So far, students who used the tool, MathVC, have said, “‘It felt just like a real classroom,’ and others became more motivated because they wanted to ‘answer before the virtual peers,’” according to Murong Yue, a Ph.D. student lead on the project.
Mathematical modeling — the process of translating real-world scenarios into mathematical problems — is a key skill for students pursuing science, technology, engineering and math fields, according to the researchers. But creating activities that help students practice this is often difficult, particularly in schools with limited staff and resources.
According to a recent preprint of the project’s findings, MathVC is the first system to use an LLM to simulate multiple student characters who work together with a human learner to solve math problems. The system is designed to be as realistic as possible, with AI student characters having realistic strengths and weaknesses in math and moving through conversations in ways that resemble real problem-solving patterns.
HOW IT WORKS
One early critique of LLMs was that they struggled with math reasoning, but models have improved with time. Recent models have demonstrated stronger capabilities in both solving math tasks and simulating role-specific dialog, which helps lay the foundation for tools like MathVC.
“In education, we don’t need endless new problems — classic math problems are sufficient to inspire students, and most of these have already been encountered in model training,” Yue said via email. “MathVC builds on this stability by introducing task structures and error injection, so virtual students reason step by step but are not always correct, which better matches the needs of authentic learning.”
MathVC is a two-part system. A meta-planner organizes the conversation into stages of problem-solving, including agreeing on what the problem is asking, proposing possible approaches, doing calculations and reviewing results. The second part is character simulations representing the reasoning, errors and adjustments of the individual AI student “classmates.”
WHY THIS APPROACH?
MathVC can help personalize learning for students with different backgrounds and different propensities for class participation, Yue said. Whether a student learns in a different language or is talked over by a more confident peer, the tool can offer more opportunities for collaboration.
In order to make the interactions useful, the student characters have human-like fallibility, demonstrate collaborative behaviors and mimic an age-appropriate social voice.
Unlike all-knowing LLMs or models that simulate a teacher or teaching assistant, MathVC does not supply direct answers. Its student characters make mistakes, which Yue said offers unique learning advantages.
For example, in one sample problem about soup, a simulated student named Charlie miscounted the number of people who ordered tomato soup, prompting the human student to correct him.
“One virtual peer might suggest an incomplete solution, and another might challenge it,” Yue wrote in an email. “This type of exchange stimulates deeper thinking than simply receiving an answer from a teacher.”
It also helps students practice persuading others why their viewpoint is correct, rather than just listening. The simulated students ask questions and challenge reasoning, Yue said.
Throughout these interactions, the simulated students remain informal, sending short messages meant to sound like middle schoolers.
“This is important because it makes the interaction feel more like a real peer discussion, encouraging students to participate more actively,” Yue wrote.
Each character’s understanding of the math task is tracked over time. If they are corrected, they learn from it, just as in real life.
CURRENT STATUS
The project is still in development and is now focused on prototype evaluation. According to a news release from the university, the team introduced MathVC to students at George Mason’s Math EdVentures Camp this summer, where middle school students explored STEM problems and gave feedback on the system. They also ran studies with 14 middle school students.
According to the project’s website, upcoming work includes collecting more student interaction data, expanding the range of student interactions that can be simulated and developing a more user-friendly interface for use in schools.
As the project grows, safety and security are top of mind, Yue said, ensuring the conversations stay on topic is key, and are integral to the design of the model.
