Lecture Publication Series PCMI Math Forum Archive 2003 Program About the Program


Institute for Advanced Study
Questions and Comments


High School Teacher Program at Summer Session

Professional Development and Outreach groups Program

List of Professional Development and Outreach groups

Affiliated Programs

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 for 2003 is Sums and Differences: the Art and Craft of Adding and Subtracting.  How do you find a polynomial function of smallest degree that agrees with a table of data? What's the sum of the fourth powers of all the integers between 1 and 100? What's the sum of the reciprocals of the perfect squares? What's the sum of the squares of all the complex numbers whose fifth power is 1? Why, if the third differences in an input-output table are constant, is there a cubic polynomial fit? What's the probability that two integers, chosen at random, have no common factor? And, most importantly, what do all these questions have to do with one another? This course will look at the calculus of finite differences as a unifying theme for these questions and others that connect to the middle and high school curriculum.

 2. 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 and ideas for teaching specific mathematical topics selected from the secondary curriculum

3. Working Groups (2 hours, 4 days a week): As part of their summer activities, each participant selected for the 2003 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 

Connections to the PCMI Mathematical Theme
Data analysis and probability
 Physics in the mathematics curriculum
Geometrical concepts from constructions, models, and investigations
Japanese lesson study
Mathematics in the Middle Grades
Note that these topics may change before the Summer Session.  All participants will be notified of any changes.

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.

blue_arrow.GIF (140 bytes)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, June 29-July 6.  Those in the Math Specialists program will take part in the morning sessions of the High School Teacher Program and will meet together in a special working group in the afternoon.  (See the working group page for a description of this group's focus and activity.) 

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

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

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 (Northwest Mathematics Interaction); 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 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.