IAS/Park City Mathematics Institute
The PCMI Summer Session High School Teacher Program is a paradigm for the lifelong professional development of high school teachers, just as PCMIs 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:
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:
The system of Gaussian integers, Z[i], consists of all
complex numbers a+bi where a
and b are integers. Geometrically,
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
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.
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.
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:
theory and algebra
1 to 3 years, the working groups will:
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.
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.
Year-long Program of Professional Development and Outreach Groups
Teachers in the PDO groups meet regularly to
The classic PDO group is facilitated by a cooperating university or college faculty person.
Development and Outreach groups currently active:
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: firstname.lastname@example.org.)
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:
questions or concerns should be directed to C. Giesbrecht