Re: TI-89 virtue email needed
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Re: TI-89 virtue email needed
Ray Kremer writes (and I respond) as follows:
> It's a very tough argument. In the real world, everyone uses calculators
> to do things, and the 89 will quickly become common. However, in
> class, how important is it that the students learn the CONCEPT behind
> the math, thus making it necessary to deny them access to the calculator
> so they can't have it do the work for them? I'm not sure myself.
> I would like everyone to know how to take derivatives and integrals
> (simple ones, at least) by hand, but if you need a calculator for the
> complex ones, why not use the calculator for all of them?
Perhaps it will not be taken as blasphemous if I paraphrase the well-known
piece of folk wisdom and say "God grant me the power to perform simple
calculations by inspection, the expertise to tackle complex calculations with
the help of technology, and the wisdom to know the difference." The type of
calculations that it is reasonable to undertake at any give time are really a
function of available technology. Once pen-and-paper (and the algorithms that
were developed to support ther use) became widely available, a great lot of
mathematics was discovered/invented that never would have come to light under
the old ways of doing business. I think it is safe to say that in just the
past 10 years more people have graphed more functions than in the entire
history of our civilization to date, simply because of the availablity of
graphing calculators. Now that inexpensive symbolic calculation is here, what
sort of new explosion are we going to see?
Has the _concept_ behind the math involved been lost as we have moved from
technology stage to technology stage? There are certainly some lost
technologies. We are likely never to know how some of the major engineering
feats of antiquity were accomplished, or how Archimedes and Diophantus came up
with their amazing results in the absence of modern symbol systems and
algorithms. Some of the old technology is known, but has been quietly put to
sleep on library shelves. Most people in the world today could not start a fire
without matches (even if they have served time in the Boy Scouts). Every now
and then I pull down the book on my shelf titled "Advanced Abacus" and leaf
through it a bit out of curiosity, bit I don't make any effort to actually
develop a usable level of skill in the techniques explained. If these skills
were _needed_ I am sure that it would not be long before society saw to it that
they were being learned by the next generation. But in the meantime, there are
more interesting things to learn and do. Let's ask _why_ it is we want to be
able to find derivatives and antiderivatives, and what we will be able to do
once we can calculatoe them with the push of a button. Then let's start doing
it!
> In today's era of GPS satilite guidance systems, the U.S. Navy still teaches
> navigation by the stars. This is so they can still find their
> way around if the satilites fail...
One of the postings I put up on our departmental bulletin board this last year
was a clipping from the New York Times noting that Annapolis had just dropped
its last course in celestial navigation, as this skill was now totally
outmoded.
> Science fiction often depicts a society entirely dependend on computers,
> in which the people themselves have forgotten everything. I can think
> of at least two Star Trek episodes alone with this topic. So, how
> do we make things convenient by allowing calculators, yet still ensure
> learning takes place? And as the available technology increases, where
> do we draw the line, and how do we know when to move it?
Since Isaac Asimov first introduced this idea (daring at the time) some 50
years ago, it has become something of a SF cliche. As you see from my
commentary above I don't see much point to the argument once the initial
amusement of the presumption has worn off. There will always be plenty to
learn. It is my job as instructor to stay one step ahead on this.
I think I can do it!
RWW Taylor
National Technical Institute for the Deaf
Rochester Institute of Technology
Rochester NY 14623
>>>> The plural of mongoose begins with p. <<<<