In this age of the calculator, why should you have to learn to do arithmetic in your head?

Surely the reason that we have the calculator is to help us do our calculations, and it is a tool for all of mankind, including school children, just like the motor car is a tool to get us from one place to another to save on walking.

In many ways these arguments have some value. It is true that the calculator is used to help us in performing calculations, and the calculators are very useful, and often indispensable, for certain professionals such as financial consultants, engineers, and scientists. Builders need to perform calculations quickly, and accurately, such as determining how much paint they will need for a house.

But the argument should be rephrased as “now that we have the calculator to help us, do we still need to learn mental arithmetic“? And I think that this is a better question for us to consider.

For me, the answer is a definite yes. I firmly believe that mental arithmetic is important for the reason that there are many cases in which the calculator is too slow for us to use when we need quick answers, and if we can do these more simple calculations in our heads, then we do not need the calculator.

But surely the calculator is always faster than using your head? Well not really, since using the calculator means picking it up, typing on the keypad, reading the result, and finally making use of this result. For larger calculations, such as this is reasonable, but not when you are wanting the value of . So we need to ask “when should we used the calculator, and when will it be faster to just recall the result from our head?“

This defines what I mean by “mental arithmetic” which is calculations which you can perform faster in your head than using pencil and paper or using a calculator.

Consider the sum . Would you consider taking out your calculator for this, or will you just “know” the answer which you can recall from information which you have previously memorized?

I am hoping that you knew the value of this sum and that you did not think about reaching for your calculator. If you thought about using your calculator for this then I hope you realize that something is wrong and that this something must be fixed.

It should be now clear that there are some calculations which you should be able to do in your head, like and others which are too complex to do in your head, such as . The question now is “how far can we develop our mental mathematics skills, and when is it better to use the calculator?“

There are many simple calculations which you should always learn, and many of these are introduced into the early grades, as one of the few areas of mathematics in which you have to memorize facts rather than to develop your understanding of the mathematical topics processes.

As learners move through the curriculum, and especially in Grades 7-9 and on to the more advanced mathematics covered in Grades 10-12, there is an increasing demand for performing arithmetic calculations as quickly as possible.

There are many types of calculations which you should be able to do in your head, without using a calculator and without using pencil and paper, and I will be addressing the following in this series of articles (which are still under development):

• addition of single-digit numbers
• addition of double-digit numbers
• number bonds
• simple subtractions
• simple multiplications
• simple divisions
• special cases of multiplication and division: 10, 20, 25, 50, 100 
• doubling and halving
• determining divisibility
• dividing numbers into factors
• identifying prime numbers
• dividing numbers in prime factors
• reducing common fractions
• percentages, decimal numbers and common fractions

In the following pages of this Mental Mathematics series I will be covering each of these mental arithmetic topics in turn and I will also be providing some documents which you can download use to help you with improving your powers of mental arithmetic and to test yourself.