> And Lou Talman replies:
>>For starters, the time non-technology-based courses spend on the
>>syntax of algebra. The problem of Mathematica syntax replaces the
>>problem of algebra syntax.
And Greg Armstrong adds:
> Of course, the syntax of algebra is part of the universal language of
>mathematics, while the syntax of Mathematica is specific to one
>particular computer program. Which would you prefer to spend time on?
>
An old Chinese (I believe) proverb says that "The fish does not see
the water in which it swims". The most difficult point for students to
appreciate is the fact that there _is_ such a thing as syntax, and that their
instructors are not simply being picky when they cricize them for just
stringing everything together with "=" signs. Student work in any
situation requiring formal syntax (calculator, computer algebra, whatever)
can be a great boon to the instructor in this respect, if the attitude is taken
that it is an opportunity to make hay rather than a nuisance to be suffered.
Systems with helpful diagnostics (e.g. the TI-92) can be of even more use.
It's nice to have students see a _real_ use of the word "domain" in a context
that makes practical sense, for example! There is, at least in my own
opinion, a lot of value in exercises that force students to map calculations
or statements from one syntax to another (try going back and forth between
traditional notation and APL, for example). Isn't this just the sort of
exercise that is at the heart of "real" (higher) mathematics? Trying to
catch the nature of the wine as it gets poured from bottle to bottle, you
might say.
As far as "the universal language of mathematics" goes, I doubt that
anyone who has taken more than a superficial look at the history of mathematical
notation believes in such an animal. I have already seen a number of changes
(improvements) in accepted notation in my lifetime, and I certainly believe
that in 100 years mathematics, when written, will be written more logically
and consistently than it is today. Part of this will be due to the hard
thinking about syntax that is forced by implementation of formal electronic
calculation.
RWW Taylor rwtnts@rit.edu
National Technical Institute for the Deaf
Rochester Institute of Technology
Rochester NY 14623