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Re: if using Mathematica to solve an algebraic problem

On 4/5/2010 1:26 PM, David Park wrote:
> Why is using Mathematica similar to copying someone else's homework?
instead of looking around your classroom and trying to identify the 
student most likely to get the right answer and
be willing to share it with you,  you look around on your computer (or 
phone!) and see if there is a program
that will solve the problem for you.
> Putting the question of the motivation and economics of student cheating
> aside, the question is: how can Mathematica be used to promote learning by
> students actually interested in learning?
Well, you have already cut the sample size considerably, since some 
students are mostly interested in
getting a grade.  That is one consequence of having required courses 
(like calculus??) that some
students resent.

> How about the following as one possible method? Use an Axiom Set - Problems
> approach. Give the students the axioms or rules of his subject (with
> descriptive names) in an active form and then have them solve problems by
> choosing and applying the axioms step by step. If they could do that, would
> it satisfy you, even though the computer was doing the dog work?
I think that some teachers would like to know that the students could do 
the algebra "by hand".
What you or I might find satisfactory is not necessarily relevant.

> Would you object if the students didn't actually memorize the axioms but
> worked from a table or palette? Would they sort of memorize them just by
> repeated use?
> Or is it your position that students have only learned what they can recall
> from memory and apply using pencil and paper?
Apparently being able to solve problems on a final exam is what was 
expected at MIT.
The "new knowledge paradigm" that you don't have to know anything other 
than how to
look up something is, perhaps, being oversold these days.

> More generally, is it your position that Mathematica can't ever be helpful
> in learning,
not my position
>   or that it hasn't been shown to be useful,
yes, that is approximately true.  Do people "learn more calculus" at 
Univ. of Illinois if they use Mathematica?
Do people learn "extra" stuff like computer programming along with 
calculus? Probably. Just that Mathematica
is most likely NOT the kind of computer programming that would be taught 
by a computer science department.

> or that we just
> haven't learned ourselves how to make it useful.
Yet.  There is of course the possibility that something really useful 
will be developed that will make it
possible to teach all students everything they need to know.  
Experiments in "computer aided instruction"
have not been all that successful, although there are a few (e.g. there 
is a statistics course at Berkeley
with computer technology in learning and testing;  there are many ways 
of making computer programming
"more automated" that help teach the subject.)


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