IAS/Park City Mathematics Institute
HIGH SCHOOL TEACHER PROGRAM (HSTP)

The PCMI Summer Session High School Teacher Program is a paradigm for the lifelong professional development of high school teachers, just as PCMI’s graduate summer school/research component is a paradigm for the lifelong professional development of a research mathematician. As such, the high school teacher program includes the following three components:

1. continued rigorous mathematical learning
2. reflection on (analysis of) classroom practice
3. becoming a resource to colleagues and the profession

Reflecting these components, the PCMI summer session for high school teachers has three strands:

 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.   The course slated for 2002 is “Applications of the Gaussian integers and related systems” a deep, yet eminently accessible topic that links closely with the other mathematical topics of the 2002 Summer Institute, from the sums of squares which Deborah Ball will explore with 6th graders to combinatorial questions and (via factorization) to the zeta function in the undergraduate program and (via theta functions) to the research topic of automorphic forms and applications:

 Applications of the Gaussian integers and related systems
15 two-hour guided problem sessions 

The system of Gaussian integers, Z[i], consists of all complex numbers a+bi where a and b are integers.  Geometrically, Z[i] can be represented as the lattice points (the points with integer coordinates) in the complex plane. Z[i] can be used to illustrate, deepen, and tie together many important ideas in secondary mathematics. This course will look at some of the applications of the system to topics in arithmetic, algebra, geometry, and discrete mathematics. In addition, we'll look at how algebraic systems like Z[i] can be employed in task design, the craft of writing problem sets and activities for one's students.  The course will develop the arithmetic of Z[i], comparing and contrasting it to the ordinary number theory of integers. We'll then apply this arithmetic to topics like Pick's theorem, generating Pythagorean triples, and counting the number of ways an integer can be written as the sum of two squares. The ideas and machinery we develop will be applied to related problems: finding other ``triples'' related to Pythagorean triples, writing numbers as the sum of four squares, and looking at asymptotic estimates for functions that arise in arithmetic.

 2. Math in the Classroom – reflections on practice (1 hour per day, 5 days per week, plus opportunities for informal sessions in late afternoon and evenings):  The participants will actively investigate, consider, and discuss what it means to teach school mathematics and how knowledge of content is interwoven with the practice of teaching.  They will ground the discussion in actual tasks involved in teaching such as grading student work, designing assessments, managing discussions, or planning lessons, all within the context of a central mathematical topic or course common to the secondary mathematics curriculum but related to the overall mathematical theme of the institute.  For example, the topic of functions at the high school level may be considered when harmonic analysis is the topic for the undergraduate program in 2003.

A framework for the work of the participants will be the NCTM Principles and Standards and the National Board for Professional Teaching Standards (NBPTS) for certification in mathematics (nbpts.org). NBPTS candidates are required to describe, analyze, explain, and reflect on their practice, providing insight into what is happening in their classroom as well as a rationale for those events and processes.  They are required to systematically analyze student work, class work, assessments, and other instructional materials (NBPTS, 2001), just as will be done at PCMI.  Throughout a two-year cycle, PCMI participants will also study the use of videotapes as a medium to provide authentic and complete views of teaching and illustrate ways in which students can be engaged in learning.  They will examine how teachers translate knowledge and theory into practice and use this knowledge to consider their own practice and what it would involve for them to become NBPTS candidates.

3. Working Groups (2 hours, 4 days a week): Every participant in the High School Teacher Program pre-selects a working group from a set of options.  For example, the 2001 working groups consisted of:

Number theory and algebra
Data analysis statistics, and probability
Physics in the mathematics curriculum
Geometrical concepts
Making mathematics meaningful
Japanese lesson study

 Over 1 to 3 years, the working groups will:

•  Review and critique existing materials and activities for the selected topic in the secondary curriculum

• Prepare and pilot 1 to 3 units or activities, together with the associated mathematics

• Prepare the activities for eventual publication in some form

 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. Mathematicians from the Institute who are knowledgeable about the topic will critique the products prior to publication.  The products may take many forms such as an on-line course for professional development, a web-based bibliography of resources for a particular topic, 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 many participate in a variety of ways depending on their area of expertise, e.g. writing, creating, technology.

In addition to the formal program components listed above, several small volunteer focus groups will be formed based on the interests of the participants and the background of the staff and participants.  For example, a group may be formed around the use of the internet in mathematics classrooms or around how to use a new piece of software in a statistics course.

Applicants will be asked to 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 group.

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 Year-long Program of 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

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

Rutgers University-Newark Campus, Newark, NJ; David Keys, keys@andromeda.rutgers.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 Washington, Seattle, WA; James King, king@math.washington.edu

Alumni groups:

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 involvmenet in PCMI. Groups of 5-10 teachers and 1-2 university support persons are invited to apply. (Groups interested in applying should contact Catherine Giesbrecht, PCMI Administrator, at 609-734-8290 or by email: giesbrec@ias.edu.)

Affiliated Programs

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.

Other Links:

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.

PCMI Summer Session Page

PCMI Home Page

questions or concerns should be directed to C. Giesbrecht