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

2026-04-05

AI Summary

This study addresses the limited cognitive and linguistic authenticity of student simulations generated by current large language models under zero- or few-shot prompting, which hinders teachers’ accurate insight into student thinking. For the first time, it systematically compares three approaches—fine-tuning, multi-agent collaborative reasoning, and Direct Preference Optimization (DPO)—to develop high-fidelity student simulators in mathematical learning contexts, complemented by qualitative evaluation through educational interviews. Results indicate that all three methods significantly enhance simulation authenticity: multi-agent and DPO approaches explicitly articulate problem-solving rationales, facilitating pedagogical observation, whereas fine-tuned models produce concise responses that constrain elaboration of reasoning. The findings reveal critical trade-offs between authenticity and instructional utility across technical paradigms, offering a novel framework for designing AI-driven student simulations in teacher education.

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.

Problem

• simulated learners
• authenticity
• teacher learning
• student thinking
• large language models

Innovation

• Fine-tuning
• Multi-agent simulation
• Direct Preference Optimization
• Authenticity
• Teacher noticing