Calculators
in the Classroom |

** Since
the development of small, inexpensive, electronic calculators in the early
1980's mathematicians and teachers of mathematics at all levels have seen
the great potential that these instruments have for changing how mathematics
is taught, and for changing the way that mathematics is learned.
From Principles and Standards for School Mathematics, produced
by the National Council of Teachers of Mathematics (N.C.T.M., 2000):**

** "Technology
is essential in teaching and learning mathematics; it influences the mathematics
that is taught and enhances students' learning." "In the mathematics
classroom envisioned in the Principles and Standards, every student
has access to technology to facilitate his or her mathematics learning
under the guidance of a skillful teacher."**

** On the
other hand, I believe that the availability of calculators should be limited
to students in 7th grade and above, and does not eliminate the need for
students to learn algorithms. Proficiency with paper and pencil computational
algorithms is important, but such knowledge should grow out of problem
situations that have given rise to the need for such algorithms.
Students should be able to decide when they need to calculate and whether
they require an exact or approximate answer. They should be able
to select and use the most appropriate tool. Students should have
a balanced approach to calculation, be able to choose appropriate procedures,
find answers, and judge the validity of those answers.**

** I believe
that graphics calculators can help students visualize otherwise abstract
mathematical concepts. They empower students to take more control
of their learning by offering a visual way of discovering mathematical
relationships. Appropriate use of graphing calculators also includes
use on what I refer to as coincidental computation. Coincidental
computation is the arithmetic that occurs during the solving of real problems.
That is, when the focus is not on the algorithm, but on the solving of
a problem that has been translated from a real situation into an expression
that requires evaluation. When the focus is on the algorithm I call
the exercise, contrived computation. This is the abstract manipulation
of mathematical (algebraic) expressions/equations whose sole purpose is
the learning of the computational steps (algorithm) required to simplify
or quantify.**

** I would
like to set the minds of my students and their parents to rest on the subject
of calculators in the classroom. My students will learn how to do
every algebraic manipulation, including graphing, with a pencil and paper
because I advocate BASICS FIRST. In addition, every one of the manipulations
that it is possible to do on a graphics calculator will be taught on the
TI-84+ graphics calculator. Students will be required to know how
to use both pencil and paper and graphics calculators for the mathematics
taught in my classroom. Students will
be led to understand the power of graphics calculators as well as their
limitations (as Shoe discovered, above, calculators can't do everything.)
Even though calculators will be available most of the time in my classroom
(beginning with SAT preparation) there will always be some exercises/problems
on test/quizzes that it will be of no help.**

** I am
a firm believer in using technology in the math classroom for all of the
following purposes: emphasizing concepts, discovering patterns and
relationships, coincidental computation, graphing, developing mathematical
intuition, confirming solutions, solving all types of problems (including
problems that would not be attempted without the use of graphics calculators)
and to encourage higher level thinking skills.**

** For
those who would discourage calculator use for fear the users will become
calculator dependent I would give the following example: Suppose
you lived on a farm where you often had to dig post holes. Your father,
and his father before him, had always used a manual post hole digger.
Then you discovered you could dig five times as many holes in the same
amount of time using a post hole digging auger on the back of a tractor.
I am pretty sure that you could come to prefer to use the auger
over the manual post hole digger, but I don't think you would ever lose
your ability to use the manual tool. I would agree, however, that
you just might become dependent on the auger to give you better post holes
in less time, and you may wind up not being able to use the manual digger
as well as your father, but I'll wager that you would be willing to give
up a little skill with the post hole digger to learn great technique with
the auger. And in the end, aren't you really just trying to dig a
hole?**

** It is
for all of the above reasons that I recommend that parents of students
in my classes purchase TI-84+, or TI-84+ Silver Edition graphics calculators
for their children. After the first 6-weeks we will be using the
class set of graphics calculators that have generously been provided by
the Academys. Often, the work will require that students use a graphics
calculator on homework. Students who do not have one at home will
have to complete the work at school. Graphics calculators can be
purchased at most any office supply store or discount store. This
same calculator is used extensively at most high schools, so students can
expect to be able to use theirs for many years. Owning a calculator
is not required for success in Algebra I, but owning one will go a long
way towards facilitating the learning of both Algebra I and graphics calculators.**

** The
bottom line here is that the human instinct to take the path of least resistance,
and to use the easiest method available to solve a problem, often encourages
overuse of technology. For this reason there will always be problems
on algebra tests that cannot be solved/answered using a calculator.
There will also be problems that require graphing calculator use on most
tests.**

** As adults
in the real world we have lots of "tools" that we use in our everyday lives
and in our work that we could do the job without, but that we have become
addicted to using to make life/job a little more pleasant with a little
less drudgery. The graphing calculator holds the same position in
the lives of my students. They can always do the job without the
tool, but if the point is to understand the problem and find a solution
then the calculator ought to be available to facilitate that end.**

** I recommend
that students
not bring their graphics calculators to school as
the possibility of damage or loss is too great. There will always
be TI-84+'s available in my room for students to use. Students should
leave their personal graphics calculators at home for use on homework.**

** One
final thought. I believe that many people cannot learn to do mathematical
computation at a level that used to be necessary for success in higher-level
mathematics classes. I also believe that no individual should be
excluded from these courses just because they lack fluent computational
skills. Having poor computational skills is not necessarily an indication
that a person lacks the ability to problem-solve at the most difficult
levels. Therefore, if a student lacks manual computational skills,
but he can understand complex real-world problems, define variables, and
write equations that model the situations, I believe he should have access
to the highest levels of mathematics and science classes even if he needs
a calculator to do every computation. No student should be denied
access to higher mathematics simply because he lacks manual computational
skills.**