> <snip>
> Very likely, the plotted path of the baseball they throw or hit is not a
> factorable function, so why should we leave our developmental students with
> the misconception that the function is factorable? However, it would be great
> if they get the concept that the function is quadratic.
Not to split hairs, but every quadratic involving the height above the ground of
a baseball in flight is factorable over the reals. You mean factorable over the
rationals, I suppose - but, we do have that nifty formula due to Al Kwarizmi....
> We all know that there are many examples where technology has been used as a
> button pushing device to replace learning skills or concepts. Surely, we can
> learn from past mistakes without blaming the technology itself as the culprit.
Well, there is some evidence that, in fact, technology itself is the culprit.
While it may be argued that people may be numb-skulls with or without
technology, I refer readers to Neal Kobitz' article in the Mathematical
Intelligencer (Vol 18, No 1, 1996) in which he makes the following arguments:
"Cost is an issue not only for schools but also for individual students.
Ironically, it is sometimes the colleges with the highest proportion of
working-class students that become most enamored of expensive new gadgetry for
teaching mathematics."
Yeah, tacking a $200 calculator on to the price of the textbook is pretty
severe.
Koblitz goes on to say, "Computers reinforce the fascination with gadgetry, as
opposed to intellect, that is endemic in American popular culture. <snip>
Computers are generally used in the classroom in a way that fosters a
Golly-Gee-Whiz attitude that sees science as a magical black box, rather than as
an area of critical thinking. <snip> Most software is based on immediate
gratification and does not encourage sustained mental effort. While physically
playing an active role, the pupil is intellectually passive, and has little
opportunity to be creative; that is, the pupil is programmed to follow a path
already laid out in detail by others."
He makes that point that the fetishization of computers by the media and
educational establishment is a kind of Cargo Cult, and that it is quite
possible, even preferable, to teach computer science without computers and that
computers have been foisted off on education by money-corrupted businesses such
as TI and MS and Apple.
Just some food for thought. Meantime, how about having students compute the
probability that four keys are pressed at random will produce a sum?
Geoff Hagopian,
Palm Desert
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