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Topic:  Shodor lessons 
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Subject:  RE: Shodor lessons 
Author:  Craig 
Date:  Jan 26 2006 
I agree with Mathman that just showing a quick dynamic slider to illustrate the
effects of different parameters in the graph of a function does not lead to the
fundamental understanding that most teachers want and expect from their
students. In fact, I have not used the "function flyer" applet I mentioned in a
few years, because I didn't think my students needed that level of
visualization. However, I have had students in the past (and probably will
again) for whom that extra visual step provided just the impetus needed, either
to break through a fog of misunderstanding or as a catalyst for much
higherorder thinking (proving effects of parameters, for example). Bottom
line, I don't endorse using the function flyer as a cureall, or a oneshot
"this is how slope works" lesson. I think a good teacher will hold this tool
for use when it becomes apparent that a student (or class) would benefit from
it.
Here's a slider I'd like to see, just for fun (and I have almost succeeded in
creating one in Geometer's Sketchpad): an "eccentricity" slider. Slide from 0
through 3, say, and see a conic section change from a circle, through ellipses,
to a parabola, then through hyperbolas. I can get the effect by using overhead
transparencies with parallel lines and/or concentric circles...
 
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