One of the distinguishing features of a Math Cirlce is the variety of presenters. The students participating in a Math Circle will be exposed to not only a variety of mathematical ideas but also to a variety of mathematicians. Here are some key points to keep in mind when preparing a presentation for the Washington University Math Circle.
  1. The most important thing is that the students are working (alone or together) for 50-90% of the time and listening to you for about 10-20% of the time (no more than this!).

  2. The emphasis of a presentation should be on Problem Solving. Students might forget most topics they see in the Math Circle, but they are likely to remember the problem solving techniques that they encounter.

  3. Make the presentation explorative and interactive.
    • Divide the students into groups to work on a problem.
    • Let students do computations together, draw pictures, etc.
    • Give the students plenty of time to work things out.
    • While the students are working, you can walk around the room and offer suggestions and insights.

  4. Do not do proofs at anything but the most basic level (and even then it will take some real thought to get the level right).

  5. Try to arrive a bit early (~5 minutes) and give the students an initial problem to work on. Write the problem on the board and let the students work on it for 5-10 minutes. This is very helpful to get them immediately engaged in the topic! Make sure you tell the students to get working on the problems you give them!

  6. There is a wide age range for our math circle---5th grade to 9th grade. It is important that we try to make sure there is something for everyone. Give the younger students something easier to work on and give the older student something more difficult. Check in with the younger students more often to make sure they are following, or at least accomplishing something.

  7. Try to have some problems to give to the kids who finish their tasks early (e.g., "here, figure this one out!"). This will keep everyone on task.

  8. The main point is not to demonstrate some fantastic mathematics (although, if you can that is great). The main point is to get the kids engaged in mathematics by giving them problems to work on that they can actually do.

  9. Focus your presentation on a set of activities for the kids to do.

  10. If you are willing to type up some notes (or share your handwritten notes), I would love to have them so that we can maintain an archive of such materials.

Math Circle
Washington University