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I found myself wondering about the amount of paper used. In the first

narrative it was almost 15 pages. If its a small classroom of 25 that is

almost a ream of paper.

Hmm, its beginning to look more like an Activity system.

Mike Cole wrote:

*> Interesting questions, interpretations, and observations regarding the
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*> first interactions concerning
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*> T and geometry. Some people were interested in the next installment.
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*>
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*> As I noted when posting the prior example, it was not selected as
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*> typical of the activity system where
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*> homework is imposed by the Club who are supported in this imposition
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*> by the parents and distrusted
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*> by the community for fear that they do not impose homework rigidly
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*> enough. (See paper by Nocon and
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*> colleague on "School invades after school"). Nor is T typical in her
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*> willingness to spend a lot of time
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*> on homework. Nor is it typical for an undergrad to be able to do this
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*> level of math. Mixed fractions tend
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*> to be the upper limit. If there is interest, I can try to arrange for
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*> a wide range of examples to be posted and
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*> folks can work at defining typical from the raw data. Up to 48
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*> generations of fieldnotes to choose from
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*> covering 16 years.
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*>
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*> But assuming a next example of this pairing is of interest to some,
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*> here it is.
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*> mike
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*> -----------------
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*> I noticed T was sitting at the same desk as before so I walked up to
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*> her to see if she was working on math again. Sure enough she had the
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*> blue (medium difficulty) math sheet. I exclaimed, "Blue again, common,
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*> where's the green!" T looked up and smiled and then pulled out the
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*> green (most difficult) sheet as I pulled up a chair.
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*>
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*> NARRATIVE:
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*> Once again the assignment was on volume. This time we were to find the
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*> volume of pyramids. She didn't have the formula written down, and
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*> though I thought I knew it I wanted to make sure. I asked several
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*> adults around me and we agreed that the formula was 1/3Bh but Jim got
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*> me a geometry book just in case. The first few problems were quite
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*> easy. The shape was a basic pyramid and all the dimensions were
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*> provided. T breezed through these problems. The next two problems were
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*> slightly more complicated as you needed to find the volume of part of
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*> the shape provided. The first of these problems asked you to find the
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*> volume of the base. T didn't know how to approach this problem so I
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*> asked her if she could find the volume of both the big pyramid and the
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*> top part. She said she could because they were both periods, she then
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*> understood that to find the volume of the base she would have to
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*> subtract the top from the bigger pyramid. The next problem applied
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*> this same technique. Following these problems, the assignment asked
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*> her to write down the method she had used. T had no problem describing
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*> this subtraction method so I was confident that she understood what
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*> she had done. The next few problems were even more complex volumes.
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*> The last problem was particularly tricky as it gave you the volume of
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*> a square base pyramid as well as the height, and then asked you to
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*> find the length and width. I walked T through the system of formula's
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*> that led to volume = side squared X height. I asked if, with this
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*> formula and the givens, she could find the length of the side, which
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*> we agreed was both the length and width, and she said she could. The
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*> calculations were also tricky as they involved dividing with
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*> fractions. Once I told her to put the entire volume in improper
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*> fraction form she had no problem with the long division. In the end we
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*> needed to use the square root function to find the side length. T
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*> wasn't familiar with the square root so I explained it to her. I was
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*> impressed with how quickly she caught on. Once I explained why the
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*> square root of 4 was 2 and the square root of 9 was 3, she could
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*> easily tell me the square roots of 16 and 25. This was the end of the
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*> math homework.
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*>
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*> I asked T if she had done the healthy snack activity and she said she
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*> hadn't so we decided to do that. This was a fairly straight forward
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*> activity and I found that she really didn't need my assistance. T is
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*> apparently quite computer savvy and had no problems finding the
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*> information on the web. At the end of the activity she wrote a letter
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*> to the Wiz describing her diet. Instead of a catalogue of items, she
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*> wrote in terms of what she ate enough of and what she didn't eat
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*> enough of. Once she had finished the activity she started to
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*> experiment with imputing different ages and genders into the pyramid
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*> system to see what the differences would be. At this point her father
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*> came.
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*>
*

-- Website: http://nateweb.info/ Blog: http://levvygotsky.blogspot.com/ Email: willthereallsvpleasespeakup who-is-at nateweb.info"The zone of proximal development defines those functions that have not yet matured but are in the process of maturation, functions that will mature tomorrow but are currently in an embryonic state. These functions could be termed the buds or flowers of development rather than the "fruits" of development. The actual developmental level characterizes mental development retrospectively, while the zone of proximal development characterizes mental development prospectively." - L.S.V.

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