BOX 5-1 Mathematical Circles: Teaching Students to Explorea

In 2006, an eighth-grade home-schooled student named Evan O’Dorney came to an evening meeting of the Berkeley Mathematics Circle with his mother. For an hour he listened to the director, Zvezdelina Stankova, talk about how to solve geometry problems with a technique called circle inversion. Then, during a 5-minute break, he went back to his mother and told her, “Mom, there are problems here I can’t do!”

It’s not something that O’Dorney has said very often in his life. By the time he graduated from high school, he had become as famous for academic excellence as any student can be. In 2007, he won the National Spelling Bee. From 2008 to 2010 he participated in the International Mathematics Olympiad (IMO) for the U.S. team three times, winning two silver medals and a gold. And in 2011 he won the Intel Science Talent Search with a mathematics project on continued fractions. President Barack Obama called O’Dorney personally to congratulate him after his IMO triumph, and the two met in person during the Intel finals.

It would be easy to say that a student as talented as O’Dorney probably would have achieved great things even without the Berkeley Math Circle. But that would miss the point. For 5 years, the mathematics circle gave him direction, inspiration, and advice. It put him in contact with university professors who could pose problems difficult enough to challenge him. (As a ninth-grader, he took a university course on linear algebra and found a solution to a previously unsolved problem.) By the time he was a high-school senior, he was experienced enough and confident enough to teach sessions of the Berkeley Mathematics Circle himself. The experience helped him develop the communication skills he needed to win the Intel Science Talent Search.

Not all students can be O’Dorneys, of course. But the math circle concept, imported from Eastern Europe, has begun to find fertile ground in the United States. The National Association of Math Circles now counts 97 active circles in 31 states, most of them based at universities and led by university professors. As is the case in Eastern Europe, math circles have become one of the most effective ways for professional mathematicians to make direct contact with precollege students. In math circles, students learn that there is mathematics beyond the school curriculum. And yes, they discover problems that might be too hard for them to solve. But that is exactly the kind of problem that a student like O’Dorney wants to work on. Gifted students are often completely turned off by the problems they see in their high-school classes, which for them are as about as challenging as a game of tic-tac-toe.

Dr. Stankova, who was then a postdoctoral fellow at the Mathematical Sciences Research Institute at Berkeley (she now teaches at Mills College in began the Berkeley Math Circle in 1998, hoping to replicate the experience she had as a grade-school student in Bulgaria. In Bulgaria and throughout Eastern Europe, math circles are found in most grade schools and many high schools. Just as students with a talent for soccer might play on a school soccer team, students with a talent for mathematics go to a math circle. This does not mean that the



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