Re: TI-89 virtue email needed
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Re: TI-89 virtue email needed
Bill Risher <billr1@MIDSOUTH.NET> writes:
> Would you (or any other mathematics teacher/professor) be willing to write
> a comprehensive e-mail to my AP Calculus teacher extolling the virtues
> of the 89? Despite all of my reasoning she still refuses to allow
> it even on classwork as she says it is "too powerful". Me and a few
> other students have 89's (and/or 92(+/II)'s) and were quite disappointed
> when we brought our 'great new calculator' to school just to find
> that it was totally useless to us (except for the 92's which most of
> us type class notes on in other subjects, but thats beside the point).
> I sincerely hope that she will regard the opinion of another learned
> mathematics educator more highly than she does ours.
I'd have to say that I am sympathetic to both you and your instructor (I know,
that doesn't help you much!). You are caught in the technological ramp-up that
has been a feature of mathematics instruction since the early 70's, when the
first electronic calculators became reasonably affordable.
Nobody today would deny you the use of a standard scientific calculator or
(probably) even a common graphing calculator, and insist that you practice
numeric calculations (even square roots) with pencil and paper because you
might sometime not have a calculator, or require you to make tables of function
values by hand and plot out the graphs on graph paper on the grounds that this
is a skill you need to have for future work. Both of these arguments were
seriously put forward in the days when calculators were new, expensive and
rare, and no-one had yet worked out ways to teach with them that were as much
of an intellectual challenge to students as the old ways were. But now there
are many good textbooks around that put students to work _using_ the new
technology to get at those really interesting mathematical questions that
students in the old days never got to because they were fully occupied carrying
out the "busy work". I myself am much happier teaching in this new
environment.
Symbolic manipulators are the next step, and it's a big one! All of a sudden,
much of what people used to spend their time on (pages of algebraic
calculation) has also become "busy work" that should probably be shortcut by
pressing a few keys. Of course, symbolic manipulation is as yet by no means as
pervasive in our society as electronic calculation, and it is halfway
reasonable to still gain some personal skill with pencil-and-paper manipulation
(besides which it is kinda fun sometimes). I tell my students that they are in
the unfortunate position of having to learn it both ways, that in the future
they will be expected to be in control of electronic computation, but they will
still be in frequent situations where they will be expected to demonstrate
traditional methods. You are just going to have to accept that, and deal with
it.
As far as the classroom goes, it's partly a question of equity. If your
instructor had the power to require everyone to gain access to use of a TI-92
or TI-89 (preferably right in the classroom) and had the time and authority to
develop a whole new curriculum based on this power, then your class could do
some wonderful things that would still meet the original spirit of the course.
If only _some_ of the members of the class have access to symbolic calculation,
and if the only thing they do with it is to trivialize the assignments that
students without a calculator have to sweat over, then the instructor is right
to say "don't do that, do it the long way".
So what do you do in order to get the value out of that calculator you paid
for? You should recall that the purpose of taking a course is to _learn_
something. There are a number of ways that you can use the TI-92 or TI-89 to
help you catch the _idea_ of the assignments you will encounter. You've got to
learn the math, anyway, to even understand where the designers of the
calculator are coming from. If there is a really messy calculation, who is
going to complain if you (on your own) explore the steps with the aid of your
calculator until you understand them, as long as you can eventually create a
clear convincing set of steps on paper. Practice of this sort ought to
_increase_ your ability to do this kind of work without a calculator (as you
probably will need to be able to do on tests).
But you can also explore beside and beyond the material minimally covered in
the course, if you are of a mind to, tackling more difficult examples for
instance. An excellent way to develop mathematical understanding is to develop
a _script_, including comments, that shows step by step how to perform a
certain calculation. You might try working with your instructor to develop a
project or two along these lines, showing her that you are not just interested
in getting through the assigned homework problems in the easiest way.
There is a special difficulty in this being an AP course, because of the
unknown situation in which you will eventually be wanting to claim credit for
the experience. Surely some of the students in the course will be going on to
situations where they will need to take course work where the instructor has
had neither the time nor the inclination to consider the use of symbolic
calculators, and will ban their use even more firmly than your present
instructor has. So, I would say that your instructor is right to some extent.
But, as I said, you really need to learn it both ways. Don't give up -- work
with the situation, and at some point you will be mighty glad that you
understand how to handle that calculator too!
RWW Taylor
National Technical Institute for the Deaf
Rochester Institute of Technology
Rochester NY 14623
>>>> The plural of mongoose begins with p. <<<<
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