The Need to Understand How Functions Fool Graphing Calculators
Graphing calculators are relatively recent and innovative tools in
mathematics education. There is quite a debate in today's mathematical
community concerning their proper use. Proponents of the use of
graphing calculators claim that the technology allows their
students to investigate the behavior of more graphs than traditional means
allow, to investigate more complicated graphs reflecting more realistic
problems, and to develop valuable
technological skills. Opponents claim that that use
of the graphing calculator really has nothing to do with mathematics and,
worse, the graphing calculator creates a cruch that the student
will always depend upon.
Let me say a couple of things to prevent a flood of protest from either
So, I guess I come down in the middle somewhere.
My belief is that technology in education is here to stay and educators
make sure that our students understand how to use this technology
In particular, students must understand that computers are stupid
and make stupid mistakes. Understanding what types of mistakes graphing
calculators make helps students use them more intelligently and, also,
requires the students to understand the mathematics involved, which is the
whole point behind mathematics education in the first place.
- I refer to and use not only graphing calculators regularly in my
classes, but also, powerful computer algebra systems. I, also,
encourage the responsible use of these tools by my
- I believe that serious steps need to be taken to make sure that
mathematics is being taught, rather than a course on how
to use a calculator, and to prevent students from becoming dependent on
Understanding the types of mistakes a graphing calculator will make
is, also, beneficial to instructors of mathematics. The knowledgable
instructor is able to pose questions on a test, quiz, or homework
which will fool a graphing calculator in a subtle way. Continually
doing this is a great way to combat dependence on the graphing
calculator. Personally, I like to go over such examples in class in
the following sequence:
I've found that this approach encourages students to experiment with
graphing calculators, while imparting an understanding of the
- Graph the function using standard analytic techniques (pencil,
paper, and brain).
- Graph the function blindly with a graphing calculator.
- Compare the two (there should be differences).
- Attempt to refine the calculator's graph by changing the viewing
rectangle and/or settings of the calculator.
Math Dept. |