INTEGRATING SYMPY INTO COLLABORATIVE LEARNING FOR PARTIAL FRACTIONS AND INTEGRATION: A QUALITATIVE STUDY IN CALCULUS
Abstract
This qualitative classroom study explores how collaborative learning (CL) supported by Python (SymPy) can strengthen university students’ understanding of partial fraction decomposition and its application to integration. Thirty‑two second‑year mathematics majors participated in four weekly sessions that blended manual problem solving with computational checking. Students worked in six small groups with defined roles (problem solver, coder, recorder, presenter), engaged in real‑world tasks (e.g., economic growth, fluid flow, and motion analysis), kept reflective journals, and delivered group presentations evaluated with an analytic rubric. Data sources comprised observations, journals, and presentation assessments. Thematic analysis indicates improved participation, clearer conceptual linking between algebraic manipulation and integral calculus, and more systematic error‑checking when Python was used to validate manual work. Groups demonstrating stronger within‑group communication tended to employ Python more effectively and reached higher rubric scores. The study discusses practical design choices for CL tasks that combine traditional and computational approaches, and reflects on limitations such as heterogeneous prior programming experience and the absence of pre–post achievement testing. Implications for practice include structuri
References
Adigun, A., Osofisan, O., Robert, B., & Kolawole, M. (2021). The Development of Adaptive Collaboration in a Dynamic Environment for Information Sharing. Current Topics on Mathematics and Computer Science Vol. 4, 134-141. https://doi.org/10.9734/bpi/ctmcs/v4/11931D
Akilandeswari, V., Kumar, A., Freeda, A., & Kumar, S. (2015). Elements of Effective Communication. New Media and Mass Communication, 37, 44–47.
Biktagirova, G. F., & Kasimova, R. S. (2017). Communicative abilites and their formation at primary school children. Modern Journal of Language Teaching Methods, 7(3), 597.
Boye, T. (2019). The collaborative classroom in computing higher education. Proceedings of the 2019 ACM Conference on International Computing Education Research, https://doi.org/10.1145/3291279.3339436
Callo, E. M. E., & Ubayubay, R. M. (2024). Perceptions of peer coaching technique by the alternative learning system community implementer. International Journal of Research Publications, 144(1), 29-49. https://doi.org/10.47119/IJRP1001441320246138
de Oliveira Santos, F. A. (2018). A tool for assisted correction of programming exercises in Java based in computational reflection. Journal on Computational Thinking (JCThink), 2(1), 51-51. https://doi.org/10.14210/jcthink.v2.n1.p51
Faniyi, A. O. (2023). Enhancing student academic performance through educational testing and measurement. Edumania-An International Multidisciplinary Journal, 1(2), 162-171. https://doi.org/10.59231/edumania/8981
Flynn, D., Hughes, J., & Robb, J. (2023). Improving Mathematics Learning Through Computational Participation. Journal Of Educational Informatics, 4(1). https://doi.org/10.51357/jei.v4i1.214
Gorjão, L. R., Hassan, G., Kurths, J., & Witthaut, D. (2022). MFDFA: Efficient multifractal detrended fluctuation analysis in python. Computer Physics Communications, 273, 108254. https://doi.org/10.1016/j.cpc.2021.108254
Goswami, L., Zeinoddin, P. S., Estier, T., & Cherubini, M. (2023). Supporting Collaboration in Introductory Programming Classes Taught in Hybrid Mode: A Participatory Design Study. Proceedings of the 2023 ACM Designing Interactive Systems Conference, https://doi.org/10.1145/3563657.3596042
He, S., Shi, X., Choi, T.-H., & Zhai, J. (2023). How do students' roles in collaborative learning affect collaborative problem-solving competency? A systematic review of research. Thinking Skills and Creativity, 50, 101423. https://doi.org/10.1016/j.tsc.2023.101423
Hsu, T.-C., Chang, S.-C., & Hung, Y.-T. (2018). How to learn and how to teach computational thinking: Suggestions based on a review of the literature. Computers & Education, 126, 296-310. https://doi.org/10.1016/j.compedu.2018.07.004
Jahara, A., & Daulay, N. (2023). Solution-focused group counseling: A solution to enhance students’ self-confidence. KONSELI: Jurnal Bimbingan dan Konseling (E-Journal), 10(1), 59-64. https://doi.org/10.24042/kons.v10i1.16606
Joglar, C., & Rojas, S. (2019). Overcoming obstacles to the formulation and use of questions in the science classroom: Analysis from a teacher reflection workshop. Research in Science Education, 49(4), 1125-1139. https://doi.org/10.1007/s11165-019-9857-5
Johnson, D. W., & Johnson, R. T. (2015). Theoretical approaches to cooperative learning. Collaborative learning: Developments in research and practice, 17-46.
Kamalov, F., Santandreu, D., Leung, H. H., Johnson, J., & El Khatib, Z. (2023). Leveraging computer algebra systems in calculus: A case study with SymPy. 2023 IEEE Global Engineering Education Conference (EDUCON), https://doi.org/10.1109/EDUCON54358.2023.10125108
Kazeni, M., & McNaught, C. (2020). Using Group Discussion and Reflection for Developing Student Teacher Autonomy. International Journal of Work-Integrated Learning, 21(1), 1-12.
