A Hierarchical Probabilistic Framework for Incremental Knowledge Tracing in Classroom Settings

TL;DR

This paper introduces KT$^2$, a hierarchical probabilistic framework for knowledge tracing that effectively models student learning in low-resource classroom settings with online updates.

Contribution

We propose KT$^2$, a novel hierarchical probabilistic model using a tree structure and EM algorithm for incremental knowledge tracing in low-resource environments.

Findings

KT$^2$ outperforms baseline models in low-resource online settings.

The hierarchical structure improves knowledge estimation accuracy.

Incremental updates enable real-time student performance prediction.

Abstract

Knowledge tracing (KT) aims to estimate a student's evolving knowledge state and predict their performance on new exercises based on performance history. Many realistic classroom settings for KT are typically low-resource in data and require online updates as students' exercise history grows, which creates significant challenges for existing KT approaches. To restore strong performance under low-resource conditions, we revisit the hierarchical knowledge concept (KC) information, which is typically available in many classroom settings and can provide strong prior when data are sparse. We therefore propose Knowledge-Tree-based Knowledge Tracing (KT$^2$), a probabilistic KT framework that models student understanding over a tree-structured hierarchy of knowledge concepts using a Hidden Markov Tree Model. KT$^2$ estimates student mastery via an EM algorithm and supports personalized prediction through an incremental update mechanism as new responses arrive. Our experiments show that KT$^2$ consistently outperforms strong baselines in realistic online, low-resource settings.