When research mathematicians get together, they exchange stories and favorite problems. They marvel at the way some things were solved, and share their amazement that certain problems that sound simple don't have solutions. They talk about what they have been doing, what they are working on, and what they wish they could learn if they only had the time. In short, they inspire each other. We hope that young mathematicians in school classrooms will have the same experience.
Perhaps one of the best-kept secrets about mathematics is that it is easy to get a feel for the kinds of questions that are at the wide-open frontiers of knowledge. We already know that students enjoy speculating about what happened to the dinosaurs, pondering the shape of the universe or imagining the Big Bang. We think that they can get as much intriguing puzzlement from wondering about the size of infinity and finding out that there are some very simple-sounding problems that would take huge computers longer than the estimated age of the universe to solve. We are concerned that so much of the ``good stuff'' doesn't make it's way into the math classrooms until graduate school.
Good mathematics ultimately comes from and returns to good stories --- and questions that bug you! We will have succeeded if you, and the children in your care, enjoy the stories and activities and come away from them with some annoying unanswered questions.
All of the activities involve hands-on exploration, and lots of opportunities for mathematical thinking, problem-solving and communication. All of the topics are live, important areas of current mathematical research. When mathematicians consider these subjects, they do just what you will be doing---wrestling with interesting ideas, and having that special kind of fun that comes from tenacious and satisfying thinking.
Mike Fellows
mfellows@sol.uivc.caNancy Casey
casey931@cs.uidaho.edu