3389/fpsyg.2021.787210

Mohammed Alharbi, S., Ibrahim Elfeky, A., & Sultan Ahmed, E. (2022). The Effect of E-Collaborative Learning Environment on Development of Critical Thinking and Higher Order Thinking Skills. Journal of Positive School Psychology, 2022(6), 6848–6854. http://journalppw.com

Mujib, A., & Firmansyah. (2022). Improvement habits of minds in constructing mathematical proof using DNR-model. AIP Conference Proceedings, 2577(1). https://doi.org/https://doi.org/10.1063/5.0096095

Ndebil, M. B., & Ali, C. A. (2024). Cooperative learning as a strategy of improving mathematics performance and attitudes. International Journal of Educational Innovation and Research, 3(1), 62–74. https://doi.org/10.31949/ijeir.v3i1.7163

Nurlaila. (2019). Pengembangan Model Cooperative Learning. Jurnal Ilmu Tarbiyah Dan Keguruan, 22(2), 213–22.

Nurrahmah, A., & Karim, A. (2018). Analisis Kemampuan Pembuktian Matematis Pada Matakuliah Teori Bilangan. JURNAL E-DuMath, 4(2), 21. https://doi.org/10.26638/je.753.2064

Pangantihon, A. L. D., & Tantiado, R. C. (2024). Cooperative Learning Strategies and Students ’ Well -being. 07(06), 2732–2745. https://doi.org/10.47191/ijmra/v7-i06-41

Poggiolesi, F., & Genco, F. A. (2021). Conceptual ( and hence mathematical ) explanation , conceptual grounding and proof.

Rahmawati, F. A., & Purwaningrum, J. P. (2022). Penerapan Teori Vygotsky dalam Pembelajaran Matematika. Jurnal Riset Pembelajaran Matematika, 4(1), 1–4. https://doi.org/10.55719/jrpm.v4i1.349

Ruijuan, L., Srikhoa, S., & Jantharajit, N. (2023). Blending of collaborative and active learning instructional methods to improve academic performance and self-motivation of vocational students. Asian Journal of Education and Training, 9(4), 130–135. https://doi.org/10.20448/edu.v9i4.5211

Rukmini, D., & Rahardjo, W. (2021). The effect of cooperative learning on students’ mathematical proof skills. International Journal of Instruction, 14(3), 205–220. https://doi.org/https://doi.org/10.29333/iji.2021.14313a

S. Kaymak, Zh.Kassymbek, A. Kalamkas, & F. Saydenov. (2021). The Effect of Cooperative Learning on Students Academic Achievement. Management Studies, 9(6). https://doi.org/10.17265/2328-2185/2021.06.009

Schwartz, N. H., Click, K., & Bartel, A. N. (2022). Educational Psychology: Learning and Instruction (Issue May). https://doi.org/10.1007/978-3-030-28745-0_67

Silva, H., Lopes, J., Morais, E., & Dominguez, C. (2023). Fostering Critical and Creative Thinking through the Cooperative Learning Jigsaw and Group Investigation. International Journal of Instruction, 16(3), 261–282. https://doi.org/10.29333/iji.2023.16315a

Simelane, B., & Engelbrecht, J. (2023). Measuring the Mathematical Maturity of Students in an Academic Development Programme. International Journal of Research in Undergraduate Mathematics Education, 10, 1–30. https://doi.org/10.1007/s40753-023-00222-2

Stylianides, A. J., & Stylianides, G. J. (2022). Introducing students and prospective teachers to the notion of proof in mathematics. Journal of Mathematical Behavior, 66(April), 100957. https://doi.org/10.1016/j.jmathb.2022.100957

Stylianides, G. J., Stylianides, A. J., & Moutsios-Rentzos, A. (2024). Proof and proving in school and university mathematics education research: a systematic review. ZDM - Mathematics Education, 56(1), 47–59. https://doi.org/10.1007/s11858-023-01518-y

Sümmermann, M. L., Sommerhoff, D., & Rott, B. (2021). Mathematics in the Digital Age: The Case of Simulation-Based Proofs. International Journal of Research in Undergraduate Mathematics Education, 7(3), 438–465. https://doi.org/10.1007/s40753-020-00125-6

Tupouniua, J. G. (2022). Differentiating between counterexamples for supporting students’ algorithmic thinking. Asian Journal for Mathematics Education, 1(4), 475–493. https://doi.org/10.1177/27527263221139869

Wattanawongwan, S., Smith, S. D., & Vannest, K. J. (2021). Cooperative Learning Strategies for Building Relationship Skills in Students With Emotional and Behavioral Disorders. Beyond Behavior, 30(1), 32–40. https://doi.org/https://doi.org/10.1177/1074295621997599

Winer, M. L., & Battista, M. T. (2022). Investigating Students’ Proof Reasoning: Analyzing Students’ Oral Proof Explanations and their Written Proofs in High School Geometry. International Electronic Journal of Mathematics Education, 17(2), em0677. https://doi.org/10.29333/iejme/11713

Yudha, S. I. D., Qohar, A., & Sisworo, S. (2024). Metakognisi Mahasiswa Dalam Menyelesaikan Masalah Pembuktian Matematis. SJME (Supremum Journal of Mathematics Education), 8(2), 253–263. https://doi.org/10.35706/sjme.v8i2.10964

Zazkis, R., & Zaskis, D. (2014). Script writing in the mathematics classroom : Imaginary conversations on the structure of numbers. https://doi.org/10.1080/14794802.2013.876157

Downloads

Published

2026-01-18

How to Cite

Kesumawati, N., Lusiana, L., & Fuadiah, N. F. (2026). Investigation of the Mathematical Proof Ability of Prospective Teacher Students Through Cooperative Learning Approach. Edumatica : Jurnal Pendidikan Matematika, 16(1), 1–18. https://doi.org/10.22437/edumatica.v16i1.43191