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One day more than a year ago, an 8-year-old named Andrew told his parents he wanted to learn to do long division. His dad, Tim Sylvester, looked up a YouTube video explaining the basic steps and began working with him through simple problems on a whiteboard in their house. A half-hour later, the child was dividing two-digit numbers into 20-digit numbers.

“He was ecstatic, running around,” said Sylvester, describing the moment as a “math high.” Several months later, when Andrew’s third-grade class at a public school in Santa Cruz, California, began tackling long division, the boy had it down cold and read a book on his own during the lessons.

Sylvester and his wife, Barbara Meister, wanted to keep Andrew, who is profoundly gifted with numbers, engaged and learning. So last fall, the father launched the Santa Cruz Math Circle: a six-week enrichment program that brought in mathematicians for two hours on Sunday afternoons to explore and discuss fascinating numerical puzzles and concepts with fourth- through eighth-graders. Math circles are an Eastern European and Russian tradition that spread across the U.S. in the last two decades. The goal wasn’t to plod through the standard formulas in preparation for a test, but to provide a stimulating and interactive environment in which Andrew and other kids with a knack for numbers could experience “math that was challenging and fun at the same time,” said Sylvester, a software engineer who works in Silicon Valley.

The new course in Santa Cruz has been “a huge success,” said Evelyn Strauss, whose 10-year-old son was an avid participant. “There’s a wide range of kids who are really enjoying the program.” Most students go through elementary school thinking that mathematics is only about adding and subtracting and arithmetic, “but there’s this whole world of math that’s not typically covered in school and that’s really interesting,” she said. Math circle reveals that world to kids.

Creating a math circle takes a lot of energy and planning — from finding dynamic instructors to booking classroom space — but it can be well worth the effort if no similar enrichment opportunities are available nearby. Parents might consider forming a circle when their children come home from school saying they’re bored with the level of mathematics that’s being taught, Sylvester said. “If your kid comes back and wants more challenging math, or if they love math or they love puzzles, then start one.”

One Sunday last November, the fledgling program was underway at a community center, with around 19 boys and seven girls mulling over a game called Conway’s checkers. The visiting instructor that day was Zvezdelina Stankova, a Mills College professor and director of the Berkeley Math Circle. Each student was given a sheet of paper with a grid of squares — divided in half by a thick line — and a pile of pennies to serve as checkers. Beginning at one end of the board, and given particular rules for checker-jumping and a theoretically endless supply of coins, Stankova asked: How far could the coins be advanced?

Students experimented with jumping the checkers to the third row on the other side of the line, and then the fourth, and Stankova demonstrated the winning solutions. What about the fifth row? Many kids became so engrossed, chattering among themselves, they didn’t want to stop to hear the next part of the lesson. “No touching the coins!” Stankova finally admonished. “It’s impossible to reach the fifth row,” she said, briefly explaining that the reason had to do with the quadratic equation and the Golden Ratio.

Stankova grew up in Bulgaria, where it was common for children to attend circles in math, physics, chemistry and poetry. “Kids went to the math circle because they loved what was happening in class and they wanted more of it,” she said. By contrast, in the U.S., “most of the kids come to the math circle because they don’t like what they see in school and they’re looking for something else.”

A COMFORTABLE PLACE FOR MATH GEEKS

About three years ago, Sylvester wanted to take Andrew to a math circle after hearing of the programs at Berkeley as well as Stanford, but those courses are popular and hard to get into. He and his wife have fostered their son’s passion for numbers in various ways, including online courses and a summer camp in mathematics, as well as math competitions. Although UC Santa Cruz was offering a monthly math circle at one point, that course was put on hold when the professor who ran it went on sabbatical.

Last summer, Sylvester decided to start a circle through the X Academy, a nonprofit that he founded to offer enrichment activities, and he reached out to math professor Paul Zeitz, co-founder of the San Francisco Math Circle. Zeitz promptly volunteered to give an introductory math circle session in Santa Cruz and connected him with Stankova and other willing expert instructors.

“I thought I’d be lucky to get five kids in a room on a Sunday afternoon,” Sylvester said. To his surprise, 50 students and their parents signed up to attend the free kickoff session by Zeitz. Through an application process, the Santa Cruz Math Circle ended up with around 25 regular attendees for the rest of the fall course; registration cost $75, but scholarships were available.

