Learning from Teaching Labs Summary
Monday - Friday, July 11 - 15, 2005
Today we met with Deborah Ball and staff in a debriefing meeting where introductions were done and "lab" class was explained. We were given a copy of the lesson plan for this first class to read and think about. She said that she expected 22 students to attend this coming week and explained how the students were recruited. We were asked to sign waivers since our face might appear in the video, which everyone did. She also gave us a paper explaining the Observer Guidelines we were to follow. Dr. Ball then asked us to wait until 10:15 before we came to observe so she would have time to talk to the parents and students. After the parents left, we were allowed to quietly enter the lab and observe the class. Dr. Ball had each student introduce themselves and tell why they were there. Then she explained the notebook and how it would be used. The students would be writing and doing work in it every day and each day would start on a new page with the date written on that page. The class discussed different ways to write the date. Then Dr. Ball asked the class to write in their notebook what they thought "The Real Line" was or could be. She told them to use pen and not markers. The markers were for diagrams. The students worked quietly for several minutes. After giving the students time to write, she asks them to share what they wrote. As the class continued, we observed and had an opportunity to walk around and look at the students working, without interacting with them. Dr. Ball kept to her lesson plan as outlined. Near the end of the class, the students were told they would have homework and that was explained - how to get it (download from their computer) and what kind of problems they might encounter and to read everything carefully. The students were then escorted to lunch. We agreed to sit together, if there was a table available, and talk about what we had observed, which we did. At approximately 1:15, we gathered in the lab room to discuss with Dr. Ball and other guests what had taken place during the lab class. It was a good discussion of questions and comments about the lesson, the students and their work. Then our working group met briefly to discuss Tuesday and our "work-in-progress" project.
We decided our product for PCMI is the electronic discussion group we are creating. We may need to work on an abstract and a link to the web page for the Friday presentation. (Possibly use pieces of the format provided and the Japanese Lesson study page as a guide)
We focused on finalizing information needed for the web page our group is creating. Nicole is working on getting a more permanent home for our electronic discussion group. Once this is established, all participants will log on and give input regarding whether it is user friendly and whether the information posted makes sense. (Our backup plan is to formalize the shared information on our current site and transfer it to the new site when it is up and running)
Revised purpose: An electronic community for those interested in discussing the teaching and learning of secondary school mathematics.
We decided that assigned glossary words that may not need defining can be eliminated and some words may need to be added. The annotated bibliography summaries can be in the first person and they should contain enough information to be useful to teachers and brief.
We finished the day by specifying what each person would do to help finish our product.
Today we started class by watching Deborah Ball's video on the "Pool Border Problem". Again Laurie Sleep was with us and asked us to look through two "lenses" while watching the video: 1) mathematical knowledge for teaching and 2) what the teacher is doing to scaffold and support student explanations. We talked about picking just one or two "lenses" to look through when watching videos of teaching because trying to do too much can be difficult. After watching the video we discussed some of our observations. We talked about D. Ball's use of student mistakes as learning opportunities for the entire class and validating misconceptions as teaching tools. We also talked about intellectual complements compared to just compliments. Most of our discussion took place around the idea of Deborah Ball's ability or knowledge of when to hold back and let the students work out their confusion on their own and knowing when to step in and direct the student conversation. This discussion led to "knowing your goals for your students". By this wee meant that as a teacher you focus on certain goals that you want to accomplish for the day and focusing on those goals you can keep students "on track". But, we also discussed the way Deborah Ball is able to use quick judgment about whether to keep students "on track" or whether to let the students take hold of their misconceptions and go with them and discover the facts for themselves. Some of the key terms that where brought up today were: 1) audience shift - having student that are in the front of the class demonstrating talk to the entire class not directly to the teacher. 2) teacher moves - this is like a teacher's bag of tricks (correcting errors and knowing when to do so and when not to do so, strategies used to get things moving . . . ) 3) mathematical participation - we are still "chewing" on this idea. Some thought were: students teaching students, giving answers, asking a question, trying someone else’s method, sharing errors, sharing thought processes/reasoning, productive disagreements, engaged in mathematical thinking...
We spent the day editing and refining our newly formed website. Attention was given first to content and then to appearance. It is our hope that this site will be completely operational in time for the presentation tomorrow.
We gave presentation on our electronic community we plan to use throughout the coming year. This website contains information about: (1) How we created our community; (2) A glossary of terms and ideas; (3) An annotated bibliography of our favorite sources; (4) Discussion Schedule; (5) A link to our EPost monthly discussion community; (6) Our discussion norms; and (7) reflections on our experiences in our working groups at PCMI.
Our website is public. All are welcome to participate in our monthly online discussions, provided that one reads and adheres to our community norms for discussion.
Community Website: http://depts.washington.edu/pcmillab/
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This material is based upon work supported by the National Science Foundation under DMS-0940733 and DMS-1441467. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.