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Re: if using Mathematica to solve an algebraic problem
*To*: mathgroup at smc.vnet.net
*Subject*: [mg109010] Re: if using Mathematica to solve an algebraic problem
*From*: Murray Eisenberg <murray at math.umass.edu>
*Date*: Sat, 10 Apr 2010 06:53:26 -0400 (EDT)
I quote, third-hand, what a student at my university said a few years
ago to his chemistry instructor: "Professor, I know what you're trying
to do: you're trying to get us to think. And we don't like that!"
On 4/9/2010 3:32 AM, Richard Fateman wrote:
> 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?
>
>
>
>
>
--
Murray Eisenberg murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower phone 413 549-1020 (H)
University of Massachusetts 413 545-2859 (W)
710 North Pleasant Street fax 413 545-1801
Amherst, MA 01003-9305
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