We were originally inspired to start a math circle by the book “Math from Three to Seven” by Alexander Zvonkin. This book is a diary of a Russian father in the 1980s who led a math circle for his daughter and son. It describes both the activities he did and the children’s reactions to the problems.
We wanted to do math with our daughter, but noticed that she didn’t respond well in a 1-on-1 situation. We wanted to show her that math is something fun you can do with your friends. The kids are always excited to see their friends each week, and it’s a lower pressure environment to explore math concepts.
The primary principle of our teaching philosophy is to do problems, not exercises. The kids all get plenty of practice for core skills such as counting, addition, and subtraction. However, we’ve noticed that there is less of a focus on logic and open-ended problem solving. We try to construct activities where the kids don’t initially know how to solve the problem and have to come up with their own method. One important part of this is the parents generally sit in the other room during circle, so they’re not tempted to give help or advice.
For example, consider the problem of sorting cards numbered from 1 to 60. One approach would be to teach them sorting techniques (e.g., put all the 20’s together, all the 30’s together, etc.) and have them apply the techniques several times. Our approach was to give them a pile of shuffled cards and say “sort as many of these as you can in 10 minutes”. The kids had to work together with no adult leader (a challenge). In a few run-throughs, they came up with several promising approaches to the problem.
We try to include a mix of group and individual activities in each circle. We also try to vary the difficulty of the problems.