[IAEP] GPA Notes 7/23/09

[Maria Droujkova]

On Thu, Jul 23, 2009 at 9:38 PM, Anurag Goel <agoel23 at gmail.com> wrote:

> The kids used the following sequence to make the turtle point in different
> hour directions:
>
> seth() --> forward(100) -- back(100)
>
> Note: The kids started off by experimenting with different values for
> "seth"
>
> I feel most kids struggled with this because they had not learned too much
> about geometry, particularily concepts involving degrees and radii. However,
> kids experimented with a lot of different values to better predict
> increments. Some kids realized that if they input a really large number they
> would get the same result as importing a really small number (ex: 12 and
> 732). As expected, the kids did not understand why that was. Perhaps we need
> to give a brief geometry lesson before letting the kids play with heading
> directions.
>

I had good luck with paper folding activities to go with clock activities,
for example, making snowflakes with different number of segments. Clock is a
highly multiplicative structure, and kids who have weak multiplicative
reasoning (e.g. reunitizing) struggle with it. I have an online snowflake
maker to introduce the activity:
http://www.naturalmath.com/special-snowflake/index.php

Just leaving 4 out of 12 clock numbers (3, 6, 9, 12) helps a lot, too,
because quarters are easier cognitively, the angles are familiar and so on.
However, this is the "attenuation" approach (simplifying the environment)
and I don't like to attenuate too much. With paper folding, you can give
kids angle experience in an interesting context.

I started to sketch a Zoombini-like paper folding activity, where you need,
for example, to construct (match) certain folds to build a stained glass
window. You construct everything out of prime number folds. So, to make the
clock (1/12th) fold, you need to use a 3-fold and a 2-fold twice. This
relates to "the splitting conjecture" by Confrey et al, and the ways young
kids can construct numbers multiplicatively instead of additively. However,
you can't use 3-folds with paper at the start, so there is the added fun
complexity here. In physical space, I use coffee filters for this work.


Cheers,
Maria Droujkova

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