What is the purpose of mental arithmetic in the modern world? In what way does it benefit someone to be able to do mental calculations considering that a calculator can be bought for about the same price as a bar of chocolate – if not less.

In the past when schoolchildren have questioned the use of mental arithmetic, teachers were at least able to say “Well you won’t always have a calculator handy”. Well I think that’s just not true at all now – everyone has a calculator practically all of the time in their pocket, although it’s usually known now as a phone rather than a calculator. So what do you say to schoolchildren now?

Unfortunately, at least for mental arithmetic, there isn’t really anything that’s going to convince schoolchildren now of the use of mental arithmetic. Some will happily learn mental arithmetic but the vast majority won’t. That’s not to say that being able to do mental arithmetic isn’t useful, it’s just not as obvious how it’s useful. Considering how little time is spent on mental arithmetic in schools and the little mental arithmetic abilities that many students have now it certainly seems that teachers have just about given up on this one.

Maybe they’re right. Maybe there is no need for mental arithmetic. Pocket calculators are faster than humans, more efficient, less prone to error – why bother learning the times tables? Isn’t it just a complete waste of time? Well…yes and no.

When you consider how abundant electronic calculators are in the modern day then mental arithmetic really is mostly a waste of time for doing calculations. With a calculator it’s a cinch to multiply huge numbers together; I can tap into a calculator a list of numbers and it will do all kinds of statistical analysis for me on those numbers – whereas once upon a time it would have taken a good five minutes to manually calculate the variance of a list of numbers, now my calculator does it in less than a second. Why should anyone even bother trying to compete with that? Maybe at some time in past decades computers (of the human kind) were important – people who could do calculations quickly were essential before pocket calculators came along. I don’t know whether being a ‘calculator’ was a particularly lucrative job to have but it was a job. Which company or organisation would be crazy enough to employ someone to sit there doing manual calculations nowadays?

However, letting an electronic calculator do the work for you all the time has some downsides. Just like using a car to always get you from A to B is far easier and quicker than walking or running, you end up getting lazy and out of shape (at least physically). Similarly, using an electronic calculator all the time means that you get lazy and out of shape (at least mentally). I come across many maths students right up to A Level who struggle with mental arithmetic – and it shows. It’s not because they’re incapable it’s just that they’ve never been discouraged from using a calculator – it saved classroom time in the past but now it comes and bites them on the backside.

As it turns out – not being able to do simple mental arithmetic such as addition and subtraction of two-digit numbers and not knowing your times tables means that you lack, to a certain degree, understanding of how numbers work so you don’t have any real idea how to start extending those ideas to algebraic problems where an electronic calculator might not be able to help (though, you can buy calculators that deal with algebra now but they’re a bit more pricey).You also end up using all of your energies trying to figure out really simple things like 12×15 in the middle of a complex algebraic problem and then you don’t have any energy left to do the more complicated parts of a problem; the result is a very bumpy stop-start, stop-start solution to a problem which can be compared to driving a car and slamming on the brakes every fifty yards – you might get where you want to be but with much more wasted effort.

I don’t think it’s necessary to be able to do huge mental calculations; there are people around today who can carry out huge mental calculations. They do it either because it’s something that they can just do or because mental arithmetic is something that they enjoy doing and have spent many hours learning how numbers work in great detail. However, I can’t see that mental arithmetic will be making a comeback in the classroom any time soon – I think that maths students are impoverished because of it’s absence and lack of mental arithmetic skills makes their lives more difficult further down the line if they decide to go on to do higher level maths; but even if they don’t want to do higher level maths they will still lack the confidence of dealing with numbers in a world where numbers and statistics are everywhere you look. Sadly, I think that mental arithmetic is a dead skill.