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
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
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:
- 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 ...
-- 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:
- Web page - Nicole is working on getting a permanent site for our electronic
- 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
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
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
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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.