From Mastery Profile to Simulated Response: Stochastic Student Knowledge Graphs (SSKG) for Faithful LLM Student Simulation

Abstract

Large language models (LLMs) are increasingly used to simulate students at different mastery levels to generate synthetic training data and stress-test tutoring systems. Existing approaches primarily leverage an LLM to answer questions or perform tests while instructing it to simulate various skill levels. However, LLMs tend to execute at their full built-in capability regardless of target skill levels. We demonstrate this limitation on SAT questions across five mastery levels, where three LLMs consistently achieve 96.8-100\% accuracy. To faithfully simulate student behavior, we propose a Stochastic Student Knowledge Graph (SSKG)-based approach that leverages the strengths of LLM in different ways. Using human-in-the-loop workflows, LLMs extract a Curriculum Knowledge Graph (CKG) from course materials, decompose solution paths into CKG triples, and map incorrect distractors. A student's mastery profile is represented as an SSKG, assigning mastery probabilities to CKG triples. When solving a problem, the SSKG is sampled to determine the outcome, after which an LLM generates a rationale consistent with the sampled result. Compared to seven baselines which fail to separate profiles and maintain 86.5-100\% accuracy, our SSKG-based approach achieves 44.1-85.2\% accuracy from low to high-mastery profiles, creating a clear monotonic gradient. An ablation study demonstrates that taxonomy awareness contributes most significantly to these fidelity gains, particularly for lower-mastery profiles.