A Calculator is a Device

8/3/2019 A Calculator is a Device

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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.



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.



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



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.



• 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



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



• 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



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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A Calculator is a Device