The PCMI 2005 Program

« Secondary School Teacher Program

Secondary School Teacher Program Working Groups

This group will develop lessons that use technology, such as the statistical software FATHOM, as a tool for understanding the mathematics and the application of mathematics in contexts that require data analysis and statistical concepts. The goal is to produce lessons, describe teaching strategies, or present an issue related to the mathematics content at different mathematical levels from beginning algebra to Advanced Placement Statistics.

Discrete Mathematics

Counting, networks and relations are discrete mathematics topics that have applications to mathematical biology, the research topic for PCMI this year.  Participants in this working group will explore both the mathematics and biology in some of these applications, and work together to develop resource materials to help educators incorporate these interdisciplinary topics in their teaching.

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 Labs

For ten days during PCMI, the distinguished math educator Deborah Ball will be teaching a group of fifth grade students at our site and reflecting on the student learning that takes place. This math education component of PCMI is the Teaching Lab. The lab will be open to some live observation, and it will also be videotaped extensively.
> The Working Group will focus on learning from video of classroom practices. We will center our work on the Teaching Lab, which will be done in collaboration with Professor Ball and her team. Participants in the  Working Group will attend the Lab in person one or two times, but most of the work will be done during Working Group time using video from the lab. We will construct ways of talking about classroom practices and student learning, as well as how we can continue our conversations beyond PCMI using tools like instant messaging or web chats.

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 colloquium 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 and 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.