The PCMI 2004 Summer Session has three strands:

Stories that Count: The Art and Craft of Combinatorial Proofs

(2 hours per day, 5 days per week)

Combinatorics, sometimes called, "the art of counting without counting" has made some inroads into the middle and high school curriculum. This course will look at how combinatorics itself can fit into the 5-12 program, but it will also look at how combinatorics and combinatorial thinking can be used to illuminate ideas from more mainstream courses like algebra, arithmetic, and geometry. Look at any row of Pascal's triangle. What is the sum of the entries? What is the sum of the squares of the entries? Combinatorial proofs allow you to answer questions like these by "telling a story" - establishing a formula by showing that each side of the formula represents a different way to count the same thing. Starting from scratch, we'll learn in this course how to use combinatorial proofs to create and establish - in very simple ways - many beautiful results that will delight your students.

 

Reflecting on Practice: Connections to Research

(1 hour per day, 5 days per week, plus opportunities for informal sessions in late afternoon and evenings)

After considering research related to teaching and learning mathematics, participants will reflect on the implications of this research for what takes place in classrooms. The discussion will be grounded in the development of lessons, student work, and videos of classroom practice. Participants will conduct small research investigations around some topic of interest in the secondary curriculum.

 

Working Groups

(2 hours, 4 days a week)

As part of their summer activities, each participant selected for the 2004 High School Teacher Summer Program will be assigned to a small subject-specific working group, which will prepare an activity or resource for the profession (with the associated mathematics) for piloting during the following year.