Mathematical modeling (MM) is considered a fundamental skill for students in STEM disciplines. Practicing the MM skill is often the most effective when students can engage in group discussion and collaborative problem-solving. However, due to unevenly distributed teachers and educational resources needed to monitor such group activities, students do not always receive equal opportunities for this practice. Excitingly, large language models (LLMs) have recently demonstrated strong capability in both modeling mathematical problems and simulating characters with different traits and properties. Drawing inspiration from the advancement of LLMs, in this work, we present MATHVC, the very first LLM-powered virtual classroom containing multiple LLM-simulated student characters, with whom a human student can practice their MM skill. To encourage each LLM character's behaviors to be aligned with their specified math-relevant properties (termed "characteristics alignment") and the overall conversational procedure to be close to an authentic student MM discussion (termed "conversational procedural alignment"), we proposed three innovations: integrating MM domain knowledge into the simulation, defining a symbolic schema as the ground for character simulation, and designing a meta planner at the platform level to drive the conversational procedure. Through experiments and ablation studies, we confirmed the effectiveness of our simulation approach and showed the promise for MATHVC to benefit real-life students in the future.

翻译：数学建模（MM）被视为STEM学科学生的基本技能。当学生能够参与小组讨论和协作解决问题时，MM技能的练习通常最为有效。然而，由于监测此类小组活动所需的教师和教育资源分布不均，学生并不总能获得平等的练习机会。令人振奋的是，大语言模型（LLMs）近期在数学问题建模和模拟具有不同特质与属性的角色方面展现了强大能力。受LLM发展的启发，本研究提出MATHVC——首个由LLM驱动的多角色虚拟课堂，包含多个LLM模拟的学生角色，人类学生可与之共同练习MM技能。为使每个LLM角色的行为与其指定的数学相关属性保持一致（称为"特征对齐"），并使整体对话流程贴近真实的学生MM讨论（称为"对话流程对齐"），我们提出三项创新：将MM领域知识融入模拟过程、定义符号模式作为角色模拟的基础、以及设计平台层面的元规划器驱动对话流程。通过实验与消融研究，我们验证了模拟方法的有效性，并展示了MATHVC未来造福真实学生的潜力。