Learning from Teaching Labs Summary

Monday - Friday, July 4 - 8, 2005

Visitors were welcomed and our group focus was described to them. Our common vocabulary list was revisited and a few words were added (eg. status and sociomathematical norms). The group revisited a clip from the "Status Treatment" video to continue our discussion on what status problems are and how to combat them in the classroom. How do we deal with status issues when they occur in the classroom? What qualities do we value in our group work and classroom environments? How do we work with students to understand these values? The group watched a 10 minute video clip from a sheltered Algebra class of students discussing an expression for the perimeter created with algebra tiles. The group focused observations on the status problems that arose and how the teacher showed students what was valued. The group concluded with a discussion of ideas for a final product that can be used as a resource for teachers next year. Discussion focused on something that can be "under construction" during the year--something that can be added to as we learn more and have more successes or needs in our classroom.

Today's Learning Lab was extremely interesting and helpful thanks to a special guest, Laurie Sleep. Her introduction provided us with a different resource for discussion of mathematics teaching in a practical and insightful manner. The premise of her discussion was based on three important ingredients: practice-base approach, mathematical knowledge for teaching, and how teachers teach math or work of teaching. As expected, each member of our learning lab came up with some excellent questions and points of discussion that lead to greater understanding of how intricate and strategic practices are incorporated in order to insure that a teacher is using mathematical knowledge throughout a math lesson. This introductory activity was followed by a short video of Deborah Ball's teaching, taped during May of the 1989-90 school year. We watched the video through the lenses of mathematical knowledge for teaching and made notes of specific instances. After discussion of the video we concluded our session by narrowing down options for the Learning Lab Product. We made some revisions of our plan (work in progress) and added "mathematical knowledge for teaching" to our glossary. Finally, our recorder marked the term "what is valued" with double stars!! Great job everyone!! :)

Laurie Sleep continued as the group facilitator for our discussion of portions of Deborah Ball's videos. We are looking at specialized mathematical knowledge that teachers need to teach math effectively. Our definition of mathematical practices includes "tools, skills habits of mind and actions that form the basis for learning, doing and using mathematics." Teachers must not only develop these mathematical practices in themselves but they must help students learn to use mathematical practices.

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.

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 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:

  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 ...


Other Tidbits:
-- Our CURRENT community web site: http://groups.msn.com/PCMILearningLab/
-- We plan to include an annotated bibliography of our resources with our product, so stay tuned. If anyone would like to contribute to our annotated bibliography, please contact Nicole: nicdavis at u.washington.edu
-- This is our schedule for our PRODUCT:

  1. Web page - Nicole is working on getting a permanent site for our electronic community
  2. Books - we are all writing our own annotated bibliographies
  3. How to start your own group - Nicole and Meghan
  4. Title - everyone
  5. Purpose - Mark and Steph
  6. What our site is and is not (norms) - Natan and Cheryl
  7. Reflections (what we like and would do differently next time) - this will be our first discussion on our site
  8. 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 :)

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IAS/Park City Mathematics Institute is an outreach program of the Institute for Advanced Study, 1 Einstein Drive, Princeton, NJ 08540
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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.