The PCMI 2017 Summer Session has three strands:

Math Course: Recursion and Matrices

(2 hours per day, 13 days in session)

Many sequences of numbers can be described recursively. Probably the most famous of these is the Fibonacci sequence: 0, 1, 1, 2, 3, 5, 8,.... In this course, participants will explore these recursive sequences and develop tools for analyzing them. The development of these tools will take participants into a deep dive into the study of matrices and their many applications.

What happens when you multiply matrices repeatedly and how does that connect to recursive sequences of numbers? The course will investigate questions like these, tying them to the precollege mathematics curriculum. No prior background is necessary; the contexts and methods developed in the course will be low-threshold, high-ceiling, with plenty of interesting mathematics for any grade level.

 

Reflecting on Practice: Making Inquiry a Core Teaching Practice

(75 minutes per day, 13 days in session, plus opportunities for informal sessions in late afternoon and evenings)

What role does inquiry play in developing students' insights about and understanding of mathematics? Participants will consider research related to teaching and learning mathematics with a particular focus on how active learning can produce both conceptual knowledge and procedural fluency. The discussion will be grounded in the study of lessons and classroom practice in both the United States and other countries as participants work collaboratively to better understand how they can design experiences for students that enable them to make sense of mathematics.

 

Working Groups

(2 hours per day, 13 days in session)

As part of their summer activities, each participant selected for the Teacher Leadership Program will be assigned to one of three options: 1) a small team that will focus on an developing an activity related to providing resources to support teachers as they implement standards for mathematical proficiency in their schools and districts or on an TLP academic year outreach project, 2) a special working group attending a course related to the PCMI research math topic Random Matrices or 3) a working group on lesson study, which will design and deliver a lesson to area high school students during the three-week session and revise the lesson for use by other mathematics educators.