Using calculator in elementary math teaching

This article discusses whether or not calculator should be used in teaching math in elementary grades and gives ideas on how to use it wisely.

The 'battle' over calculator use

Some people say calculator enables children to concentrate on understanding and studying mathematical concepts instead of spending time on tedious calculations.  They say calculator helps develop number sense, and makes students more confident about their math abilities.

National Council of Teachers of Mathematics (1989) has recommended that long division and "practicing tedious pencil-and-paper computations" receive decreased attention in schools, and that calculators be available to all students at all times.

Others are against using calculator in lower level math teaching, saying that it makes children not to learn their basic facts, prevents students from discovering and understanding underlying mathematical concepts and instead encourages them to randomly try different operations without understanding what they're doing.

They say calculators 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.

There IS a balance

In my opinion, calculator can be used in the teaching in a good way or a bad way - it all depends on the teacher's approach.  Calculator in itself is not bad or good -- it is just a tool.  It is used a lot in today's society, so students should learn to use it by the time they finish school.

At the same time, children SHOULD learn their basic facts, be able to do mental calculations, and master long division and other basic paper-pencil algorithms.  Mathematics is a field of study that builds on previously established facts.  A child that does not know basic multiplication (and division) facts will have hard time learning factoring, primes, fraction simplification and other fraction operations, distributive property, etc etc.  Basic algorithms of arithmetic are a needful basis for understanding the corresponding operations with polynomials in algebra.  Mastering long division precedes understanding how fractions correspond to the repeating infinite (non-terminating) decimals, which then paves way to understanding irrational numbers and real numbers.  It all connects together!

For this reason, it is probably very wise to restrict the calculator use in the lower grades, until a child knows her basic facts and can add, subtract, multiply, and divide even large numbers with pencil & paper. THIS, in my opinion, can build number sense — as do mental calculations.

This does not mean that you couldn't use calculator occasionally in the elementary grades for special projects or when teaching specific concepts, or for some fun.  It could be used for example in science or geography projects, or for exploring certain new concepts, or for some number games or checking homework.  See below for some ideas.

The discussion here does not apply to graphical calculators in high school.  I am strongly in favor of using graphical calculators or a graphing software when studying graphing of functions and calculus.  Even there though, one certainly needs to learn the basis of how the graphing is done on paper.

Things to keep in mind when using calculator

When calculator is used more freely, one should pay attention to following points:

• Calculator is a tool to do calculations.  So is the human mind, and paper & pencil.  Children should be taught when to use calculator, and when mental computing (or even paper & pencil) are more effective or appropriate.  Choosing the right 'tool' is part of effective problem-solving process.
• It is very important that students learn how to estimate the result before doing the calculation.  It is so very easy to make mistakes when punching in the numbers, and a student must not learn to 'rely' on the calculator without checking the reasonableness of the answer.
• Calculator should not be used for a random trying out of all possible operations and seeing which one produces the right answer.  It is crucial that the child understands the different mathematical operations so she knows WHEN to use which one - whether the actual calculation is done mentally, on paper, or with a calculator.

Ideas for calculator use in elementary grade math

If you use these ideas, make sure the kids don't get the idea that calculator takes away the need to learn mental math.  It can serve as a tool to let children explore and observe, but afterwards the teacher should explain things, justify the math rules, and put it all together.

