Assessing course difficulty and student performance using bayesian networks
EDN: VUGPPL
Abstract
This article proposes an approach to jointly assessing course difficulty and student performance based on Bayesian networks. Unlike traditional methods based solely on GPA or the number of credits, this approach takes into account both objective and subjective factors influencing course difficulty and individual student performance. Using Bayesian methods allows for the integration of prior information (e.g., placement test results or historical course data) and updating assessments based on observed learning outcomes, ensuring transparency and interpretability of findings. This method not only facilitates a more equitable ranking of students based on the difficulty of the courses they complete but also identifies teaching characteristics associated with specific instructors or educational institutions, which can be useful for analyzing the quality of the educational process and its subsequent optimization.
Keywords
Supporting agencies: Mathematical Center in Akademgorodok under the agreement No. 075-15-2025-348 with the Ministry of Science and Higher Education of the Russian Federation.
About the Authors
E. V. Efremov
Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
Russian Federation
Russian Federation
Egor V. Efremov, Postgraduate Student, Research Intern
Novosibirsk
A. V. Logachev
Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
Russian Federation
Russian Federation
Artem V. Logachev, Candidate of Sciences (Physics and Mathematics), Associate Professor, Senior Research Fellow
Novosibirsk
V. I. Nikitina
Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
Russian Federation
Russian Federation
Vitalina I. Nikitina, Postgraduate Student, Research Intern
Novosibirsk
E. I. Prokopenko
Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
Russian Federation
Russian Federation
Evgeny I. Prokopenko, Candidate of Sciences (Physics and Mathematics), Associate Professor, Senior Researcher
Novosibirsk
M. D. Tokareva
Novosibirsk National Research State University
Russian Federation
Russian Federation
Maria D. Tokareva, Junior Specialist
Novosibirsk
References
1. Kostromitina M., Naismith B., Burstein J., Plonsky L. Beyond GPA and language proficiency: A systematic literature review of international students’ academic success factors, Review of Education, 2025, vol. 13, no. 2. DOI: 10.1002/rev3.70089. Available at: https://bera-journals.onlinelibrary.wiley.com/doi/abs/10.1002/rev3.70089
2. Marin Y.R., Huatangari L.Q., Tuesta J.N.A. et al. Analysis of factors affecting the academic performance of university students using machine learning, Scientific Reports, 2025, vol. 15, no. 1. DOI: 10.1038/s41598-025-28870-1.
3. Rochev K.V., Kudelin A.G. Problemy prognozirovaniya uspevaemosti studentov: vzaimosvyaz' rezul'tatov EGEh i akademicheskih uspehov [Problems of Predicting Student Academic Performance: Corelation Between Unified State Exam Results and Academic Success], Psihologicheskaya nauka i obrazovanie [Psychology and Education], 2025, vol. 30, no. 1, pp. 158–170. DOI: 10.17759/pse.2025300112
4. Hoffman H.J., Elmi A.F. Comparing Student Performance in a Graduate-Level Introductory Biostatistics Course Using an Online versus a Traditional in-Person Learning Environment, Journal of Statistics and Data Science Education, 2021, vol. 29, no. 1, pp. 105–114. DOI: 10.1080/10691898.2020.1841592.
