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Running Circles Around Math

Story by
Nancy Joseph

Julia Pevtsova and colleagues in the Department of Mathematics weren’t sure what to expect when they organized an on-campus lecture for middle school students in 2010. After all, it was being held on a Sunday afternoon, on a math topic that was unfamiliar to most people. How many tweens and teens would give up their Sunday for math?

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UW graduate student Chris Aholt helps Math Circle participants work through a problem. Media credit: Jacob Lambert

As it turns out, quite a lot.

The reserved room filled up half an hour before the talk. The organizers quickly switched to a larger lecture hall but still ended up with a standing room only crowd. “It was clear there was a lot of interest,” says Pevtsova, associate professor of mathematics.

With that vote of confidence, the Department decided to expand its offerings for middle schoolers, presenting three mathematics lectures annually, an annual math Olympiad, and weekly Math Circles that explore challenging math topics on an ongoing basis. All offerings are free.

The programs for middle school students grew out of an after-school math program offered by the Department at two Seattle elementary schools, Montlake and Stevens. Montlake fifth-graders urged then-UW graduate student Steve Klee, who led the sessions, to consider starting a similar program at their assigned middle school the following year. Klee obliged, but the middle school program never gained traction, so the Department decided to offer a program on the UW’s Seattle campus instead.

“Middle school is an important age to show that math can be fun and that there’s a lot you can do with it,” says Pevtsova. “A lot of kids are really capable at math, but if they get one boring class, then another, they get lost and decide they’re not good at it. This is especially true for girls, who will just start doing something else.”

The UW Math Circle, explains Pevtsova, is modeled after its Russian namesake, started in Saint-Petersburg in the 1930s. The idea is simple: the person leading the group presents an intriguing math problem; participants must use logic and reasoning to come up with solutions.

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Math Circle instructors (from left) Kolya Malkin, Alex Vaschillo, Dylan Wilson, and Chris Aholt. Media credit: Jacob Lambert

“Our goal is not to bring up a generation of mathematicians per se,” says Pevtsova. “The students are learning universal skills that can be used anywhere. It’s about making connections and seeing the bigger problem.”

Last year the Department began offering  a weekly Math Circle for seventh graders; this year an eighth grade section was added. The groups are led by UW students—graduate student Chris Aholt and undergrads Kolya Malkin, Dylan Wilson, and Alex Vaschillo. “The instructors bring all this energy,” says Pevtsova. “They’re always looking for new problems, new topics, new ways to make it exciting. And I think they connect much better to younger people than faculty would.”

The instructors receive a small quarterly stipend thanks to National Science Foundation funding, but that nominal support is not what motivates them to lead a Math Circle. “The main reason that I do this is because I want the students to understand that math can be so much fun,” says Aholt. “And it's not just the enjoyment that comes from having the best answer to a problem, or from really understanding why something is true.  Rather, I think the best times come at that moment when you realize that your awesome solution is actually not optimal. There's nothing more exciting than finding out that something which you thought was difficult and intricate and deep and beautiful is actually even more intricate and deep than you thought it was.  Those are the things you're going to go home and talk about at dinner.”

Some participants do, in fact, talk about Math Circle problems over dinner. As one parent wrote to Pevtsova, “I wanted to send a note of gratitude…. You have captured the fire in my child!”

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UW students Alex Vaschillo (far left) and Kolya Malkin lead a Math Circle. Media credit: Jacob Lambert

To keep that fire alive, the instructors search for problems that will challenge and inspire without overwhelming. There’s one problem that involves saving 100 pirates from cannibals (“Math problems are notoriously gruesome,” says Aholt), and others that are less story-based. The key, says Malkin, is to find “the right balance of fun story problems and theoretical problems…for them to get a grasp of the material without compromising their interest.” Aholt has even used puzzle-type questions that software engineers are asked during job interviews. “It's a great boost of confidence to the students when we tell them that these are actual questions they ask people applying for jobs at Microsoft or Google!” he says.

Both sections have held “mathematical auctions” to encourage students to find the best solution to a problem, and have organized the students into teams for added motivation.  The teams earn points for their solutions, with one team winning a prize at the end of the quarter. “In many cases, students are more driven by the competitive factor of winning the most points on a given day than they are interested in the prizes at the end of the quarter,” says Vaschillo. “The point system gives the circle a healthy level of cooperative competition.”

The Department has not yet decided whether it will add a ninth grade Math Circle next year. “If there is enough interest among the current eighth graders, we are likely to continue teaching them,” says Pevtsova. Either way, the hope is that the lessons learned and the fire sparked through the Math Circle will inspire its participants for years to come.

“My experiences with such a program led me to an incredible interest in mathematics and a much deeper understanding of the beauty of math,” says Vaschillo. “I hope that our Math Circle can similarly open doors for these students.”

For more about the Department of Mathematics Math Circle program, visit www.math.washington.edu/~mathcircle/circle