• Let preschoolers or first graders explore numbers by adding 1 repeatedly (which can be done with first punching in 1 + 1 =, and then pressing the = button repeatedly) or subtracting 1 repeatedly.  Observe their faces when they hit negative numbers!  Or, let them investigate what happens to a number when you add zero to it.
• Calculator pattern puzzles:   An extension of the idea above, where first-third grade children add or subtract the same number repeatedly using a calculator.  Children will observe patterns that emerge when you add 2 or 5 or 10 or 100 repeatedly, or will make their own "pattern puzzles" which are simply number sequences with a pattern where you omit some numbers, for example 7, 14, __, __, 35, __, 49. The activity can connect with the idea of multiplication very easily.
• Place value activity with calculator:  Students build numbers with the calculator, for example:
  Make a three-digit number with a 6 in the tens place; OR Make a four-digit number larger than 3,500 with a four in the ones place; OR Make a four-digit number with a 3 in the tens and a 9 in the hundreds place; etc.
  Afterwards teacher lists several on the board and discusses what the numbers that students made have in common, like all might be sixty-something etc.
• Write number one million on the board.  Ask students to pick a number that they will add repeatedly with the calculator to reach one million within reasonable class time.  If they pick small numbers like 68 or 125 they won't reach it!  This can teach children about how vast and big the number one million is.
• When introducing pi, have students measure the circumference and the diameter of several circular objects, and calculate their ratio with a calculator (which saves time and can help keep the focus on the concept).

Sources

Calculators in the Classroom Article by Eisenhower Southwest Consortium for the Improvement of Mathematics and Science Teaching, 1998

Educators Battle Over Calculator Use: Both Sides Claim Casualties

The Role of Long Division in the K-12 Curriculum
"The role of long division is not just to divide one rational number by another, but the algorithm itself contains the initial exposure of topics which become crucial in the core applications of mathematics in our society today. ...we discuss methods for teaching long division in such a way that the underlying concepts can be understood by students."

The Use of Calculators Gets at the Heart of Good Teaching

Comments

I think both should be used. I agree we need to learn the basics in elementary school, addition, subtraction, etc.) However, When you go to Macy's, Olive Garden or Mc Donald's, the cashier doesn't use paper and pencil. Computers (calculators) are used. We live in a computer age. We are no longer in the Industrial Revolution, so let's come into the 21st century.

Bev

Hi I'm Kelly. I'm a freshmen in college at St. Charles community college in Missouri. Your site is wonderful. I was looking it over for my younger sister. Something I would really like to tell everyone and anyone who plans on going to college is to stop using a calculator immediately. Only use it for graphing logs and necessary things like that. I finished high school in a calculus class using a calculator for even the simplest multiplication and division problems, and when I got to college I had to start all over in BEGINNING ALGEBRA because I didn't know how to multiply and divide without a calculator. So please do everyone a favor and ask them or tell them to stop using a calculator. They will thank me for it later. Kelly

Hello my name is Rafeek and I am a freshman at Hobart and William Smith colleges in Geneva, NY. I am doing a paper on technology and its effects, so I decided to pick the calculator. I came across this site in my research. I want to stress what Kelly said. The same thing happened to me, I was great in high school math, practically aced all math exams, then I came here for orientation and they told me I have to take a math placement test W/OUT a calc. I didn't realize I couldn't do a lot of the simple problems because I always plugged it into my calc and got the answer. This is becoming something serious, I already took away my younger brother and sisters calc. and told them until they are in college they will not be using a calc (at least not in front of me). Now I am taking pre-calc. and my goal it to not use a calc. DO NOT DEPEND ON YOUR CALCULATOR!!!

Rafeek

When in University taking math courses for my BMath we weren't allowed calculators for many of the exams (to prevent people smuggling in pocket computing devices). For anyone doing higher level math I would say that being able to do sums on paper is essential.

Emily Bell

I've never been good at math and so when i got a hold of my calculator and how encouraging it is in highschool i fell in love with it. that is until i took my colege placement test. I did horrible. I couldn't even remember how to do a simple division problem mentally. The problem with schools today is that they worry and encourage too much about calculators. Students should have a good sturdy base of mental math before they learn to use the calculator and if u ask me K-3 grade isn't enough. it should not be permitted until college.

Yaymi

I am a recent college graduate. My major was Electrical Engineering. As my course of study involved a great deal of mathematics, I feel obligated to speak on this important issue. In my opinion, calculators should never be used for any mathematics class, even at the college level. Using a calculator for any subject will cause the user to become mentally lazy and incapable of basic mathematics skills. You should never use a calculator when learning how to multiply, do long division, or even graph a function.

