The PCMI 2006 Program

« Secondary School Teacher Program

Secondary School Teacher Program Working Groups

Please note these descriptions are subject to change. If you have any questions regarding the SSTP Working Groups, please contact the PCMI office at pcmi@ias.edu.

Participants will explore ideas relating to data and chance using teh Navigation Series from the National Council of Teachers of Mathematics as a resource.  Technology, such as the statistical software of FATHOM, will be used as a tool for learning.  The goal is to produce lessons, describe teaching strategies, or present an issue related to statistics or probability.  Content related to the study of data in beginning secondary courses as well as in AP Statistics will be explored.

Exploring Discrete Mathematics

Members of this working group will explore topics from the rich field of discrete mathematics, which is increasingly important in both various applications and K-12 education.  Possible topics include counting techniques, graph theory, logic games, and in the light of this year's research topic, coloring maps on bagels.  Participants will develop resources to help their peers incorporate this material into their classrooms.

Investigating Geometry

Participants will consider one or more rich geometry topics from multiple mathematical and pedagogical perspectives with special emphasis on "hands-on-investigations," model building, dynamic software, and other active approaches.  From this work, the group will create lessons, activities, or discussion documents that relate to the classroom and geometrical investigations.

Learning from Teaching Cases

Participants will discuss readings and video of classrooms, using video taken from a variety of sources, including some classes taught by Deborah Ball at PCMI.  We will construct ways of talking about classroom practices and student learning in order to elarn and benefit from observing video.  The product will be a record of the group discussions during the summer session and afterwards.

Teacher Professional Continuum Wirting Group

As a part of the Teacher Professional Continuum (TPC) program the National Science Foundation has funded PCMI to create and disseminate ourse materials
based on the Developing Mathematics course. The TPC working group will make decisions about what support facilitators would need to teach these courses, and then work on creating that facilitator support.

Implementing Lesson Study

Lesson study, Jugyuu Kenkyuu, is a professional  development activity that is at the heart of much of the professional development for teachers in Japan.  In this group, participants will select a daily goal for a "study lesson," spend an extended period of time collaboratively creating a detailed lesson plan, observe a participant teach the lesson to students, participate in a collogquium to discuss the lesson, and revise and refine the lesson to share with others.

Visualizing Functions

Participants will explore selected functions from multiple perspectives.  Functions of interest may include polynomials adn trigonometric functions, but also matrix functions and geometrical transformations.  One possible topic would be the use of computer algebra systems to work with functions, and how these can support or hinder learning.  For this topic teachers could study relevant research, design and evaluate lessons based on this study, or discuss implications for their own work with students.

Advanced Geometry

This group will have a different structure from the other groups. It will be based on a course on Knot Theory taught by Colin Adams as part of the
Undergraduate Faculty Program. This is a course designed to teach college faculty the elements of knot theory in a ways that they could use with their
students.  Thus it is a college level course, but a particularly interesting and accessible one.

The teachers in the group will attend the course, along with the PCMI SSTP resource person Jim King, of the University of Washington.  Then the working
group will move to another room from 2-3 to discuss the points raised in the class, do problems, and eventually consider ways that the mathematics of the
course might be adapted to a secondary math classroom.

A description of the course is on the PCMI website:

http://www.admin.ias.edu/ma/current/program_undergradfaculty.php

Adams, a professor at Williams College, is well-known as an excellent teacher. He has also written a very readable book called Knot Theory and another book of knot theory activities published by Key Curriculum Press. So the course should be well-taught at the level of an accessible college class.

This plan is quite different from the way that all the other Working Groups are organized. Working groups are in general more informal and planned to a great
extend by the participants.

For some PCMI teachers, this Knot Theory course may be just what you are looking for -- really interesting math, an outstanding instructor, and
discussion and problems.  But this does mean that the subject matter is more prescribed and there will be homework!  Some teachers may prefer the structure
of the other groups -- or prefer to explore another part of geometry.