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So What Exactly Is a Math Circle?

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I had never heard the term, "math circle," until a few weeks ago when I stumbled across an article in The Atlantic about the growing number of American kids excelling in the highest levels of math. It mentioned the growing popularity of math circles as a driver of that trend, and I was intrigued:

In New York City last fall, it was easier to get a ticket to the hit musical "Hamilton" than to enroll your child in certain math circles. Some circles in the 350-student New York Math Circle program run out of New York University filled up in about five hours.

Math circles are meetings between mathematicians and K-12 students or teachers where they work on problem solving. These gatherings typically take place outside the regular school day. The instructors are often university professors or graduate students in math. And these programs are having a huge impact, according to The Atlantic article:

...but a cadre of American teenagers are reaching world-class heights in math—more of them, more regularly, than ever before. The phenomenon extends well beyond the handful of hopefuls for the Math Olympiad. The students are being produced by a new pedagogical ecosystem—almost entirely extracurricular—that has developed online and in the country's rich coastal cities and tech meccas.

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The National Association of Math Circles assists school districts that would like to start math circles by providing training and helping to facilitate partnerships with universities. The group reports that math circles have grown in the United States from about 30 in the 1980s to nearly 200 now.

To help me make sense of this phenomena, I reached out to the two women who lead the association. Diana White is the group's director. She has a Ph.D. in mathematics and teaches mathematics and mathematics education at the University of Colorado Denver. Brandy Wiegers is the group's associate director. She has a Ph.D. in applied mathematics and teaches mathematics at Central Washington University.

Diana and Brandy recently talked to me via phone about their work. Below is a lightly edited version of our conversation.

So what goes on during a math circle?

Diana: Mathematics professionals lead sessions with either K-12 students or teachers that really focus on the process of doing mathematics, on mathematical problem solving, and on understanding mathematics as a discipline of inquiry where you're conjecturing and communicating and exploring mathematics with other people as opposed to, like in a lot of school mathematics, you're often just learning set procedures. This is really more like a mini-mathematical research experience where you're learning to do mathematics just like a mathematician would, only obviously the people learning it don't have the same massive background with math coursework, and so they're doing it at a level that's appropriate to the background that they do have.

Where does this term come from?

 Brandy: A lot of them that were started initially around 20 years ago were started based on inspiration from people's experience in Eastern Europe. They had grown up with these math circles, these after-school and out-of-school experiences where mathematicians from the local universities came and supported students' exploration of problem solving. So many professors that were involved in starting the math circles in the United States had these experiences themselves as youth. They used that as inspiration for the programs that they started in the United States.

How does a math circle differ from a traditional K-12 math class?

Diana: In a typical K-12 math class, there's set content that a teacher is responsible for covering at a given grade level. Whether that aligns with the Common Core State Standards or whatever state standards their state happens to be using, there's specific content and benchmarks for each grade. In a math circle, the focus isn't on any particular content per se but much more about the process of doing mathematics and solving mathematical problems. So it can be taken from content that wouldn't typically be seen in K-12 mathematics. You might see some stuff with number theory or cryptography or other areas of geometry that aren't done in K-12 mathematics typically.

Are math circles primarily for whiz kids?

Brandy: That was the initial motivation for some people to get involved. They were looking for challenging programs for talented youth. But I've been involved in the San Francisco Math Circle, which ever since it was founded has always had a focus on bringing mathematical opportunities to under-enriched youth, providing opportunities for students that just really love mathematics but aren't the top of their class but want to explore and do problem solving.

Can an average or below-average math student benefit from a math circle?

Brandy: I believe so. As I'm structuring my math circle program, I really focus on mathematical play. So here's this question, go and see what you can discover. That provides an opportunity for every student in the classroom to discover something new.

 Diana: Just testing at an average or below-average level isn't necessarily a real indicator of that student's creativity or that student's potential in mathematics. That could be a reflection of the mathematical experiences they've had to date much more so than aptitude or what they could develop into.

Photo: A student at Lincoln Elementary School in Ellensburg, Wash., takes part in the Kittitas Valley Math Circle. (Brandy Wiegers)


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