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Topic: Fractals
Replies: 29   Last Post: May 9, 1995 10:14 AM

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Michael Paul Goldenberg

Posts: 7,041
From: Ann Arbor, MI
Registered: 12/3/04
Re: Fractals
Posted: May 7, 1995 7:20 PM
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On Sun, 7 May 1995, Andrei TOOM wrote:

> Thank you, Han, for this very interesting message.
> I must apoligize: I wrote something which seemed to
> mean that I am against speaking about fractals in
> middle school. Of course, not. Let me make a comparison.
> Suppose somebody asks: Does it make sense to put
> on bosoms of cheerleaders' T-shirts a sign: `E=MC^2'.
> Why not ? After all, it is not obscene.
> But, PLEASE, do not call it physics.
> This is the point. You may discuss quantum mechanics
> with small children and it may make some sense.
> But it is NOT a study of quantum mechanics.
> You may (perhaps, should) some time show middle school
> students fractal pictures and in may have a positive
> effect on their development. (Everything what intelligent
> adults do WITH children has a positive effect on their development,
> including, for example, practical joking.)
> But, PLEASE, do not call it mathematics.
> And do not do it INSTEAD of a regular course.
> Andrei Toom

I'm not clear on what the potential crime is here: what bad thing(s) would
happen if someone talked about fractals with kids to give them a taste of
a fascinating phenemenon? At worst, the kids might be bored or turned
off; another possibility is that they'd say to themselves, "Gee, that's a
pretty interesting thing. I'd like to learn more about that" which
potentially could motivate them to pursue more mathematics; in some
cases, kids might simply find it a novel but ultimately unengaging topic.
So what?

I also don't share the apparent fear of "mislabeling" something as
mathematics which "really" isn't mathematics. Do we all share an
identical set of meanings for that word? I seriously doubt that we do.
I'll grant that we don't want to mislead kids to think that something
trivial, or a trivial understanding of something, is in fact deep. But we
don't have to be dishonest: when someone demonstrates a new piece of
software, you don't expect to "get it" entirely in one gulp, and only a
very silly demonstrator would expect you to do so. Should we only taste
that which we're ready to gulp? Should we fear that kids will suffer if
they sample ideas "prematurely"? I read Joyce's ULYSSES as a college
freshman. I didn't get much from it. I made an erroneous evaluation based
on my perspective as an 18-year-old. Guess what? I got older and reread
the book with vastly more appreciation. Why? Because part of the growth
process is gaining the ability to reflect on one's previous judgments.
One "bad" taste of something shouldn't keep most folks away from
anything; most of us are pretty resilient creatures.


Michael Paul Goldenberg
University of Michigan 310 E. Cross St.
4001 School of Education Ypsilanti, MI 48198
Ann Arbor, MI 48109-1259 (313) 482-9585
(313) 747-2244 email:

"Truth is a mobile army of metaphors." F. Nietzsche

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