Efficient Knowledge Tracing with Optimal Question Selection
Research Overview
This ongoing research focuses on developing an efficient mathematical framework for knowledge tracing that can dynamically update with new information and optimally select questions to accurately estimate student knowledge.
Research Questions
1. Efficient Knowledge Representation
How can we mathematically model a student’s knowledge in a way that allows efficient updates when new information is acquired?
- Developing a structured representation of knowledge states
- Creating update mechanisms that scale with the knowledge base
- Ensuring computational tractability for real-time applications
2. Optimal Question Selection
How can we optimally choose which questions to ask a student to make our knowledge estimator converge quickly to the student’s true knowledge state?
- Formulating information-theoretic approaches to question selection
- Balancing exploration (discovering new knowledge gaps) vs. exploitation (confirming existing assessments)
- Minimizing the number of questions needed for accurate assessment
Research Goals
- Mathematical Modeling: Develop a rigorous mathematical framework for knowledge state representation
- Efficient Updates: Design algorithms that efficiently incorporate new assessment data
- Convergence Guarantees: Establish theoretical bounds on estimator convergence
- Practical Implementation: Create scalable solutions for real-world educational systems
Status
Early stages of research. Exploring foundational mathematical models and algorithmic approaches.