[IAEP] GPA Notes 7/23/09

[K. K. Subramaniam]

On Tuesday 28 Jul 2009 2:25:29 am Caroline Meeks wrote:
> On Sat, Jul 25, 2009 at 5:55 AM, K. K. Subramaniam <subbukk at gmail.com>wrote:
> > On Friday 24 Jul 2009 7:08:05 am Anurag Goel wrote:
> >> ..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.
> > The circular movement is not about geometry but differential calculus.
> > Watch
> > the movie clips on Talking Turtles in http://logothings.wikispaces.com,
>
> The one with the yellow turtle?
No, the BBC video "Papert and Talking Turtle" shown in five parts. See part 2:

  http://www.youtube.com/watch?v=BTd3N5Oj2jk

Papert [1:37] : The essential point about the turtle is its role as a 
transitional object. That is, transitional between the body, self and the 
abstract mathematical ideas. The turtle, you can identify with it. You can 
move your body in order to guess how you can command the turtle. So it is 
related to you, your body, your movement and it is also related to 
mathematical ideas."

Papert's genius lies in creating an environment in which children can not only 
experience distances, turns and geometrical shapes but also digitize them into 
countable numbers for operating the turtle. Pen trails help children to detect 
and correct any encoding errors. In this process, children use principles of 
differential calculus (countable offsets from current location), integral 
calculus (accumulate counts), arithmetic (modulo operators) and not geometry 
(compass-ruler constructions).

The teacher in the video summarizes it very well:

Teacher [4:13]: The great thing is it provides a mathematical environment for 
the children. While the children are working around the turtle, if you listen 
to what they are talking about, it's all mathematical. Verbalization in 
Mathematics is very important and I think that half of the problems with 
Mathematical teaching is that students don't communicate mathematically, talk 
about mathematics and experience mathematical problems...

The numbers on the clock (and its shape) encode experiences that many adults 
take for granted but which inspire awe in children. Why deny them the wonder 
by jumping into encodings right away?

Subbu