Sylvester ran the course with help from X Academy board members (including Meister) and other parent volunteers, who assisted with promotion and setup. Meeting the needs of students from fourth through eighth grades in a single class proved too wide of a spread in ability and maturity to manage, so the software engineer brought in an extra instructor and split the students into two tracks; but younger kids such as Andrew who were ready for the math of the upper-level group could move up.

For many attendees, being in a place where they could dive into math and interact with other number-loving geeks was a welcome shift from the standard school environment, where the subject isn’t exactly popular. The circle “creates this community where it’s safe to come and talk about math,” said teacher Nicholas Bugayong of Rolling Hills Middle School in Watsonville, who volunteered to drive four eighth-grade math students, all from Latino families, to the Sunday sessions. Some of these pupils were otherwise unable to make the 17-mile trek — their parents couldn’t bring them — or to afford the course without X Academy scholarships.

“Other people don’t like math and they say it’s a waste of time, but I think it’s interesting to learn things that you don’t learn in school,” said Rolling Hills student Monica Alvarez, 13. Listening to the other students as they volunteered different ideas and strategies for tackling challenging problems “helps you to learn other ways to solve a puzzle,” she added.

As for Andrew Sylvester, now age 10, the program prompted some more “math highs,” such as when he got into thinking about the Conway’s checkers conundrum. And the lessons spurred lively discussions. During one pizza break, he stayed behind in the classroom with two other boys who are also profoundly gifted at math. “They were bent over a piece of paper scribbling, in animated conversation,” recalled Strauss, whose son was part of the confab.

“I just like learning the math and arguing with my friends about math stuff — for example, stuff like if one over infinity equals zero,” said 10-year-old Olin Ottemann-Strauss.

MATH CIRCLE STARTUP LESSONS

The Santa Cruz Math Circle resumes this spring. A major challenge will be continuing to arrange for high-quality instructors, Tim Sylvester said. While ideal teachers include math professors or scientists or engineers with doctorates in math, not all such experts have the experience or classroom management skills to instruct young pupils in a dynamic way. But Sylvester hopes to eventually join forces with UC Santa Cruz’s math circle.

Even if there is no nearby college to collaborate with, anyone interested in launching a math circle program can find helpful, step-by-step resources on the National Association of Math Circles website, including lesson plans from the book, Circle in a Box. Teachers at some Bay Area schools have created their own programs, Sylvester noted, such as Nueva School in Hillsborough.

Sustaining a circle does require adequate financing, which can be an ongoing challenge if registration fees are to remain affordable. The Santa Cruz program recently got a donation from Cisco Systems, where Sylvester used to work, and parents can make contributions to X Academy through its website. The academy has also applied for a seed grant from the Berkeley-based nonprofit Mathematical Sciences Research Institute, which has funded many math circles over the years. But the institute is currently reviewing that grant program and has ended its support of the San Francisco Math Circle.

While many students often question why they need to learn algebra or calculus that they might not use later in life, Sylvester sees the ability to figure out tough math problems as being an essential life skill.

“One of the reasons you learn math is for the thought process and the problem-solving process,” he said. “That’s why you do it.”

Correction: An earlier version of this story misidentified Barbara Meister as Barbara Sylvester. It also stated that Andrew Sylvester’s third grade lessons in long division were at a private school, which is incorrect. He was attending a public school.

  • David Cordeiro

    The west coast Math Circles mentioned in the article are all great examples of the growing math circle community. For families in the Dallas-Fort Worth area there are two established math circles to choose from. The Metroplex Math Circle (http://www.metroplexmathcircle.org) and the Mid-Cities Math Circle (http://www.midcitiesmathcircle.org).

    • Lisa Norris

      Anyone have this going in the clearwater, Florida area?

  • Martin Fischberger

    Great. More enrichment opportunities for rich white kids. I suppose there’s nothing inherently harmful about that. Meanwhile, the rest of us are trying to figure out how to get the poor brown and black kids into the elite colleges and universities. Here’s the real question — can young Black and Latino students become more successful if they adopt the cultural masks and mores of the whites? Or is it not PC to say that? Or are we all color-blind Americans (and a few Canadians)? Or are we race-neutral when it’s convenient, and race-aware when it’s convenient?

