Re: [Phys-l] Should equation solving be done with calculators and robots or by hand?

[John Denker <jsd@av8n.com>]

On 02/27/2008 07:49 AM, Steve Highland wrote in part:

> .... doing the dirty work with something like QuickMath (see
> http://www.quickmath.com) or MAPLE or a calculator with symbolic
> manipulation abilities 
....
> .... ³QuickMath is down again², 

Let me start with a remark at the nuts-and-bolts level ...
and then segue to the more philosophical issues that were
at the core of the original question.

You can download _maxima_ (a variant of macsyma) for free.  
It has versions for Linux, Windoze, and Mac OS X.
  http://maxima.sourceforge.net/

Some pros and cons:
 -- quickmath is free but very limited, for instance when it
  comes to chaining together a long calculation, AFAICT.
 -- MAPLE is kinda pricey.
 -- maxima has low-end price and almost-high-end capability
 -- maxima is 10 years behind macsyma, but you won't notice
  if you're just doing algebra.
 -- maxima is both more powerful and easier to use than a 
  hand calculator, when doing algebra.
 -- students might be allowed to use hand calculators during
  an in-class test, but usually not allowed to use PCs.

============================

The computer algebra train has already left the station.  Not 
all students, but some students know about this stuff and use 
it on their homework.  

School should teach people to live in the real world.  And
that's a moving target, because new technology is always
coming along.

IMHO, schools are (with rare exceptions) too slow to adopt 
new technology.  Computer algebra capability has been around 
for 40 years;  you might think that the math department would
have noticed before now, and incorporated it in to the basic
math courses.  By the same token, spacetime has been around
for 100 years, and is taken for granted even in low-brow TV
shows;  you might think the physics department would have 
noticed before now, and incorporated it at all levels
(introductory and otherwise).  Other examples abound.

A simple calculator allows you to automate the calculation
when R=1.2345, while computer algebra allows you to automate
the calculation when R is just R, a symbolic variable.  IMHO
computer algebra is in no ways worse and in many ways better
than using a simple numerical calculator, better in the sense
of facilitating understanding.  So unless you disallow basic
calculators, you shouldn't disallow computer algebra.

The biggest practical problem at the moment is lack of support.
The computer algebra documentation is not very Muggle-friendly.
Somebody needs to write a nice tutorial that covers the tiny
subset of features that is needed in an introductory course.
This includes documenting how to avoid the usual neophyte
mistakes (such as expecting the system to be more capable
than it actually is).  Somebody needs to rewrite everything 
else, so as to integrate computer algebra into the syllabus.

As for the proverbial student who can't divide by 10 without
a calculator, that's a problem, but the problem wasn't caused
by the calculator, can't be cured by the calculator, and *can*
be cured by standard prosaic teaching.  The same applies to
computer algebra:  If somebody doesn't understand the principles
of algebra, the computer isn't going to make things better.  It
won't make the pre-existing problems worse, but it may make them
more obvious.  As the proverb says, it is a poor workman who
blames his tools.