{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T10:23:24Z","timestamp":1775039004759,"version":"3.50.1"},"reference-count":32,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T00:00:00Z","timestamp":1775001600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>Accurately modeling student knowledge evolution is a central challenge in personalized learning and adaptive educational systems. Traditional sequential or static approaches often fail to capture both the temporal dynamics of learning and the relational structure between students and concepts. This study introduces a Temporal Graph Neural Network (TGNN) framework for modeling student knowledge acquisition and predicting learning trajectories using fine-grained interaction data from the ASSISTments_skill dataset. The TGNN represents students and skills as nodes in a dynamic bipartite graph, with temporal edges encoding correctness, attempts, hints, and interaction timestamps. Experiments demonstrate that TGNN significantly outperforms state-of-the-art baselines, including Deep Knowledge Tracing (DKT), Self-Attentive Knowledge Tracing (SAKT), and static graph convolutional networks, achieving an Area Under the Curve (AUC) of 0.892, Accuracy of 0.846, F1 score of 0.842, and a Mean Absolute Error (MAE) of 0.078 for trajectory prediction. Ablation studies reveal the critical role of temporal encoding, edge features, and graph connectivity in accurately modeling learning dynamics. Concept-level analysis indicates high prediction accuracy across both high-frequency and low-frequency skills, while temporal attention mechanisms enable interpretable insights into the influence of prior interactions on future performance. These results highlight the effectiveness of integrating temporal dynamics, graph-based relational modeling, and pedagogically meaningful features in predicting student learning outcomes. These results demonstrate the potential of temporal graph-based modeling for capturing student\u2013skill relationships and learning dynamics in educational interaction data. Rather than introducing a fundamentally new graph architecture, this study systematically adapts the Temporal Graph Network (TGN) framework to educational data and evaluates its effectiveness for modeling knowledge evolution and forecasting student learning trajectories. The findings provide practical insights for applying temporal graph learning methods to personalized learning, adaptive intervention design, and real-time performance forecasting.<\/jats:p>","DOI":"10.3390\/a19040263","type":"journal-article","created":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T08:08:34Z","timestamp":1775030914000},"page":"263","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Temporal Graph Neural Networks for Modeling Student Knowledge Evolution and Predicting Learning Trajectories"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7940-060X","authenticated-orcid":false,"given":"Deborah","family":"Olaniyan","sequence":"first","affiliation":[{"name":"Department of Computer Science and Informatics, Faculty of Natural and Agricultural Sciences, University of the Free State, Qwaqwa Campus, Kestell Road, Phuthaditjhaba 9866, South Africa"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3733-3485","authenticated-orcid":false,"given":"Ruth","family":"Wario","sequence":"additional","affiliation":[{"name":"Department of Computer Science and Informatics, Faculty of Natural and Agricultural Sciences, University of the Free State, Qwaqwa Campus, Kestell Road, Phuthaditjhaba 9866, South Africa"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,4,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"27777","DOI":"10.1007\/s11042-024-20207-w","article-title":"Toward an adaptive learning system by managing pedagogical knowledge in a smart way","volume":"84","author":"Chergui","year":"2025","journal-title":"Multimed. Tools Appl."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"770","DOI":"10.3390\/psych5030050","article-title":"An introduction to Bayesian knowledge tracing with pyBKT","volume":"5","author":"Bulut","year":"2023","journal-title":"Psych"},{"key":"ref_3","unstructured":"Ma, C. (2024). Deep Knowledge Tracing Based on Behaviour in the Item Response Theory Framework. [Master\u2019s Thesis, University of Alberta]."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"4512","DOI":"10.1109\/TKDE.2025.3552759","article-title":"Deep learning based knowledge tracing: A review, a tool and empirical studies","volume":"37","author":"Liu","year":"2025","journal-title":"IEEE Trans. Knowl. Data Eng."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Qadhi, S. (2023). Knowledge dynamics: Educational pathways from theories to tangible outcomes. From Theory of Knowledge Management to Practice, IntechOpen.","DOI":"10.5772\/intechopen.1002979"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"455","DOI":"10.3758\/s13421-022-01361-8","article-title":"Enhancing learning and retention through the distribution of practice repetitions across multiple sessions","volume":"51","author":"Walsh","year":"2023","journal-title":"Mem. Cogn."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"23817","DOI":"10.1007\/s10639-024-12782-0","article-title":"Unlocking learner engagement and performance: A multidimensional approach to mapping learners to learning cohorts","volume":"29","author":"Kim","year":"2024","journal-title":"Educ. Inf. Technol."},{"key":"ref_8","unstructured":"Khan, M.A. (2024). A Learning Analytics Approach Towards Monitoring Coregulation by Human Tutors, in a Virtual Classroom Environment. [Doctoral Dissertation, UCL (University College London)]."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"427","DOI":"10.3390\/computation3030427","article-title":"Computational modeling of teaching and learning through application of evolutionary algorithms","volume":"3","author":"Lamb","year":"2015","journal-title":"Computation"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"137621","DOI":"10.1109\/ACCESS.2023.3335196","article-title":"Deep representation learning: Fundamentals, technologies, applications, and open challenges","volume":"11","author":"Payandeh","year":"2023","journal-title":"IEEE Access"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1003","DOI":"10.1109\/TLT.2025.3630276","article-title":"Graph Neural Network Empowers Intelligent Education: A Systematic Review From an Application Perspective","volume":"18","author":"He","year":"2025","journal-title":"IEEE Trans. Learn. Technol."