The PCMI 2010 Summer Session has three strands:

Over and Over

(2 hours per day, 5 days per week)

Pick a positive number, take the reciprocal and add 1. Then take the reciprocal of that and add 1. Then again, and again, until.... Many mathematical problems can be explored and solved through the study of iteration. This course will explore how iterative processes can be used to investigate Fibonacci numbers, image processing, the calculation of square roots, and more. No specific mathematical prerequisites are necessary, but by the end of three weeks, participants will have a useful toolkit of techniques that can be applied to many different areas.

 

Reflecting on Practice: Connections to Research

(75 minutes 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 with a particular focus on student thinking and how it can be used to shape instruction. The discussion will be grounded in the study of discourse in lessons and classroom practice in both the United States and other countries. Participants will work collaboratively to consider different approaches to managing discussions that better enable students to learn mathematics.

 

Working Groups

(2 hours, 4 days a week)

As part of their summer activities, each participant selected for the 2009 Secondary 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. The working groups are:

• Reasoning from Data and Chance
• Exploring Discrete Mathematics
• Investigating Geometry
• Implementing Lesson Study
• Visualizing Functions
• Learning the Mathematics of Image Processing