## Learning from Teaching Cases Summary## Monday - Friday, June 26 - June 30, 2006
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.
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.
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?
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 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.
- When assigning competence, teachers must make sincere and intellectual comments.
- Formative assessment - Teachers take notes while observing group work to help assigning competence better next time.
- We all noticed the status problem in group work.
- What does it mean to be "smart" in math?
- What does it take to do group work well?
- How do you assign groups?
- What are multiple abilities for a math classroom?
- Training resources: http://www.teachersdg.org
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 Grant No. 0314808. |