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