Date: Apr 20, 1995 3:07 PM
Author: Ted Alper
Subject: Re: mathematics as a historical entity


Edward S. Miller <edmiller@lcsc.edu> writes:

>On Thu, 20 Apr 1995, Ted Alper wrote:
>

>> 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?

>
>> 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.

>
>I seed to have missed the point to these statements.


The point was in response to the idea that the secondary school
curriculum should somehow include some of the "new mathematics
developed since world war II". I know a portion of that math, and have
a passing familiarity with a lot more (and am quite ignorant of somem
I'll confess -- but this is true of most mathematicians, I think), and
I doubt that much of it has any role in the secondary math curriculum.


>I recall that the
>physics, chemistry, biology, english grammer, spanish grammer,
>literature, and even the history was largely a century or more old. I
>also came away with the impression that all of these areas of human
>endeavor were constantly evolving (pardon the biological pun) and that
>human understanding of even small areas of study in them were also
>changing. I did not get a similar impression of mathematics.
>


I don't remember getting that impression in my English or history classes,
but no matter.

In any case, while one can quibble at the details, the fact remains:
there is an enormous core of mathematics that is pretty rock-solid. A
vague awareness of those hammering away at the frontiers of knowledge
is fine -- but what specifically do you want to teach about those
frontiers?

>In hindsight, that was (is? I hate temporal mechanics) a problem. I
>graduated from high school equating mathematician with actuary or some
>similar object.


Of course, actuarial science is ALSO a dynamic, growing field -- even
in its pure mathematical components. How much of a problem is/was it to you
that you feel otherwise?

Actually, I doubt many students graduate high school even knowing what
actuaries do. So perhaps your condition was an improvement over the
norm.

>
>After lamenting the problem, I will give my first guess at a solution. I
>try, and would suggest that others also try, to place mathematical ideas
>that are being taught in their historical perspective. If you are
>teaching classic geometry, talk about the Greeks; include Greek
>philosophy and drama. I teach calculus, so I get to talk about the
>parallel development of physics.
>
>Maybe if we place math in its historical perspective, and talk about when
>the stuff we're talking about didn't exist, then we can impart the idea
>that math isn't like latin: mostly dead and easily forgotten.


Isn't the study of latin also constantly evolving, etc.? But I can
agree with this, up to a point. I certainly think it's useful to
stress that the math in the textbook wasn't made all at once and just
for the purpose of filling a textbook. Historical context in its
development and refinement can give a broader sense of the power and
dynamism of math -- in the sense that one sometimes applies ones tools
to a problem and sometimes one first has to craft the tools
themselves. I could also see including all the false starts and errors
in the history of math that tend to drop out of the finished textbook
and give too pat an impression.

(I'm not sure that spending time in math class talking about Greek
drama is such a good idea -- kids may pick up the wrong message from
the desire of a teacher to talk about something other than the subject
he or she is supposed to be enamored of.)

Still, ultimately, the speed which with math will be forgotten may
have more to do with whether you can make students see either the
power, utility or beauty of what they learn, quite apart from whether
they think it was discovered last week or two thousand years ago.



Ted Alper
alper@epgy.stanford.edu