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.