2006 Index Page
2006 Photos
2006 Roster
Class Notes
Daily Schedule
Getting Started
Participant Outreach Activities
Project Abstracts
Update Contact Info
Send Note: Suzanne & Richard
Site Map
Working Groups
Reasoning, Data, Chance
Exploring Discrete Math
Investigating Geometry
Learning from Teaching Cases
Implementing Lesson Study
Visualizing Functions
Advanced Geometry
Teacher Prof Continuum
Related Programs
Designing and
Implementing Professional Development
Remote Sites
Etable  McAllen
Etable  Cincinnati
username/password required
Contact List
Discussions
Email addresses
Morning Announcements
Portrait Photos
Forms

The PCMI 2006 Summer Session has three strands:
 Developing Mathematics: Some Applications of Geometric Thinking
 (2 hours per day, 5 days per week)
 While geometry is a wonderful field in its own right, geometric ideas
are also useful tools for studying and understanding all kinds of
phenomena inside and outside mathematics. Teachers in this course
will look at some basic geometric habits of mind like studying
continuous change and looking for things that don't change, and
they'll apply these habits to a wide variety of situations. For
example, we may look at
Geometric optimization: what are some generalpurpose tools for
minimizing paths or maximizing area?
Geometric invariants: what attributes of a figure stay the same when
the figure is changed in some regular way?
The fundamental theorem of algebra: what does it say, why is it
fundamental, and why is it true?
Fixed points: If you pick a positive number, take its square root,
take the square root of that, and keep up the good work, what
happens and why?
What geometric thinking is common to all these and similar
questions?
No background with any of these questions will be assumed. One of the tools
we may use in the course is a dynamic geometry environment (like The Geometer's Sketchpad® or Cabri). Here, too, we'll start from scratch. By the end of week three, we promise some beautiful and exciting applications of geometry.
 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. 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 use problemsolving and openended approaches.

 Working Groups
 (2 hours, 4 days a week)
 As part of their summer activities, each participant selected for the 2006 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 and Data and Chance
 Exploring Discrete Mathematics
 Investigating Geometry
 Learning from Teaching Cases
 Implementing Lesson Study
 Visualizing Functions
 Advanced Geometry
 Teacher Professional Continuum
