How to Start a Circle

To help you create your own Math Circle, we offer this text adapted from Emily McCullough and Tom Davis (So You’re Going to Lead a Math Circle). We also suggest that you check out the wealth of resources available at https://mathcircles.org/

You would like to lead a mathematical circle and you have never done it before. Here we give you a few pointers on what it takes, how to prepare and what you can expect.

What is a math circle?

A math circle is a group of students (usually motivated high school or middle school students) led by a mathematician who get together each week to learn mathematics. It is helpful if the person in charge has an assistant (students and parent volunteers are welcome!) to ensure the smooth running of the activity.

Often the leader changes regularly which has a few advantages:

  • The leader doesn’t get burned out; it’s easy and fun to prepare a couple of presentations per year for motivated students.

  • The students see different mathematical styles and different topics.

  • The leader can make the same presentation at multiple circles if there is more than one circle in the area.

Math circles are different from the typical high school “math club”:

  • Circles emphasize problem solving.

  • Circles don’t necessarily cover material from the standard curriculum.

  • Circles get students to think; they are generally not designed to drill the students for mastery of a skill or topic (although sometimes they can be designed to do this and the students don’t even realize that it’s happening).

To assure that the circle session you lead goes as well as possible:

  • Circle sessions often concentrate on problem solving techniques applicable in many areas. Sample circle topics include: symmetry, the pigeon-hole principle, divisibility, counting, probability, invariants, graphs, induction, plane geometry, or inversion in a circle.

  • Hand out a set of problems a week before your session. Not too many, perhaps three or four, but seductive. Include an easy one and a challenging one.

  • Try not to lecture. Even though introducing new theory and techniques is an integral part of math circles, your sessions should be as interactive as possible. Score yourself: 1 point per minute you talk; 5 points per minute a student talks; 10 points per minute you argue with a student; 50 points per minute the students argue among themselves.

  • Divide students into groups of 2-4 to solve problems. Have them present their own solutions.

  • Be encouraging, even about wrong answers. Find something positive in any attempt, but don’t be satisfied until there is a rigorous solution. Wrap up each problem by reviewing the key steps and techniques used.

  • If the kids cannot answer your question immediately, don’t just tell them the answer; let them think. If they’re still stuck, give hints, not solutions.