Japanese Lesson Study Summary

Tuesday, July 15, 2003

Yesterday we debriefed the sample lesson right after our volunteers left. This is a record of our comments and suggestions.

We first talked about how Celeste felt about the class since she had the role of the teacher of the lesson. She said that the class felt artificial since it was made up of experienced, knowledgeable teachers. However, she did have suggestions on how the lesson could be improved. Next time, she would like to be more directive in turning papers around to see the squares on the side and how it looked backwards and forwards. The group that had concentrated on the sums of the volumes (a Calculus example) seemed to be an example of positive/negative transfer since these teachers have been spending a lot of time looking at similar problems in the morning number theory course. This prompted the question of whether the directions had been clear, since this group really did not answer the question. We will plan to have the comments posted on white butcher sheets for Thursday's lesson. Next, we discussed whether or not we needed to discuss the a/b scale factor in case it comes up with the students and if it should be brought up even if they don't bring it up. Do we need a model to demonstrate this idea? At the beginning of the lesson, some students (teachers as students) seemed to have confusion over the grid lines and graph paper. We decided that Celeste should say something like, "Use the grid lines to your advantage". Gail wondered whether Celeste had been the first to use the word "iteration" and whether we should use it, define it, or use something simpler like, "repeat the process". Art mentioned that this word might very well be brought up by the students since many of them play video games.

We discussed each person's role and what they had observed.

Jennifer (How can we improve the questions and better anticipate student reponses?) She brought up the group which did the wrong task and did not answer the question. This is where the idea of having clear written as well as spoken questions was suggested. Jennifer thought that Celeste did a good job of following the questions that we had designed. Celeste used good judgement and built nicely on what students said. She especially liked the question about, "Were there any relationships between what the 3 groups presented?" Jennifer also asked about what part was the summing up? Celeste commented that it was easy to sum up because of the group work on the white butcher paper sheets and the notes on the board. The question, "Are you impressed" was discussed and we felt it might be good to say something like, "On a scale of 1 to 5, how impressed are you by this first set of cuts?"

Jill (How do students use prior knowledge? Did we have the correct level of difficulty?) She was impressed by how well each group was able to apply prior knowledge and really produce a lot of mathematics from the task. She was impressed that all groups seemed to be challenged but capable of the task presented. She did, however, suggest that our question, "What did you see and what did you wonder?" should be followed by a statement to take a moment to jot down your ideas on the back of the directions and we should collect these from the students.

Tony (Observe 3 students) He was impressed by how the students went right where we had wanted them to with the lesson. Except for the group who did the summation of the volumes, we did a pretty good job of anticipating student responses and leading them towards our math objective. He also thought the discussion went really well with participants getting others to clarify their thoughts. He was impressed that the group he observed (5 students actually) brought up the idea of scaling by 1/3 on their own.

Joyce (When/how did the math appear? When were the key statements made?) She was impressed by how easily the math unfolded for each group from the model. All groups were able to make mathematical connections from the stair step fractal and pull meaningful ideas, conjectures, and formulas from the model. Over and over, Celeste asked questions which brought forth the mathematical points and clarified their ideas. She did a nice job of comparing the various groups' work and summing up the ideas brought forth discussing scale factor. Some of the questions Celeste used were not part of our lesson, but should be added since they were just what was needed.

Jerry (Timing of the parts of the lesson)

     10 minutes     Cutting and folding
      7 minutes     Make lists
     17 minutes     Group work
      7 minutes     Presentations
      7 minutes     Summation
      2 minutes     Extra examples from box of samples
      2 minutes     Discuss homework assignment
      2 minutes     Comments to group on process

Gail (Took copious notes and looked for overall comments) She noticed that the charts really need to be written much bigger and clearer. Also, more needs to be said about the concept of scale factor. We still need to spend some time polishing the summary. She commented that this was a good lesson and that it was great to see all of it come together so well especially after all of our work and collaboration.

Today, we watched the video and revised our draft of the lesson. These comments and suggestions have now been added in red. The draft can be downloaded (requires password)

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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.