Grouping Students' Learning Outcomes on Questions regarding Exponents and Roots through the K-Means Approach Utilizing Unsupervised Learning

Ruth Helen Simarmata; Esterlina Esterlina; Danny Matthew Saputra

doi:10.33541/edumatsains.v11i2.8784

Authors

Ruth Helen Simarmata Universitas Sriwijaya
Esterlina Esterlina Universitas Pendidikan Indonesia
Danny Matthew Saputra Universitas Sriwijaya

DOI:

https://doi.org/10.33541/edumatsains.v11i2.8784

Keywords:

Student Assessment Analysis, Principal Component Analysis, K- Means Clustering, Exponent and Roots

Abstract

This study aims to explore patterns of student academic performance specifically about questions on exponents and roots using K-Means clustering and Principal Component Analysis (PCA). An exploratory quantitative method was employed, using data from a final mathematics examination involving 100 ninth-grade students and 10 questions. Twenty students who gave no answers were excluded from the analysis, leaving 80 students for the clustering process. The function of K- means in this research were defined students on the same group with same categorize with similarities responses. PCA was used for dimensionality and visualize for reduce data distribution groups that found. The analysis revealed two distinct groups where 75 students in the primary group scored a mean of 7.36 while 23 students in the secondary group scored a mean of 3.12. The highest silhouette score from these two different groups is 0,3128 that shows different significant patterns that seen. PCA results showed that primary and secondary principal components accounted for 42.70% and 14.89% of the variance with a cumulative explained variance of 57.58%. K-Means grouping effectively shows variations on these findings based on students’ responses with exponents and roots question. However, the diverse for the result between grouping that was written down, some overlap shows that the patterns are not entirely separate. These clustering results can serve as a basis for more detailed diagnostic investigations into how students respond to mathematical problem-solving.

References

Alaoui, G. M., Zouhair, A., & Khabbachi, I. (2026). Students’ performance clustering for future personalized in learning virtual reality. International Journal of Electrical and Computer Engineering (IJECE), 16(1), 297. https://doi.org/10.11591/ijece.v16i1.pp297-310

Alvarez-Garcia, M., Arenas-Parra, M., & Ibar-Alonso, R. (2024). Uncovering student profiles. An explainable cluster analysis approach to PISA 2022. Computers and Education, 223. https://doi.org/10.1016/j.compedu.2024.105166

Azmi, M. F., Abidin, D. Z., & Jasmir, J. (2026). K-Means Clustering with Elbow Method and Validity Indices for Classifying Student Academic Achievement Based on Knowledge Scores at SDN 48 Kota Jambi. Jurnal Teknik Informatika (Jutif), 7(1), 571–586. https://doi.org/10.52436/1.jutif.2026.7.1.5349

Christian, H., Friansa, K., Pradipta, J., Haq, I. N., & Leksono, E. (2024). Comparasion of HVAC Energy Consumption Prediction in an Academic Building using LSTM and DNN. Jurnal Ecotipe (Electronic, Control, Telecommunication, Information, and Power Engineering), 11(1), 77–87. https://doi.org/10.33019/jurnalecotipe.v11i1.4488

Christian, H., Pradipta, J., Haq, I. N., Hanadi, Friansa, K., Leksono, E., & Esterlina. (2024). Reliability Evaluation of Advanced Metering Infrastructure Based on Isolation Forest Anomalies Detection. International Conference on Artificial Intelligence and Mechatronics System, AIMS 2024. https://doi.org/10.1109/AIMS61812.2024.10512537

Farha, I., Nola Febriana Saputri, Melati Elvita, Andri Azmul Fauzi, & Fidia Deny Tisna Amijaya. (2024). Klasterisasi Potensi Mahasiswa Program Studi Matematika Universitas Mulawarman Menggunakan Metode K-Means Untuk Menyaring Mahasiswa Berprestasi. MILANG Journal of Mathematics and Its Applications, 20(2), 89–99. https://doi.org/10.29244/milang.20.2.89-99

Feng, G. , & F. M. (2024). Research on learning behavior patterns from the perspective of educational data mining: Evaluation, prediction and visualization. Elsevier, 237.

Harahap, A. A., Raihan, M., Amani, N., & Andini, R. (2023). SENTIMAS: Seminar Nasional Penelitian dan Pengabdian Masyarakat Comparison of Unsupervised Learning Techniques for Clustering Data on the Number of Villages in Indonesia Perbandingan Teknik Unsupervised Learning untuk Pengelompokan Data Jumlah Desa Di Indonesia. https://journal.irpi.or.id/index.php/sentimas

Hilyawan, F. R., Syafrullah, M., & Sudija, I. (2025). A Systematic Literature Review on the Optimization of K-Means and Agglomerative Clustering for Student Performance Segmentation: A Comparative Analysis of Elbow and Silhouette Methods. Edcomtech: Jurnal Kajian Teknologi Pendidikan, 10(1), 73–88. https://doi.org/10.17977/um039v10i12025p73-88

Ilonga, H. K., & Chirimbana, M. (2024). Iilonga, H. K., & Chirimbana, M. (2024).

