Last summer there were eighty students, mostly from high school, who had strong interests in math. The students never recieve scores on the problem sets. They are instructed to finish as much as they can, and recieve comments. Finishing the problem sets becomes steadily more difficult as the program progresses, and few students come close to finishing the problem sets in the second half of the program. The lack of grades enables the program to keep competition to a minimum.
Students constantly work together and discuss the problems.
This brings us to the role of counselors. I commented on their problem sets, and discussed their work with them. We talked about the course and tried to resolve some difficulties. Besides his or her five students, the counselor is responsible for all of the students in the program. Students work with students, students work with counselors, counselors work with counselors.