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 dwell on.

For me, the answer is yes, that mental arithmetic is important, and 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.

This defines what I mean by “mental arithemetic” which is calculations which you can perform in your head, rather than using a pencil and paper. For example, consider the sum . Would you considering taking out your calculator for this, or will you just “know” the answer which you extract from the prior knowledge in your head?

I guess that almost all of you will be able to determine the answer without using your calculator, and if you are already reaching for your calculator then clearly something is wrong.

So there are some calculations which you can do in your head, like and others which you cannot do in your head, and which appear to be too difficult such as . So I now ask how far can we go with developing our mental arithmetic, and when should we use the calculator?

There are a range of common, and simple, calculations which you should always learn, and some of these are introduced into the early grades, as one of the few areas of mathematics in which you have to memorise large number of facts.

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 many simple arithmetic calculations and to perform these as quickly as possible.

Here is my list of the types of calculations which you should be able to do in your head, without support from pencil and paper, and without reaching for your calculator:

- simple additions of numbers
- number bonds for a given number
- simple subtractions
- simple multiplications
- simple divisions
- determining divisibility
- identifying prime numbers
- dividing numbers into factors
- reducing fractions

In the following posts I will be covering each of these mental arithmetic topics in turn and I will also be providing some useful documents which you can use to help you with improving your powers of mental arithmetic.