Q&A #1659

Teachers' Lounge Discussion: Graphing calculators

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From: Loyd

To: Teacher2Teacher Public Discussion
Date: 2001111110:31:11
Subject: Re: When to use graphing calculators

On 2001111020:15:56, A. Booth wrote:
>	I am a new teacher although I got my bachelors degree in math about
>25 years ago.  I would like to know when and when not to allow
>students to use graphing calculators.  I learned to do all this stuff
>without them, but now my students do all kinds of shortcuts with them
>and I want to make sure they can perform the tasks they need to
>without them.  Am I being too picky?

The graphing calculator is very useful for algebra II students and
higher.  It is not absolutely necessary for a student to get through
the course but increases greatly the understanding of functions and
graphs.  It takes some algebra skill to get the equations in the
proper form for graphing.  Also, the graphing operation makes clear
what a root or zero is; the meaning of minimums, and maximums become
much clearer than they did with purely mechanical means.  I learned
how to graph 46 years ago and then went on to major in mathematics. 
Still, after I got my TI-83 in 1999 so I could tutor algebra II
students, I found that even now, the ability to graph with ease
increased my understanding and gave me permanent visuals to store in
my memory.  I found myself reviewing all my old calculus books and
graphing the myriad of functions in the back of the book.   

I have watched a lot of students use these calculators and some only
use them as a scientific calculator replacement.  They aren’t always
taught how to use them with understanding.   

In the hands of a good math teacher, they are a great asset.  In my
opinion, the algebra I teacher should teach the fundamentals of using
the graphing calculator and the algebra II teacher should teach it a
little more to use as a tool.  I have not found a student who is poor
at math without a graphing calculator that is good at math with a
graphing calculator.  Most of these capable students are good with
math either way.  

When I took matrix algebra (linear algebra) in my junior year in
college, matrices were taught at a very abstract level so that even
simple matrix multiplication was difficult to understand at first.
Most of the students didn’t know what the German Professor was even
talking about.  I finally learned by going to the library where I
found a high school textbook that “spilled the beans” with a lot less
rigor.  Then, I could finally understand the what appeared to be “hen
scratches” used by the textbook and professor.  Then finally we tried
to solve 5x5 systems of equations using the matrix method using
elementary row operations.  I was able to do maybe one or two problems
in my entire college career (5x5 system) because the odds of making an
arithmetic mistake were very great.  Try it some time.

Now with the TI-83 you can punch in coefficients of a 5 by 5 system of
equations and find the roots very easily. You can use row operations
or you can use the matrix inverse method; the latter is simple with
the TI-83.  This power gives you the ability to experiment with in a
lot of ways that is not possible with only pencil and paper.  

However, I would not encourage a student to graph linear equations or
even quadratic equations until they understand the manual process. 
Algebra should start with established methods so that the students can
get an appreciation for the process.  Then they will appreciate the
graphing calculator more.   

There is thinking that goes on with a graphing calculator that would
not be available to a student that was educated in say late 40s and
early 50s or even 60s and 70s.  In the computer age, this thinking is

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