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 Discussion: Roundtable Topic: Teaching the Concept of Functions

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 Subject: RE: Teaching the Concept of Functions Author: Susan Date: Sep 24 2004
On Sep 24 2004, gene wrote:
> Hi Susan,

For the composition of functions I like the applet
> http://mathforum.org/mathtools/tool/2149/ (Jon, is this like the BBN
> "function machine" you allude to on 5/24?) This takes a little bit
> of effort to get oriented, but after you do you can put in any
> functions you wish and see how a change in the inside function
> effects the whole thing. It gives pretty good graphs, although a bit
> small so everything fits in together.

- gene

Gene,
I really liked the applet, especially the fact that you could grab points with
your mouse and reshape the graph....definitely cool, and seeing the composition
change was wonderful.  Now how do we help kids see how it all fits together.  We
can find good analogies for compostions,like the one on this powerpoint
http://mathforum.org/mathtools/tool/15246/
and good graphs, but I'm wondering if the students ever make the connection
between the analogy and the graph.  Maybe the thing to do is start out with
something that makes sense...like f(x) = x-2 and
g(x) = sqrt x.  Seeing the square root function shift 2 to the right should make
sense, and the composition would hopefully be clearer. I couldn't get the applet
to take parenthesis for some reason.  Gene, can you help?  Any other ideas about
how to connect function anologies to the algebraic processes?

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