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Secondary School Teachers Program

PCMI 2009 — Application DEADLINE January 28, 2009

The Park City Mathematics Institute (PCMI) of the Institute for Advanced Study, Princeton, NJ, offers comprehensive professional development for mathematicians and teachers of mathematics, as well as programs for students aspiring to a career in mathematics.

The Secondary School Teachers Program (SSTP) Summer Session is a 3-week residential program in Park City, Utah, and is part of the larger PCMI program. Teachers are given full support and a stipend during the Summer Session. In addition, 6 quarter-credits of 400-level mathematics are available from the University of Washington for a modest fee. A related but separate program is a special one-week session for mathematics supervisors, curriculum coordinators, or university mathematics educators involved in designing and delivering professional development.

The SSTP is structured around three goals:

All teachers should be involved in
• continuing to learn and do mathematics
• analyzing and refining classroom practice
• becoming resources to colleagues and the profession.

Each of these goals is reflected in the three strands that comprise the summer courses and activities.

Some Questions and Problems in Arithmetic (2 hours per day, 5 days per week)
This course will investigate questions like these:
- In how many ways can an integer be written as the sum of two squares?
- In how many ways can an integer be written as the sum of four squares?
- What's the probability that an integer picked at random has no perfect square factor?
- What's the probability that two integers picked at random have no common factor?
- Which linear functions f(x) = ax+b (a and b integers) generate infinitely many prime numbers for integer values of x?
- What is the probability that an integer picked at random between 1 and 1020 is a prime number?
The real goal of the course is to answer the following quesiton:
How are all of the above questions related?
In this three week course, you will investigate questions like those above and develop underlying structural similarities among them. In particular, you will see how to use the algebra of sequences and series as a general- purpose tool for these investigations. No prior knowledge of number theory or sequences and series is assumed, and by the end of three weeks, you'll be astounded at what you've discovered about arithmetic and its applications to the 7-12 curriculum.
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.
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
- Learning from Teaching Cases
- Implementing Lesson Study
- Visualizing Functions
- Algebraic Number Theory
Note that these topics may change before the Summer Session. All participants will be notified of their working group assignments prior to the Institute.

The Working Groups will collaborate with others in their group to produce some product that can be shared with others at PCMI and across the larger mathematical education community. Each working group is composed of a small group of teacher participants and a resource person. The group works together to research existing classroom materials and techniques, technologies, and other materials related to the topic, for dissemination and eventual publication by PCMI. The focus of the work should be on:
- creating and elaborating meaningful tasks
- designing activities to extend content knowledge
- illustrating the use of technology as a way to enhance learning and teaching
Applicants should rank their first, second, and third choice of Working Group on the application form. After applicants are accepted and named to a Working Group, some preparation in the form of reading or materials review may be suggested by working group leaders.