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

            -   Consent forms

10 min

            -   Circulate sheet for email addresses

               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 are your overall goals for your students?

                  -   What should your instruction look like to achieve your goals?

                  -   What knowledge do you need to be able to teach in this way?

               Debrief teachers on what they KNOW about:

10 minutes (50 min)

Group discussion

                  -   Reform efforts

                  -   Instruction in other countries

                  -   Mathematical expectations of students around the country and in other countries

                  -   Professional practices that differ from theirs

               Opinions of past professional development experiences

15 minutes (65 min)

Ask them to think of examples of _____, then write what you think the attributes of that experience made it ______.

Have teachers write these responses individually

                  -   Ask for attributes of EXCELLENT professional development

                  -   Ask for attributes of POOR professional development

                  -   Ask what they think are the objectives of professional development

               PCA Exam

45 minutes (110 min)

Need to be careful how this is framed. They must not think that they are being EVALUATED. We are getting baseline information so that we can track growth and so that we can make better decisions about designing and adapting the course.

Ask them to show their work (explain why we ask this)

               BREAK

15 minutes (125 min)

               Discuss items on the PCA

?? min

Items 3, 8, 19, 22, 24 on version H

                     Question for class discussion

                        -   What mathematics does this problem get at?

What must students understand to understand these problems?

What must students be able to do to solve these problems?

What are common misconceptions that might obstruct students' solving these problems?

To what mathematics are these problems connected?

               Give teachers Question 15 (H) to take home with above questions to recapitulate class discussion

               Read Teaching Gap

                  -   Hand out assignment sheet