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Prerequisite Structure Discovery in Intelligent Tutoring Systems

Louis Annabi, Sao Mai Nguyen

TL;DR

This work tackles KS discovery for ITS by learning a prerequisite KS graph directly from learner trajectories through Prerequisite Knowledge Tracing (PKT), which treats the KS as a learnable parameter via an adjacency matrix $M$. The authors couple PKT with a KS-guided tutoring strategy, ZPDES-KS, to evaluate how discovered KS supports content recommendation and learning progress. Empirical results on synthetic data show that PKT-derived KS improves tutoring over several baselines and can rival KT-based approaches, though using ground-truth KS remains superior. The findings suggest that explicit KS discovery can meaningfully enhance personalized instruction and that KS-based curricula hold promise for improving learning outcomes in ITS, with future work focusing on data efficiency and forgetting dynamics.

Abstract

This paper addresses the importance of Knowledge Structure (KS) and Knowledge Tracing (KT) in improving the recommendation of educational content in intelligent tutoring systems. The KS represents the relations between different Knowledge Components (KCs), while KT predicts a learner's success based on her past history. The contribution of this research includes proposing a KT model that incorporates the KS as a learnable parameter, enabling the discovery of the underlying KS from learner trajectories. The quality of the uncovered KS is assessed by using it to recommend content and evaluating the recommendation algorithm with simulated students.

Prerequisite Structure Discovery in Intelligent Tutoring Systems

TL;DR

This work tackles KS discovery for ITS by learning a prerequisite KS graph directly from learner trajectories through Prerequisite Knowledge Tracing (PKT), which treats the KS as a learnable parameter via an adjacency matrix . The authors couple PKT with a KS-guided tutoring strategy, ZPDES-KS, to evaluate how discovered KS supports content recommendation and learning progress. Empirical results on synthetic data show that PKT-derived KS improves tutoring over several baselines and can rival KT-based approaches, though using ground-truth KS remains superior. The findings suggest that explicit KS discovery can meaningfully enhance personalized instruction and that KS-based curricula hold promise for improving learning outcomes in ITS, with future work focusing on data efficiency and forgetting dynamics.

Abstract

This paper addresses the importance of Knowledge Structure (KS) and Knowledge Tracing (KT) in improving the recommendation of educational content in intelligent tutoring systems. The KS represents the relations between different Knowledge Components (KCs), while KT predicts a learner's success based on her past history. The contribution of this research includes proposing a KT model that incorporates the KS as a learnable parameter, enabling the discovery of the underlying KS from learner trajectories. The quality of the uncovered KS is assessed by using it to recommend content and evaluating the recommendation algorithm with simulated students.
Paper Structure (15 sections, 4 equations, 4 figures, 2 tables)

This paper contains 15 sections, 4 equations, 4 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Context
  3. Problem and Contribution
  4. Related Work
  5. Intelligent Tutoring Systems
  6. Knowledge Tracing
  7. Knowledge Structure with Prerequisite Structure Learning
  8. Methods
  9. KS Discovery
  10. Tutoring model
  11. Experiments
  12. Synthetic data generation
  13. Prerequisite Structure Learning
  14. Exploiting prerequisite relations for recommendation
  15. Conclusion

Figures (4)

  • Figure 1: Domain knowledge (top) and student models (bottom) can be exploited by tutoring models. The KC-exercise graph gives the KCs practiced on each exercise. The Knowledge Structure (KS) is represented as a directed acyclic graph where the edges represent prerequisite relations between KCs. Knowledge Tracing (KT) models predict the learner's level on each KC at each step of practice, here for a learner trajectory of length T=3.
  • Figure 2: Illustration of the ZPDES-KS method applied on a toy example. Learner progress can unlock new KCs and add new exercises to the ZPD, and can also deactivate exercises when success becomes too frequent.
  • Figure 3: Example of simulated learner trajectory. KC 3 is never practiced.
  • Figure 4: Results with the ZPDES-KS algorithm on one of the datasets, with the KS discovered by the PKT method. Left: learner skills over time, averaged on 300 learners. Right: activated KCs in the ZPDES-KS algorithm over time, averaged on 300 learners (clear=activated).