PS2: Parameterized Control for Fine-Grained Student Proficiency Simulation

Understanding how students with different proficiency levels respond to educational materials is a critical issue within the field of AI for Education. However, acquiring sufficient real student response data for a robust evaluation is often hindered by cost, ethics, and security constraints. Consequently, LLM-based student proficiency simulation, especially prompt-based methods, has emerged as a practical alternative under data-scarce conditions. Despite their promise, current methods still exhibit limited controllability with coarse-grained proficiency representations, high sensitivity to prompt design, and the lack of calibration with academic performance. Therefore, we propose Parameterized Student Proficiency Simulation (PS2), an unsupervised and parameterized model-level framework that simulates students with different proficiencies by interpolating between a strong upper-bound LLM and a weaker, cognitive error-informed lower-bound student LLM via a hybrid ratio. Specifically, the lower-bound model is constructed by fine-tuning the weaker LM to exhibit cognitive errors when responding to educational materials. To ensure alignment with target proficiency levels, PS2 further calibrates the interpolation ratio with academic performance. Experiments on two public datasets demonstrate that PS2 achieves finer-grained and consistent proficiency simulation compared to existing baselines, leading to superior performance in student behavior similarity and item difficulty prediction.