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Re: where's the math? so?
Posted:
Apr 20, 1995 6:55 PM


On an earlier message, Ted Alper wrote:
>Presumably everyone on this list has loved mathematics from a fairly young age. >How many owe that love to a sense that there were modern mathematicians out >>there, tackling tough modern problems? > Later, Judy Roitman responded: (parts of her response)
>Nope, I didn't. I thought math = calculations (including algebraic) and >overly formalized proofs of uninteresting statements = uncreative and >dreary. Except for having run into the proof that the reals were >uncountable in George Gamow's 123 Infinity back in junior high... > (cut...)
>So how to teach kids what math is? I think Ted is right  you have to >give kids something they can work with and understand themselves. But >surely it doesn't hurt to give a glimpse of some of the more understandable >modern developments, both theoretical and applied. ...(cut...)... Strange and >>interesting and attractive things were going on in physics. Why didn't we >know >about strange and interesting and attractive things in mathematics? > > My comments:
Thought that I would ride out this "Where's the math? so?" conversation without jumping into the fray...but, alas, I can't resist.
Kudos to Judy for trying to strike the practical middle ground...both approaches can and should be employed within the school mathematics setting...some educators are better at integrating, or highlighting, different perspectives of mathematics than others...
However, we need to understand that the everevolving mathematics of today (post WWWII) was/is not developed in isolation of the rich history of mathematics of previous eras...Conceivably, (and shallowly), I could write a novel without any deep understanding of the middle age epic poem, but it is impossible to develop new mathematics without any rich sense of the mathematics of old...New mathematics does not follow a replacement theory...it truly is an accumulating evolution...
Let me offer an example: I recently had the opportunity with my student teachers in a methods class to higlight this interconnection aspect of mathematics...One of the students engaged the rest of the class in an activity that developed the idea of using graph theory as a modeling tool in problemsolving...She used the wellknown problem of the lion, the llama, and the lettuce (orcrossing the river with dogs, or...etc.) where the owner of the three l's had to cross with one other object at a time, return back for one other, etc. until he/she had all threethe lion, the llama, and the lettuceon the other side of the river...all under certain prescriptions of which two things could be left alone with each other.
After allowing the other students solve the problem, and having developed the threed model of representing the problem with graphs, she then led the students to the connection to the Tower of Hanoi problem...
What she and the other student teachers did not realize at first was that this type of modeling that is connected to the Tower of Hanoi problem was/IS connected to the Sierpinski Triangleconnected to the Cantor setconnected to Pascal's Triangleall of which is connected to ideas of selfsimilarity, chaos, and fractalsvery modern mathematical ideas...
We even explored further (couldn't resist to follow up) that these newer mathematical topics which had their roots in the Sierpinski Triangle, Cantor Set, and Pascal's Triangle, which, in turn, have in their roots, geometric series, binomial distribution, probability, the powers and divisibility of both 2 and 11, etc. all of which are connected to Fibonacci sequence numbers, the geometric idea of triangular numbers and tetrahedral numbers, the Golden Mean, continued fractions, and Farey fractions, just to name a paltry few!
While slightly (ha!) overwhelming, the excitement and the realization that students in secondary school can: (1) study things that we *normally* study in school mathematics; (2) make connections to the historical mathematics in an active, involved, and evolving way; and (3) examine the development of newer advances in mathematics both in terms of their origins as well as their application in the real world...
Well, we all left with a renewed vision of what school mathematics can be...
I dunno about everyone else...but I vote for strange and interesting and attractive! Moreover, I am tickled pink that the strange, interesting, and attractive is only so because of its rich undergirding of historynot dead (date occurred history), but vital (recreating, interpreting)history.
Tim
***************************************************** Tim Hendrix (hendrix@uxa.cso.uiuc.edu) * Division of Mathematics Education * Department of Curriculum & Instruction * University of Illinois * ***************************************************** 382 Education Building * 1310 South 6th Street * Champaign, Il 61820 * ***************************************************** (217) 3333643 * *****************************************************