    To put it another way, is the success of the math circle generalizable beyond the population of rich, two-college-graduate white families?

    • Cristina Smiley

      Everyone is free to learn.

    • Tim Sylvester

      Mr. Fischberger – I am befuddled by your comment and the insinuation that the Santa Cruz Math Circle is just an “enrichment opportunity for rich white kids.” If I wanted to create an enrichment opportunity for “rich white kids”, I would have just spent my time and money creating an enrichment opportunity for one “rich white kid” – my son. Instead, I created a non-profit organization, donated money to the non-profit, reached out to the leaders of math circles in the Bay Area and created a math circle in Santa Cruz because I knew there were more kids and families that would benefit. I then reached out to all of the schools in Santa Cruz County and invited their students to participate. I also contacted the organizers of the Bruce Woolpert Algebra Academy in Watsonville, a wonderful math program for middle schools students – mostly Latinos from low income families, and invited them to bring some of their students to the Math Circle, free of charge. Four students participated and their teacher is quoted in the article. During the admissions process, I specifically selected students from
      schools all over Santa Cruz to make sure that we had a diverse group of
      students, both ethnically and economically diverse. I had to turn away some of
      the “rich white kids” from the most affluent schools in Santa Cruz because we
      already had several students from the same school. We admitted a diverse group of 36 students from 16 schools across Santa Cruz County and 40% of them were girls.

      To answer your question “is the success of the math circle generalizable beyond the population of rich, two-college-graduate white families?” – YES. The San Francisco Math Circle actively reaches out to teachers to find students from different backgrounds that would not normally know about this type of enrichment activity. Dr. Tatiana Shubin from San Jose State University started the Navajo Nation Math Circles Project to bring math circles, teacher workshops and a two-week summer camp to the Navajo Nation.

      The response to the Santa Cruz Math Circle from the leaders of the Bay Area math circles, the students, and the parents has been overwhelming positive. It is sadly ironic that the only critical, cynical responses to the Santa Cruz Math Circle have come from two “educators” – you, a retired educator and another educator.

      This spring the X Academy is sponsoring another six week session of the Santa Cruz Math Circle and will host a test center for Math Kangaroo, a national math competition for K-12 students. I started the X Academy and the Santa Cruz Math Circle for ALL kids who love math. I encourage other parents, teachers and mathematicians to start math circles and I will gladly help anyone start a math circle.

  • ja

    Dear Mr. Sylvester, Don’t let comments like Mr. Fischberger’s get to you. Some people are not interested in listening or in the facts, they are just detractors. Your Math Circle project is inspiring and I plan to see how we can bring a Math Circle to our community. Keep up the good work.

  • Eunice

    Just because a child can apply a learned algorithm “dividing two digit numbers into 20 digit numbers” does not make them a gifted mathematician…..

  • Ricky

    As a student that is highly interested in math, reading
    about these math circles definitely piqued my interest, and I love the concept
    of an extracurricular, dedicated group of students that can freely explore the
    world of math. I also agree with the point about why we learn math: not to
    memorize and regurgitate random concepts, but to hone our problem-solving
    skills and imagination. However, I feel that ideas similar to math circles
    could be applied to other subject areas in school, and not just for advanced
    students. Teaching from the book and to the test is seen more and more
    frequently nowadays, and many people can find themselves stifled by public
    education. There are many subject areas where ideas like this could be
    implemented; for example, book clubs could serve as a creative outlet for students
    who are passionate about literature, but dislike the way it is taught in
    school.

    Here is a list, in my opinion, of some of the best English
    novels ever written. These would be great choices for a book club:

    http://www.modernlibrary.com/top-100/100-best-novels/

  • Daniel

    Dear Chen

    I enjoyed your blog on math circles. I enjoy math and I
    wished that there had been a math circle by my school when I was growing up. I
    think math circles are important because they offer a way to enrich the
    learning of kids who are interested in math. I agree with you that the
    classroom setting is not always the best way to teach kids math. Kids need to
    have access to programs where they are introduced to interesting math problems.
    Did you have a math circle by your school when you were growing up? Also, do
    you have a favorite math subject?

Author

Ingfei Chen

Ingfei Chen is a freelance writer in Northern California whose work has appeared in Scientific American, the New York Times and Smithsonian.

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