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Topic: Demise of Green Globs


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Subject:   RE: Demise of Green Globs
Author: Alan Cooper
Date: Aug 5 2005
On Aug  4 2005, Mathman wrote:
>  Sorry, but I can't agree with it in principle.
> What is fundamentally being asked is for the student to guess at
> the "best-fit" parabola that will pass through some random points.  

It may not be consciously algorithmic mathematics, but it's certainly not just
"guessing".

The act of drawing or imagining a curve of a particular type passing through a
number of given points is not typically done as a conscious  exercise in
mathematics, but like throwing a basketball through a hoop in the face of
interference from a number of opponents, it is done subconsciously using
algorithms that noone yet fully understands. I believe that this practice, while
not strictly-speaking mathematical, exercises cognitive skills and geometric
intuition that are useful in the practice of mathematics and its applications in
the real world.

>    . . . .

> They'd do well with a good graphing program that
> will show effects upon the graph when a parameter changes
> dynamically.  . . . .

Well, I did say that lack of immediate feedback as the sliders are moved in the
Explorelearning 'ZapIt' game was one reason for prefering my own (not yet ready
for prime time)version (see first draft at
http://www.langara.bc.ca/~acooper/mathlets/meanies/ ).

The applet at http://www.langara.bc.ca/%7Eacooper/GeX/v2/Grapher.htm was
intended to be a "graphing program that will show effects upon the graph when a
parameter changes dynamically". If there are ways it could be improved please
let me know.
Thanks.
   Alan

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