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Topic: Understanding Distance, Speed, and Time Relationships
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Subject:   RE: Understanding Distance, Speed, and Time Relationships
Author: Craig
Date: Jan 20 2007
On Jan 20 2007, lanius wrote:
> I'm curious. Are students today introduced to the term "modeling"? I
> don't think I ever heard anything about "mathematical modeling"
> until I was out of college and started teaching. It seems to me that
> is a pretty sophisticated idea, and I'm interested in knowing how
> teachers handle it.

I agree with the "newness" of the terminology... but "model" has crept into
textbooks, particularly those written since the first publication of NCTM's
standards in 1989.  It seems that "the equation for a projectile's motion is..."
has been replaced by "a model for a projectile's motion is..."  I like the new
formulation much better.  First, by using "a" instead of "the," students get the
idea that there may be several different approaches.  Second, "model" can
incorporate many different ways of thinking about the topic at hand: an
algebraic equation, a graph, a table of values, a recursive relationship, a
computer or calculator program.  Third, the term model, itself, implies a
stand-in, with inherent approximation and error; an attempt to describe a
phenomenon, rather than a rule or law that the phenomenon must follow (gee, I'd
better hurry up, or my motion won't fit the prescribed equation).  I haven't
observed that students think about the term model differently than they thought
about any other term loosely categorized as "word problem," so they're not
particularly tripping over the subtleties.

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