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From: mroussel@alchemy.chem.utoronto.ca (Marc Roussel)
Subject: Re: The use of calculators in teaching calculus
Message-ID: <1990Dec5.030314.26463@alchemy.chem.utoronto.ca>
Keywords: Calculators, calculus
Organization: Department of Chemistry, University of Toronto
References: <4608@umbc3.UMBC.EDU> <1990Dec4.153552.29699@javelin.es.com>
Date: Wed, 5 Dec 90 03:03:14 GMT

In article <1990Dec4.153552.29699@javelin.es.com> pashdown@javelin.es.com
(Pete Ashdown) writes:
>In my higher math classes, I tend to bang out derivatives on the
>48 rather than waste time doing them by hand.
>However, we all know the "square root"
>arguement as you mentioned it.  Should these tasks be designated for
>computers/calculators?  Is "hand-math" a dying breed?  In my opinion, I
>certainly hope so.  If I can do a problem quicker and more accurately on a
>calculator, I'll use the calculator.

     Let's take another example.  Some (primary) educators have
suggested that long division should be removed from the curriculum.
However long division is the basis of polynomial division, and if you'd
never done polynomial division, I don't think you'd ever be able to
write a polynomial deflation routine (for instance).
     Perhaps the actual taking of derivatives is more like square roots
(boring and arguably not terribly educational) than like long division
(a technique with interesting generalizations), but the traditional
introductory calculus course includes a substantial discussion of Newton
quotients and of epsilon-delta proofs.  These topics must not be lost in
the shuffle to computer assisted education as they form the basis for
understanding the generalization of calculus to higher dimensions.

				Marc R. Roussel
                                mroussel@alchemy.chem.utoronto.ca