# T and I two days later

From: Mike Cole (lchcmike@gmail.com)
Date: Sat Apr 30 2005 - 11:16:58 PDT

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.

NARRATIVE:
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.