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# Knowledge Tracing with Math Solutions

## Motivation
Knowledge Tracing (KT) is a core research task that models the evolution of a learner’s knowledge state based on their problem-solving history.  
This capability is essential for **Intelligent Tutoring Systems (ITS)** to provide adaptive feedback and personalized guidance.  

Traditional KT research has primarily relied on student–item interactions in the form of binary correctness (1/0).  
While deep learning-based models such as **DKT, SAINT, and AKT** have brought notable improvements,  
they still face **limitations in transferability and generalization** across datasets.

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## Challenges
KT continues to face long-standing issues:
- **Cold start problem**  
- **Lack of interpretability**

Recent approaches have introduced natural language as a new modality:  
- **LKT**: models questions as natural language prompts to mitigate cold start  
- **EFKT**: applies cognitive frameworks to enhance interpretability  
- **LBMKT**: uses LLM encoders to summarize a learner’s knowledge state in natural language  

These works suggest the potential of natural language to overcome KT limitations, but their performance gains remain modest.

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## Related Progress in Programming Education
Programming education has seen stronger improvements by leveraging **richer interaction data** such as:
- Students’ code submissions  
- Textual questions  

Recent studies integrating these signals into KT architectures have shown significant improvements.  
For example, an **ACL 2025 paper** demonstrated that student question texts yielded **state-of-the-art performance** in programming education KT.

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## Advances in LLMs
Recent LLMs have enabled more **systematic and consistent step-by-step reasoning** through reinforcement learning and alignment:
- **Math-Shepherd**: leveraged verifiable reward signals → substantial gains on GSM8K and MATH  
- **PRM-Guided GFlowNets**: improved reasoning trace quality and diversity → better generalization on unseen datasets  

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## Our Approach
Building on these developments, our project integrates **LLM-generated step-by-step math solutions** into KT inputs.  
This provides **richer interaction signals** beyond simple correctness.

**Hypothesis:**  
Modeling student–item interactions with synthesized solutions can break through the current performance ceiling of KT models.

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## Research Question
> Can incorporating LLM-generated mathematical solutions into KT inputs  
> push Knowledge Tracing beyond its existing limitations?