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"6295","DOI":"10.1007\/s10462-022-10321-2","article-title":"A survey of graph neural networks in various learning paradigms: Methods, applications, and challenges","volume":"56","author":"Waikhom","year":"2023","journal-title":"Artif. Intell. Rev."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"87","DOI":"10.3233\/WEB-210458","article-title":"Graph-based knowledge tracing: Modeling student proficiency using graph neural networks","volume":"19","author":"Nakagawa","year":"2021","journal-title":"Web Intell."},{"key":"ref_14","unstructured":"Rossi, E., Chamberlain, B., Frasca, F., Eynard, D., Monti, F., and Bronstein, M. (2020). Temporal graph networks for deep learning on dynamic graphs. arXiv."},{"key":"ref_15","first-page":"0150105","article-title":"Development of a Framework for Predicting Students\u2019 Academic Performance in STEM Education using Machine Learning Methods","volume":"15","author":"Abdrakhmanov","year":"2024","journal-title":"Int. J. Adv. Comput. Sci. Appl."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Akpan, B. (2020). Mastery learning Benjamin bloom. Science Education in Theory and Practice: An Introductory Guide to Learning Theory, Springer International Publishing.","DOI":"10.1007\/978-3-030-43620-9"},{"key":"ref_17","first-page":"45","article-title":"Bloom\u2019s taxonomy and its digital evolution: A framework for school education","volume":"7","author":"Khokhar","year":"2025","journal-title":"Int. Res. J. Mod. Eng. Technol. Sci."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Cui, J., Qian, H., Jiang, B., and Zhang, W. (2024). Leveraging pedagogical theories to understand student learning process with graph-based reasonable knowledge tracing. Proceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, Association for Computing Machinery.","DOI":"10.1145\/3637528.3671853"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"9813","DOI":"10.1007\/s10639-024-13069-0","article-title":"Graph-based effective knowledge tracing via subject knowledge mapping","volume":"30","author":"Yang","year":"2025","journal-title":"Educ. Inf. Technol."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"128724","DOI":"10.1016\/j.eswa.2025.128724","article-title":"Leveraging graph neural network for learner performance prediction","volume":"293","author":"Hakkal","year":"2025","journal-title":"Expert Syst. Appl."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"142306","DOI":"10.1109\/ACCESS.2024.3471681","article-title":"Multi-Graph Spatial-Temporal Synchronous Network for Student Performance Prediction","volume":"12","author":"Zhou","year":"2024","journal-title":"IEEE Access"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"117681","DOI":"10.1016\/j.eswa.2022.117681","article-title":"SGKT: Session graph-based knowledge tracing for student performance prediction","volume":"206","author":"Wu","year":"2022","journal-title":"Expert Syst. Appl."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Cheng, P., and Long, Z. (2024). A method for Analyzing and Predicting Students\u2019 Competitive Performance via Temporal Knowledge Graph. Proceedings of the 2024 International Conference on Artificial Intelligence, Digital Media Technology and Interaction Design, Association for Computing Machinery.","DOI":"10.1145\/3726010.3726033"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1109\/TLT.2023.3301011","article-title":"Multivariate Knowledge Tracking Based on Graph Neural Network in ASSISTments","volume":"17","author":"Xia","year":"2023","journal-title":"IEEE Trans. Learn. Technol."},{"key":"ref_25","unstructured":"Xia, J. (2024). Graph Model-Based Deep Learning for Student Learning Analytics. [Doctoral Dissertation, Deakin University]."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Mai, N.T., Cao, W., and Liu, W. (2025). Interpretable knowledge tracing via transformer-Bayesian hybrid networks: Learning temporal dependencies and causal structures in educational data. Appl. Sci., 15.","DOI":"10.3390\/app15179605"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Zhang, Y., Wang, S., Li, E., Zhu, Y., and Li, J. (2025). AEKT: A Multi-dimensional Knowledge Tracing Model Integrating Student Cognitive Ability and Knowledge Acquisition. International Conference on Advanced Data Mining and Applications, Springer Nature.","DOI":"10.1007\/978-981-95-3459-3_8"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Hashemifar, S., and Sahebi, S. (2025). Personalized Student Knowledge Modeling for Future Learning Resource Prediction. International Conference on Artificial Intelligence in Education, Springer Nature.","DOI":"10.1007\/978-3-031-98420-4_18"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"510","DOI":"10.1016\/j.ins.2021.08.100","article-title":"Jkt: A joint graph convolutional network based deep knowledge tracing","volume":"580","author":"Song","year":"2021","journal-title":"Inf. Sci."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"108274","DOI":"10.1016\/j.knosys.2022.108274","article-title":"Bi-CLKT: Bi-graph contrastive learning based knowledge tracing","volume":"241","author":"Song","year":"2022","journal-title":"Knowl.-Based Syst."},{"key":"ref_31","unstructured":"Ding, X., and Larson, E.C. (2021). On the interpretability of deep learning based models for knowledge tracing. arXiv."},{"key":"ref_32","unstructured":"Jain, K. (2025, May 10). ASSISTments Skill Data. Kaggle. Available online: https:\/\/www.kaggle.com\/datasets\/kanishkjain03\/assistments-skill."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/19\/4\/263\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T08:13:20Z","timestamp":1775031200000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/19\/4\/263"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,4,1]]},"references-count":32,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2026,4]]}},"alternative-id":["a19040263"],"URL":"https:\/\/doi.org\/10.3390\/a19040263","relation":{},"ISSN":["1999-4893"],"issn-type":[{"value":"1999-4893","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,4,1]]}}}