  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.
