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Article

A Knowledge Tracing Model Based on Hierarchical Heterogeneous Graphs

1
School of Mathematics and Computer Application, Shangluo University, Shangluo City, Shaanxi Province, Shangluo 726000, China
2
Department of computer science, University of California Davis, Davis, CA 94555, USA
*
Author to whom correspondence should be addressed.
Mathematics 2026, 14(3), 500; https://doi.org/10.3390/math14030500
Submission received: 7 October 2025 / Revised: 20 December 2025 / Accepted: 22 December 2025 / Published: 30 January 2026
(This article belongs to the Special Issue Applied Mathematics for Information Security and Applications)

Abstract

Whether learners can correctly complete exercises is influenced by multiple factors, including their mastery of relevant knowledge concepts and the interdependencies among these concepts. To investigate how the structure of the knowledge space—particularly the complex relationships among learners, exercises, and knowledge points—affects learning outcomes, this study proposes the Hierarchical Heterogeneous Graph Knowledge Tracing model (HHGKT). A hierarchical heterogeneous graph was constructed to capture two types of interactions—“learner–knowledge concept” and “exercise–knowledge concept”—and incorporate the interdependencies among knowledge concepts into the graph structure. By leveraging this hierarchical representation, the model’s ability to characterize learners and exercises was enhanced. A hierarchical heterogeneous graph encompassing users, exercises, and knowledge concepts was built based on the ASSISTments dataset, and simulation experiments were conducted. The results indicate that the proposed structure effectively represents the complexity of the knowledge space. Incorporating knowledge concept interdependencies improves prediction accuracy by 1.79%, while the hierarchical heterogeneous graph outperforms traditional bipartite graphs by approximately 1.5 percentage points in accuracy. These findings demonstrate that the model better integrates node and relational information, offering valuable insights for knowledge space modeling and its application in educational contexts.
Keywords: hierarchical heterogeneous graph; adaptive attention mechanism; knowledge tracing hierarchical heterogeneous graph; adaptive attention mechanism; knowledge tracing

Share and Cite

MDPI and ACS Style

Li, B.; Zhang, Y.; Du, H.; Chen, Y.-c. A Knowledge Tracing Model Based on Hierarchical Heterogeneous Graphs. Mathematics 2026, 14, 500. https://doi.org/10.3390/math14030500

AMA Style

Li B, Zhang Y, Du H, Chen Y-c. A Knowledge Tracing Model Based on Hierarchical Heterogeneous Graphs. Mathematics. 2026; 14(3):500. https://doi.org/10.3390/math14030500

Chicago/Turabian Style

Li, Bin, Yan Zhang, Hongle Du, and Yeh-cheng Chen. 2026. "A Knowledge Tracing Model Based on Hierarchical Heterogeneous Graphs" Mathematics 14, no. 3: 500. https://doi.org/10.3390/math14030500

APA Style

Li, B., Zhang, Y., Du, H., & Chen, Y.-c. (2026). A Knowledge Tracing Model Based on Hierarchical Heterogeneous Graphs. Mathematics, 14(3), 500. https://doi.org/10.3390/math14030500

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