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Topic: A statement on what is wrong with standard calculus
Replies: 15   Last Post: Sep 21, 2004 11:26 AM

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p.kent@ic.ac.uk

Posts: 67
Registered: 12/6/04
Re: A statement on what is wrong with standard calculus
Posted: Feb 23, 1996 11:14 AM
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>Date: Thu, 22 Feb 1996 17:26:22 -0700
>From: Matthias Kawski <kawski@akaikuma.la.asu.edu>
>

>>As a matter of fact, laziness, the desire to have convenient tools
>around is a major driving force for innovation. Rather than changing
>the people (a la socialist re-education camps), we change the envi-
>ronment in such a way that even without any technical expertise the
>average citizen can use very sophisticated machinery, from cars to
>Macinstoshes. If the American citizenry had been too well educated
>we might have never seen the Macintosh and instead still use the
>DOS-prompt, take square-roots by hand, and enjoy wasting our days
>with long integrations by parts ....
>


I disagree with this, quite fundamentally. It's really quite
striking how after 15 or so years, the philosophy of the
Macintosh Operating System ("windows"/"desktop") is still
not much understood. MacOS was *not* designed for average
people to use computers - it was designed for all those
people (even really bright ones) who wanted to spend more
time using a computer to get their work done than messing
around with computers.

In the same way, computer mathematics software (Mathematica,
Maple, Derive, ...) offers *everyone* a tool with which
they can spend more time doing "mathematics" and less time
doing all those routine "manipulations" that are something
less than "mathematics".

The complication is, there is no agreement in the maths
profession on what is real "mathematics" and what is plain
"manipulation" - and how much of the latter you need to
do in order to understand the former.

As someone else said, properly-designed curriculum experiments
are needed to find out how much "algebra" people need to know
in the era of mathematical software, in order to do mathematics
or physics or whatever else. But diluting mathematics courses
for political reasons (pressures from outside the profession)
can only lead to trouble.

There's a recent UK report looking at the dilution of "high
school" maths and its effect upon mathematics at university:

http://www.qmw.ac.uk/~lms/tackling/report.html


Regards, Phillip Kent.

----------------------------------+----------------------------
Dr Phillip Kent | tel: +44 (0)171 594 8503
Transitional Mathematics Project | fax: +44 (0)171 594 8517
Mathematics Department |
Imperial College | p.kent@ic.ac.uk
180 Queen's Gate |
London SW7 2BZ, U.K. | http://othello.ma.ic.ac.uk
----------------------------------+----------------------------
"An impossible probability is preferable to an improbable
possibility" - Aristotle ["Poetics"]





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