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.

中文翻译：

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MathVC：用于数学教育的法学硕士模拟多角色虚拟教室

数学建模 (MM) 被认为是 STEM 学科学生的一项基本技能。当学生能够参与小组讨论和协作解决问题时，练习 MM 技能通常是最有效的。然而，由于监督此类团体活动所需的教师和教育资源分布不均，学生并不总是能获得平等的机会进行这种实践。令人兴奋的是，大型语言模型（LLM）最近在数学问题建模和模拟具有不同特征和属性的角色方面表现出了强大的能力。从法学硕士的进步中汲取灵感，在这项工作中，我们推出了 MATHVC，这是第一个由法学硕士支持的虚拟教室，其中包含多个法学硕士模拟的学生角色，人类学生可以与他们一起练习他们的 MM 技能。为了鼓励每个 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”），并使整体对话过程接近真实的学生 MM 讨论（称为“对话程序对齐”），我们提出了三项创新：将 MM 领域知识集成到模拟中，定义符号模式作为角色模拟的基础，并在平台级别设计元规划器来驱动对话过程。通过实验和消融研究，我们证实了模拟方法的有效性，并表明 MATHVC 有望在未来使现实生活中的学生受益。