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appropriate use of calculators



It seems to me that programmable and graphing calculators are simply
_creating_ more teachable moments for us. As such, I welcome them
into my classrooms and exams.

One person mentioned the problem of innumeracy among today's students.
Is this due to the pervasive presence of calculators? Perhaps, in that
people do fewer estimates these days. However, as instructors we can
counter this by simply asking if and why an answer is _reasonable_.
Answering such a question requires understanding of magnitude and
relationships.

Another wrote of students blindly performing sophisticated curve fits
to data. This is a problem which becomes an opportunity. Example:
Several times students I've worked with have performed a Boyle's Law
experiment, usually acquiring the data with a CBL. Now, the typical
graphing calculator performs many curve fits, among them y=a*x^b,
where a and b are the fitted parameters. The students would see the
apparent power relationship on seeing the Pressure vs. Volume graph,
and then fit the calculator's power function to the data. The fit
would inevitably be excellent, but the power would not be -1, but
something more like -0.9. The appropriate fit, of course, is just y =
a / x (which most calculators won't do, by the way). That the student
performed an easy but ultimately not informative fit creates another
teaching opportunity. How does one choose a function to fit to data?
Is it useful to fish for a function which fits well, but whose
coefficients cannot be interpreted? These will generate good
discussions.

In exams, one can pretty much remove any advantage to having stored
equations in a calculator by asking questions that require more than
numerical answers. The recent suggesting of "taxing" the use of
equations with a required explanation of the equation's meaning and
applicability is an excellent one. So what if a student recovers one
of those specialized, limited use relations from a calculator? If he
or she can fully explain it, then fine. If not, there's no advantage
to the calculator.

Banning calculators or equation sheets from exams creates artificial
situations. In professional life we all use calculators and references
in solving hard problems. It seems to me that not using calculators in
class and exams only _encourages_ shallow understanding of the machine
results. Why not use them fully, but at the same time demand
understanding?

--
John E. Gastineau (304) 296-1966
900 B Ridgeway Ave. gastineau@badgerden.com
Morgantown, WV 26505
www.badgerden.com/~gastineau