Date: Apr 20, 1995 4:32 AM Author: Ted Alper Subject: Re: where's the math? so? (was Re: 5th Grade Activity)

Michael Paul Goldenberg <mikegold@umich.edu> wrote:

>I think that at least one point here is that mathematics is an open

>enterprise, constantly evolving, never to be completed. While that may be

>a commonplace in the mathematics community, it's hardly well known to the

>general public. Few of us are taught that mathematics is a growing body

>of knowledge that represents human ingenuity and inventiveness. Until I

>met graduate students in mathematics during my college years, I didn't know

>there WAS any mathematics past calculus.

Why is it important to teach that mathematics is a growing body of

knowledge? I mean, it's certainly true, and it is better to

be aware of the wide world than not -- but how much attention should be

paid to this in an 8th grade math class?

Oh sure, one wants the NSF to get funding, etc., so people need to be

wordly enough to recognize the existence of researchers. Then, too, as

a mathematician, I would like to see more people develop the

world-view of mathematicians and apply the general principles of

abstraction and reason to every aspect of their lives (though even

many mathematicians do a poor job of this -- for example, some think

their internal proofs of their own political prejudices somehow carry

as much weight as the proofs they produce in more appropriate

contexts). But what does this have to do with changing the curriculum

to reflect all the new math developed since WWII?

The bulk of the mathematics students learn in K-12 dates from the 18th

century or earlier. It is dressed up in 20th century notation, and

takes some of its emphases from the late 19th/early 20th century --

and is frequently applied to modern contexts -- but there is little

"modern" mathematics in it. Perhaps a few topics in the BC calculus

saw their first rigorous proofs in the 19th century -- not that the BC

calculus students are given complete proofs.

One could do quite well (at least as far as mathematics content is

concerned) with textbooks well over a century old. US Math Olympiad

students know, for instance, that Hall and Knight's "Algebra"

(it may be called "Higher Algebra" -- I don't have it in front of me), an

English textbook dating from the 1880s, aimed at preparing students

for University entrance exams, is an INCREDIBLE encyclopedia of useful

concepts and tricks.

Clearly one wants to give students a sense of modern applications.

But the essential core of mathematics is actually pretty ancient.

(That doesn't need to be so horrible, does it? Isn't there a thrill

in being part of an ancient tradition, imparting the distilled wisdom

of generations long past to the next generation? Is there no romance

at all in seeing a child wrestle with a concept the Greeks wrestled

with over two millenia ago?)

Ted Alper

alper@epgy.stanford.edu