AI plus mathematical modeling equals a new tool for teaching

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"Where am I going to use that?" is, according to Jennifer Suh, a common complaint in math classrooms. The real-world applications of algebra, geometry, and probability are often lost in the shuffle of textbook questions and equations. But this professor of mathematics leadership education is hoping to change the narrative.

Ziyu Yao, PI, assistant professor in the Computer Science Department in the College of Engineering and Computing; Suh, co-PI, professor of mathematics specialist leadership in the College of Education and Human Development; and collaborative site-PI Janice Zhang of William and Mary received a grant from the National Science Foundation's Research on Innovative Technologies for Enhanced Learning (RITEL) program to develop MathVC: a virtual classroom where middle school students can work through mathematical modeling problems with AI-powered chatbot students. A preliminary version of this project was sponsored by Microsoft's Accelerating Foundation Models award, also led by Yao.

"We're trying to build these 21st-century skills in collaborative problem-solving while preparing students to solve global challenges, all while making math modeling a more inclusive practice," said Suh.

Mathematical modeling creates a mathematical representation of a real-world scenario to help teach students math concepts in context. These can be small scale scenarios-calculate costs for a party-or global challenges-supplying clean water to a city after a major flooding event.

A demo of MathVC with Yao communicating with the virtual students. Photo provided.

These types of math problems combine computational skills and soft skills like critical thinking, collaboration, and communication: identifying the problem, defining the variables, analyzing solutions, iterating on the model, and reporting findings.

"These are problems with real-world applications," explained Suh. "It helps students understand the value."

While mathematical modeling is an incredibly effective tool for math education, it comes with its own set of challenges. "Schools vary greatly in their access to classroom resources, teacher resources, education research...and as a result not all students are given the opportunity to engage with this type of learning," Suh said. "And on an individual level, some students find the communication aspect of this more challenging than others."

MathVC is one way to bridge those gaps of accessibility.

Within the virtual classroom, the human student can collaborate with generative AI students to work through these mathematical models.

"We see the benefits for multilingual students, as well as for students who want to develop their communication skills for math reasoning and justification through math talk," said Suh. And for teachers, MathVC allows students to ask questions and be prompted through the problem without their intervention: a benefit for teachers with large classroom sizes who are otherwise unable to monitor every group.

Once the program is deployed, access will be as simple as logging into a website. "Our system is developed using state-of-the-art Large Language Models (LLMs). The cost of these tools is reducing, the programming required is reducing, so it's an incredibly practical solution," said Yao.

From the student perspective, MathVC's success is dependent on how accurate the generative AI student voices are. Part of the grant supports the development of Math EdVentures Camp, a week-long program for students to build their skills in mathematical modeling, as well as an opportunity for Suh and Yao to collect valuable data on student problem-solving and communication techniques.

"AI safety is paramount," explained Yao. "Authentic simulation prevents the students from losing the social skills of communicating with real-life peers, as well as makes the human-AI interaction more engaging."

Students in Math EdVentures Camp explore how many water drops could fit on a coin. Photo provided.

This past summer, students in the Math EdVentures Camp explored STEM problems both large and small-from bridge engineering to calculating the number of water drops that could fit on a coin-in three-person teams. Teachers provided feedback as they worked through the modeling problems. On the last day, Yao led the students through a demonstration of the MathVC and asked for their feedback.

All of this is helping mold the generative AI.

"We found that students don't want to be told the answer," said Yao. "They prefer the interactive learning, where they get thought-provoking questions that help them find the solution."

Math EdVentures Camp leadership. Photo provided.

"Watching our fantastic team of Math EdVentures instructors and George Mason student researchers work with the middle schoolers was also a rich source of data to improve how the AI will support student problem-solving and critical thinking," said Suh.

Yao and Suh discovered some surprises, too.

"They were actually really interested in how we developed the program," said Yao. "Students were asking me what classes they needed to take in high school or college in order to develop a platform like this themselves. And we had good discussions about keeping a critical mind while using AI."

MathVC represents one way that George Mason researchers are leveraging transdisciplinary collaboration to advance 21st education for all, a part of the university's Grand Challenge Initiative. And there's another goal as well-changing the narrative of math education.

"When we talk to middle schoolers, a lot of them have math phobia. But these more collaborative learning models get them excited and interested," Suh said. "We want all kids to see that they are math people."

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