From: kraai4712@iscsvax.uni.edu (jim kraai)
Newsgroups: sci.math
Subject: Afraid of the future? (WAS DEREGISTERe: An interesting limit problem.
Date: 28 Jul 92 16:51:37 -0500
Organization: University of Northern Iowa

In article <1992Jul28.191037.28756@gdr.bath.ac.uk>, mapsj@gdr.bath.ac.uk (Simon Juden) writes:
> >                            Mathematica should be viewed as a fancy calculator
> > (which, essentially, is what it is). Very good and very useful, BUT undergrads
> > HAVE to learn basic concepts and manipulative skills before they're let near
> > it. Otherwise they will never become mathematicians, but rather computer
> > operators. Also they'll never FULLY understand subtle concepts or follow harder
> > arguments used in difficult proofs if they haven't had to do things with their
> > bare hands first. Like any good similar system Mathematica can be very helpful
> > to the professional mathematician. But I believe such gadgets can also do
> > irreparable harm unless used appropriately. I also believe children should not
> > be given calculators until they can do sums without them. But doubtless these
> > views will get me flamed...
                      ^^^^^^
You are certainly correct, they'll get you flamed.  Could you show us some
evidence?

Ok, let's take Simon a few steps further (and get myself flamed, too).  All
Mathematica is is a tool.  Just like the decimal number system.  Would you have
us give up our positional number system for something else like Roman numerals?

I don't believe you understand the purpose of tools.

How are we to stand on the shoulders of those before us (as Newton said) with
people spouting rhetoric like this?

I would guess that using tools like Mathematica to derive tedious results will
be viewed much the same way in 50 years as we view grabbing a handheld
calculator to do square roots today.  It won't be given a second thought.

Simon, do you still force your students to figure square roots by hand?  Do you
force them to learn to figure them by hand before allowing them to use a
handheld calculator?  Do you believe that your students understand what a
square root is without having to go through the fun and excitement of figuring
them by hand?  (I should say at this point that I found it very interesting
when I learned how to figure square and cube roots by hand, but I'm just not
that interested in doing it every time I need to take a root.)

Well, let me remind you that people used to go to college to master the art of
multiplication and division, things which we gripe about if they aren't
mastered in junior-high-school today.  In the same spirit, we will take
symbolic manipulation software for granted someday. 

If your curriculum isn't compatible with today's technology, then maybe you
need to change the content of your courses.  Technology certainly will not stop
falling into the hands of the next generation simply because you and a few
others want it to stop.

People like this should dedicate their lives to safeguarding the past instead
of preventing the next generation from moving on into the future.

IMHO                                                                        

jim kraai

young, progressive undergrad math major who has never used Mathematica in his
life, but who does keep 2-3 extra graphing, progammable calculators around to
loan out to students he is tutoring -- because they are a fantastic _tool_
Newsgroups: sci.math