A Bayesian Approach to Inferring Prerequisite Structures and Topic Difficulty in Language Learning

Understanding how linguistic topics are related to each another is essential for designing effective and adaptive second-language (L2) instruction.We present a data-driven framework to model topic dependencies and their difficulty within a L2 learning curriculum.First, we estimate topic difficulty and student ability using a three-parameter Item Response Theory (IRT) model.Second, we construct topic-level knowledge graphs-as directed acyclic graphs (DAGs)-to capture the prerequisite relations among the topics, comparing a threshold-based method with the statistical Grow-Shrink Markov Blanket algorithm.Third, we evaluate the alignment between IRTinferred topic difficulty and the structure of the graphs using edge-level and global ordering metrics.Finally, we compare the IRT-based estimates of learner ability with assessments of the learners provided by teachers to validate the model's effectiveness in capturing learner proficiency.Our results show a promising agreement between the inferred graphs, IRT estimates, and human teachers' assessments, highlighting the framework's potential to support personalized learning and adaptive curriculum design in intelligent tutoring systems.