Large Language Model (LLM) simulations, where LLMs act as students with varying approaches to learning tasks, can support teachers' noticing of student thinking. However, simulations using zero- or few-shot prompting often yield inauthentic knowledge and language, directing teachers to unrealistic reasoning. We evaluate three approaches (Fine-tuning, Multi-agent, and Direct Preference Optimization; DPO) to improve the authenticity and pedagogical utility of simulated students. All approaches improve cognitive and linguistic authenticity, compared with few-shot prompts. Interviews with elementary mathematics pre-service teachers and researchers (\textit{n} = 8) reveal distinct pedagogical affordances. The fine-tuned model produces realistic, brief responses but limits opportunities to extend students' thinking. Meanwhile, the multi-agent and DPO approaches generate explicit reasoning behind student strategies. We discuss implications for designing LLM simulations that balance authenticity with instructional utility for teacher learning.
@article{arxiv.2604.04361,
title = {Developing Authentic Simulated Learners for Mathematics Teacher Learning: Insights from Three Approaches with Large Language Models},
author = {Jie Cao and Ha Nguyen and Selim Yavuz and Boran Yu and Shuguang Wang and Pavneet Kaur Bharaj and Dionne Cross Francis},
journal= {arXiv preprint arXiv:2604.04361},
year = {2026}
}