Discussion:  Roundtable 
Topic:  Computer Tools at PreK2 
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Subject:  RE: Computer Tools at PreK2 
Author:  Mathman 
Date:  Oct 4 2004 
> When I read work such as the VanHeile's Levels of Geometric
> Reasoning, it occurs to me that we need to be able to have a picture
> (mental model) of all math concepts. I think that is one of the many
> functions of using models in math class and defines the real value
> of concrete manipulatives for students of all ages.
To a point. Certainly, a mental image is a great asset, especially at a very
young age. However:
(i) not all mathematics lends itself readily to some immediate image. At the
simple level it is easy to have a picture of four objects or five ...but not of
371. Later, it is difficult to picture the product of complex numbers.
(ii) not all can readily visualise in 3 dimensions. This capability or lack of
it causes some to carry on in their studies, and some to halt in them. A former
math head I knew had enormous difficulty picturing a hole cut through a sphere,
and then having the sphere expanded. He could only shake his head in
dismay.
At an entirely different level, Albert Einstein made history [again] with his
"thought experiments", using extremely simple diagrams [an elevator pulled by a
rope] to demonstrate some of his theories quite clearly. A demonstration to
emulate the "coriolis force" stuck forever in my mind; just a ball bearing
rolling across an LP turntable.
Whatever works!
David.
 
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