Learning from Teaching Cases Summary

Monday - Friday, July 9 - 13, 2007

Monday July 9, 2007

SSTP Participants: Nicole, Connie, Kelley, Bree, Mitch, Amy, Angie, Rey, Sarah, Joe, Sandy

Visitors: John Schweig from Math for America

Daily Summary:

  1. We reviewed norms for Productive Disussion (created last week). We added a norm where during the first round everyone should speak based on facts from the reading/video, then during the second round everyone could make comments and during the third round everyone could respond to questions or other people's comments.
  2. Groups were randomly assigned using playing cards. The suits of the cards corresponded to group roles of team captain, recorder and resource manager.
  3. Each group worked on the Tile Pattern Task Card where they were to present thier solutions using multiple representations. Groups were asked to present solutions on graph paper and tape it to the wall. Groups then were allowed to comment on or question other groups work using post-it notes.
  4. While the groups were working, "huddles" were done by asking the team captain and recorder (not at the same time) to meet with the facilitators.
  5. While groups were working, facilitators were writing observations on how the group roles were being used and how it impacted group activity. These observations were posted on large paper for the whole group to see. At the end of the activity, the whole class was allowed to read and discuss the observations with the following questions in mind:
    • What instructional choices did you notice? What was the purpose of it?
    • What are the features of the Tile Pattern Task?
    Some comments:
    • Huddles were important to help undo the effects of status on group members. (ie. a dominant person could be removed from the group allowing the rest to work , or a quieter person could be removed and return with important information that the group must pay attention to.)
    • random assignment of group roles allowed students who would otherwise choose thier roles or are more comfortable with thier certain roles could try out other roles. (ie. allows for students to develop new skills and talents like leadership if team captain)
    • the open endedness of the problem allowed for multiple solutions
  6. At the end of the class, we watched a video of a group of students doing the Tile Pattern Task.

Summary by: Angelica Vega

Tuesday July 17, 2007

SSTP Participants: Nicole, Connie, Kelley, Bree, Mitch, Amy, Angie, Rey, Sarah, Joe, Sandy

Visitors: n/a

Daily Summary: What instructional choices did you notice? What was their purpose?

What are the "group worthy" features of the Tile Pattern Task?
What abilities do students need in order to access,/complete the Tile Pattern Task?
What can we do to positively manage or influence status. How does the Tile Pattern Task and/or instructional choices help manage status?
On the previous day, we were divided in groups and each came up with a lesson on how to model so students could predict the area of a sequence of cubes. Today's assignment was to discuss how the four questions above were addressed in our lessons. This was done as a group discussion and then as a whole class. We then disccussed the "aha" moment we experienced as a group and individually. Our group pointed out that when students groups present to the class, one method is to have the group with the weakest understanding present one idea they understand well. This idea is picked by the instructor so he/she must be familiar with the each student's group understanding. The group with the most undersanding will present last. So as not to present twice, most likely, the latter groups will refer to the findings of previous group(s). This will empower and raise the status of the lowest performing group and cut down on the amount of each group's presentation time.
What I gained from this activity helped me examine the ideas we use in developing a lesson and why they are good.

Summary by: Joe Rice Gonzales

Thursday July 12, 2007

SSTP Participants: Nicole, Connie, Kelley, Bree, Mitch, Amy, Angie, Rey, Sarah, Joe, Sandy

Visitors: Melissa Smith from Horizon Research, Inc.

Daily Summary: We began the session with a discussion on status. Everyone had the opportunity to comment on their personal perception of their status at the assigned table groups in the morning sessions. We have become keenly aware of status and its effects since it was presented to us in our Case Study Group.

It was mentioned that there is no cure for status even though status is not necessarily considered a disease. Adults have a greater ability to deal with status issues than children. Consequently, what can educators do to alleviate negative status issues in their classrooms?
Before watching today's video, we were given a handout that included an explanation of the lesson plan and an English translation of the Spanish conversation that took place among the students. A second handout explained the Video Club Roles and Norms. The reverse side of the second handout offered a place to take notes on "What I Noticed" and "Questions I Have" concerning the two observation questions:

  1. What do these students understand about the mathematics?
  2. What is the role of teacher questioning?

The video was entitled "Where is the 10?" The events in this teaching extract take place in a ninth grade sheltered Algebra I class where students are taking the class for the first time. The lesson plan instructions include finding the perimeter of an arrangement built with Lab Gear blocks. Students are to combine like terms in their answer.

A short discussion in relation to the obervation questions followed the video presentation. The discussion will be continued on Monday, June 16. Homework for Monday includes thinking of more ideas for our Case Study project. Tomorrow, Friday, June 17, we are to attend Aki's teaching demonstration from 1:00 to 3:00 p.m. Case Study sessions will resume on Monday, June 16.

Summary by: Sandra Peterson Nesbitt

Friday July 13, 2007

SSTP Participants: Nicole, Connie, Kelley, Bree, Mitch, Amy, Angie, Rey, Sarah, Joe, Sandy

Visitors: John (Math for America), Melissa (MSP)

Daily Summary: We had the opportunity to observe Akihiko Takahashi's teaching lab. He is guiding a group of 11 students (5th and 6th graders) through lessons he has prepared to emphasize the process of learning through problem solving to develop formulas for parallelograms, triangles, and trapezoids.

Aki has post-it posters all along the walls illustrating the progression of their sessions on discovering ways to develop formulas for parallelograms. The kids were engaged and excited and most were eager to struggle through the tasks. Aki encouraged the students to use scissors and tape to cut their parallelograms into puzzle pieces that could be manipulated to form a rectangle.

I loved seeing the direct application of what Aki has been teaching us in our morning groups. He celebrated with the kids as they discovered ways that didn't work and ways that did work. He encouraged each student to come up and share their method with the class. At the end of the class the students took time to write down what they had learned that day.

I enjoyed observing the way he interacted with his students as well as the way he assessed their performance. He walked around with a clipboard, and I brainstormed things that he might be writing down. What would I be interested in knowing about what each group was working on? Ways that worked/didn't work, correct/incorrect math sentences, how many times I talked to each group/individual ... When I peeked over Aki's shoulder, I was surprised. He was drawing pictures of what each student had created.

I have so many thoughts: Will I be able to set-up and maintain healthy working groups? Will I be able to motivate my students to delight in discovery? Can I hold my tongue and refrain from leading my students by the nose? Do I have the resources available to complete such tasks? Do I start the first week of school? Is it something that the kids need to be eased in to?

Who's to say what the perfect method of approaching this in a classroom is? I plan on jumping in the first week of school and learning with my students. We will practice and practice, and I hope that this idea of teaching through problem solving will eventually become a procedure that my students are used to. I want to eliminate initial confusion so that we will be able to have maximum time to engage in discovery lessons.

Summary written by: Amy Bateman

Back to Journal Index

PCMI@MathForum Home || IAS/PCMI Home

© 2001 - 2018 Park City Mathematics Institute
IAS/Park City Mathematics Institute is an outreach program of the Institute for Advanced Study, 1 Einstein Drive, Princeton, NJ 08540
Send questions or comments to: Suzanne Alejandre and Jim King

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.