Developing Authentic Simulated Learners for Mathematics Teacher Learning: Insights from Three Approaches with Large Language Models

TL;DR

This paper evaluates three methods—Fine-tuning, Multi-agent, and DPO—to enhance the authenticity of LLM-based simulated students for mathematics teacher learning, improving realism and pedagogical usefulness.

Contribution

It introduces and compares three novel approaches to improve the authenticity and pedagogical utility of LLM simulations in teacher education.

Findings

All approaches improve cognitive and linguistic authenticity over few-shot prompts.

Fine-tuning yields realistic but brief responses, limiting extended reasoning.

Multi-agent and DPO generate explicit reasoning behind student strategies.

Abstract

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.