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Re: if using Mathematica to solve an algebraic problem

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  • Subject: [mg108991] Re: if using Mathematica to solve an algebraic problem
  • From: "David Park" <djmpark at comcast.net>
  • Date: Fri, 9 Apr 2010 03:33:19 -0400 (EDT)

Well, if the students are truly incapable of thinking it hardly seems fair
to take their money, or to fool the public by credentialing them. If you
want to teach broader based thinking skills you need more mentoring,
projects, essay questions and fewer "grind out the answers" type tests. But
then that would be much more expensive to provide, wouldn't it?

But this is a Mathematica news group so the real question is: what role, if
any, can Mathematica play in education? It seems obvious that Mathematica
should be useful in education - but the obvious isn't always true or easy. I
consider it as an ongoing problem to be solved. Mathematica is something of
an amorphous object depending on how we adapt it. It isn't fair to just
treat it as a fixed thing that doesn't work. There are a lot of educators
out there who are trying to adapt Mathematica to educational uses and some
are doing very impressive things. It would be nice to hear more from them
about their successes and frustrations, and how they are using it and what
techniques they use.


David Park
djmpark at comcast.net
http://home.comcast.net/~djmpark/  


From: Richard Fateman [mailto:fateman at cs.berkeley.edu] 

David Park wrote:
> Sometimes I find it difficult to understand these discussions.
>
> For example, Richard's: "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." What kind of something would that be, and
in
> what way would it make it possible? It seems like a rather vague but
> expansive goal.
>   
Something like "No child left behind" :)
Maybe better teaching technology. Or
 Perhaps something like an injection with "smartDNA".
Or surgery. ("I spoke excellent French, as soon as I recovered from the 
surgery..")




....

> But another way to use Mathematica is to try to set up the rules or axioms
> for some subject matter and then practice using them to carry out various
> derivations or prove various theorems. Mathematica may do the dog work but
> you have to decide the steps and see why various axioms are necessary. 
Sorry, you are expecting students to think.  Unless you can teach them 
to think, some of them won't be able to
do this. (Seriously, I have encountered students who have done very well 
in school whose skills include
excellent memorization, rote substitution into examples, neatness and 
courtesy.  But they have never been
expected to show any independent thought.)  Will using Mathematica 
change something here?

> There
> might be various ways to do this for teaching. Should the teacher provide
> the axioms and the student just uses them? Or should you start with a
vague
> discussion of some subject and have the students and teacher together
> develop the axioms, something like the Math Circles?
>   
Look at textbooks and you will find piles of examples. Generally NOT 
algorithms to follow.
How is it that something like the (complete!) description of a 
programming language like Pascal can take
20 pages, but "Pascal for Dummies" can be 20X larger?







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