MATHVC is an LLM-powered virtual classroom designed to simulate multiple student characters for mathematics education. The system aims to provide a platform where human students can practice mathematical modeling (MM) skills through collaborative discussions with AI-simulated peers. The key innovations include integrating MM domain knowledge into the simulation, defining symbolic schemas as the foundation for character behavior, and implementing a meta planner to guide conversational procedures. These components ensure that the simulated characters exhibit behaviors aligned with real students and that the discussions closely resemble authentic MM discussions. The system features a modular architecture with a meta planner for organizing conversations and a character simulation module for creating and updating student characters. The character schemas represent the dynamic understanding of mathematical problems, incorporating potential errors and evolving thought processes. The meta planner ensures that conversations follow stages typical of collaborative problem-solving, enhancing the realism of interactions. Experiments and ablation studies demonstrated that MATHVC outperforms traditional simulations in terms of characteristic and procedural alignment. The system effectively simulates student interactions, allowing for more realistic discussions and improved MM skill development. The results indicate that MATHVC has significant potential for real-world application in mathematics education, particularly for students in resource-limited environments. The system addresses two main challenges: characteristic alignment (ensuring simulated characters behave like real students) and conversational procedural alignment (ensuring discussions follow authentic stages of collaborative problem-solving). These challenges are tackled through symbolic schemas and a meta planner, which guide the simulation process and ensure realistic interactions. MATHVC has the potential to enhance mathematics education by providing a platform for students to practice MM skills without the need for teacher supervision. The system can be integrated into the curriculum to support collaborative learning and improve student engagement. Future work includes personalizing the simulation based on student needs and ensuring ethical considerations are addressed. The system is designed to be flexible and adaptable, with potential applications beyond mathematics education.MATHVC is an LLM-powered virtual classroom designed to simulate multiple student characters for mathematics education. The system aims to provide a platform where human students can practice mathematical modeling (MM) skills through collaborative discussions with AI-simulated peers. The key innovations include integrating MM domain knowledge into the simulation, defining symbolic schemas as the foundation for character behavior, and implementing a meta planner to guide conversational procedures. These components ensure that the simulated characters exhibit behaviors aligned with real students and that the discussions closely resemble authentic MM discussions. The system features a modular architecture with a meta planner for organizing conversations and a character simulation module for creating and updating student characters. The character schemas represent the dynamic understanding of mathematical problems, incorporating potential errors and evolving thought processes. The meta planner ensures that conversations follow stages typical of collaborative problem-solving, enhancing the realism of interactions. Experiments and ablation studies demonstrated that MATHVC outperforms traditional simulations in terms of characteristic and procedural alignment. The system effectively simulates student interactions, allowing for more realistic discussions and improved MM skill development. The results indicate that MATHVC has significant potential for real-world application in mathematics education, particularly for students in resource-limited environments. The system addresses two main challenges: characteristic alignment (ensuring simulated characters behave like real students) and conversational procedural alignment (ensuring discussions follow authentic stages of collaborative problem-solving). These challenges are tackled through symbolic schemas and a meta planner, which guide the simulation process and ensure realistic interactions. MATHVC has the potential to enhance mathematics education by providing a platform for students to practice MM skills without the need for teacher supervision. The system can be integrated into the curriculum to support collaborative learning and improve student engagement. Future work includes personalizing the simulation based on student needs and ensuring ethical considerations are addressed. The system is designed to be flexible and adaptable, with potential applications beyond mathematics education.