Japanese Lesson Study Summary

Thursday, July 3, 2003

Gail started us off by asking what plans we all had for the weekend.

We caught Jerry up on our discussion from yesterday and the problem that we had selected to do. We showed him how to construct the stair step fractal and explained how it could be used to compare changes in side length, area, and volume.

The question was posed as to whether students should build the fractal. We know how important it is to give students a chance to reflect on the mathematics involved so we need to be very careful not to short change the mathematics. We need to be very careful as well in formulating our teacher questions.

Debbie mentioned that there is a web site where you can manipulate the Tower of Hanoi. Check this out:
    http://math.bu.edu/DYSYS/applets/hanoi.html

Joyce mentioned that there are two members of the U. of W. PDO (Professional Development Organization) which have web sites with bits on this fractal and/or the Tower of Hanoi. They are:
    http://www.ac.wwu.edu/~mnaylor
and
    http://www.faculty.whatcom.ctc.edu/wwebber

We discussed what our objective should be. Jennifer suggested: Students will be able to articulate how length, area, and volume will be affected by scaling one of these measurements. Jill suggested: Make connections between dimensionality and scale factor.

Leo mentioned that we could consider scale factors that are fractional as well (hince the concept of a fractal).

On Wednesday, we spent an hour cutting various fractals and have come to the conclusion that we should start with the original fractal suggested by Debbie. We talked about just starting out with how the area and volume change as we double or halve the length of the steps. Jill's objective is really the over riding unit objective with Jennifer's objective being the lesson objective. In other words, the over riding goal is dimensionality and the first day goal (our lesson) would be simply the connections between the side length, area, and volume as the side length is cut in half.

We divided up into two groups, including the supervisors who were joining us for the last day. We will really miss them because they have really contributed a lot to our group and been an integral part of the group.

In my small group (Celeste, Tony, Miguel, and myself) we talked about what we should do first. Tony suggested that we start by having the students build the fractal. Miguel said that we should have them build the fractal and then immediately generate questions. Thus, by their questions and observations we will learn what they know about this topic and it can act as a quick assessment of what they do and do not know.

We think that some of their observations and questions might be:
Are the heights of the steps the same?
Identify the scales involved.
How do the sizes of the squares compare? How do the sizes of the steps compare?
Identify the shapes they see.
They might group the figures into two and three dimensional shapes.

We ended our session feeling like we were well on the road to writing our lesson, but with much work to do this next week.

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