The Ross Summer Mathematics Program is an excellent example of how vertical integration of mathematics students, teachers, and researchers can be pursued in a deep and meaningful way. By considering simply stated questions from several directions and depths, students attain an understanding of how professional mathematicians and scientists work: gathering data, looking for patterns and analogies, making conjectures, and finally testing and proving those conjectures.
In the Ross Program for 2001 we began a new component for high school teachers. The Ross Program has involved teachers several times in the past. In fact, Arnold Ross began a teacher training program at Notre Dame in 1947 that eventually evolved into a program for students by 1960. That program moved to Ohio State in 1964 and has now become the Ross Summer Mathematics Program.
The current version of the teacher component began in 2001 with a start-up grant from the Park City Mathematics Institute. During this first summer we had five teacher participants attending for 3 weeks. Those teachers were enthusiastic about the ``exploration method'' used in the Ross Program. They were eager to try some of those pedagogical techniques in the classes they teach. They supported the idea of having occasional meetings during the academic year. Those meetings would serve as forums for those teachers to explain how they applied the Ross techniques in their own classes, and as a platform for recruiting some of their colleagues to have the Ross experience next summer. We plan to organize three such short meetings per year.
The teacher participants are involved in the program for the first 3 weeks, spending 4 hours in classes each day. They begin each day by attending the morning lecture on number theory along with the young students. The following two-hour workshop and a one-hour seminar focus on the number theory problems and various approaches and strategies to solve them. During the workshop and seminar times they work interactively on the assignments, discussing the ideas with one another with some guidance by the instructors. The crucial ingredient is the formation of a culture of exploration among the participants.
This teacher component of the Ross Program is an excellent outreach opportunity for the Department. It could have a real positive impact on the local schools, and will improve the articulation between the University and local high schools. We expect that this program will help improve the standing of the Department within the local math education community.
We propose to expand the teacher program to a class of 15 teachers. Such an extension is rather expensive since the teachers require stipends and since a low ratio of instructors to participants is needed for the exploration method to work effectively. In addition, we plan to organize three meetings per year for high school teachers during the academic year.