Date: Jun 29, 1995 11:35 AM
Subject: Re: re:graphing calculators

>I think that the ability to analyze the behavior of functions is critical.
>How can you even use a graphing calculator if you don't have some idea of
>what to expect?

Absolutely. Although I am not an engineer, I trained in a discipline that was
suffciently related that I had some distribution requirements in electrical
engineering and diff eq, including some analog computing. I also took
coursework in lingusitics. I was involved (much later, when I'd forgotten it
all) in real-time programming. Also, I read magazines like Science News and
Scientific American.

Why the boring bio? Since my physics intuition and skills are really quite poor
for someone with mathematical training, the one thing I remember and can "use"
from all of this is the importance of sinusoidal functions. And I'm sure the
reason I kept that much was because I understood what these curves look like,
from the homework assignments and classwork on how to graph them. (I also
found this intensely beautiful, even in high school). Even when the crew of
the Enterprise is talking about being "out of phase" I have mental images that
I can rely on of combining sine curves with different phase shifts.

I too believe strongly in the use of computing technology to simplify the kind
of learning experiments that kids need to do to grasp material. But, just as I
would be aghast if learning the multiplication tables, or good penmanship, were
totally dropped, so I believe that if your own hands don't do it, you don't
learn it.

Let's not forget that when slide rules were the hot technology, studenst were
expected to know (a) enough arithmetic (including logs and exponetials) to
validate the answer; (b) error analysis to know how much the answer could be
trusted; and (c) how the system they were making computaions about behaved.

I think we owe today's kids at least this much.