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A calculator is a device, usually hand-held, for calculating
mathematical expressions. In the past, calculations were done in
the head, on paper or by a semi-manual machine.
There are now many advanced variations of calculatorsavailable, each performing a specific function. For example, the
scientific calculator is designed for advanced mathematics like
trigonometry and statistics. The financial calculator will help in
accounting and real-estate deals. The mortgage ones will show
you what exactly you have to pay on your house. Apart from
these there are loan, lease, time, love, area, temperature and the
most advanced of them all, graphing calculators. These are all
basically online calculators but they do have certain anomalies,
like, if the numbers get too big or too small, some errors in
calculations can occur.
. Some believe that using calculators hamper the basic
mathematical skills of people, especially students, by making
them poor in instant calculations.
In many countries, students are allowed to use calculators in
their school-work because it is felt that problem-solving and
estimation techniques can be taught more easily throughcalculators. Others worry that students may use the calculator in
the wrong way unintentionally and, yet, believe the answer
because that was the result shown. This type of error can take
place outside school rooms also. Anyone using the calculator
incorrectly will believe the wrong answer to be the right one.
This might happen in shopping malls or even during business
transactions.
In schools, teachers try to tackle this by asking the students to
first make an approximation of the answer manually and then
compare it to the calculated result. But, overall, this does
hamper the child`s learning process because he or she may not
understand the logic behind the answer. In such a case,
calculators become more of a hindrance than a help.
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A prime example of the technology debate is calculator use in
schools. Calculators should only be allowed on a regular basis in
elementary schools after the student has mastered the basics of
adding, subtracting, multiplying,. Students should be proficient at
adding, subtracting, multiplying, and dividing without the use of a
calculator. Calculators should only be used after students have
gained a firm grasp of math basics to alleviate the tedious and
repetitive work.Calculators can actually create problems for
students when the calculator becomes a crutch. Students
become dependent on their calculators and have difficulty doing
math problems when they don’t have a calculator available. In
recent years many teachers have noticed that because of
calculator dependence students do not simplify problems.
Instead, students leave as much as work as possible for the
calculator. This means that the natural intuition gained when
students simplify their work to make the problem easier to solve
by hand is being lost. These simplifying skills learned through
practice in the lower grades are no longer being carried through
by the student into college level math. This makes math more
challenging for students later on because they do not possess
the natural intuition and skills needed to approach a hard
symbolic problem and simplify.
There has also been a fundamental shift in math from a focus on
problem solving to a focus on getting the right answer. Students
put numbers into a magic black box and get an answer, write it
down, and teachers grade on whether the answer is correct
instead of focusing on the process. If the students work problems
out by hand then they are forced to go through the problem
solving steps and gain thorough understanding. Calculators
should not be allowed when the point of the problem solving is to
develop a skill in math. Educators should ensure that the student
has a good understanding of math concepts before calculator use
should be allowed to replace paper and pencil problem solving.
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Take factoring for example, complex calculators today can factor
with ease. However, factoring is an important skill that is used in
all kinds of higher-level classes and is a basic necessity much
like adding. The calculator should not be used to get the final
answer by having the calculator solve the entire problem. Instead
calculators should be used to help the student find common
factors by checking the student’s hypothesis about the factored
term.
In conclusion, calculators are a tremendous tool of technology
that have a worth while place in our education system. They
should be limited, however, to simplifying work by replacing only
the tedious tasks that the students have already mastered.
Educators must be careful, especially in the elementary levels,
that the calculator is not being used to replace the practice and
conceptual understanding students need to succeed. Calculators
have their place as long as the student is getting the maximum
education benefit from their use.
Con: Mechanization of fundamental classroom skills may leave
kids unable to do
simple math on paper.
Some calculators cost as little as $20, or about the same as
some textbooks, and
instructors say they could
become required equipment in advanced math classes. The
pocket-sized units are
Opponents of calculators say that kids won't know how to count
if their
calculator batteries ever go dead, just as TV-oriented students
no longer seem
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to know the basics of grammar and spelling. The device, critics
contend, will
make pencil-and-paper math obsolete.
"The calculator doesn't think for you; it doesn't have abrain."
Educators Batte Over Calculator Use: Both Sides Claim
Casualties
The philosophical war rages. On one side: the accused
"kill and drillers," dedicated to times tables and long
division, preaching the gospel of repetition and
memorization. On the other side: alleged "fuzzy math"
reformers preaching concept over content, insight over
"right." Between them: the most visible symbol of the
continuing conflict -- the classroom calculator.
• Depending on one's perspective, the use of calculators at
the elementary school level is seen as either the solution to or
the cause of many of the problems
AND IN THIS CORNER: THE CALCULATOR CRITICS
Critics say calculators
• produce students who can't perform basic tasks without a
calculator.
• encourage students to randomly try a variety of
mathematical computations without any real understanding of
which is appropriate or why.
• prevent students from discovering and understanding
underlying mathematical concepts.
• keep students from benefiting from one of the most
important reasons for learning math -- to train and discipline the
mind and to promote logical reasoning.
• inhibit students from seeing the inherent structure in
mathematical relationships.
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• give students a false sense of confidence about their math
ability.
