Posted by K. K. Subramaniam on May 30, 2007; 6:02pm
URL: https://forum.world.st/Discovering-Pi-in-Squeak-tp114410p114412.html

On Wednesday 30 May 2007 5:35 pm, Alan Kay wrote:
> Hi --
> For example, you can make a big circle with a turn by 1 and sum the
> forwards, and also remember max y and min y to get the diameter. This
> will give you a pretty good value for Pi.
Unfortunately, what they will discover is the number programmed into the Float
class initialize method :-). I wanted to explore a method without built in
bias.
> You didn't mention the ages of your children.
10 and 6. The exercise is for the older one (and her
friends/classmates/cousins). The younger one went to a Montessori and watches
everything the elder one does :-).
> But it is always good to get them to do some reasoning about measures
> of various kinds and areas. I think that the manipulation of the
> strings, etc.,  might be too awkward (but see the discussion in the
> "Powerful Ideas" book about measurement).
I used 'string' in the generic sense. Actual stuff could be anything that we
can find around the house - strip of paper, cloth or ribbon, buntings etc
(e.g. cutting a wrap for a round pencil holder). There is a long tradition in
India of learning by immersion and many lessons are woven into daily
activities, so there is no awkwardness in using 'strings'.

"Powerful ideas..." is not available in bookstores here in Bangalore :-( and
Amazon doesn't ship direct to India. Shipping it in is quite unreliable (a
great incentive to go online :-)).

> I would just give them squares of different sizes and see if they can
> work out how a side might relate to the perimeter, and if so, why
> something like that would also work for a diagonal. The idea that the
> relationship is the same regardless of scale is a biggie for
> children. Discovering the relation for the area is even bigger.
Perimeter to side ratio is grasped quickly because 'addition' is readily
apparent. Diagonals and Circles require deeper thinking. I will try out your
suggestions.

> This is a very good way to show how and why
> proportions work (and many studies have shown that proportions and
> the normalizations associated with them are not learned well by most
> children).
Very true. The casual way proportions are treated in math text books is
disturbing. I always wondered how a child looks at things like shadows or
dolls before discovering proportions. This is something my daughter could
teach me.

Thank you very much for your suggestions .. Subbu
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