John Jamieson says that numeracy depends on daily practice of mental arithmetic.
Having reached what Ogden Nash has called the sixth age of man, I can look back on many humbling experiences. The morning I walked into Campbell Henry was one such. I had just left school at the age of 17 and, while waiting to see whether I would get into university, had taken up employment with this long-established firm of wholesale grocers in a part of Glasgow now called the Merchant City - it's odd that we didn't call it that when it was but now call it that when it isn't.
I was set to work adding invoices. There were a succession of sums like 8cwt of sugar at Pounds 5 0s 6Fd a ton. Having a facility for maths and arithmetic, the task wasn't difficult. It was what my schooling had prepared me for. Except for the final two years of secondary education, there had been daily drill and practice. But my drubbing came mid-morning. "Is that all you have done so far?" said the senior clerkess as she lifted the not insubstantial pile of completed invoices off my desk.
The rebuke had not been said with any intention of hurting, but out of surprise that this was all that someone who had just sat his Highers, about to go to university to do mathematics, could achieve. Graduates did not work in firms of wholesale grocers. My embarrassment deepened with the discovery of errors in my sums. If a catchphrase of the time - speed and accuracy - was associated with arithmetic, I may have passed the test at school, but not at Campbell Henry.
It was this salutary experience of my first morning at work coupled with the fact that I clearly got better at adding up invoices in the ensuing days that taught me that performance in arithmetic improves with practice. Some years later as a graduate scientist I was able to put this idea to the test when I routinely helped the meteorologists I worked alongside with their daily balloon flight. We picked up data transmitted by radio from airborne instruments at a rate of 30 messages a minute.
Essentially the exercise was arithmetic. We did our computations at a furious pace so as to keep up with the incoming signals. Whereas my companions always did their sums on hand-cranked calculators - it was the time before the electronic version - I did mine mentally. We made a race of it, and usually the mental operations won, both in speed and accuracy. Arithmetic indeed improves with practice.
The first hand-held electronic calculator, introduced by Hewlett-Packard in 1972 and costing Pounds 175, was fantastic. At a stroke it did away with the tedium of computations of up to eight significant figures of trigonometric functions. However, I did not personally benefit from this new technology. My contract of employment as a scientist came to an end and I took up physics teaching. A short while later the electronic calculator had become ubiquitous.
A generation later, I am no longer a classroom teacher, but do occasional tutoring to oblige friends and neighbours. What I find is that no young person can do basic arithmetic operations such as multiplication, division or handling factions. One Higher physics student could not use his calculator to multiply or divide by powers of 10. For instance, to obtain the quotient of 108 V 10-7 you subtract the indices taking -7 from 8, which gives 15. So the answer is 1015.
It's elementary by mental arithmetic, but because this boy was utterly dependent on his calculator he was unwilling to be taught how to do this calculation by his own wits. He was in fact incapable of working with numbers. There was really no point in teaching him the correct button-pressing sequence because he had no idea of ever knowing whether his answer was right. The calculator should be an aid to people who understand, not a substitute for understanding. It should be a pole for the vaulter, not a crutch for the lame.
The ostensible benefit of allowing children to work with calculators is that by removing the supposed tedium of arithmetic it provides more opportunity for higher level mental processes such as problem-solving and investigations. This fine thinking has simply not worked. Because of calculator dependence, children stop practising arithmetic and cease to be able to handle numbers. It would seem that their facility to multiply by mental reckoning, a skill which presumably every child is taught at primary school, is allowed to atrophy from lack of practice.
Throughout my days as student and teacher, the accepted value g in m s-2 was 10, which was convenient in mental arithmetic. Yet to make calculations more realistic, in the 1980s the exam board changed the accepted value to 9. 8 (it's back to 10 again, I think). It was a tacit acceptance that nearly everyone then used calculators. By the same act it reflected the fact that many pupils were not capable of multiplying or dividing by 10, which is one of the basic processes of numeracy.
The easy route is by the broad way and wide gate. Many follow it, but it doesn't lead anywhere, The other route is narrow, hard to follow, being overgrown with briars. But it is worth taking because it leads to life. The calculator should be forgotten. It is directly to blame for the young being incompetent at arithmetic. Once upon a time, most of the calculations that anyone needed to do could be carried out with the assistance of the digits on a pair of hands, But to understand the present age - from the smallness of the nucleus, to the vastness of the universe - orders of magnitude spanning many decades have to be comprehended. There has never been a greater need to be numerate, but we are failing to provide young people with this facility.
The Inspectorate's concerns about overuse of the calculator in schools have led to a proposal that its introduction should be "delayed until late primary or early secondary school". I disagree. It should be removed from all levels of school. Even the more complex calculations with trigonometric or other functions can be expeditiously solved by approximation and ready reckoning. The need to practise should continue through all stages of schooling. The supposed notion that arithmetic is tedious should be replaced by one that mental reckoning is cool.
Its complement is also worth bearing in mind - calculators produce numpties.
John Jamieson is senior associate of STS, national support services in science, technology and safety.