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 Discussion: All Tools in Algebra II on Sketchpad Topic: Functions as objects?

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 Subject: RE: Functions as objects? Author: Mathman Date: Nov 30 2005
On Nov 29 2005, Susan wrote:
> I was wondering if there is a way to plot a function in Sketchpad,
> and then have it behave as an object.  For example, I can graph f(x)
> = sqrt (x), but I would like to make it an object so that I could
> move it freely.  I would also like to be able to reflect it over the
> x or y axis using the transformations menu.  I know that I can do
> this algebraically by writing and graphing a new function, but I was
> thinking about just being able to do it geometrically.  Any ideas?

I believe that what you are asking is not possible in any software I have ever
seen.  Basically, you are asking to transform a graph equation by moving the
image.  All that I am familiar with is, as you say, the other way around: state
the function, then plot it.  You can arrange perhaps to have a slide-show,
which might be just as educational.  Graphmatica allows some graphing with
variable parameters, but still might not fit what you are attempting.  It is as
close as I can find, at least.  So, you might want to take a look there.  It is
available from http://archives.math.utk.edu , along with much other useful
material.

This might be one case where the old-fashioned methods are best?  I'd not
throw the baby out with the bathwater, as has been done so often, and hang onto
a few of those.  I'm referring to the possibility of projecting  [overhead?]
pre-done plastic sheet images as overlays.  Way back in the dark ages, we used
to teach, and a hired technician did all of that sort of thing ten times better
than any teacher ...that was his job, after all [and secretaries who could type
at over 100wpm did the rest.  I still slog it out at round 5wpm or bust.]  Ours
prepared some overheads for me on use of the slide rule that knocked me over.
They made explanation [and my part ofthe job] simple.  I'm suggesting a possible
alternative?

The very best alternative I can offer is likely not well met, but I mean it
sincerely:  Get them to calculate and plot points by hand.  Rather than memorise
situations, they really get a handle on things.  it makes a difference from
being a cookbook chef and being up to the elbows in flour.  For transformations,
I generally set up a series of functions which they'd plot.  Then the real
teaching/learning came with lengthy discussion back and forth about similarities
and differences. The start is tedious ...but it sinks in with the time
spent.

David.