Learning from Teaching Cases Summary

Monday - Friday, June 26 - June 30, 2006

Monday June 26, 2006
SSTP Participants: Nicole, Connie, Shenaz, Anastasia, Maribel, Amy, Carole
Visitors: Lani Horn (DIPD), Nancy (DIPD), Zende (DIPD), Charlie Patton (DIPD), Katie (DIPD)
Summary: (by Nicole)
Welcome to the Learning from Teaching Cases working group! We began our day with an overview of the group, its history, and the goals Nicole has for the group (making sense of instructional tasks, the teacher's role and practices, and the fundamental connection between them; learning to talk about video productively).

After a few technical problems, we dove into our task for the day: thinking about the cognitive demand of instructional tasks. We performed an initial sort of mathematical tasks from the "purple book"; classifying them as hi or lo demand (or medium or both :-P). Partner groups then shared out their thinking - especially when there was contention on how tasks should be rated. We're still thinking about these ideas: What is a hi/lo level task? What is a task? Do we look for cues in how tasks are presented before we *think* about them? How do the reading demands of the task influence the cognitive demand? (cog level of math vs. cog level of reading/writing) What's the teacher's role?

After the task sorting activity we transitioned to our first video case: the Border Problem. We watched the video with an eye toward these ideas: (1) What is the instructional task? (2) What is the cognitive demand of the task? (3) Evidence of student thinking? After the video our time was nearly up, so we had a quick debriefing that we will continue tomorrow.

HW: read "Chapter 2" (from the purple book). Does this influence/change your thinking about your initial sorting of tasks?

Tuesday June 27, 2006
SSTP Participants: Nicole, Connie, Shenaz, Anastasia, Maribel, Amy, Carole
Visitors: Zende (DIPD), Nancy (DIPD), Charles (DIPD)
Summary: (by Shenaz)
Checking In:
Nicole checked in with the group about how the mornings were working out for each member of the group.
Findings/Comments:
Building Math in the classroom helps generate good discussions Our group will have a chance to observe Deborah Ball teach and debrief with her.
Discussion:
We reflected on our reading for the day: Analyzing Mathematics Instructional Tasks. The Task Analysis Guide has four categories of tasks. We thought about the inherent hierarchy of the categorizations. These categories are not cut and dry. They do provide good pointers and are helpful in generating ideas we need to be mindful of when selecting tasks. What is the task? How should it be set up? How will the student implement it? What will it accomplish? Instead of thinking about tasks as hi/lo, it may be helpful to ask 'how hard is it to enact a task as a "high tasks?" It appears that value judgment is associated with categorizing tasks as hi/lo. Different parts of the brain are used when performing a high or low level task. It may be appropriate in certain cases to use tasks characterized as low.

We then re-sorted the mathematical tasks from the purple book. We continued to disagree on task A, B, and C. We also looked at the authors' characterization of these tasks and briefly studied their rationale. Our session concluded with debriefing the border problem we had observed in Cathy Humphries' video lesson from yesterday's session.

Parking Lot (to be revisited):
Teacher Moves: What do we do as teachers? What do we do with discussion tangents? What is the point of covering curriculum if there is no learning? How do we establish a Classroom Culture so that there is learning? What are good questions?

HW for Thursday:
Five Categories of Teacher's Questions
Questioning Your Way

Suggested Readings:
Nicole has some articles written by Deborah Ball
Nancy recommended reading Gramstom Costa's book on Baptist Schools (Teacher Moves/Physical positioning)

Thursday June 29, 2006
SSTP Participants: Nicole, Connie, Shenaz, Anastasia, Maribel, Amy, Carole, Megan
Visitors: Nancy, Charlie, Zendi
Summary: (by Anastasia)
The group jumped into our "Parking Lot" to address the Lemonade Problem from our previous discussion. The key point of the discussion was about different models of assumptions made before solving the problem - by both teachers and students. Can we make a conclusion without an assumption?

Furthermore, how a question/task/assumption is treated can lead to a more open or more specific discussion, which could lower or raise the level of cognitive demand. In discussing an "open-ended" approach, we saw the beauty of students being able to make assumptions, make connections, feel ownership, and make their thinking explicit enough for others to understand.

Ultimately, what is the teacher's role in maintaining or raising cognitive demand? How does teacher questioning play a role? We observed another clip of the "Border Problem" with a focus on questioning in the discussion. A framework for looking at these questions includes questions for managing, clarifying, orienting, prompting mathematical reflection, and eliciting mathematical thinking.

Again, as the previous two work sessions came to a close, the last few minutes spawned a pool of interesting queries left to investigate. "What is EVIDENCE of student thinking?" What do WE do as teachers? Are we leading the students to one place? What role does discussion play in this display of evidence and how does all of this tie back to assessment?

Friday June 30, 2006
SSTP Participants: Nicole, Connie, Shenaz, Anastasia, Maribel, Amy, Carole, Megan
Visitors: Nancy, Charlie
Summary: (by Carole)
Discussion on Lani's talk

Their process involved brainstorming of the current crisis, and analysis of the current data. They have all (or most) math teachers' cooperation to be trained and to teach differently - they "de-track" students, and they use a rigorous curriculum, and the "diagnose / anticipate / response" method as mentioned by Aki. They emphasize on evidence of students' thinking using formative assessments. As a result, they have managed to raise the standard of all students. Of course, having administrative support is also an important factor for the success.

We talked a bit about the current system as opposed to what it used to be. An example is the fact that students used to have to just get enough units to graduate, regardless of the nature of the subjects. Now students have to do so many units of English, Math, Science, - in order to graduate. Ironically, many schools are at the same time "dumbing down" their classes and tests so more students can graduate. Is this a good thing or not? (Charles pointed out that there were statistics claiming that student's success is related to the number of years in school.

Then we talked about some social-economic problems, poverty, parents involvement, NCLB, assessment, - These are noted for further discussion, but we are all keen to know and learn what we can do to solve these problems, at least in our classroom.

We watched the video: Status Treatments in the Classroom -- Designing Group work: Strategies for the Heterogeneous Classroom

Status Problems happens when students with lower status order do not get to participate, particularly in group work. Status order in classroom is formed due to the perceived academic ability, in attractiveness as a friend, or in popularity. Some teachers may see low status students as passive and not hard-working rather than realizing that they actually cannot get access to the work because of their low status.

To weaken this status effect in the classroom, teachers can use the Multiple Activity Treatment. Teachers convince students that the activity is going to involve multiple skills, and no one person can do it alone. He/she encourages students to share the work appropriately.

Another strategy is to have teachers assigning competence to low status students. With this strategy, the power of teacher as evaluator is used. Teachers go around telling students what they are competent in. This can be a powerful strategy because in general, students believe that their teachers know best.

Important Points

  1. When assigning competence, teachers must make sincere and intellectual comments.
  2. Formative assessment - Teachers take notes while observing group work to help assigning competence better next time.
  3. We all noticed the status problem in group work.
  4. What does it mean to be "smart" in math?
  5. What does it take to do group work well?
  6. How do you assign groups?
  7. What are multiple abilities for a math classroom?
  8. Training resources: http://www.teachersdg.org

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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 Grant No. 0314808 and Grant No. ESI-0554309. 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.