A Successful Equation

A Teaching Fellowship in Undergraduate Mathematics helps energize learning.

Matthew Gherman is on a mission to bring more joy, and a little less anxiety, to young minds studying mathematics. While many first-year students arrive to the Institute with a natural affinity for and significant experience with mathematics, for others, this is their first in-depth exposure to the advanced math required as part of the core curriculum.

As the Phoebe Hearst Teaching Fellow in Mathematics, Gherman is helping ensure undergraduates receive the support and encouragement to persevere in future careers as scientists and engineers.

Unlike most postdoctoral fellowships which center around research, Gherman's fellowship allows him to focus on teaching and improving pedagogical approaches within the math department. The Hearst fellowship, named in honor of Phoebe Hearst—the first woman regent at the University of California, Berkeley—is funded through 2027.

It is in fact Gherman's success in the role over the last two years that has catalyzed a call for a permanent Teaching Fellowship in Undergraduate Mathematics position at the Institute. As a result, a $500,000 gift was recently made towards a $3 million endowment to provide for ongoing support in teaching and learning in the division of Physics, Mathematics and Astronomy (PMA).

The Tower of Hanoi

"Students really love Matt's classes," says Professor of Mathematics Thomas Graber who serves as the executive officer for the mathematics department. "His office is two doors down from me, and it's just packed with students for his office hours." In addition to his work with undergraduates, Graber also points to Gherman's collaboration with faculty and other postdoctoral scholars in helping to apply research-based strategies for more effective instruction.

"He's here as an educator and that is what he's thinking about all the time," adds Graber. "It's a different mindset than a researcher."

Making math more accessible drives Gherman's work, including volunteering with students as young as elementary school age when math anxiety can first emerge. "Somehow, along the way, a lot of students are pushed away from math," says Gherman, who helped reinstate the Caltech Math Circle with a local polytechnic school following the COVID pandemic. The Math Circle Network, a project of the American Institute of Mathematics, offers extracurricular activities designed to be "frunstrating"—an experience that is both challenging and rewarding.

"These math circles provide students with joyful math experiences," he adds. "I think a lot of Caltech faculty had fun with math in the past, that's why many of us are here, but many people never get to see how math could be fun."

In the game the Tower of Hanoi, for example, players are asked to move a stacked tower of disks of various sizes and colors from one peg to a series of others. The puzzle is solved when a player can move the disks by following such rules as no disk may be placed on top of a disk that is smaller in size. While the puzzle elicits laughter and shouts of excitement from the elementary school students, more importantly it introduces mathematical concepts and logic in a fun way.

In prior learning experiences, Gherman has witnessed first-hand the consequences of undergraduates who become demotivated by a math course. "They literally give up," he says. "And normally it's not just math they quit. They quit the STEM field all together. Math is essential, but it shouldn't be so inaccessible that it stops a student from becoming a biologist or engineer."

Hallmarks of a Caltech Education

Gherman, who joined Caltech in 2023 after earning his PhD in mathematics from UCLA, has taught a special section of Math 1a designed for students who may not have had as much access to advanced math. In this course and others Gherman applies innovative approaches to motivate students such as flipped classes (using formal class time for problem-solving and delivering traditional content outside of class) and the use of an alternative grading system where points are gained, not lost, throughout the term.

"These pedagogical enhancements advance critical thinking, collaboration, and research, which are all hallmarks of a Caltech education," says Fiona Harrison, the Kent and Joyce Kresa Leadership Chair and Harold A. Rosen Professor of Physics. "We look forward to the continuing impact of Matt's work, and we are grateful to the Hearst Foundation in leading the initial investment in our teaching fellowship in math."

Gherman also has led teaching demonstrations for PMA teaching assistants and hosted a series of seminars called "Conversations about Math Teaching" featuring guest speakers on topics ranging from alternative assessments and active learning to AI in education.

"The Hearst Foundations are proud to support undergraduate math instruction at Caltech," says Paul "Dino" Dinovitz, executive director at the William Randolph Hearst Foundation. "When students feel confident in their math abilities, they're more likely to persist in challenging disciplines. By investing in effective teaching strategies, we're helping Caltech create an environment where all students can thrive."

A Passion for Math

"I never thought that someone could be so passionate about math—and I especially never thought that that person's passion could make me excited about math," says an undergraduate in one of Gherman's Math 1d sections.

Like many of the students he inspires, there was a time when Gherman also felt challenged by mathematics. Although he had excelled in math in the past, he found himself having to work much harder in his doctoral program. Fortunately, he found a mentor in his academic advisor Alexander Merkurjev. "He gave me a project that he knew I could manage," recalls Gherman. "He would meet with me every week and was very supportive as I went through the highs and the lows of the program. He was always there to answer my questions."

With a permanent teaching fellowship in place, undergraduates will continue to have a dedicated resource committed not only to answering questions but to fostering a culture of academic engagement and support.

If you would like to contribute to the Teaching Fellowship in Undergraduate Mathematics, we invite you to contact Brian Yocum, senior director of development, at (626) 395-5705 or [email protected].