"Some people say calculator enables children to concentrate on understanding and studying mathematical concepts instead of spending time on tedious calculations. They say calculator helps develop number sense, and makes students more confident about their math abilities."

The above statement is the total hogwash. The only way to develop number sense and understand mathematical concepts is to pour over hours of tedious calculations. The only way to develop confidence in one's math abilities is to use a pencil and paper whenever you are confronted by a math problem. If a mathematics teacher agrees with the above statement, he or she should be fired immediately. The NCTM should be publicly disgraced for going along with such ruinous ideals.

The only time calculators should be used in school is in the laboratory class when you are doing calculations on numbers with more than 4 significant digits. Otherwise, the student should rely on a paper, a pencil, and his or her brain.

Eugene

I use a paper calculator to teach the basics and it works as fast as the real thing. The students do mental math with the calculator face as a reference. It is a DOTMATH paper calculator. You can get info on it from the DOTMATH for kids website or email me at owenbprince(AT)hotmail(DOT)com

Owen

I do come across situations when caculator are not available or not allowed, how to make fast calculations then in the brain?

rohit jain

There are several books available that teach you efficient mental math methods, if you don't yet know any. For example:

Mental Math for grades 4-8

50 Easy Ways to Add, Subtract, Multiply, and Divide Without a Calculator

How to Calculate Quickly

Speed Mathematics

Question: What are the main reasons for not using calculators in forms one to three of secondary schools?

I'm not quite sure what forms one to three are, but I guess you are talking about high school.

I personally would not deny calculator use of high schoolers. Children need to learn to use calculator, and to use it wisely - which means they should learn WHEN it's good to use it and when not. Maybe one would deny calculator use in high school if a student was constantly misusing it, in other words using it for 6 x 7 etc., in which case such a student might need to review lower grades math.

I am a current sixth grader, I know most kids my age prefer using a calculator not for checking there work, but doing a large portion of they're math with calculators. Calculator should be used only for checking work,recently my math teach has practically been forcing us to use TI30 xa calculators,as you know,the school provides a calculator that can add,subtract,multiply,and divide, and that seems to be enough. Lately I have been catching myself relying on calculators to do all my work, but today during my math class I decided no more calculator,one problem I had to solve was 3.8892 divided by 3 and I couldn't remember how to do it. And the other day my mom gave me a simple math problem while getting gas and it took me 5 minutes to do this basic addition problem. My parents didn't use calculators when they were in school and if they didn't need them then we don't either. But once all of our current middle schoolers are full grown adults, our school system will see that the adults will be way behind in math while relying on computers, and calculators to do all there deeds. I am officially Anti calculator!

Bre

I was lucky enough to learn basic math facts (multiplication, division, fractions, estimation, etc) before getting a calculator in 8th grade, but I grew really dependent on my TI 83 graphing utility for my high school algebra/precalc classes. I would graph the function to find the zeros instead of using the quadratic formula and stuff like that.

My freshman calculus class didn't allow calculators, and I failed it. This was after doing quite well in honors high school precalculus. I went into an easier life/social science series (still had to struggle for B's/C's when I'd had easy A's in high school) and eventually repeated the harder calculus class much more prepared. My life/social science series classes allowed 4-function but not graphing utilities. Also, in college I had to show my work to get any credit, even if the answer was right. I think one problem is that I got too hung up on finding the answers rather than learning the process.

My sister on the other hand has had a calculator since 3rd grade, and she literally can't multiply 6*7 without a calculator or do a word problem, though she does get B's in high school math.

Laura

As a Senior majoring in Early Childhood/Elementary Education, I understand the importance of having the knowledge on how to use a calculator, because yes, we live in an age where technology is widely used. However, like many of you, when I first came to college and had to take exams without use of the calculator, I was in big trouble! I still did very well, but it took me a long time to relearn all of the basic functions of math. From my own personal experiences in the field and through my own courses, I recommend a consistent balance between the two methods!!

Heather

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