Developing Authentic Simulated Learners for Mathematics Teacher Learning: Insights from Three Approaches with Large Language Models
This work addresses the challenge of creating realistic simulated learners for elementary mathematics pre-service teachers, though it is incremental as it builds on existing LLM simulation methods.
The paper tackled the problem of inauthentic knowledge and language in large language model (LLM) simulations for mathematics teacher learning by evaluating three approaches (Fine-tuning, Multi-agent, and Direct Preference Optimization) to improve authenticity and pedagogical utility, finding that all approaches enhanced cognitive and linguistic authenticity compared to few-shot prompts.
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.