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Topic: Graphing Tool
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Subject:   RE: Graphing Tool
Author: markovchaney
Date: May 19 2007
One of the more intelligent posts I've seen on this topic, here or on other
boards. Last time I checked, kids have a natural interest in play and a natural
interest in learning, and the two are not so separate as some of the purists and
educational conservatives ("No pain, no gain") seem to believe.

This isn't to suggest that mathematics is a painless process, if by "pain" we
mean "taking pains to focus, think, concentrate, bring to bear our best," etc.
But all too often, for the folks I generally disagree with in these sorts of
discussions, "pain" really means "suffering." And there's nothing in mathematics
that requires that sort of thing. It's the way we make that so for kids, often
during early elementary school, that we lose so many of them. And I think that
for some of these Schwartzeneggar, iron-pumping types of thinkers, that's
actually a GOOD thing. Keeps their sense of achievement, merit, and elite status
intact. I could hack it, you couldn't. That makes me one hell of a person, even
if I can't communicate what I know to anyone who isn't exactly like me. The
whole model is predicated on a scarcity philosophy: there's only so much praise,
so much credit, so much success to go around, so the less there is for you, the
more there is for me. Since I'm not a professional mathematician, it doesn't
actually hurt me all that much if highly-competetitive, egotistical math gods
want to play at that game, but keep them out of the K-16 classrooms as much as
possible and don't let them set the rules for the rest of us, especially not for
kids.

Technology in math, be it pencil and paper, chalk and board, knots in strings,
pebbles in the sand, beads on rods, slide rules, hand-held calculators, or pcs
with various levels of programability and powerful software, is a necessary and
wonderful part of how mathematics is done. And also how it is communicated to
others. If some purist can do it all in her/his head, great, but don't expect me
to have to learn that way. And don't tell me or my students or the teachers I
train that we can't play and explore in any way we see fit. Or that we can't
play with these things until we're in Grade X. For one thing, no one has the
authority to stop us, and for another, it's WAY too late. :)


On May 18 2007, I-Heng wrote:
> I think we can have goals and objectives even while students
> play...that is, guide the play so students discover something.  For
> example, when we play games, we have a goal and yet it's still play.
> The art is in providing enough but not too much guidance...in order
> to preserve the feel (freedom, openness, choice, challenge,
> surprises, etc.) of play.

A little more concretely, I like the
> idea of 15 minutes of play with the tool before more beginning
> structured activities with the tool.  I would guide this initial 15
> minutes with a general goal...maybe something like:

Play with the
> settings to generate as many drastically different graphs as you
> can.

(I'd have to find some way for students to easily record
> their results...shots of the graphs with settings, or hand-written
> quick sketches and the corresponding settings, or printouts....)
> We would then have some shared experience and examples to use as the
> basis of a more formal discussion of what's going on with these
> graphs.

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