
Re: A statement on what is wrong with standard calculus
Posted:
Feb 23, 1996 11:14 AM


>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 reeducation 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 >DOSprompt, take squareroots 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, properlydesigned 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"]

