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Topic: Understanding Distance, Speed, and Time Relationships Using Simulation Software
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Subject:   RE: Understanding Distance, Speed, and Time Relationships Using Simulation Software
Author: Mathman
Date: Aug 20 2007
On Aug 20 2007, Kathy522 wrote:
> When students realize that what we are
> working with is actual and potentially found in their world, they
> learn more.

What will you do when that is not entirely possible?  Some math is abstract, but
has application none the less.  Well, I suppose it all is if we want to get to
the nitty gritty.  Natural Numbers are just squiggles on paper that represent
what is seen.  Any number greater than 9 is dependent on the Arabic numeral
representation, arbitrary and abstract.  Complex numbers, that they will meet
later, have uses in electronics [with infinite application in their "real
world".]  The arithmetic of numbers must include radicals as part of the real
number system, and that arithmetic skill is very dependent upon patterns studied
in algebra ...which is intrinsically abstract.

Whether or not they "learn more" will depend upon a point of view being short
term or long term.  Their education should be as whole as possible.  To give
them less is to stunt their academic growth.  That is not to go overboard with
discussions on abstraction, but to surely include it to some degree.  The
properties of geometric figures is well worth knowing.  Their formal derivation
is also well worth knowing. ...and so on.

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