Calculators are NOT the enemy

In December I wrote a post entitled “Why calculators should be banned.” It caused a bit of a stir and opened a wider discussion, which was great. Colin Beveridge, (@icecolbeveridge) co-host of the great “Wrong, but useful”, (Which you can read a review of here) has been in touch and has written this guest post:

You could – if you were the benevolent dictator of the world – reduce the number of deaths on Britain’s roads to zero overnight, in one fell swoop, by simply abolishing the car.

Brilliant, effective solution, with many side benefits: no more car crime, much less pollution, no more traffic jams, fitter populace, probably a rejuvenation of town centres. It’s a fantastic idea.

Except, of course, if you want to get anywhere that’s not served by public transport, or need to get to the hospital in a hurry, or pick your kids up from the school disco. I would suggest that, if you were to implement such a policy, you wouldn’t be seen as a benevolent dictator for long.

The trouble is, making decisions to ban tools to eradicate problems often leads to losing the benefit of the tools. Cars may have many negative side-effects, but on the whole they’re a Good Thing for society. The biggest problem isn’t people using cars, it’s people using cars inappropriately: driving 300 metres to school, racing down the M1 flashing your lights at people you don’t think are driving fast enough, having a flag of St George stuck to the roof.

This article isn’t about cars. This article is about calculators.

There is a school of thought that would like to see a ban on calculators in the classroom, reasoning that they detract from students’ number skills. I can see their point of view: I sigh a scornful sigh when a student automatically reaches for the calculator when given a simple sum; the Mathematical Ninja is rather more violent in his responses.

It goes almost without saying that students need some manner of number sense – I once had a student who insisted that Mars was five centimetres away because his calculator said 5 – and I’m very keen on Rob Eastaway’s idea of ‘zequals’ – effectively doing all of your sums to one significant figure before you get the calculator involved – just so you have an idea of whether your number is correct. There is also a calculator on the market (the QAMA: http://qamacalculator.com/ ) that won’t give you an answer unless you give it an acceptable estimate first – which looks like a terrific tool that even the Mathematical Ninja would allow in his classroom.

Reluctantly.

Like with the car, the problem is not with the use of calculators, but in using them when they don’t need to be used – or using them wrongly. (To extend the analogy, some students use the calculator in way that’s like using a car as a sofa.)  I would argue, all the same, that the calculator can – and should – be used as a tool to extend the boundaries of what topics are available to students to learn.

It’s only a fairly recent invention – calculators have only been commercially available since the 1970s or so; before that, students of maths relied on slide rules and books full of lists of the values of trigonometric functions, logarithms, and so on. If you wanted to know the value of a complicated expression, you’d be in for a long, hard, and probably inaccurate slog.

Why would you want a student to spend literally hours pounding away at something tedious – say a long list of four-digit multiplication sum – when a calculator can do it in the blink of an eye? Would you not rather they spend the time learning how to solve mathematical problems? Developing models that may need a calculator (or even a computer) to solve? Doing the things humans are better than machines at doing, and leaving the drudge work to our silicon slaves?

If we want to help students develop the skills they’ll need to succeed in jobs that can’t be automated away, we need to turn the calculator from an unnecessary crutch into something that makes difficult problems possible, and tedious problems quick. We should be encouraging students to use spreadsheets and explore what they can do. We should be getting them to write computer programs to avoid repetitive tasks. And we should be using computers to explore things like the Collatz Conjecture or the Twin Primes Problem to show that there are accessible, unsolved problems where a school student could conceivably spot something the brainiac professors had all missed.

Calculators are not the enemy, any more than cars are.

Colin is a Weymouth maths tutor, author of several Maths For Dummies books and A-level maths guides. He started Flying Colours Maths in 2008. He  has a PhD in mathematics and even has an equation named after him! He lives with an espresso pot and nothing to prove.