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Reasoning from Data and Chance
Exploring Discrete Math
Investigating Geometry
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Visualizing Functions
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The PCMI 2008 Summer Session has three strands:
 Applications of Algebra and Geometry to the Craft of Teaching
 (2 hours per day, 5 days per week)
 How do you generate Pythagorean triples? Scalene triangles with integer sidelengths and a 60degree angle? Cubic polynomials with integer zeros and extreme points? Triangles on the Cartesian plane whose vertices have integer coordinates and whose side lengths are integers? A mathematical analysis of how to design problems that "come out nice" leads to investigations into foundational ideas from number theory, algebraic geometry, and analytic geometry. We'll use this theme as a springboard into investigations of the structure of different algebraic systems and geometric curves. This applied mathematics — choosing and designing tasks — is mathematics applied to the work teachers do.

 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, student work, and classroom practice. Participants will work collaboratively to develop teaching and learning resources in order to implement ideas from their discussion. The focus will be on teaching strategies that enable students to learn mathematics.
 download: Research References for Week 1 [username/password required]

 Working Groups
 (2 hours, 4 days a week)
 As part of their summer activities, each participant selected for the 2008 Secondary School Teacher Summer Program will be assigned to a small subjectspecific 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
 Learning from Teaching Cases
 Visualizing Functions
 Algebraic and Analytic Geometry
