[IAEP] [etoys-dev] TED - Alan Kay - Example(8:44)
Edward Cherlin
echerlin at gmail.com
Tue Feb 23 19:23:26 EST 2010
On Tue, Feb 23, 2010 at 11:42, K. K. Subramaniam <subbukk at gmail.com> wrote:
> On Tuesday 23 February 2010 09:13:59 pm Edward Cherlin wrote:
>>We also know that simply asking the question and making careful observations
>>also gives astonishing results, as, for example, in the careers of Maria
>>Montessori and Jean Piaget. Also Jerome Bruner
> Yes. But these people followed the child. Jean Piaget discovered that children
> in the 2-7 age group do not comprehend conservation of quantity or use logical
> thinking. Children don't come with fast forward buttons :-).
It is easy to demonstrate what children are capable of, when you can
see them do it. It is much harder to demonstrate what they are not
capable of, or what some can do but not others, or what is dependent
on development or prior experience. But consider this, from Piaget's
Genetic Epistemology.
This example, one we have studied quite thoroughly with many children,
was first suggested to me by a mathematician friend who quoted it as
the point of departure of his interest in mathematics. When he was a
small child, he was counting pebbles one day; he lined them up in a
row, counted them from left to right, and got ten. Then, just for fun,
he counted them from right to left to see what number he would get,
and was astonished that he got ten again. He put the pebbles in a
circle and counted them, and once again there were ten. He went around
the circle in the other way and got ten again. And no matter how he
put the pebbles down, when he counted them, the number came to ten. He
discovered here what is known in mathematics as commutativity, that
is, the sum is independent of the order. But how did he discover this?
Is this commutativity a property of the pebbles? It is true that the
pebbles, as it were, let him arrange them in various ways; he could
not have done the same thing with drops of water. So in this sense
there was a physical aspect to his knowledge. But the order was not in
the pebbles; it was he, the subject, who put the pebbles in a line and
then in a circle. Moreover, the sum was not in the pebbles themselves;
it was he who united them. The knowledge that this future
mathematician discovered that day was drawn, then, not from the
physical properties of the pebbles, but from the actions that he
carried out on the pebbles. This knowledge is what I call logical
mathematical knowledge and not physical knowledge.
>>> > Concepts
>> > like product (a*b), square, square root, symbols to represent quantity
>> > and manipulating them will take some more time. The constructional
>> > technique adopted by Julia Nakajima is so beautiful because it uses
>> > growth instead of symbols.
>>
>> Can you give me a URL for that?
> See page 7 second last para of
> http://www.vpri.org/pdf/m2007007a_revolution.pdf
>
> I typed the name wrong :-(. The correct name is Julia Nishijima.
>
> Also see http://dobbse.net/thinair/2008/12/growth-and-polygons.html
>
> Subbu
>
--
Edward Mokurai (默雷/धर्ममेघशब्दगर्ज/دھرممیگھشبدگر ج) Cherlin
Silent Thunder is my name, and Children are my nation.
The Cosmos is my dwelling place, the Truth my destination.
http://www.earthtreasury.org/
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