MathVC: An LLM-Simulated Multi-Character Virtual Classroom for Mathematics Education
This addresses the problem of limited resources and peer dynamics in mathematics classrooms for middle school students, representing an incremental application of existing LLM technology to a new educational context.
The paper tackled the challenge of fostering collaborative problem solving in mathematics education by developing MathVC, an LLM-simulated virtual classroom platform, which resulted in 14 middle school students reporting increased engagement, motivation, and confidence through constructive interactions and shared solutions.
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.