Date: Apr 20, 1995 1:45 PM
Author: Ted Alper
Subject: Re: where's the math? so?


W. Gary Martin <gmartin@kimiyo.ed.Hawaii.Edu> writes:

>Ted Alper <alper@Ockham.Stanford.EDU> writes:
>>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? <etc.>

>
>This is not just a "fact" to be conveyed to students. It is a mindset, a
>way of looking at the study of mathematics. Mathematics is not something
>dead people who lived years ago did. Mathematics is a continuing creative
>enterprise of developing knowledge done by people who are LIVING.
>Mathematicians do this for a living; we share in that enterprise as we make
>sense of the mathematics we are studying, no matter what level that may be.
>Too often students see mathematics as a body of knowledge to be assimilated
>(a product). To me, seeing mathematics as an exciting and worthwhile
>activity (a process) is at the very heart of the Standards.


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