# MathVC: An LLM-Simulated Multi-Character Virtual Classroom for Mathematics Education

arXiv: https://arxiv.org/abs/2404.06711 · HTML: https://mlsanity.com/paper/2404.06711/

## Key facts

- Cited by 37 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 108 references that are in the map.
- First posted on arXiv 10 Apr 2024.

## Builds on (most cited first, 19 of 19)

- [MetaGPT: Meta Programming for A Multi-Agent Collaborative Framework](https://mlsanity.com/paper/2308.00352/) (2023)
- [LaMP: When Large Language Models Meet Personalization](https://mlsanity.com/paper/2304.11406/) (2023)
- [Character-LLM: A Trainable Agent for Role-Playing](https://mlsanity.com/paper/2310.10158/) (2023)
- [MedAgents: Large Language Models as Collaborators for Zero-shot Medical Reasoning](https://mlsanity.com/paper/2311.10537/) (2023)
- [Learning Discourse-level Diversity for Neural Dialog Models using Conditional Variational Autoencoders](https://mlsanity.com/paper/1703.10960/) (2017)
- [MathDial: A Dialogue Tutoring Dataset with Rich Pedagogical Properties Grounded in Math Reasoning Problems](https://mlsanity.com/paper/2305.14536/) (2023)
- [Systematic Biases in LLM Simulations of Debates](https://mlsanity.com/paper/2402.04049/) (2024)
- [On Learning to Summarize with Large Language Models as References](https://mlsanity.com/paper/2305.14239/) (2023)
- [A User Simulator for Task-Completion Dialogues](https://mlsanity.com/paper/1612.05688/) (2016)
- [EduAgent: Generative Student Agents in Learning](https://mlsanity.com/paper/2404.07963/) (2024)
- [The TalkMoves Dataset: K-12 Mathematics Lesson Transcripts Annotated for Teacher and Student Discursive Moves](https://mlsanity.com/paper/2204.09652/) (2022)
- [Writer-Defined AI Personas for On-Demand Feedback Generation](https://mlsanity.com/paper/2309.10433/) (2023)
- [Gentopia: A Collaborative Platform for Tool-Augmented LLMs](https://mlsanity.com/paper/2308.04030/) (2023)
- [Learning Agent-based Modeling with LLM Companions: Experiences of Novices and Experts Using ChatGPT & NetLogo Chat](https://mlsanity.com/paper/2401.17163/) (2024)
- [Mathemyths: Leveraging Large Language Models to Teach Mathematical Language through Child-AI Co-Creative Storytelling](https://mlsanity.com/paper/2402.01927/) (2024)
- [Reflective Linguistic Programming (RLP): A Stepping Stone in Socially-Aware AGI (SocialAGI)](https://mlsanity.com/paper/2305.12647/) (2023)
- [One Prompt To Rule Them All: LLMs for Opinion Summary Evaluation](https://mlsanity.com/paper/2402.11683/) (2024)
- [Can Language Models Employ the Socratic Method? Experiments with Code Debugging](https://mlsanity.com/paper/2310.03210/) (2023)
- [Interrogating AI: Characterizing Emergent Playful Interactions with ChatGPT](https://mlsanity.com/paper/2401.08405/) (2024)

