• Notes on TPC course
- Course to focus on a few big ideas and how they provide coherence to a wide body of content
- PLCs to focus on design of instruction
• Course Content
• Focus like a laser on variation and covariation
- Force the issue of interpreting all settings in terms of them
- Force the issue of interpreting common symbolizations in terms of them (e.g., what is an equation from a covariation

perspective?)
• Relate course content to issues of their students' learning and to the curricula that they teach
- The kind of learning we envision students achieving will be alien to the students that the teachers teach, and they will resist in subtle ways. They likely will be disequilibrated by the focus on developing meaning, reasoning from meaning, focusing on metarepresentational and methodological issues. SO ... we need to design the PLCs so that they support teachers' trying things out and dealing with the simultaneous transition of their and their students' to these new ways of thinking.
- Students' thinking about covariation (or OTHER's thinking about covariation). Point of this? So that they realize that success in teaching is not simply about their performance, but is instead about their students' understandings.

Day 1, Aug. 17th:

Introductions and Consent forms: 15 minutes

Frame Course Purpose (15 minutes)

Three questions to frame purpose of course (30 mins: 15 min writing, 15 min discussing)
Have teachers write responses to each, then open discussion
- What knowledge do you need to be able to teach in this way?

Introduce "Rules of Engagement for Course" (15 minutes)

General “rules of engagement” that I would like for us all to practice and enforce:

1) Speak meaningfully—what you say should carry meaning;

2) Exhibit mathematical integrity--base your conjectures on a logical foundation; don’t pretend to understand when you don’t ;

3) Strive to make sense—persist in making sense of problems and your colleagues’ thinking.

4) Respect the learning process of your colleagues—allow them the opportunity to think, reflect and construct. When assisting your

colleagues, pose questions that will help them construct meaning.

Break (15 minutes)

Box Problem (60 minutes)

-Intro.to Graphing Calculator

Functions Inventory (45 min.)

Course Forum