From: dwp@cci632.cci.com (Dana Paxson)
Newsgroups: sci.math
Subject: Re: Computational aids.  Was:  Re: An interesting limit problem.
Date: 30 Jul 92 12:40:53 GMT
Organization: [Computer Consoles, Inc., Rochester, NY

In article <1992Jul29.210135.16840@seas.smu.edu> mhosea@seas.smu.edu (Mike Hosea) writes:
>In article <55402@mentor.cc.purdue.edu> hrubin@pop.stat.purdue.edu (Herman Rubin) writes:
>>In article <1992Jul29.000223.27339@massey.ac.nz> news@massey.ac.nz (USENET News System) writes:
>>>In article <1992Jul28.191037.28756@gdr.bath.ac.uk>, mapsj@gdr.bath.ac.uk (Simon Juden) writes:
>>
>>>> >mattm@lure.latrobe.edu.au writes:
>>
>>>> [stuff deleted]
>>
>>>> >Will someone please back me up, and say that no one learning
>>>> >Calculus should ever be allowed anywhere _NEAR_ Mathematica?
>>
>> [stuff deleted]
>>
>>Only researchers and teachers need to know the mechanics.  It is useless
>>to know how to differentiate if one does not know what a derivative means.
>>No amount of memorizing formulas and tricks helps in understanding.
>
> [stuff deleted]
>
>This question pops up from time to time, and the strongest reactions
>occur when someone suggests a total abandonment of hand calculation
>or a total abandonment of modern computational tools (in the context
>of education).  Either extreme is a poor choice IMO.  Why must we 
>go to an extreme?
>
>Regards,
>Mike Hosea (mhosea@seas.smu.edu)

I second Mike's point.

When I was taking a basic course in differential equations, many years 
ago, I was impressed by the variety and complexity of methods needed to 
solve these equations.  I had little trouble learning useful methods of 
attack on a given equation, but some of the problems required PAGES of 
algebraic manipulation to arrive at a demonstrated solution.  Half my 
time was spent in factoring, multiplying through, reorganizing terms,
etc., none of which required the application of great intelligence but 
all of which demanded fanatical detailed accuracy and unflagging attention.
I would much rather have spent that time learning new solution methods or 
better use of the ones I had.  Worse yet, the time often doubled when I 
introduced minor procedural errors into these endless mantras of symbolic 
contortion.  It might have been character-building, as some less-
sympathetic soul might put it; but when I was juggling a family, a full-
time job, a long commute, and two night classes, it was physically 
draining to the point of illness.  Is this necessary?

Mathematica or Maple or some other such package would have been a 
blessing, and an enhancement to the learning process; BUT on the other 
hand, I wouldn't want the tool to present the result if I needed to 
learn the methods.  At some point in our mathematical education, we must 
learn the underlying ideas well enough to apply them meaningfully, and 
then get on to the next stage founded on those ideas.  What looks so 
simple on the page only reveals its complexity and subtlety when the 
reader tries to explore it in detail.  This exploration is a vital part 
of the learning process.  Tools cannot substitute for it.  After all, 
tools are founded on numerical and symbolic methods, which for some 
branches of mathematics are only approximations of the true ideas to
be learned.


Dana Paxson
Network Applications Systems Group
Northern Telecom
97 Humboldt Street
Rochester, New York  14609

1 716 654-2588

Disclaimer:  The opinions expressed above are mine personally,
	     and do not necessarily reflect the views of my 
	     employer.