## Built on by (most cited first, 30 of 37)

- [A Survey of Self-Evolving Agents: What, When, How, and Where to Evolve on the Path to Artificial Super Intelligence](https://mlsanity.com/paper/2507.21046/) (2025)
- [From LLM Reasoning to Autonomous AI Agents: A Comprehensive Review](https://mlsanity.com/paper/2504.19678/) (2025)
- [Simulating Classroom Education with LLM-Empowered Agents](https://mlsanity.com/paper/2406.19226/) (2024)
- [From Individual to Society: A Survey on Social Simulation Driven by Large Language Model-based Agents](https://mlsanity.com/paper/2412.03563/) (2024)
- [LLM Agents for Education: Advances and Applications](https://mlsanity.com/paper/2503.11733/) (2025)
- [MEDCO: Medical Education Copilots Based on A Multi-Agent Framework](https://mlsanity.com/paper/2408.12496/) (2024)
- [Social Science Meets LLMs: How Reliable Are Large Language Models in Social Simulations?](https://mlsanity.com/paper/2410.23426/) (2024)
- [Embracing Imperfection: Simulating Students with Diverse Cognitive Levels Using LLM-based Agents](https://mlsanity.com/paper/2505.19997/) (2025)
- [Very Large-Scale Multi-Agent Simulation in AgentScope](https://mlsanity.com/paper/2407.17789/) (2024)
- [A Survey on LLM-based Conversational User Simulation](https://mlsanity.com/paper/2604.24977/) (2026)
- [Quantifying and Optimizing Global Faithfulness in Persona-driven Role-playing](https://mlsanity.com/paper/2405.07726/) (2024)
- [From MOOC to MAIC: Reshaping Online Teaching and Learning through LLM-driven Agents](https://mlsanity.com/paper/2409.03512/) (2024)
- [Classroom Simulacra: Building Contextual Student Generative Agents in Online Education for Learning Behavioral Simulation](https://mlsanity.com/paper/2502.02780/) (2025)
- [GFlowNet Fine-tuning for Diverse Correct Solutions in Mathematical Reasoning Tasks](https://mlsanity.com/paper/2410.20147/) (2024)
- [FACET: Teacher-Centred LLM-Based Multi-Agent Systems-Towards Personalized Educational Worksheets](https://mlsanity.com/paper/2508.11401/) (2025)
- [Towards Valid Student Simulation with Large Language Models](https://mlsanity.com/paper/2601.05473/) (2026)
- [Position: LLMs Can be Good Tutors in English Education](https://mlsanity.com/paper/2502.05467/) (2025)
- [When LLMs Learn to be Students: The SOEI Framework for Modeling and Evaluating Virtual Student Agents in Educational Interaction](https://mlsanity.com/paper/2410.15701/) (2024)
- [CP-Env: Evaluating Large Language Models on Clinical Pathways in a Controllable Hospital Environment](https://mlsanity.com/paper/2512.10206/) (2025)
- [Digital Twin AI: Opportunities and Challenges from Large Language Models to World Models](https://mlsanity.com/paper/2601.01321/) (2026)
- [Can LLMs Simulate Personas with Reversed Performance? A Systematic Investigation for Counterfactual Instruction Following in Math Reasoning Context](https://mlsanity.com/paper/2504.06460/) (2025)
- [Synthesizing High-Quality Programming Tasks with LLM-based Expert and Student Agents](https://mlsanity.com/paper/2504.07655/) (2025)
- [Evolution in Simulation: AI-Agent School with Dual Memory for High-Fidelity Educational Dynamics](https://mlsanity.com/paper/2510.11290/) (2025)
- [Unveiling the Learning Mind of Language Models: A Cognitive Framework and Empirical Study](https://mlsanity.com/paper/2506.13464/) (2025)
- [INSIDE the Student's Mind: Jointly Modeling Latent Reasoning and Action in LLM Student Simulators](https://mlsanity.com/paper/2608.10492/) (2026)
- [Is your multimodal large language model a good science tutor?](https://mlsanity.com/paper/2505.06418/) (2025)
- [Exploring Communication Strategies for Collaborative LLM Agents in Mathematical Problem-Solving](https://mlsanity.com/paper/2507.17753/) (2025)
- [OnlineMate: An LLM-Based Multi-Agent Companion System for Cognitive Support in Online Learning](https://mlsanity.com/paper/2509.14803/) (2025)
- [Student Development Agent: Risk-free Simulation for Evaluating AIED Innovations](https://mlsanity.com/paper/2510.09183/) (2025)
- [DebugTA: An LLM-Based Agent for Simplifying Debugging and Teaching in Programming Education](https://mlsanity.com/paper/2510.11076/) (2025)

## Abstract (arXiv)

Collaborative problem solving (CPS) is essential in mathematics education, fostering deeper learning through the exchange of ideas. Yet, classrooms often lack the resources, time, and peer dynamics needed to sustain productive CPS. Recent advancements in Large Language Models (LLMs) offer a promising avenue to enhance CPS in mathematical education. We designed and developed MathVC, a multi-persona LLM simulated virtual classroom platform to facilitate CPS in mathematics. MathVC combines a meta planning controller that monitors CPS stages-sense-making, team organization, planning, execution, validation, and predicts the next speaker, with a persona simulation stack that encodes mathematical thinking via a task schema and error-injected persona schemas seeded from teacher-specified misconceptions. We evaluated MathVC with 14 U.S. middle schoolers. Students reported constructive interaction and reaching shared solutions, describing gains in engagement, motivation, and confidence through diverse perspectives, immediate scaffolding, and human-like fallibility. Our findings also provide insights into simulating peers via LLM-based technologies for collaboration to support learning.