Ke Ting, C., Ibrahim, N., Huspi, S. H., & Wan Kadir, W. M. N. (2024). Multidimensional Context Clustering to Analyse Student Engagement in Online Learning Environment. International Journal of Innovative Computing, 14(2), 89–96. https://doi.org/10.11113/ijic.v14n2.487

Kenney, S., & Ntow, F. D. (2024). Unveiling the Errors Learners Make When Solving Word Problems Involving Algebraic Task. SAGE Open, 14(4). https://doi.org/10.1177/21582440241299245

Liawati, Huda, N., & Marzal, J. (2026). Analyzing Students’ Thinking Processes in Solving Exponential Problems Based on APOS Theory: A Qualitative Study at SMA Negeri 7 Tanjung Jabung Timur. 10(4), 69–81. https://doi.org/10.33541/edumats

Mahdy, I. F., Haqqi, M. W. N., & Oktiardi, R. N. (2025). Comparative Study Of Clustering Algorithm To Determine Student Profiles Based On Academic Ability. VARIANCE: Journal of Statistics and Its Applications, 7(2), 231–240. https://doi.org/10.30598/variancevol7iss2page231-240

Medina-Gual, L., Medina-Velázquez, L., & Parejo, J.-L. (2025). A tridimensional model of AI literacy: An empirical analysis of student performance and demographic patterns in higher education. In Australasian Journal of Educational Technology (Vol. 2025, Number 5).

Octaria, E. A., Ridwan, R., & Saputra, H. (2026). Pemetaan Kemampuan Matematis Peserta International Kangaroo Mathematics Contest Menggunakan K-Means Clustering. JPG: Jurnal Pendidikan Guru Journal, 6(1), 64–75. https://ejournal.uika-bogor.ac.id/index.php/jpg/index

Pilgrim, M. E., Burks, L. C., Ryals, M., & Hill-Lindsay, S. (2025). College algebra students’ perceptions of exam errors and the problem-solving process. Frontiers in Education, 10. https://doi.org/10.3389/feduc.2025.1359713

Rahma, F. (2025). Clustering Students Based on Academic Performance and Social Factors: An Unsupervised Learning Approach to Identify Student Patterns. International Journal for Applied Information Management, 5(3), 139–154. https://doi.org/10.47738/ijaim.v5i3.109

Sabrina Rochadi, Z., & Ridwan Yudhanegara, M. (2024). Jurnal Didactical Mathematics Analisis Cluster untuk Hubungan antara Kemampuan Pemahaman Konsep dan Kemampuan Pemecahan Masalah Matematis Siswa Menggunakan K-Means Clustering (Vol. 6, Number 1). https://ejournal.unma.ac.id/index.php/dm

Şenay, Ş. C. (2024). Analysis of Misconceptions and Errors Regarding Exponential and Radical Expressions Through the Theory of Reducing Abstraction. Research on Education and Psychology, 8(2), 281–295. https://doi.org/10.54535/rep.1520588

Shimizu, Y., & Kang, H. (2025). Research on classroom practice and students’ errors in mathematics education: a scoping review of recent developments for 2018-2023. ZDM - Mathematics Education, 57(4), 695–710. https://doi.org/10.1007/s11858-025-01704-0

Sujana, T., Astuti, R., Prihartono, W., & Hamonangan, R. (2025). Journal of Artificial Intelligence and Engineering Applications Implementation of Data Mining Using the K-Means Algorithm to Group Students Based on Academic Performance (Vol. 4, Number 2). https://ioinformatic.org/

Sulaiman, H., Saepul Rohman, R., Wintana, D., & Abdul Ghani, M. (2025). Analyzing Students’ Interest in Mathematics Through the Implementation of the K-Means Clustering Algorithm. Journal of Information and Technology) Accredited Sinta, 4.

Uddin, S., & Lu, H. (2024). Dataset meta-level and statistical features affect machine learning performance. Scientific Reports, 14(1). https://doi.org/10.1038/s41598-024-51825-x

Wu, M. (2026). ICCK Transactions on Educational Data Mining K-Means Clustering-Based Feature Generation for Student Performance Prediction. 2(1). https://doi.org/10.62762/TEDM.2026.716076

Yuting Tan, & Tao Yang. (2026). Cognitive process grouping on students’ mathematical creative problem solving: Evidence from clustering analysis, lag sequence analysis, and hidden Markov model. Elsevier, 252.