[Squeakland] Discovering Pi in Squeak

[subbukk]

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