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Let's hear it for Arithmeticians

Arithmetic is an undervalued skill

ARITHMETICIAN.  That's not a word you hear very often.

In past centuries it was a much more familiar word.  Here's a line from Shakespeare's Othello:

Forsooth, a great arithmetician, one Michael Cassio*, a Florentine.

Shakespeare never used the word mathematician in any of his plays, though in Tudor times the two words were often used interchangeably, just as 'maths' and 'arithmetic' are today - much to the annoyance of many mathematicians.

Definitions of arithmetician vary, but typically it means somebody who is extremely competent at doing calculations without the aid of a calculator.  A good arithmetician can work out in their head what 4/7 is as a percentage; can multiply 43 x 29 to get the exact answer; and can quickly figure out that in a limited overs cricket match, if England require 174 runs in 31 overs they'll need to score at a bit more than five-and-a-half runs per over.

Arithmeticians and mathematicians are not the same thing.  Many good arithmeticians - such as the guy who recently fitted my new boiler - know little about algebra, geometry or proof.  And many top mathematicians are hopeless at arithmetic.

I recently asked the Head of Maths at an independent school how many of his Maths A Level students are good arithmeticians.  "About 10% of them" he said.  I asked if he thought that was a problem.  "Yes it is," he said, "because it means they are missing a key mathematical life skill."

I agree with him.

A couple of years ago, a friend who runs an engineering company was talking with some final year engineering undergraduates about a design problem he was working on.  "And we have this pipe that has a cross-sectional area of 4 square metres," he said, "and the water is flowing through at about 6 or 7 metres per second, so how much water is flowing through the pipe?"  To his dismay, all of the students took out their calculators.

What's shocking is that many children are extremely good at arithmetic when they leave primary school, but by the time they leave secondary they have lost the knack.  They aren't helped by the fact that A level papers almost all now allow a calculator, so there's little incentive for 17-18 year olds to practise mental maths.

Yes, we do all have calculators these days.  We don't all need to be able to divide 174 by 31 and get the answer right to one decimal place.  But if you DO have this skill, then you have the ability to quickly evaluate information "in real time", which will give you valuable insights during business meetings, when shopping, when listening to politicians and so on.

You will hear lots of people saying that this country needs more mathematicians, and they are right.  But you won't hear many people saying that we also need more arithmeticians.  Yet if you think about a new employee starting almost any professional job (electrician, solicitor, accountant, estate agent etc etc), and ask which skill is likely to benefit them more, algebra or arithmetic, it's a no-brainer.

So let me say what others aren't saying.  This country needs more Arithmeticians.


* Cassio's family later went on to develop calculating machines that became popular in schools across Europe. At least that's what my friend Andy Murphy told me.