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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: Susan
Date: Nov 30 2005
Thanks for the response.  I guess I should have stated what technology problem I
was trying to solve.  The Smartboard software allows you to draw the parent
function, and you can rotate and dilate, but you can't reflect or
compress/expand horizontally or vertically independently.  So I thought, why not
try the Sketchpad, and use Sketchpad with the Smartboard.  I knew you could
definitely do reflections, and I thought if you could make the function an
object you would be able to do all these things that you wish you could do on a
Smartboard.  So, I tried, but it didn't work very well.  We've done the
translations and reflections lots of other ways, including wikki stix and just
plain graphing, but I was trying to think of ways to do it with the Smartboard.
Again, thanks for the input.
On Nov 30 2005, Mathman wrote:
> 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.

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