Fuzzy C-Means Clustering of Student Mathematical Communication Skills and Cognitive Performance and Its Association with Learning Models

Dhidhi Pambudi; Sachiko Nakano; Alfina Damayanti

doi:10.31764/jtam.v10i2.35522

Fuzzy C-Means Clustering of Student Mathematical Communication Skills and Cognitive Performance and Its Association with Learning Models

Dhidhi Pambudi, Sachiko Nakano, Alfina Damayanti

Abstract

This study applies Educational Data Mining (EDM) to examine how students’ mathematical communication skills and cognitive styles interact under different instructional contexts. A quantitative research that applies quasi-experimental design combined with EDM was employed involving 64 seventh-grade students at SMP Negeri 2 Jaten, divided into Learning Cycle 7E (LC7e) and Direct Instruction (DI) groups. The research instruments included a validated essay test for mathematical communication and the Group Embedded Figures Test (GEFT). Data were analyzed using the Fuzzy C-Means (FCM) algorithm to partition students into distinct clusters based on their cognitive-communicative attributes. The analysis resulted in a stable five-cluster model, representing progressive levels of cognitive–communicative integration. The model shows that cognitive profile predominantly creates cluster structure, whereas the Learning Cycle 7E (LC7E) model exerts a moderating influence. Students taught through LC7E were more concentrated in higher-performing clusters than those in DI classrooms. Furthermore, Field-Independent (FI) learners tended to achieve the highest communicative profiles, yet Field-Dependent (FD) learners also benefited meaningfully from LC7E activities that emphasized exploration and reflection. These results demonstrate that the LC7E model supports cognitive and communicative development across the learner spectrum, with differentiated gains linked to cognitive style. These findings highlight the utility of EDM in capturing student heterogeneity and provide a basis for educators to design adaptive learning strategies that accommodate diverse cognitive characteristics.

Keywords

Educational Data Mining; Fuzzy C-Means; Learning Cycle 7E; Mathematical Communication; Cognitive Style.

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References

Baker, R., & Siemens, G. (2014). Educational Data Mining and Learning Analytics. In The Cambridge Handbook of the Learning Sciences (pp. 253–272). Cambridge University Press. https://doi.org/10.1017/CBO9781139519526.016

Barbeiro, L., Gomes, A., Correia, F. B., & Bernardino, J. (2024). A Review of Educational Data Mining Trends. Procedia Computer Science, 237, 88–95. https://doi.org/10.1016/j.procs.2024.05.083

Bezdek, J. C., Ehrlich, R., & Full, W. (1984). FCM: The fuzzy c-means clustering algorithm. Computers & Geosciences, 10(2–3), 191–203. https://doi.org/10.1016/0098-3004(84)90020-7

Burnham, K. P., & Anderson, D. R. (Eds.). (2004). Model Selection and Multimodel Inference. Springer New York. https://doi.org/10.1007/b97636

Bybee, R. W., Taylor, J. a, Gardner, a, Scotter, P. V, Powell, J. C., Westbrook, a, & Landes, N. (2006). The BSCS 5E Instructional Model: Origins, Effectiveness, and Applications. In BSCS. https://bscs.org/wp-content/uploads/2022/01/bscs_5e_executive_summary-1.pdf

Capili, B., & Anastasi, J. K. (2024). An Introduction to Types of Quasi-Experimental Designs. AJN, American Journal of Nursing, 124(11), 50–52. https://doi.org/10.1097/01.NAJ.0001081740.74815.20

Claeskens, G., & Hjort, N. L. (2001). Model Selection and Model Averaging. Cambridge University Press. https://doi.org/10.1017/CBO9780511790485

Cramér, H. (1946). Mathematical Methods of Statistics. Princeton University Press. https://archive.org/details/in.ernet.dli.2015.223699

Eisenkraft, A. (2003). Expanding the 5E Model: A proposed 7E model emphasizes “transfer of learning” and the importance of eliciting prior understanding. The Science Teacher, 70(6), 56–59. http://www.jstor.org/stable/24156091

Gan, G., Ma, C., & Wu, J. (2007). Data Clustering: Theory, Algorithms, and Applications. Society for Industrial and Applied Mathematics. https://doi.org/10.1137/1.9780898718348

Han, Jiawei., Kamber, Micheline., & Pei, Jian. (2012). Data mining : concepts and techniques. Elsevier/Morgan Kaufmann.

Hwang, W.-Y., Chen, N.-S., Dung, J.-J., & Yang, Y.-L. (2007). Multiple Representation Skills and Creativity Effects on Mathematical Problem Solving using a Multimedia Whiteboard System. Educational Technology & Society, 10(2), 191–212. https://www.researchgate.net/publication/316239984

JASP Team. (2025). JASP (Version 0.95.3)[Computer software]. https://jasp-stats.org/

Jati, N. H. D., Budiyono, & Slamet, I. (2017). Students’ Mathematical Communication Ability using Learning Cycle 7E on Junior High School. Journal of Physics: Conference Series, 895, 012040. https://doi.org/10.1088/1742-6596/895/1/012040

Kalita, E., Oyelere, S. S., Gaftandzhieva, S., Rajesh, K. N. V. P. S., Jagatheesaperumal, S. K., Mohamed, A., Elbarawy, Y. M., Desuky, A. S., Hussain, S., Cifci, M. A., Theodorou, P., Hilčenko, S., Hazarika, J., & Ali, T. (2025). Educational data mining: a 10-year review. Discover Computing, 28(1), 81. https://doi.org/10.1007/s10791-025-09589-z

