How we do things, and why
“One of the reasons we don’t do as well as we should is that we are all over-taught.”
Many mathematicians participate in the Stanford Math Circle, and each brings to the project a distinctive approach, so it’s impossible to say what will happen in any particular meeting. But in planning and leading each session, we try always to keep in mind this penetrating observation of Fields Medalist Heisuke Hironaka:
“When a person works, he must have knowledge or he will make terrible mistakes. But at the same time, knowledge alone doesn’t do anything new. You must have instinct and somehow be conscious of making use of instinct. It is an interesting question how to give kids knowledge without having them lose their instinctive power. If you just keep pounding them with knowledge, most lose their instinct and try to depend on knowledge.”
At the Stanford Math Circle, we share Professor Hironaka's esteem for instinct, and his concerns about its vulnerability, so we strive always to avoid just pounding kids with knowledge. Rather, we try to involve them in a variety of activities — often novel games and puzzles — that subtly incorporate the deepest mathematical ideas we can think of.
Of course it’s hard work coming up with these things, and the sessions can get a little noisy sometimes. But the kids seem to like it that way.