## Learning from Teaching Labs Summary## Monday - Friday, July 4 - 8, 2005
One specific mathematical practice that we focused on today is that of developing mathematical definitions. Some of the problems with learning and teaching definitions in the classroom include: they might be simply memorized, they might not be taught at all, they might be treated parenthetically, the definitions might not be flexible, they may not be used in ways that make them part of doing math. As we viewed the video, our focus questions were: What do definitions enable? What makes a good definition? How do definitions emerge and develop? Following the video we discussed that definitions enable all sorts of reasoning to occur. To be effective definitions must be mathematically precise and they must be useful to the user community and based on already defined and understood terms. The key seems to be getting the definition complete enough that students can use it effectively. We finally divided into two groups and discussed how we might categorize
our "Learning to notice..." glossary terms. During the discussion that followed we
talked about how the "poster walk" might be used in the classroom.
- mathematical knowledge for teaching and
- 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 complements. 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 we 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 help 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: - audience shift - having student that are in the front of the class demonstrating talk to the entire class not directly to the teacher.
- 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 ... )
- 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 ...
--Meghan
- Web page - Nicole is working on getting a permanent site for our electronic community
- Books - we are all writing our own annotated bibliographies
- How to start your own group - Nicole and Meghan
- Title - everyone
- Purpose - Mark and Steph
- What our site is and is not (norms) - Natan and Cheryl
- Reflections (what we like and would do differently next time) - this will be our first discussion on our site
- Glossary
Cheryl - revoicing, wait time, add-on, making reasoning public Lynda - teacher demeanor, student agreement, teacher questions Mark - celebrate meaningful success, teacher consistency, richness of task Meghan -classroom norms, teacher moves, sociomathematical norms, making judgment calls Natan - what is valued, mathematical practices, student restatements, status Steph -teacher response, teacher focus, mathematical knowledge for teaching Tere - listening, IRE, audience shift, mathematical participation
REMEMBER: . . . we want to have this done on Wednesday so if we have to revise we can :) PCMI@MathForum Home || IAS/PCMI Home
With program support provided by Math for America 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. |