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Implementing historysensitive math
Posted:
Mar 5, 2000 6:52 PM


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 4part 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 "nonmathematicians" along university departmental lines (as per today's bureaucracies)  because many leading lights in the past _cannot_ and _should not_ be pigeonholed 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:
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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).
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2. how mathematical contributions, both historical and current, enhance our society in new and interesting ways
Given that I'm using wellknown 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).
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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).
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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 pigeonholed 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 socioeconomics, 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



