(M – F, 9:00A.M. – 5:00P.M.)
A typical teacher's day in the summer program will begin with a morning lecture attended by all PROMYS participants: teacher participants, first year and returning students alike. This is followed by work with other teachers on a daily problem set. The teachers work collaboratively and in an exploratory manner. The problem sets are not designed to test what a teacher has learned in past mathematics courses. Instead, the problem sets are designed to encourage participants to design their own numerical experiments and to employ their own powers of analysis to discover mathematical patterns, formulate and test conjectures, and justify their ideas by devising their own mathematical proofs. Like the classroom activities that PfT encourages, the problem sets are low threshold high ceiling, so there is enlightenment, discovery, and challenge for teachers from a very wide range of mathematical backgrounds.
Counselors (graduate students in mathematics, research mathematicians, and graduates of previous PROMYS programs) serve as resources for the teachers in their work. Participants' written work on problem sets will be reviewed by the counselor staff each evening and returned the next morning with written comments. Weekly problem sessions run by PROMYS staff help teachers pull together threads of ideas from the problem sets and focus on the big ideas.
Second-year participants: Returning participants take an advanced seminar and engage in research projects. Twice each week, teachers will meet with their small research group (usually two teachers and a counselor) in the exploration labs. In the fifth week, each research group will submit written reports of their work and give an oral presentation summarizing their results to the rest of the program.
Returning participants add an important dimension to PROMYS by sharing their valuable program experience and by serving as peer role models for first-time participants. The second summer of participation helps teachers cement their experience of mathematical exploration and extend their content knowledge into other mathematical fields relevant to the high school curriculum. Moreover, through their discussions with beginning participants, the returning teachers share strategies they have learned for engaging students in the process of mathematical exploration. This is an important part of the community-building that is so crucial for the long-term success of these efforts.