Khatib, M., & Hosseinpur, R. M. (2011). On the Validity of the Group Embedded Figure Test (GEFT). Journal of Language Teaching and Research, 2(3), 640–648. https://doi.org/10.4304/jltr.2.3.640-648

Khine, M. S. (2024). Educational Data Mining and Learning Analytics. In Artificial Intelligence in Education (pp. 1–159). Springer Nature Singapore. https://doi.org/10.1007/978-981-97-9350-1_1

Kim, H.-Y. (2017). Statistical notes for clinical researchers: Chi-squared test and Fisher’s exact test. Restorative Dentistry & Endodontics, 42(2), 152. https://doi.org/10.5395/rde.2017.42.2.152

Messick, S. (1984). The nature of cognitive styles: Problems and promise in educational practice. Educational Psychologist, 19(2), 59–74. https://doi.org/10.1080/00461528409529283

NCTM. (2000). Principles and Standards for School Mathematics. National Council of Teachers of Mathematics. https://www.nctm.org/standards-and-positions/principles-and-standards/

Nozari, A., & Siamian, H. (2015). The Relationship between Field Dependent-Independent Cognitive Style and Understanding of English Text Reading and Academic Success. Materia Socio Medica, 27(1), 39. https://doi.org/10.5455/msm.2014.27.39-41

Nurochmah, Arifin, S., & Surgandini, A. (2021). The application of learning cycle 7E model to improve a mathematics communication skills of junior high school students. AIP Conference Proceedings 2331, 020001. https://doi.org/10.1063/5.0041644

OECD. (2019). PISA 2018 Results (Volume I). OECD. https://doi.org/10.1787/5f07c754-en

Papamitsiou, Z., & Economides, A. A. (2014). Learning Analytics and Educational Data Mining in Practice: A Systematic Literature Review of Empirical Evidence. Educational Technology & Society, 17(4), 49–64. https://www.jstor.org/stable/jeductechsoci.17.4.49

Pérez-Ortega, J., Moreno-Calderón, C. F., Roblero-Aguilar, S. S., Almanza-Ortega, N. N., Frausto-Solís, J., Pazos-Rangel, R., & Martínez-Rebollar, A. (2024). Hybrid Fuzzy C-Means Clustering Algorithm, Improving Solution Quality and Reducing Computational Complexity. Axioms, 13(9), 592. https://doi.org/10.3390/axioms13090592

Rahmy, S. N., Usodo, B., & Slamet, I. (2020). Students’ mathematical communication ability using 7E learning cycle based on students thinking style. Journal of Physics: Conference Series, 1469(1), 012154. https://doi.org/10.1088/1742-6596/1469/1/012154

Riding, R., & Cheema, I. (1991). Cognitive Styles—an overview and integration. Educational Psychology, 11(3–4), 193–215. https://doi.org/10.1080/0144341910110301

Risdiana Chandra Dhewy. (2022). Pengaruh Learning Cycle 7E Terhadap Kemampuan Komunikasi Matematis Peserta didik. Jurnal Aplikasi Matematika Dan Statistik, 1(1), 21–26. https://doi.org/10.53625/jams.v1i1.3944

Romero, C., & Ventura, S. (2020). Educational data mining and learning analytics: An updated survey. WIREs Data Mining and Knowledge Discovery, 10(3), e1355. https://doi.org/10.1002/widm.1355

Siantuba, J., Nkhata, L., & de Jong, T. (2023). The impact of an online inquiry-based learning environment addressing misconceptions on students’ performance. Smart Learning Environments, 10(1), 22. https://doi.org/10.1186/s40561-023-00236-y

Singh, J., & Singh, D. (2024). A comprehensive review of clustering techniques in artificial intelligence for knowledge discovery: Taxonomy, challenges, applications and future prospects. Advanced Engineering Informatics, 62, 102799. https://doi.org/10.1016/j.aei.2024.102799

Tinajero, C., & Páramo, M. F. (1997). Field dependence‐independence and academic achievement: a re‐examination of their relationship. British Journal of Educational Psychology, 67(2), 199–212. https://doi.org/10.1111/j.2044-8279.1997.tb01237.x

Wani, A. A. (2024). Comprehensive analysis of clustering algorithms: exploring limitations and innovative solutions. PeerJ Computer Science, 10, e2286. https://doi.org/10.7717/peerj-cs.2286

Witkin, H. A., Moore, C. A., Goodenough, D., & Cox, P. W. (1977). Field-Dependent and Field-Independent Cognitive Styles and Their Educational Implications. Review of Educational Research, 47(1), 1–64. https://doi.org/10.3102/00346543047001001

Zhang, J., Yang, Y., & Ding, J. (2023). Information criteria for model selection. WIREs Computational Statistics, 15(5), e1607. https://doi.org/10.1002/wics.1607

Zhang, L., & Sternberg, R. J. (2005). A Threefold Model of Intellectual Styles. Educational Psychology Review, 17(1), 1–53. https://doi.org/10.1007/s10648-005-1635-4

DOI: https://doi.org/10.31764/jtam.v10i2.35522