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

>>>>> "David" == David Park <djmp@xxxxxxxxxxxxx> writes:

David> "Raymond Toy" <raymond.toy@xxxxxxxxxxxx> wrote in message
David> news:sxdveyvp9or.fsf@xxxxxxxxxxxxxxxxxx
>>
>> Perhaps students are different today, but I don't think knowing a good
>> CAS (or any CAS) when I was in high school would have made a single
>> bit of difference to me. (Well, homework would have been easier, but
>> if a CAS were available, homework questions would have been quite a
>> different.)
>>
>> It's not a replacement for knowing how to do things.
>>
>> Ray

David> Ray,

David> It's a way to get to know how to do things.

David> Your experience is not my experience. When I went to MIT in the late 1950's
David> there were many times I thought to myself that I could understand things
David> better if only I could do more calculations and examples. A good CAS would
David> have made a big difference to me, especially if I had known the basic CAS
David> usage before I got to MIT. Now that I am retired and have Mathematica I am
David> trying to learn some modern math and physics. I am especially trying to
David> learn some differential geometry, general relativity and differential forms.
David> I would like to explain how I do this because I think the approach would be
David> useful to other people, including high school students.

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. And even when
it's right, it sometimes takes quite a bit of work to figure out that
the answer it got is the same as the one you did by hand. Actually,
that's probably not a bad thing for students to do. :-)

And, at least in school, problems aren't usually so complex that you
need a CAS. The problems are usually intended to be done in a few
minutes. If it takes much longer than that, you probably missed the
point of the class or made a mistake.

But high school was a long time ago for me, so I may not remember what
it was really like back then. :-)

Ray
.

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