Re: T and I two days later

From: Mike Cole (
Date: Sat Apr 30 2005 - 11:45:56 PDT

Classroom? What classroom? These encounters took place in the hybrid space
of the
5th Dimension in a Boys and Girls Club where, despite La Wizard's resistence
thanks to La mosca cosmica!) geometry has wiggled its way in. At least there
IS a
wizard there who now provides healthy snacks to kids who achieve locally
defined mastery
of the shifting ideas of the us government on what a healthy diet is. :-)

 On 4/30/05, willthereallsvpleasespeakup who-is-at <
willthereallsvpleasespeakup who-is-at> wrote:
> 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
> > first interactions concerning
> > T and geometry. Some people were interested in the next installment.
> >
> > As I noted when posting the prior example, it was not selected as
> > typical of the activity system where
> > homework is imposed by the Club who are supported in this imposition
> > by the parents and distrusted
> > by the community for fear that they do not impose homework rigidly
> > enough. (See paper by Nocon and
> > colleague on "School invades after school"). Nor is T typical in her
> > willingness to spend a lot of time
> > on homework. Nor is it typical for an undergrad to be able to do this
> > level of math. Mixed fractions tend
> > to be the upper limit. If there is interest, I can try to arrange for
> > a wide range of examples to be posted and
> > folks can work at defining typical from the raw data. Up to 48
> > generations of fieldnotes to choose from
> > covering 16 years.
> >
> > But assuming a next example of this pairing is of interest to some,
> > here it is.
> > mike
> > -----------------
> > I noticed T was sitting at the same desk as before so I walked up to
> > her to see if she was working on math again. Sure enough she had the
> > blue (medium difficulty) math sheet. I exclaimed, "Blue again, common,
> > where's the green!" T looked up and smiled and then pulled out the
> > green (most difficult) sheet as I pulled up a chair.
> >
> > Once again the assignment was on volume. This time we were to find the
> > volume of pyramids. She didn't have the formula written down, and
> > though I thought I knew it I wanted to make sure. I asked several
> > adults around me and we agreed that the formula was 1/3Bh but Jim got
> > me a geometry book just in case. The first few problems were quite
> > easy. The shape was a basic pyramid and all the dimensions were
> > provided. T breezed through these problems. The next two problems were
> > slightly more complicated as you needed to find the volume of part of
> > the shape provided. The first of these problems asked you to find the
> > volume of the base. T didn't know how to approach this problem so I
> > asked her if she could find the volume of both the big pyramid and the
> > top part. She said she could because they were both periods, she then
> > understood that to find the volume of the base she would have to
> > subtract the top from the bigger pyramid. The next problem applied
> > this same technique. Following these problems, the assignment asked
> > her to write down the method she had used. T had no problem describing
> > this subtraction method so I was confident that she understood what
> > she had done. The next few problems were even more complex volumes.
> > The last problem was particularly tricky as it gave you the volume of
> > a square base pyramid as well as the height, and then asked you to
> > find the length and width. I walked T through the system of formula's
> > that led to volume = side squared X height. I asked if, with this
> > formula and the givens, she could find the length of the side, which
> > we agreed was both the length and width, and she said she could. The
> > calculations were also tricky as they involved dividing with
> > fractions. Once I told her to put the entire volume in improper
> > fraction form she had no problem with the long division. In the end we
> > needed to use the square root function to find the side length. T
> > wasn't familiar with the square root so I explained it to her. I was
> > impressed with how quickly she caught on. Once I explained why the
> > square root of 4 was 2 and the square root of 9 was 3, she could
> > easily tell me the square roots of 16 and 25. This was the end of the
> > math homework.
> >
> > I asked T if she had done the healthy snack activity and she said she
> > hadn't so we decided to do that. This was a fairly straight forward
> > activity and I found that she really didn't need my assistance. T is
> > apparently quite computer savvy and had no problems finding the
> > information on the web. At the end of the activity she wrote a letter
> > to the Wiz describing her diet. Instead of a catalogue of items, she
> > wrote in terms of what she ate enough of and what she didn't eat
> > enough of. Once she had finished the activity she started to
> > experiment with imputing different ages and genders into the pyramid
> > system to see what the differences would be. At this point her father
> > came.
> >
> --
> Website:
> Blog:
> Email: willthereallsvpleasespeakup who-is-at
> "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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