In Emory's Math Circle, bubbles are square and equations are cool

This summer, math graduate student Sarah Trebat-Leder is working with elementary-age children at the Children’s Museum of Atlanta (above) and with advanced college undergraduates on the Emory campus. And during the school year, she organizes the Emory Math Circle for middle school and high school students. (Photos by Tony Benner, Emory Photo/Video.)

By Carol Clark

Each June and July, the Emory math department gathers a hive of brilliant minds from around the country for Research Experiences for Undergraduates (REU), a National Science Foundation initiative. The 13 participants at Emory this summer have come from Brown, Harvard, Indiana University, Princeton, Stanford, the University of Georgia and Yale. Number theorist Ken Ono heads up the Emory REU. He and the other instructors charge the group with problems relating to elliptic curves and Galois representations, mock modular and quantum modular forms, additive number theory and distribution of primes.

“This is one of the top REUs in the country, because of the research you get to do here,” says Sarah Trebat-Leder, an Emory NSF Graduate Fellow, who is an instructor for the group this summer.

Trebat-Leder, who graduated from Princeton in 2013, came to two of the Emory REU summer programs herself as an undergraduate. “I learned how to be a mathematician,” she says of the experience. “How to read technical math papers, how to give talks, how to write math and how to go about doing research.”

Ono put her to work on extending the findings of a major discovery in the area of partitions that he had just published with colleagues. “My first REU project was generalizing this major paper that a lot of people in the math world cared about,” Trebat-Leder says. “I had taken a lot of classes, but I had never worked on a problem that no one had solved. Ken is a great mentor because he knows how to develop projects that are accessible to students and yet important to math.”

Ever seen a square bubble? Emory graduate students are giving kids a new view of math, aiming to spark wonder and a desire to learn more.

Trebat-Leder is also devoted to making math accessible and inspiring, for everyone from young kids to adults. Her career goal is to become a college professor focused on teaching and community outreach. 

In January, Trebat-Leder launched the Emory Math Circle. The free program draws students from Atlanta middle schools and high schools to campus on Saturdays for challenging and fun math enrichment sessions led by Emory graduate students. This summer, in addition to teaching for the REU, she is spending several Saturday afternoons at the Children’s Museum of Atlanta alongside other Emory graduate students, including Amanda Clemm, a co-organizer of the Math Circle. They are immersing young children in math and physics through a hands-on activity they call “3D Boxes and Bubbles."

Trebat-Leder reshapes math education.

“Who doesn’t like bubbles?” says Trebat-Leder, explaining the activity’s appeal.

First the kids build a variety of geometric structures out of ZomeTools, interlocking plastic balls and tubes. Then they use the structures to create soap bubbles in crazy shapes: Squares, cubes, spirals, wormholes and parabolas.

While the kids are busy making bubbles, the graduate students are asking them questions about what they think is happening. The reason an odd-shaped bubble forms in the middle of a 3D geometic shape? "The bubble mix is kind of lazy," Trebat-Leder explains. "It wants to connect up without having to stretch a lot and it takes less stretch for it to connect in the middle than to stretch to the outside."

The idea is to strip out complex jargon and give kids glimpses into math and physics that help them to think both logically and creatively.

It’s a far different approach than multiplication drills.

Amanda Clemm is among the Emory graduate students who are volunteering their time to give kids positive early experiences with math.

“I was getting my hair cut the other day, and the hair dresser asked what I do. I told her and she said, ‘I hated math!’” Trebat-Leder says. “I get that reaction everywhere. Everyone is always telling me about their bad experiences with math. I’d like to change that, but it takes time.”

Trebat-Leder, who grew up in Pennsylvania’s Lehigh Valley, loved teaching even as a child. “It’s in my blood,” she says. By the time she was 11, she had earned her black belt in karate and was leading a karate class herself.

She also had an affinity for math. After her sophomore year in high school, she went to a summer math camp offered by Hampshire College in Massachusetts. “I spent six weeks doing nothing but math all day, and I got a strong sense of what it was all about,” Trebat-Leder says. “I love math because it’s both logical and creative. In science, you have a hypothesis and conduct an experiment that can strongly support your hypothesis. But math is more precise. You can actually prove something and be sure that it is true.”

During her Princeton undergraduate years, Trebat-Leder participated in a Boston University summer program called PROMYS, or Program in Mathematics for Young Scientists. PROMYS immerses both high school students and teachers in the creative aspects of math and original research.

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Trebat-Leder drew on all her varied experiences to launch the Emory Math Circle. More than a dozen Emory graduate students responded to her call to lead the free math enrichment sessions on Saturday afternoons, and about 30 middle school and high school students attended throughout the spring semester.

Math Circle is not free tutoring for students who are struggling in their classes, Trebat-Leder stresses. “We’re looking for kids who really want to be here and who enjoy our sessions,” she says. “Our aim is to get the students excited about math and let them see how interesting it can be by exposing them to things they don’t learn in school.”

The middle-school level sessions might introduce the students to graph theory by showing how it can be used to model Facebook networks or to play “Cops and Robbers,” a game that explores how many policemen you need to catch a criminal in different scenarios. Another popular game in the Math Circle requires students to keep four colors from touching one another. “The four-color theorem was one of the really deep problems in combinatorics,” Trebat-Leder says. “It took a lot of computers and people to prove it. But it’s also super visual and it doesn’t require a lot of technical language and symbols to convey.”

Kids grasp the idea of math hidden in shapes.

The students that attended the Math Circle sessions last spring came from a range of races and about half were girls, Trebat-Leder says. She notes that girls were the first- and second-place winners of a problem-solving contest organized for the Math Circle middle school students.

“The kids get to learn some really cool math and see what it’s like to actually discuss it themselves and not have it lectured to them,” Trebat-Leder says. “It’s really beneficial to have graduate students, who have studied a lot of math and understand it deeply, interact with kids.”

She cites an article she read recently comparing math to art. “If art classes consisted of just reproducing other people’s paintings, than the experience wouldn’t be nearly as fun or creative,” Trebat-Leder says. “And yet, that’s the way most schools teach math.”

She hopes to keep expanding her influence as an educator, and come up with more ways to improve the math experience of kids. “I think schools are emphasizing the wrong things in an era when computers drive a lot of the work,” she says. “We’re still having kids spend a lot of time practicing long division when we should be focusing more on concepts. Technology has changed so much, and I think that what we’re teaching should be adapting to that.”

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