Abstract
Large language models (LLMs) are increasingly used to simulate students at different mastery levels. These simulations can generate synthetic training data and stress-test tutoring systems. However, common prompt-based approaches leave the answer decision to the LLM, which tends to perform according to its built-in capabilities even when instructed to simulate a student with low mastery. As a result, these approaches may have difficulty distinguishing students with low and high levels of mastery. We demonstrate this limitation using 379 College Board-calibrated SAT Algebra items and five archetypal mastery profiles. Three LLMs from three vendors (Gemini 3.1 Flash Lite, Claude Haiku 4.5, and GPT-5.4-mini) achieve 96.8-100% accuracy across all profiles. To address this limitation, we introduce a method grounded in a Stochastic Student Knowledge Graph (SSKG). A curriculum knowledge graph (CKG) is extracted from an open algebra textbook, and each SAT solution is decomposed into a chain of required triples. The SSKG assigns a mastery probability to each triple, which is sampled to determine question correctness. An LLM then generates a first-person rationale consistent with the outcome. The simulation reduces accuracy to 44.1-85.2% across profiles and produces a clear monotone mastery gradient.
Abstract (translated)
URL
https://arxiv.org/abs/2608.21668
