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Implementing history-sensitive math
Posted:
Mar 5, 2000 6:52 PM
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Based on the foregoing discussion, I think I've successfully
prototyped some materials that follows our suggested guidelines.
Here's what people asked to see:
1. the historical nature of mathematics,
2. how mathematical contributions, both historical and current,
enhance our society in new and interesting ways,
3. that most major theorems and other mathematical objects
have been named after people whose contributions to
mathematics ought to be recognized,
4. the great, interesting, and in many cases still
unsolved problems of the past, and
5. the historical partnership between mathematics and science
in the development of both fields, and the importance of
the interplay between them.
Where I implement some of these guidelines is in a 4-part essay
starting linked from:
http://www.inetarena.com/~pdx4d/ocn/cp4e.html
I call this my 'Numeracy + Computer Literacy' series, because
as per prior posts (of mine), I consider these to be convergent
goals -- partly why I'm not a big fan of rigidly dividing
"mathematicians" from "non-mathematicians" along university
departmental lines (as per today's bureaucracies) -- because
many leading lights in the past _cannot_ and _should not_ be
pigeon-holed too neatly into just one category.
Anyway, let me go through the exercise of incidating in what
way I've at least partially met our own proposed NCTM criteria:
==========
1. the historical nature of mathematics,
(a) I go back as far back as BC times, with Erastosthenes,
showing how his thinking is still relevant to today.
(b) In mentioned that the Chinese were familiar with Pascal's
Triangle, I'm showing how different cultures may follow
similar threads using different terminology and conceptual
frameworks.
(c) And in talking about how the lowly numberline, introduced
in early grades, might be recast as an implementation of
vectors, ala Grassmann, Clifford, Gibbs et al, I'm showing
how later work has the effect or recontextualizing the
earlier stuff.
All of the above are indicative of important patterns, which
we encounter over and over, when studying the history of
mathematics (continued relevance, parallel/convergent tracks,
recontextualization of the old by the new).
==========
2. how mathematical contributions, both historical and current,
enhance our society in new and interesting ways
Given that I'm using well-known mathematics as a basis for
phasing in a recent, state of the art, VHLL (very high level
language), this theme is somewhat implicity: "Thanks to
mathematical contributions at many levels, you the student are
able to learn math using fancy computers and languages like
Guido's Python, relatively easy to use compared to what your
ancestors had to struggle with".
Given this same computer language, and synergy of Python + Povray,
is what's used to produce the majority of the illustrative graphics,
this message is also clear: your aesthetic environment is being
altered by pioneering work in mathematics (hits home with kids,
given how many are already immersed in video games and computerized
cartoons).
==========
3. that most major theorems and other mathematical objects
have been named after people whose contributions to
mathematics ought to be recognized
I don't mention a many theorems, but I do mention Goldbach's
Conjecture (still unproved), and Grassmann algebra (naming an
algebra for a guy). Objects such as vectors, quaternions,
turtles (graphics cursor), polyhedra etc. are _not_ named
after individuals. So I guess I'm sort of making the opposite
point as well: many important objects in math are not named
after people. Johann Carl Friedrich Gauss has the Guassian
Distribution named after him -- and he's definitely one of the
heros in this presentation (starting from early boyhood).
Others mentioned: Blaise Pascal, Rene Descartes, Waclaw Sierpinski,
Sir William Hamilton, Willard Gibbs, Robert Gray, David Chako,
Leonard Euler, Russell Towle, Tim Peters, Tom Ace, Gerald de Jong,
Jim Nugent, Leonardo Fibonacci (some of these just get a "thanks"
in the source code).
==========
4. the great, interesting, and in many cases still
unsolved problems of the past, and
Ibid: Goldbach's Conjecture. I also branch to the topic of
prime number explorations, which push the computing frontier.
Only thanks to modern high speed computers do we have such a
huge list of verified primes (still growing).
5. the historical partnership between mathematics and science
in the development of both fields, and the importance of
the interplay between them.
This is especially important to my approach, and I agitated to
retain point 5 in earlier discussions. Among those cited in
my essay who might not be neatly pigeon-holed as "just
mathematicians" are: Isaac Newton (physicist), Willard Gibbs
(scientist), Johannes Kepler (astronomer), William Barlow
(crystallographer), R. Buckminster Fuller (philosopher), Alexander
Graham Bell (inventor) and Hermann Grassmann (he got into sanskrit,
when more established mathematicians of his day were more into
ripping him off than giving him credit (another important pattern
in math (see (a))).
Yes, I know these are "dead white males" (dunno about Erastosthenes
for sure), but I consider the genetic commonalities fairly
irrelevant: it's the memes, not the genes, we need to be
focussing on, when doing intellectual history (which doesn't mean
we should ignore socio-economics, sexism, racism or classism,
all relevant factors when explaining how "mathematics" came to
be as we know it -- or refuse to recognize it -- today).
Kirby
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