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Re: if using Mathematica to solve an algebraic problem

  • To: mathgroup at smc.vnet.net
  • Subject: [mg108989] Re: if using Mathematica to solve an algebraic problem
  • From: Richard Fateman <fateman at cs.berkeley.edu>
  • Date: Fri, 9 Apr 2010 03:32:57 -0400 (EDT)

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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