Here is a message that should be of interest to us
especially those who teach two-year tech degree students.
...
Robert L Kimball 919-662-3602 (Office)
Chair, Mathematics and Physics Dept 919-266-0850 (Home)
Wake Technical Community College Raleigh, NC 27603-5696
---------- Forwarded message ----------
Date: Tue, 22 Dec 1998 22:10:06 +0000
From: Mark E. Furber <mfurber@computer.org>
To: ET List <etd-l@OIT.EDU>
Subject: Re: calculation skills
> Date: Mon, 21 Dec 1998 16:07:05 -0500
> From: steve ryan <s_ryan@tec.nh.us>
> Organization: NH Technical Institute
> To: ET List <etd-l@OIT.EDU>
> Subject: calculation skills
> Reply-to: s_ryan@tec.nh.us
>
> Maybe it's just that I've got end-of-the-semester grading on the brain,
> but it seems to
> me that some (many?) of my students would either not be in a technical
> program or
> might be doing much better if not for the calculator. For so long, the
> slide rule provided
> a real litmus test: if it was not mastered, then goodbye, don't let the
> door hit you on the
> way out. It also encouraged one to understand and set up a problem
> thoroughly, to avoid
> having to recalculate. It forced assessment of order of magnitude, and
> it limited significant
> figures. I am not advocating a return to the slide (I used mine to work
> through an exam
> a few months ago and it almost killed me), but I am planning to assign
> some "naked"
> problems in class next semester. No books, no notes, no calculator.
> Just make some
> estimates, dredge the brain, work it out on paper. Skip the
> forest-for-the-trees obstacles
> and get them to really think about the question and solution. I'd
> appreciate hearing other
> thoughts on this issue.
>
As one of Professor Ryan's former colleagues, having taught in the EET/CPET
department at NHTI during 1996-1997, I agree with his observation. I am not
suffering from any end of the semester grading fatigue, since I now work, once
again, for a defense contractor.
My observations were that the traditional college-age students I encountered at
NHTI:
1. Could not estimate orders of magnitude and did not pay attention to the
nature of the answers they calculated. They therefore could not find gross
errors (such as using 10^6 instead of 10^-6) in their work.
2. Were resistant to the concept of memorization, even for basic values or
relationships. In the electronics field, you should not have to look up Ohm's
law. Period. You also should know what "a factor of 3 dB" means without
having to calculate anything.
3. Did not use calculators to assist them in their calculations, but rather to
do their calculations for them. This is the way they are taught in their math
courses, at least as the NHTI math faculty explained it to me, and it is not
the way one would do things with a slide rule.
A simple example: A phase locked loop problem requires solving an equation
something like f = k/RC for C, given a target for f and values for R and k.
The old way: Solve the equation by hand in your lab notebook for C = k/fR,
put in the numbers and turn the crank, writing down some intermediate results.
The only thing computational aids do for you here is make turning the crank
more efficient, and the approach with a simple calculator is the same as with a
slide rule. You still see how the calculation is performed, and if nothing else
you can see how the exponents work out and get an idea of whether C is
nanofarads or picofarads. Anyone who gets megafarads (and I have seen that)
will have a problem finding the component he wants in even a well-equipped lab.
Today's way: Get a calculator that solves equations, type in the equation,
press the "Solve" key and write down the number that appears on the display.
You don't see the process, you just get an answer. If you do get an answer in
megafarads and suspect that something is wrong, it is hard to back up and see
what happened and where, since there is no paper trail.
As a attempt to counter this problem, and just to be odd, I used to give
electronics tests with "essay questions." No calculations required at all. An
example in an introductory electronics course: "You have a dual trace
oscilloscope, an ohmmeter and a roll of duct tape. Explain how to measure the
AC collector current in the transistor amplifier shown." This can be answered
easily with a few sentences and a sketch or two.
I also gave oral exams, where students had to convince me they understood
something by talking it through with me on the board, with chalk, for 10
minutes or so. No calculators, notes, books or computers allowed, or needed.
This approach does produce tests that are more time consuming to administer or
grade, but I found it quite effective at identifying students who did not know
what was going on, and that was my real goal. A "pass or fail" test to identify
students in trouble.
A better solution, of course, would be to have the engineering technology
faculty closely involved with the prerequisite math courses, so they can make
sure that students receive appropriate preparation. The subjects and techniques
that some mathematicians, or mathematics education faculty, want to teach may
not be what we need ET students to know. I suspect, however, that manpower
considerations and academic turf issues would work against such an approach in
most institutions.
Mark E. Furber
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