The PCMI 2003 Summer Session has three strands:

1. Sums and Differences: the Art and Craft of Adding and Subtracting
   (2 hours per day, 5 days per week)
   How do you find a polynomial function of smallest degree that agrees with a table of data? What's the sum of the fourth powers of all the integers between 1 and 100? What's the sum of the reciprocals of the perfect squares? What's the sum of the squares of all the complex numbers whose fifth power is 1? Why, if the third differences in an input-output table are constant, is there a cubic polynomial fit? What's the probability that two integers, chosen at random, have no common factor? And, most importantly, what do all these questions have to do with one another? This course will look at the calculus of finite differences as a unifying theme for these questions and others that connect to the middle and high school curriculum.
   
   
2. Reflecting on practice: Connections to Research
   (1 hour per day, 5 days per week, plus opportunities for informal sessions in late afternoon and evenings)
   Participants will consider research related to teaching and learning mathematics and reflect on the implications of this research for what takes place in classrooms. The discussion will be grounded in the development of lessons and ideas for teaching specific mathematical topics selected from the secondary curriculum.
   
   
3. Working Groups
   (2 hours, 4 days a week)
   As part of their summer activities, each participant will be assigned to a small subject-specific working group, which will prepare an activity (with the associated mathematics) for piloting during the following year.