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Discussion: Traffic Jam Applet tool
Topic: Computer Tools at PreK2
Related Item: http://mathforum.org/mathtools/tool/10/


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Subject:   RE: Computer Tools at PreK2
Author: Mathman
Date: Oct 4 2004
On Aug 26 2004, Teach Math wrote:
> 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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