Re: Pedagogical uses of a CAS with high school or undergraduate students


"Raymond Toy" <raymond.toy@xxxxxxxxxxxx> wrote in message
news:sxd7jbanhqt.fsf@xxxxxxxxxxxxxxxxxx
> >>>>> "David" == David Park <djmp@xxxxxxxxxxxxx> writes:
>
>
> I didn't mean to imply that it would be useless. Having a CAS doing
> some work for you is beneficial, but most CAS aren't meant to help you
> learn how to do things. It just spits out answers.

I suppose that a CAS can be used that way - but that's not the way that I am
suggesting.

I think of a CAS as an extension of a piece of paper that I write on,
develop arguments, do derivations, present diagrams and animations. If a
certain principles is used in understanding an argument, then I write a
routine that applies the principle. With a little practice I learn how to do
these routines in a somewhat general way. For example, if we are using
linearity I will write a routine that will do a linear breakout of functions
we are dealing with. I have to pretty well understand that I will be using
that principle, and that it is one of the 'axioms' of the math I am doing to
write the routine. And I have to pretty well understand how linear breakout
works to write the routine. Then once I have the routine I use it in doing
various derivations. This is not just 'spitting out the answer' but actually
understanding and implementing that understanding in a active manner.

Take another idea: the fact that one can always construct an equilateral
triangle from a line segment. A student might undertake to implement that
graphically and analytically on a CAS. He would have to learn how to specify
a line segments by clicking off two points on a blank graph. He would have
to write a routine to get the length of the line. He would have to learn how
to specify a circle of a given radius about a given point. He would have to
use the CAS two obtain the two intersection points of the circles. Then he
would have to draw the two equilateral triangles. He could explain each of
the steps and then assemble them together to make a general routine. If a
student could do that he would know a lot about how to do math and how to
use a CAS.

David Park
djmp@xxxxxxxxxxxxx
http://home.earthlink.net/~djmp/


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