Every parent with an appreciation of science wants her child to love math. But not all of us are equipped to help them see the beauty in numbers.
Recently, I came across an approach that seems to be catching on. “Math Circles” are informal math clubs for kids run by mathematicians who often hail from the former Soviet bloc. The small groups spend their time working out problems, solving various riddles and puzzles, and going on math field trips to places like art museums.
Math circles originated in Eastern Europe more than a century ago but did not arrive in the United States until quite recently – one account dates their arrival to the launch of a math circle in Boston in 1994. Today, there are more than 200 groups across the country.
While math circles—or matematicheskie kruzhki in Russian—have traditionally been for middle and high-school students, Natasha Rozhkovskaya, associate professor of mathematics at Kansas State University, recently wrote the first guide to math circles for elementary school children. Rozhkovskaya, who hails originally from Novosibirsk, Russia, leads a math circle at KSU in Manhattan, Kansas. I asked her why these clubs are, well, multiplying.
What is a math circle?
A math circle is a type of math club. It’s organized by a grown up who likes math very much and has some mathematics-based education. Usually, he or she works with a group of kids, and the background of the kids can be different. I work with kids who have a strong interest in math.
What kinds of things do students in math circles work on?
We work on challenging problems and discuss different techniques. Some people prepare for math competitions. So, it depends on the leader. And there are many different styles. There’s not just one particular way to do this.
What math competitions have your students participated in?
The most popular ones are [the Mathematical Association of America’s] American Mathematics Competitions which are geared to middle school students, and Math Kangaroo, which are for children of any age.
How do children learn differently in a math circle than they do in school?
The main difference is, most math circle leaders ask kids to build arguments, not just learn formulas and plug in numbers and get a different result. When you solve a problem you have to give a proof.
For example, what if I asked you how many ways are there to choose two apples out of 6? Now I need some time to compute that ... [pause] … It’s 15. But it’s not enough just to give the answer. You have to explain how you got to 15. You have to give the argument; you have to prove it.
Another topic is logic problems. For example, you have some people who are telling the truth, and others who are lying, and you have to figure out which statement is true. This teaches kids a very logical, structural kind of thinking. And also it helps them understand where formulas come from. If you just saw a formula in a nice box with some pictures in a book, okay, you can memorize it, but it’s better if you know where it comes from, because then you can better understand how and when to use it.
Tell me about the math circle you lead now.
We have 2 age groups: one goes up through fourth grade; a second is for 5th and 6th graders.
I have 25 children in the youngest group and 10 in the older group who attend on a regular basis. Each meets every two weeks. We try to invite special guests. The idea is that we talk not only about math itself, but we also try to talk about how, once you know math, you can do incredible things in your life.
And we invite people who can send the same message. Once, we had a speaker from NASA’s Johnson Space Center in Houston. He came and talked about the current space program, about his work at NASA, he showed beautiful pictures, brought us a piece of the space shuttle and a huge astronaut glove. It was incredible. And he said, yes, you should learn math if you want to work at NASA.
We also had an engineer from our department, a student, who gave a talk about robotics.
We also have game and puzzle days where we do wooden puzzles and brain teasers.
We take field trips. Each year we go to our art museum, and this is our joint project with the museum. We come after-hours when the museum is closed. We discuss one particular piece in the museum that is related to math, and each time it’s a different piece. It can be symmetry or probability.
How can you find a circle in your area?
Go to the Web site of the Association of Math Circles. There’s a link that lists circles around the world.
If there isn’t one in your area, how can you get one started?
The main thing is to find the right person. Sometimes, people in math departments don’t see right away the benefit of doing a math circle. But it’s very beneficial. First of all, if you start a math circle at the department of math, the local community respects the department and appreciates it a lot.
Second, mathematicians have historically thought of themselves as the elite. We often complain that people don’t understand us or that education is not good. When journalists write about math, they don’t quite write it correctly. But nobody but us is going to explain why math is beautiful and important. If there are any professional mathematicians reading this: we should go and explain to people why math is beautiful. We should not wait, and a math circle is one of the ways to do that.
What is the difference between how math was taught in Russian schools when you lived there and how it is taught in U.S. schools?
The difference probably is the following: In the Soviet Union we were granted a good math education. You go to school, and if you are a good student it’s enough to gain a good understanding of the culture of math, because textbooks were written by very prominent mathematicians. It was taken very seriously. In the United States, you are not always granted this when you go to school. Still, you can get a good math education if you look for it.
*Answer: Kaleidoscope symmetry is based on a system of mirrors, so only the bicycles and the letter K patterns could appear as a picture in a kaleidoscope. Only these two patterns have the correct, reflective type of symmetry. [Adapted from "Math Circles for Elementary School Students," by Natasha Rozhzovskaya, a co-publication of the American Mathematical Society and the Mathematical Sciences Research Institute.]
More to Explore:
Browse or order “Math Circles for Elementary School Students,” by Natasha Rozhkovskaya.
Find a Math Circle near you.