Multiple Relations and Time Enhanced Knowledge Tracing Model

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Multiple Relations and Time Enhanced Knowledge Tracing Model

Knowledge tracing (KT) is a critical technology in intelligent tutoring systems (ITS), aiming to accurately track learners’ knowledge mastery levels and predict their responses to exercises. Existing KT methods often fail to fully explore the multiple relationships between concepts or simultaneously consider the effects of knowledge interactions and time on knowledge states. To address these limitations, this paper introduces the Multiple Relations and Time Enhanced Knowledge Tracing Model (MRTKT), which improves upon traditional KT models by incorporating richer knowledge relationships and learning-forgetting patterns.

Introduction

The rapid development of ITS has created opportunities for personalized learning. KT, as a key technology in ITS, plays a crucial role in dynamically assessing learners’ knowledge states and predicting their performance. However, most existing KT models suffer from two major shortcomings: (1) they do not deeply explore the multiple relationships between concepts, and (2) they inadequately model the combined effects of knowledge interactions and time on knowledge states.

Cognitive assimilation theory suggests that new knowledge interacts with existing knowledge in three primary ways: superordinate learning, subordinate learning, and combinatorial learning. Superordinate learning involves deriving meaning through generalization, subordinate learning involves integrating new knowledge into existing knowledge structures, and combinatorial learning occurs when new and existing knowledge are neither hierarchical nor categorical but still influence each other. Additionally, knowledge mastery is influenced by time—learners may forget knowledge due to lack of practice or reinforce it through repeated exercises.

Current KT models either focus on knowledge interactions without considering time or model forgetting effects without accounting for knowledge relationships. For example, models like GKT and SKT incorporate knowledge structures but overlook time effects, while HawkesKT and LPKT model forgetting but ignore knowledge interactions. MRTKT addresses these gaps by simultaneously modeling multiple knowledge relationships and time effects, leading to more accurate and interpretable predictions.

Knowledge Structure and Relationships

Knowledge Structure Representation

The knowledge structure is represented as a graph where nodes correspond to knowledge concepts, and edges denote relationships between them. Three types of relationships are considered: superordinate, subordinate, and combinatorial.

Identifying Knowledge Relationships

Unlike previous methods that rely on expert annotations, MRTKT automatically extracts knowledge relationships from learner interaction data using statistical approaches.

  1. Subordinate Relationships (Class-Inclusion): These relationships are identified based on the probability that mastering one concept aids in understanding another. For example, understanding “rectangle area” helps in learning “square area.” A transition probability matrix is computed, and edges are established if the probability exceeds a threshold.

  2. Superordinate Relationships (Generalization): These are derived from subordinate relationships. If concept A is a subordinate of concept B, then B is a superordinate of A.

  3. Combinatorial Relationships (Co-occurrence): These relationships are identified when concepts frequently appear together in exercises but lack hierarchical dependencies. A co-occurrence probability matrix is computed, and edges are formed if the normalized probability exceeds a threshold.

By constructing this enriched knowledge graph, MRTKT captures a more comprehensive representation of how concepts influence each other.

Modeling Knowledge Interactions

To model the propagation of influence among concepts, MRTKT employs a Gated Graph Neural Network (GGNN). GGNNs are particularly suitable because they allow bidirectional message passing and can handle multiple relationship types through edge-specific parameters.

Message Passing Mechanism

At each time step, the model aggregates information from neighboring nodes based on the type of relationship (superordinate, subordinate, or combinatorial). This ensures that each concept’s state is updated by considering its interactions with related concepts.

  1. Feature Embedding: The model combines knowledge embeddings with interaction history to form input vectors. Time-related features (repetition interval, sequence interval, and past repetition count) are processed to generate temporal embeddings that influence the update mechanism.

  2. Neighbor Aggregation: For each concept, the model computes a message vector by aggregating information from its neighbors. The aggregation weights depend on the relationship type, allowing different influences to propagate differently.

  3. State Update: A GRU-like mechanism updates each concept’s hidden state by combining its previous state, aggregated neighbor information, and temporal features. This update process simulates how knowledge mastery evolves due to learning and forgetting.

Incorporating Time Effects

Time plays a crucial role in knowledge retention and forgetting. MRTKT integrates three key temporal features:

  1. Repetition Interval (Δr): The time gap between consecutive exercises on the same concept.
  2. Sequence Interval (Δs): The time gap between adjacent exercises in the interaction sequence.
  3. Past Repetition Count (Δc): The number of times a concept has been practiced before the current interaction.

These features are processed to generate two temporal vectors that modulate the GRU’s update and reset gates. The update gate determines how much the knowledge state should change, while the reset gate controls how much past information should be forgotten. By incorporating these temporal dynamics, MRTKT more accurately simulates the learning-forgetting process.

Prediction and Training

The final knowledge state is used to predict the probability of a correct response. A sigmoid-activated fully connected layer maps the hidden state to a prediction score. The model is trained using binary cross-entropy loss, minimizing the difference between predicted and actual responses.

Experimental Evaluation

Datasets

MRTKT was evaluated on three public datasets:

  1. ASSIST2009: Contains 4,163 students, 123 concepts, and 283,105 interactions.
  2. ASSIST2017: Contains 1,709 students, 102 concepts, and 942,816 interactions.
  3. Algebra2005: Contains 574 students, 436 concepts, and 607,025 interactions.

Baselines

MRTKT was compared against eight state-of-the-art KT models, including DKT, DKVMN, GKT, DKT+Forgetting, SAKT, SKT, HawkesKT, and CL4KT.

Results

  1. Performance Comparison: MRTKT achieved the highest AUC and accuracy across all datasets, demonstrating its superiority over existing models. Statistical tests confirmed that the improvements were significant.
  2. Ablation Studies: Removing either knowledge interactions or time features led to performance degradation, confirming that both components contribute to MRTKT’s effectiveness.
  3. Interpretability: Visualization of knowledge state evolution showed that MRTKT captures meaningful concept relationships and temporal dynamics. Clustering analysis revealed that related concepts were grouped together, validating the model’s ability to discover meaningful knowledge structures.

Conclusion

MRTKT advances knowledge tracing by simultaneously modeling multiple knowledge relationships and time effects. By leveraging GGNNs to propagate influence across different relationship types and incorporating temporal features to simulate learning and forgetting, MRTKT provides more accurate and interpretable predictions. Experimental results demonstrate its superiority over existing models, making it a valuable tool for personalized learning systems. Future work could explore additional cognitive factors to further enhance KT models.

doi.org/10.19734/j.issn.1001-3695.2024.07.0301

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