5. Pumpuang P., Srivihok A., Praneetpolgrang P. Comparisons of classifier algorithms: Bayesian network, C4.5, decision forest and NBTree for Course Registration Planning model of undergraduate students, IEEE International Conference on Systems,ь Man and Cybernetics, 2008, pp. 3647–3651. DOI: 10.1109/ICSMC.2008.4811865. Available at: https://ieeexplore.ieee.org/document/4811865/
6. Pumpuang P., Srivihok A., Praneetpolgrang P., Numprasertchai S. Using Bayesian Network for Planning Course Registration Model for Undergraduate students, Second IEEE International Conference on Digital Ecosystems and Technologies, 2008, pp. 492–496. DOI: 10.1109/DEST.2008.4635194. Available at: https://ieeexplore.ieee.org/document/4635194/
7. Premalatha M., Viswanathan V. Course Sequence Recommendation with Course Difficulty Index Using Subset Sum Approximation Algorithms, Cybernetics and Information Technologies, 2019, vol. 19, no. 3, pp. 25–44. DOI: 10.2478/cait-2019-0024
8. Swart A.J. Evaluation of Final Examination Papers in Engineering: A Case Study Using Bloom’s Taxonomy, Journals & Magazines >IEEE Transactions on Education, 2010, vol. 53, iss. 2, pp. 257–264. DOI: 10.1109/TE.2009.2014221
9. Goodarzi M.H., Amiri A. Evaluating Students’ Learning Progress by Using Fuzzy Inference System, Sixth International Conference on Fuzzy Systems and Knowledge Discovery, 2009, vol. 3, pp. 561–565. DOI: 10.1109/FSKD.2009.313
10. Hernandez A., Herrera-Flores B., Tomas D., Navarro-Colorado B. A Systematic Review of Deep Learning Approaches to Educational Data Mining, Complexity, 2019, pp. 1–22. DOI: 10.1155/2019/1306039
11. Nawang H., Makhtar M., Fazamin A. A systematic literature review on student performance predictions, International Journal of Advanced Technology and Engineering Exploration, 2021, vol. 8. DOI: 10.19101/IJATEE.2021.874521
12. Thaker K., Huang Y., Brusilovsky P., He D. Dynamic Knowledge Modeling with Heterogeneous Activities for Adaptive Textbooks, The 11<sup>th</sup> International Conference on Educational Data Mining, 2018.
13. Tomkins S., Getoor L. Understanding Hybrid-MOOC Effectiveness with a Collective SocioBehavioral Model, Journal of Educational Data Mining, 2019, vol. 11, no. 3. DOI: 10.5281/zenodo.3594773.
14. Kaufmann R., Gupta P., Taylor J. An Active Inference Model of Collective Intelligence, Entropy, 2021. DOI: 10.3390/e23070830. Available at: https://www.mdpi.com/1099-4300/23/7/830
15. Cunningham-Nelson S., Laundon M., Cathcart A. Beyond satisfaction scores: visualising student comments for whole-of-course evaluation, Assessment & Evaluation in Higher Education, 2021, vol. 46, no. 5, pp. 685–700. DOI: 10.1080/02602938.2020.1805409.
16. Gravestock P., Gregor-Greenleaf E. Student Course Evaluations: Research, Models and Trends, Higher Education Quality Council of Ontario, 2008, 149 p. Available at: https://books.google.ru/books?id=POJ40AEACAAJ
17. Koller D., Friedman N. Probabilistic Graphical Models: Principles and Techniques. Cambridge, MA : The MIT Press, 2009, 1272 p.
18. Efremov E.V., Logachev A.V., Nikitina V.I., Prokopenko E.I., Tokareva M.D. Performance-difficulty-estimation: software implementation of Bayesian network approach for joint evaluation of course difficulty and student performance, GitHub. Available at: https://github.com/VitalinaNikitina/performance-difficulty-estimation (accessed: 04. 03. 2026).
19. Rasines D.G., Young G.A. Chapter 2 – Bayesian selective inference, Advancements in Bayesian Methods and Implementation. Handbook of Statistics, 2022, vol. 47, pp. 43–65. DOI: 10.1016/bs.host.2022.06.006.
20. Gelman A., Carlin J.B., Stern H.S., Dunson D.B., Vehtari A., Rubin D.B. Bayesian Data Analysis, Third Edition: Texts in Statistical Science, 2013, 675 p. Available at: https://books.google.ru/books?id=ZXL6AQAAQBAJ
21. Caron F. Bayesian nonparametric models for bipartite graphs, Advances in Neural Information Processing Systems, 2012, vol. 25. Available at: https://proceedings.neurips.cc/paper_files/paper/2012/file/0768281a05da9f27df178b5c39a51263Paper.pdf
Review
For citations:
Efremov E.V., Logachev A.V., Nikitina V.I., Prokopenko E.I., Tokareva M.D. Assessing course difficulty and student performance using bayesian networks. Territory Development. 2026;(2 (44)):78-94. (In Russ.) EDN: VUGPPL
Views:
78
JATS XML
Email this article 