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 High School Teacher Program is one component of PCMI.  The High School Teacher Program summer session is a three-week experience for secondary mathematics teachers.  A related by separate program is a special one-week session for mathematics supervisors or curriculum coordinators.  The HSTP is structured around three goals:

• 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.

 1.  Developing Mathematics. (2 hours per day, 5 days per week.)  Focused on learning mathematics by working problems together, this course explores the fundamental mathematics on a topic that is rooted at the secondary level but related to the mathematical theme of the Institute.  Careful work on this topic allows teachers (and students) to understand exactly how elementary and more advanced procedures in the specific content area are derived and generalize. The course is structured so that each participant can work at his/her own level. Those who are more mathematically advanced may be asked to help those with less preparation.  The course is conducted by teacher leaders from the PROMYS program at Boston University.  The focus of this strand is entirely on mathematics, although opportunity is provided within the course for reflection on the approach used by the instructors and to consider the implications of such an approach for teaching in secondary classrooms.   

Stories that Count:  The Art and Craft of Combinatorial Proofs

Combinatorics, sometimes called, "the art of counting without counting" has made some inroads into the middle and high school curriculum.  This course will look at how combinatorics itself can fit into the 5-12 program, but it will also look at how combinatorics and combinatorial thinking can be used to illuminate ideas from more mainstream courses like algebra, arithmetic, and geometry.  Look at any row of Pascal's triangle.  What is the sum of the entries?  What is the sum of the squares of the entries?  Combinatorial proofs allow you to answer questions like these by "telling a story" - establishing a formula by showing that each side of the formula represents a different way to count the same thing.  Starting from scratch, we'll learn in this course how to use combinatorial proofs to create and establish - in very simple ways - many beautiful results that will delight your students.

3. Working Groups (2 hours, 4 days a week): As part of their summer activities, each participant selected for the 2004 High School Teacher Summer Program 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.  The working groups are:

Combinatorics
Data analysis, Statistics and Probability
Functions
Geometry
Japanese Lesson Study

Note that these topics may change before the Summer Session.  All participants will be notified of any changes.

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

The products may take many forms, such as an on-line course for professional development, or a series of lessons designed to exploit the mathematics in a way that is different from that found in traditional texts.  Because the working groups are flexible, teachers may participate in a variety of ways depending on their area of expertise (e.g. writing, creating, technology.)  The work of summer 2004 will be field-tested, and reviewed by the group participants in their classroom during the 2004-2005 school year.  The final product will be posted on the PCMI website, or published in some form.  Mathematicians from the Institute as well as teachers who are knowledgeable about the topic will critique the products prior to publication.

Applicants will 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.

Click here for a more in-depth description of each working group.

The program for Math Specialists will take place during the first week of PCMI, July 11-July 17.  Those in the Math Specialists program will take part in the regular sessions of the High School Teacher Program and will meet together in a special working group at selected times.

The 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 nominal fee.

HSTP Professional Development and Outreach Groups
Teachers are strongly encouraged to take advantage of additional opportunities through involvement in PCMI’s Professional Development and Outreach groups. These groups, based at cooperating university sites around the country, meet regularly throughout the school year and are usually composed of (although not limited to) teachers living in the same geographic region of the country. Other PDO groups may be formed from common professional interests, rather than geographic proximity, and would utilize technology for virtual meetings.

Teachers in the PDO groups meet regularly to

• deepen their understanding of mathematics,
• develop their skills in and understandings of effective teaching of mathematics,
• prepare professional development workshops for high school teachers and conference presentations.

The classic PDO group is facilitated by a cooperating university or college faculty person.

Professional Development and Outreach groups currently active:
(PDO facilitator(s) in italics):

Boston University, Boston, MA (PROMYS for TEACHERS); Glenn Stevens, ghs@math.bu.edu

Brigham Young University, UT; David Wright, wright@math.byu.edu.

California State University at Northridge, Ann Watkins and Peg Cagle, pegcagle@teacher.com

California State University at San Bernardino, San Bernardino, CA; Robert Stein, bstein@csusb.edu

Duke University, Durham, NC; Jack Bookman, bookman@math.duke.edu

Ohio State University, Columbus, OH (Ross Summer Mathematics Program for Teachers); Daniel Shapiro, shapiro@math.ohio-state.edu

Rice University, Houston, TX; John Polking, polking@rice.edu

Rider University, Lawrenceville/Trenton, NJ; Charles Schwartz, schwartz@rider.edu; Ciprian Borcea, borcea@rider.edu

St. Peter's College, Jersey City, NJ (Northern NJ Professional Development and Outreach Group); Brian Hopkins, hopkins_b@spc.edu

Texas State University, San Marcos, TX (McAllen ISD); Max Warshauer, max@txstate.edu

University of Cincinnati, Cincinnati, OH; David Minda, david.minda@math.uc.edu; Charles Groetsch, groetsch@uc.edu

University of Louisville, Louisville, KY; Steven Seif, swseif01@louisville.edu; Prasanna Sahoo, pksaho01@louisville.edu; Robert Ronau, bob@louisville.edu

University of Michigan at Dearborn, Dearborn, MI; Roger Verhey, rverhey@umd.umich.edu

University of Texas Pan American, Edinburgh, TX (McAllen ISD); Miguel Paredes, mparedes@panam.edu

University of Washington, Seattle, WA (Northwest Mathematics Interaction); James King, king@math.washington.edu

Clark Atlanta University, Atlanta, GA; (facilitator position open, contact giesbrec@ias.edu)

Idaho State University, Pocatello, ID; Robert Fisher, fishrobe@isu.edu

Purdue University; (facilitator position open, contact giesbrec@ias.edu)

Rhode Island College, Providence, RI; (facilitator position open, contact giesbrec@ias.edu)

University of Illinois at Chicago, Chicago, IL; Naomi Fisher, ndfisher@uic.edu

University of Utah, Salt Lake City, UT; James Carlson, carlson@math.utah.edu

University of Texas at Austin, Austin, TX; Gary Hamrick, hamrick@math.utexas.edu

PCMI is always interested in forming new Professional Development and Outreach groups and invites teachers or university faculty to consider forming such a group for future involvement in PCMI. For information on how to apply, such groups should contact Catherine Giesbrecht, PCMI Administrator, at 801-581-7467, or by email: giesbrec@ias.edu

Three PDO groups host their own summer institutes for teachers, concurrently with the PCMI Summer Institute in Park City. Teacher participants from these regions are encouraged to complete the local summer program before applying to the Park City summer program. These groups are:

PROMYS for TEACHERS (at Boston University). This program is in session concurrently with the PCMI Summer Session.
Ross Summer Mathematics Program for Teachers (at the Ohio State University).  This program is in session concurrently with the PCMI Summer Session.
Northwest Mathematics Interaction (at the University of Washington).  This program is in session in August and throughout the school year.

NonEuclid
NonEuclid is an interactive program for studying hyperbolic geometry. It is a java applet, so it can be used through your browser. It is being developed by Joel Castellano, supported by the PCMI.