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Jerry P. Becker

Posts: 16,576
Registered: 12/3/04
No calculators allowed ?
Posted: Jan 19, 2000 3:54 PM
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From Focus [Newsletter of the MAA], January, 2000, Vol. 20, No. 1, p. 5.

A Different Pencil: What is so good about them anyway . . .

By Nora Franzova

When I typed up my first calculus exam (not so long ago), it was right on
the front in bold capital letters: NO CALCULATORS ALLOWED! I believed in it
and my colleagues did too.

I went through my school years exploring mathematics more deeply with each
passing year, and the only tools I needed were a good pencil and a clean
sheet of paper. (I did not even insist on completely clean paper, for the
sake of the forests). And up until today this has been the most enjoyable
way for me to do mathematics. It gives me a feeling of power and
accomplishment, a perfect view of an idea being born.

During those years when I had the time of my life with my pencil and my
paper and all those math problems, I watched my friends who did not share
my enthusiasm for mathematics branch off to different fields of education.
I chose math and made new friends, people who also chose math, and we used
pencils and paper, blackboards and whiteboards and supported each other in
saying NO to calculators. It worked for me.

But (and there is always a "but") now I am a teacher, trying to convince my
students that what has worked for me, will work for them. I guess I forgot
all those friends for whom math class was just a dreadful, uninspiring,
boring time. I forgot that I never managed to convince them to share my
enthusiasm for the subject. Now, as a teacher, I am trying harder than ever
to share with my students some of my math enthusiasm. But I know in many
cases it is not going to work.

And maybe the reason is that what has worked for me does not have to work
for everybody. And maybe I should try some new ways to present the
mathematical treasures I like so much. One way would be a serious devotion
to only use problems arising from applications of mathematics in our
everyday life, but that is a radical limitation. Another possibility is use
of scientific calculators or computer algebra systems (CAS) in the

Many of us decided for one, the other or both. Right here next to my left
hand is my TI92, and next to my desk is a bag full of TI eighty-something
calculators. I have taught on a campus where Calculus is presented with the
use of Mathematica and my campus today has a classroom set of Derive
software. In my mind there is no doubt that technology is here to stay.

The main advantage of using CAS with students is in the ability to bring
something new into the classroom. The graphing component of the calculators
is a wonderful help. Each time I watch the Taylor series approximate sin x
better and better with each higher degree polynomial, I become excited
about being able not only to show the students a picture in the book, but
also give them the feeling they can touch a Taylor polynomial. I can show
my students how ¼ was discovered by trying to find the perimeter of a unit
circle, and I can completely work out the details. I can simulate direction
fields and walk along the indicated directions to graph the solution of a
differential equation. I can solve problems to the end instead of stopping
a couple of steps before the finish and saying that the details are not so
important as the idea. My students like the idea of seeing the final answer
and comparing it to the one in the back of their textbook.

I very much support the idea that materials need to be technology based but
not technology driven. For me this means a constant search for "really
interesting problems." That is why I attend conferences and workshops. Many
good problems can be found on the TI web page at, and
some of the best ones I have learned about at T3 (Teachers Teaching with
Technology) summer courses.

When I wonder how the use of calculators has changed the way my students
look at mathematics, I review the many articles that have been published on
that topic. (A very comprehensive listing of them can be found at, a site maintained by
Penelope Dunham.) I also attend conferences like the ICTCM (International
Conference on Technology in Collegiate Mathematics) and watch the
enthusiasm of both the presenters and the participants.

My favorite presentation from this summer was an animated lecture by B.
Kutzler; he compared mathematics to motion. (An article based on the
lecture can be found at
Motion can be achieved without any vehicle, but with a vehicle of some kind
everyone can get farther, and for some of us a vehicle is necessary to
travel even short distances. For some of us, a good vehicle can fly us to
the moon. This is how I believe the calculators should enable our students,
both in the classroom and later on when they go on their own "lunar"

NOTE ---

Pencils are no less technological than calculators. Thus, mathematicians
and teachers of mathematics have been dealing with the issue of the
appropriate use and abuse of technology for centuries.

A Different Pencil will be our overall title for an occasional series of
articles about the use of technology in mathematics and in the teaching of
mathematics. Contributions are welcome; please submit articles for
publication to Fernando Gouvea at .
Nora Franzova ( earned her Ph.D. at the
University of Rochester in 1996 and since 1997 has been assistant professor
of mathematics at Harford Community College in Maryland.

Jerry P. Becker
Dept. of Curriculum & Instruction
Southern Illinois University
Carbondale, IL 62901-4610 USA
Fax: (618) 453-4244
Phone: (618) 453-4241 (office)
(618) 457-8903 (home)


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