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No calculators allowed ?
Posted:
Jan 19, 2000 3:54 PM


************************************************* 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 classroom.
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 eightysomething 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 ÃÂ¼ 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 http://www.ti.com, 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 http://dungeon.ti.com/calc/docs/researchb.htm, 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 http://www.acdca.ac.at/kongress/goesing/index.htm) 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" adventures.
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 fgouvea@colby.edu .  Nora Franzova (nfranzov@harford.cc.md.us) 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 629014610 USA Fax: (618) 4534244 Phone: (618) 4534241 (office) (618) 4578903 (home) Email: jbecker@siu.edu
mailto://jbecker@siu.edu