Kharitonenko, L. (2022). Innovations and traditions in Ukrainian language teaching at the educational establishments of Ukraine: cases, models of the future. Futurity Education, 2(1), 68-85. https://doi.org/10.57125/FED.2022.25.03.7
Kumar, I., & Mohd, N. (2024). Ways of Using Computational Thinking to Improve Students' Ability to Think Critically. In Infrastructure Possibilities and Human-Centered Approaches With Industry 5.0 (pp. 253-266). IGI Global Scientific Publishing. https://doi.org/10.4018/978-1-6684-9591-2.ch013
Kynigos, C., & Diamantidis, D. (2022). Creativity in engineering mathematical models through programming. ZDM–Mathematics Education, 54(1), 149-162. https://doi.org/10.1007/s11858-021-01314-6
Landau, R. H., Páez, M. J., & Bordeianu, C. C. (2024). Computational physics: Problem solving with Python. John Wiley & Sons.
Li, G., Liu, X., & Hou, J. (2023). Research on the teaching model of interdisciplinary computational thinking cultivating from the perspective of problem-solving. International Conference on Computer Science and Educational Informatization, https://doi.org/10.1007/978-981-99-9499-1_36
Martínez-Venegas, L. (2022). Towards a Collaborative Learning Framework for D-learning based on improving the teamwork skills of adolescents. Avances en Interacción Humano-Computadora, 7(1), 33-36.
Moreland, R. L., & Levine, J. M. (2014). Socialization in organizations and work groups. In Groups at work (pp. 69-112). Psychology Press.
Muller, M., Fussell, S. R., Gao, G., Hinds, P. J., Oliveira, N., Reinecke, K., Robert Jr, L., Siangliulue, K., Wulf, V., & Yuan, C.-W. (2019). Learning from team and group diversity: Nurturing and benefiting from our heterogeneity. Companion Publication of the 2019 Conference on Computer Supported Cooperative Work and Social Computing, https://doi.org/10.1145/3311957.3359440
Nagar, S. (2017). Introduction to Python for Engineers and Scientists: Open Source Solutions for Numerical Computation. Apress. https://doi.org/10.1007/978-1-4842-3204-0
O'Reilly, C. (2021). Reflection on practice: an exploration of a virtual online collaboration as preparation for the year abroad. https://doi.org/10.21827/jve.4.35781
Perez, M., & Bresciani, S. (2015). The role of visual templates on improving teamwork performance. 2015 19th International Conference on Information Visualisation, https://doi.org/10.1109/IV.2015.66
Putri, S. W., Almufidah, A., & Gusmaneli, G. (2024). Strategi pembelajaran berbasis masalah dalam meningkatkan kemampuan problem solving peserta didik. Jurnal Kajian Penelitian Pendidikan dan Kebudayaan, 2(2), 179-187. https://doi.org/10.59031/jkppk.v2i2.401
Rania, N., Coppola, I., & Pinna, L. (2021). Reflective practices to study group dynamics: Implement empowerment and understand the functioning of groups. Frontiers in Psychology, 12, 786754. https://doi.org/10.3389/fpsyg.2021.786754
Rudawska, A. (2017). Students’ team project experiences and their attitudes towards teamwork. Central European Management Journal, 25(1), 78-97. https://doi.org/10.7206/jmba.ce.2450-7814.190
Serçe, F. C., Alpaslan, F. N., Swigger, K., Brazile, R., Dafoulas, G., & Lopez, V. (2010). Strategies and guidelines for building effective distributed learning teams in higher education. 2010 9th International Conference on Information Technology Based Higher Education and Training (ITHET),
Smirnova, Z. V., Vaganova, O. L., Frolova, N. V., Ogorodova, M. V., & Rozarenov, V. V. (2018). Modern Means and Technologies for Estimation of Results of Training. SHS Web of Conferences, https://doi.org/10.1051/shsconf/20185001174
Uğurlu, C. T., & Şemin, F. K. (2020). Peaceful solution of conflicts in schools. In Empowering multiculturalism and peacebuilding in schools (pp. 198-224). IGI Global. https://doi.org/10.4018/978-1-7998-2827-3.ch009
Wayesa, N. N. (2020). Research on: Improving Students Group Discussion Skill in Mathematics Class. Science, 8(4), 9499. https://doi.org/10.11648/j.sjedu.20200804.11
Xhaferi, B., & Xhaferi, G. (2017). Enhancing learning through reflection–A case study of SEEU. Seeu Review, 12(1), 53-68. https://doi.org/10.1515/seeur-2017-0004
Zhang, Y. (2019). Fostering Practical Developers in Computer Science Classrooms: A PBL Approach. In Global Perspectives on Fostering Problem-Based Learning in Chinese Universities (pp. 55-87). IGI Global.
Zhu, J.-M., & Luo, Q.-M. (2023). Partial-fraction decomposition of a rational function and its application. Advances in Continuous and Discrete Models, 2023(1), 1. https://doi.org/10.1186/s13662-022-03734-4
Abstract views: 168
PDF downloads: 97
