ArguMath: AI-Simulated Environment for Pre-Service Teacher Training in Orchestrating Classroom Mathematics Argumentation

2026-04-24

AI Summary

This study addresses the challenge pre-service mathematics teachers face in translating theoretical knowledge of mathematical argumentation into effective classroom practice due to limited access to authentic teaching experiences. To bridge this gap, the authors propose an AI-powered simulated classroom environment built upon a large language model (LLM), which, for the first time, generates realistic student responses grounded in actual classroom transcripts. The system enables teachers to customize instructional scenarios and receive real-time pedagogical prompts and discourse-annotated feedback. A structured reflection mechanism is integrated to foster the integration of theory and practice. Preliminary user studies demonstrate that the system significantly enhances pre-service teachers’ ability to orchestrate classroom mathematical argumentation, particularly in their use of theory-aligned elicitation strategies that promote reasoned discourse.

Technology Category

• Cognitive Modeling & Cognitive Systems: Analogy
• Knowledge Representation and Reasoning: Argumentation
• Natural Language Processing: Discourse, Pragmatics & Argument Mining

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Search and Retrieval-Augmented AI: Search Tool Learning with LLM: Teaching LLMs to invoke search and make use of retrieved information
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems

Abstract

Facilitating productive mathematical argumentation, especially asking rational questions, is essential yet remains challenging for pre-service mathematics teachers (PMTs), who often have limited opportunities to apply abstract theoretical knowledge in authentic practice. At the same time, recent advances in large language models (LLMs) have expanded the potential for simulating students in educational settings, enabling low-risk environments for instructional practice. To inform the design of a system that supports PMTs in orchestrating classroom argumentation, we conducted a formative study with eight experienced mathematics teachers to identify key design requirements, including personalization, realistic simulations, structured reflection, and ease of use. Building on these requirements, we developed ArguMath, an AI-simulated classroom environment that supports PMTs in practicing the orchestration of mathematical argumentation. ArguMath comprises three core components: (1) customization of classroom settings; (2) simulation of classroom discussions with AI-based students grounded in authentic transcripts and augmented with real-time instructional suggestions; and (3) structured reflection through discourse annotation and overall feedback. Results from an exploratory user study with seven PMTs, complemented by interviews with four experienced teachers, indicate that ArguMath has the potential to support PMTs' classroom orchestration skills, particularly theory-aligned questioning strategies.

Problem

• pre-service teacher training
• mathematical argumentation
• classroom orchestration
• teacher education
• instructional practice

Innovation

• AI-simulated classroom
• large language models
• mathematical argumentation
• teacher training
• structured reflection