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

A main issue in pedagogy would be showing the steps used in a computation.
Programs like RATSIMP in Macsyma combine and simplify over a common
denominator, but it may be hard to show the steps in the way a person would
be taught. RADCAN, which performs more complicated simplifications with
powers/roots would be even harder to deal with, as people don't normally
contemplate a canonical form for their expressions (they don't normally form
a canonical form is an obligatory pun...)
For differentiation, this is at least plausible, as a CAS can use a
recursive
algorithm that dispatches off the main operator and shows the steps, closely
mimicking the human approach.
Algorithms implemented in CAS's for integration have next to nothing in
common with the
tricks, substitutions, etc that I learned when I taught myself from a book
on calculus -
the Risch and subsequent Bronstein procedures do not lend themselves to a
simple
step-by-step that a novice would understand.
Asking the student to learn a whole new language? Why can't they mostly use
a hand-held with graphing and int/diff abilities?

A friend showed me Macsyma when I was a first year physics grad student at
MIT, and I got very involved with it. A key point was doing integrals: I
asked
it a few examples and got answers, then gave it exp(x)/x, which it returned
unevaluated. Ah, but it *knows* that there is no integral in terms of
elementary
functions for that case!

<hjbortol@xxxxxxxxxxxxxx> wrote in message
news:1131799516.696134.264510@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
> Hi!
>
> I'm looking for references (articles/books)
> elaborating about the pedagogical uses
> of a CAS with high school or undergraduate
> students. Advantages? Dangers?
>
> Google shows a lot of activities for undegraduate
> students (calculus and precalculus mainly),
> none for high school ones. However, I was unable
> to find any article discussing the pedagogical
> aspects of such activities ...
>
> Thanks in advance, Humberto.
>


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