As AI transforms education, a UF mathematician aims to preserve the productive struggle of learning

As leading AI labs solve famous open problems in mathematics, educators are grappling with a fundamental question: How can artificial intelligence support student learning without replacing the thinking that makes it possible?

A University of Florida-led research team is addressing that challenge with HaLLMos, an AI tool that helps students learn to work through mathematical challenges rather than avoid them. The goal is to preserve what educators call productive struggle, the process of engaging with difficult but achievable problems to build understanding and develop independent problem-solving skills.

Vincent Vatter, Ph.D., a professor in UF’s Department of Mathematics leads the team behind HaLLMos, a freely available tool that provides feedback on students’ written proofs without supplying complete solutions.

“Part of learning mathematics is struggling with a problem,” Vatter said. “If you remove all of that struggle, you also remove a lot of the learning.”

Nearly 40,000 student proofs have already been submitted to HaLLMos, highlighting the demand for the kind of individualized feedback that instructors often do not have time to provide.

“Students learning proofs need a lot of feedback, and instructors just don’t have the capacity to give them that much feedback,” Vatter said.

Unlike other AI-tools that may generate a complete solution, HaLLMos is designed to help them identify weaknesses in students’ reasoning and work toward corrections themselves. The approach offers a potential alternative to using AI simply to produce answers, keeping students actively involved with their learning.

“We’re trying to make sure that the AI is not just giving students the answer,” Vatter said. “We want it to help students understand what they’ve done and how they can improve it.”

The tool uses an approach known as constitutional AI, in which a written set of principles guides how the system responds. Developed by mathematicians and mathematics educators, these principles help ensure that the feedback is both mathematically sound and educationally useful.

An $814,000 grant from the AI for Math Fund, supported by Renaissance Philanthropy and XTX Markets, will help the team expand HaLLMos beyond introductory proof courses to advanced undergraduate classes in linear algebra, real analysis and topology.

Expanding the system to advanced courses requires examples of effective feedback tailored to different mathematical fields. The grant will support a fellowship program involving approximately 40 mathematicians, including faculty members, postdoctoral researchers and graduate students from institutions across the country. Fellows will help curate examples of proofs paired with expert feedback to train the AI model.

“The feedback that’s useful in linear algebra is not necessarily the same feedback that’s useful in real analysis or topology,” Vatter said. “We need people who are actively teaching those subjects to help us identify what good feedback looks like.”

Co-investigators on the research team include Sarah Sword, Ph.D., principal research scientist at Education Development Center; Jay Pantone, Ph.D., associate professor of mathematics at Marquette University; and Ryota Matsuura, Ph.D., professor of mathematics at St. Olaf College.

The project builds on earlier work supported by the National Science Foundation. Vatter has incorporated HaLLMos into his teaching, allowing students to test their proofs and receive feedback before submitting assignments.

“Students can submit a proof, get feedback, revise and submit it again,” Vatter said. “That gives them an opportunity to learn from the process instead of just seeing a grade at the end.”

The goal, he said, is to help students become more capable and independent mathematical thinkers.

HaLLMos is freely available to students and instructors at hallmos.com. Students can practice writing proofs and receive immediate feedback, while instructors can create exercises for use in their courses.