Math Forum Discussions

Michael Paul Goldenberg

Posts: 7,041
From: Ann Arbor, MI
Registered: 12/3/04

Re: where's the math? so?
Posted: Apr 20, 1995 2:59 PM

Plain Text

On Thu, 20 Apr 1995, Ted Alper wrote:

>
> Sure, teaching math is or ought to be about teaching a certain mindset
> to problems that go far beyond the template problems in the textbook.
> That is not the same thing as encorporating the study of "all [or even
> any] of the new mathematics done since world war II" into the K-12
> curriculum.
>
> Developing the mindset might be done as well by studying Descarte's
> "Rules for the Direction of the Mind" (c. 1650) which applies as much
> to a beginning algebra "word problem" as it does to modern
> mathematical research. The approach is ancient; the mathematics (at
> least at the level of high school students) is also pretty old; the
> world around you, in which you apply the approach and the mathematics,
> is ever-changing.
>
>
> Ted Alper
> alper@epgy.stanford.edu
>
This seems like apples and oranges. Some of us are talking about the
importance of giving students at an early age (but not so early that they
would be incapable of understanding or benefiting from it) the notion
that one MIGHT need mathematics only up to what was developed long ago
(or relatively long ago), but that as a career pursuit, it's not
identical to the pursuit of ancient history, classical studies,
paleontology, or Chaucerean manuscripts. (And this is not to suggest
anything derrogatory about those areas of interest or to imply that
there's "nothing new under the sun" in any of them). One might become a
mathematics historian. One might become interested in teaching high
school mathematics. One might become interested in applying the
mathematical inventions of others. One might become interested in
creating new mathematics. But obviously, the last thing on this list is
less likely to pique someone's interest IF THEY HAVE NO IDEA THAT SUCH
THINGS HAPPEN EVERY DAY.

The other issue is the notion of authority and received knowledge. By
stressing ONLY the "accessible" past of mathematics, we communicate to
students that they're pretty much engaged in Bible Studies: read the
works of the masters (and I use that gendered noun advisedly), try to
grasp the ideas with your feeble mind, and some day, if you're very
lucky, you may be worthy of a few more revelations. No one here is
suggesting that students need to knock heads with Wiles' proof of Fermat,
but it seems reasonable to believe that students might get something out
of exposure to the fact that there are problems that challenge the best
mathematical minds on Earth for over 3 centuries, that some of these get
solved by folks not all that much older than they are, that it's exciting
to know about some of these problems, that there is an inexhaustable
supply of them, some of which they can grasp without too much difficulty.

Do you think kids get hooked on basketball by studying James Naismith or
by watching Michael Jordan? They may realize that what Jordan does now is
something they can't YET, but the Michael Jordan of 2010 is probably
watching the Michael Jordan of today, and getting inspiration for the ideas
that will make basketball history in fifteen years. Of course, like all
analogies, I'm sure this one can be picked apart (and also developed
further). But my sense here is that there's a pretty clear point being
made here which some folks simply don't wish to grant.

Is it our belief as a community that there's NOTHING to be gained by
giving students a more accurate picture of what real mathematicians do? I
hope not.

-michael paul goldenberg/University of Michigan

"Truth is a mobile army of metaphors." F. Nietzsche