....Calculators prevent students from seeing the underlying
structure and beauty in math." (3/11/97)
Tom Loveless, a Harvard University professor, is quoted in a Washington Post article as saying: "There are some elements of
math -- particularly at the elementary level -- where some basic
facts simply must be memorized. We have lots of teachers
reporting that they're getting kids in third, fourth, and fifth grade
who don't know their basic facts." (11/2/97)
1. To understand numbers and patterns found in nature.
2. To know when and how to use math tools.
3. To make fast and accurate predictions.4. To grow and maintain mental power.
5. To understand invisible things.
6. To think logically and clearly when solving problems.
7. To operate systems using profound knowledge.
8. To recognize long-term causes and effects.
9. To check the reasonableness of answers.
10. To feel comfortable in a technological world.
Calculators are now in use in mathematics classrooms
everywhere.
Junior High School:
This immediately suggests to some that students may be losing
skills. Surely if students are no longer doing multiplication or
division with big numbers after grade 6, they will lose these
skills.
In fac t , th is i s t rue . S tudents a re los ing sk i l l s .
Does a student need to practice long division after grade 6, in
order to be ready for the 'real world'? Of course not. We all use a
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calculator. We'll always be able to use a calculator for those
types of calculations, so it's a skill we don't need to be good
at! And it doesn't matter! These are skills that aren ' t
n e e d e d a n y m o r e .
However, this is not to say that some skills are not still useful,
and the distinction is very important. Both 'real world' problems
and Sr. High school math courses require students to be able to
be good at 'mental math'. You can't expect to pull out your
calculator every time you need to multiply 6 times 8, and if you
have to use a calculator in grade 10 math to do problems like -6 +
8, you won't finish the tests!
In Jr. High math, we still require students to be proficient at
some basic skills; operations that they can do in their headwithout a calculator. These include, for example, the times
tables , integer operations , simple powers , and the order of
operations . Stu d e n ts a re n o t a l l o we d to u se a c a lc u la to r
wh e n p ra c t ic in g th e se sk i l l s .
In addition, some paper and pencil skills are important because
they carry over into algebra, where most calculators can't (yet)
operate. So in grades 7 through 9, students are expected to be
able to do fraction operations by hand, and may not use
programmed formulas to solve problems.
Students in grade 9 who are not proficient in these
mental calculations don't often succeed in the advanced
level Sr. High mathematics courses.
Senior High School:
easons to avoid using a calculator
• It prevents you from doing the critical thinking necessary to
do more complex calculations
• Students who use a calculator are generally weaker at
analyzing their answer to make sure it makes sense
• Takes away opportunities for you to reason your way
through the problem
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• It is easy to just try different operations and see what each
answer looks like rather than reasoning through the problem
• May give you a false sense of confidence in your
calculation abilities
•
In extreme cases, calculator overuse may inhibit your ability to do even basic calculations in your head or on paper
Many teachers have procedures concerning calculator use.
Some dislike calculators and allow them to be used only when
absolutely necessary, while other teachers allow you to use the
calculator whenever you like. Calculators can be a useful tool
when used appropriately, but it is easy to get into the habit of
reaching for one before you even think about what the question
is asking. The reason that there is a debate about calculators
and their usage is that many students overuse their calculator,
which leads them to underuse their brain. You probably know
someone who starts every math problem by reaching for their
calculator. This behavior is a problem as the calculator becomes
more and more of a crutch. Some students use calculators so
much that their first reaction is to use it to simply try to add,
subtract, multiply, or divide the numbers given in the problem to
see if any of those results make sense as an answer. These
students have lost their problem-solving instincts and have
weakened their ability to judge the correctness of an answer
because they do not think through the problem enough to
determine what type of answer to expect.
The key to calculator use is
balance. Calculators can be a helpful and effective aid as you
tackle problems that require more computation. Before reaching
for a calculator, put some thought into the problem. If it is a
word problem, consider drawing a diagram or making a chart to
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help your brain organize the information. Once you have done all
this and understand what the problem is asking, use this
information to determine whether or not to use a calculator.
Most problems can be done without using a calculator, but its
use is justified whenever it will save you the time of doingproblems that you are su re you can do. Pick up the calculator to
save yourself time on simple tasks like adding or multiplying
large numbers groups of numbers. Avoid its use when the focus
of the lesson involves practicing a new computation skill such as
adding, subtracting, multiplying, or dividing with larger numbers.
For example, if you are just learning how to add three digit
numbers, you should work the problems out by hand. Using a
calculator becomes an appropriate choice later in your math
career when you are doing an Algebra problem that involvesadding a number of three digit numbers.
The bottom line
Calculators can be a great tool when used appropriately. Just be
careful and make sure that you keep the responsibility of the
“thinking” to yourself. Calculators are good at computation but
cannot be counted on to do any of the actual “thinking” required
to do a mathematics problem.
Calculators are not really smart. If a calculator is sitting in a
burning house, does it know that it needs to get out of the house?
Does it know that it needs new batteries periodically, and how to
get
them? Can it recognize a face, or tell a cat from a dog?
Calculators are very good at one particular thing, but as a rule of thumb, being very good at one kind of thing often means that
you'll be
very bad at other kinds of things.
People are very, very good at some kinds of things, and very, very
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