[nSLUG] math rant

M Taylor mctylr at privacy.nb.ca
Wed Oct 22 16:36:01 ADT 2003


On Wed, Oct 22, 2003 at 03:33:37PM -0300, Jeff Warnica wrote:
> 
> This gives me a perfect opening for my standard complaint on math and
> math education.

I disagree with you assertions that calculus is source of a problem
for math education, I contest (without arguing it here) that one major
issue is that the poor social ties we have with math, images of nerds,
teachers of elementry students who confess that they teach young children
because they don't like/aren't good at math themselves, and thus fail
to lay a concrete foundation to upon, and at some point a student stumbles
and the mass education system is unable to assist that student to help
get them back on track, and they continue to sink, and thus end up
hating math because they stuggle with it....

 
> Calculus, at least at the first year level, is a requirement for
> graduation from just about any 'higher education' in
> science/engineering. The only modern reason for this that I can see that
> it continues to be taught is a 'test of streangth' / 'if I did it, you
> should do it'. And because of that, math education in high school is all
> pre-calculus; math earlier then that is all pre-pre....

Trying to do physics or engineering without calculus would be just stupid.

Much of mathematical knowledge is cumulative; you need to know fermat's
little theorem to do neat stuff with RSA cryptography, but to do flt
you need to know about rings, and do know about rings you need to know about
associative functions, ....
 
> not all upper math is calculus. For the %99.9 of the people calculus
> should be taught because it is a convient way of sloving a certin set of
> problem types with paper and pencil.

Well it is harder to write (and understand) numeric calculations for
differential equations if you don't understand the theoric bases, and
you actually expect to correctly apply the "cookbook" algorithms. 
 
> Of course, in 2003, and for that matter in 1945, sufficently complex
> problems (and these days 'trivial' problems too...) arn't solved with
> paper and pencil, there solved with machines desigined for computation.

Numeric computations, true; mathematics, false. What tools did Wiles
use for solving Fermat's Last Theorem? (email and TeX, AFAIK)
 
> Its interesting to wonder what would happen if Jr and Sr High math
> wasent taught with the unstated goal of 'calculus in first year uni',
> but with 'programming in first year uni'.. I think, with the possible

Heck I'd be happy if a high school graduate have enough maths 
to understand mortgage calculations and how much of a rip-off
credit card interest rates and most in-store financing offers are.

I don't see why the average student should be taught with goal of
programming. Then again, I think university is a poor place to learn about
programming -- I see computer science and programming (which some wish
we could call software engineering, but cannot due to the P.Eng
name protection) as very different fields. I do believe having a 
foundation of computer science enables a programmer to understand what
she is doing in a more holistic manner, and obtain a higher level of
mastery of the technology she is working with.

E.g. The Turing Halting Problem when evaluating claims that an anti-virus
tool is perfect in detecting all known and new malicious software.

Mathematics itself is a pure and abstract 'science', which for most
pupils is an enabler; typically helping deal with abstractions 
(aka 'models' in science), but mathematics exists for its own sake as well.

> But my opinions are uninportant; Im not a member of the cult of
> university graduates.

Education, mathematics, literacy are all enablers; you don't need them,
but they can make things easier and open up new possibilities in certain 
situations. 

I just hope it was your choice not to be a university graduate.




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