Alex's Adventures in Numberland - Alex Bellos [15]
65 24
Easy, it’s 65. Almost all of us will get the correct answer in less than half a second. If you have dyscalculia, however, it can take up to three seconds. The nature of the condition varies from person to person, but those diagnosed with it often have problems in correlating the symbol for a number, say 5, with the number of objects the symbol represents. They also find it hard to count. Dyscalculia does not mean you cannot count, but suffereEasd to lack basic intuitions about number and instead rely on alternative strategies to cope with numbers in everyday life, for instance by using their fingers more. Severe dyscalculics can barely read the time.
If you were smart in all your subjects at school but failed ever to pass an exam in maths, you may well be dyscalculic. (Although if you always failed at maths, you are probably not reading this book.) The condition is thought to be a principal cause of low numeracy. Understanding dyscalculia has a social urgency, since adults with low numeracy are much more likely to be unemployed or depressed than their peers. Yet dyscalculia is little understood. It can be thought of as the number version of dyslexia; the conditions are comparable in that they both affect roughly the same proportion of the population and they appear to have no bearing on overall intelligence. However, a lot more is known about dyslexia than about dyscalculia. It is estimated, in fact, that academic papers on dyslexia outnumber those on dyscalculia by about ten to one. Among the reasons why dyscalculia research is so far behind is that there are many other reasons why one might be bad at maths – the subject is often taught badly at school, and it is easy to fall behind if you miss lessons when crucial concepts are introduced. There is also less of a social taboo around being rubbish with numbers than there is around being rubbish at reading.
Brian Butterworth frequently writes references for people he has tested for dyscalculia, explaining to prospective employers that the failure to achieve school maths qualifications is not due to laziness or lack of intelligence. Dyscalculics can be high achievers in all other areas beyond numbers. It is even possible, says Butterworth, to be dyscalculic and very good at maths. There are several branches of mathematics, such as logic and geometry, that prioritize deductive reasoning or spatial awareness rather than dexterity with numbers or equations. Usually, however, dyscalculics are not at all good at maths.
Much of the research into dyscalculia is behavioural, such as the screening of tens of thousands of schoolchildren by giving them tests on a computer in which they must say which of two numbers is the biggest. Some is neurological, in which magnetic resonance scans of dyscalculic and non-dyscalculic brains are studied to see how their circuitry differs. In cognitive science, advances in understanding a mental faculty often come from studying cases where the faculty is faulty. Gradually, a clearer picture is emerging of what dyscalculia is – and of how the number sense works in the brain.
Neuroscience, in fact, is providing some of the most exciting new discoveries in the field of numerical cognition. It is now possible to see what happens to individual neurons in a monkey’s brain when that monkey thinks of a precise number of dots.
Andreas Nieder at the University of Tübingen in southern Germany trained rhesus macaques to think of a number. He did this by showing them one set of dots on a computer, then, after a one-second interval, showing another set of dots. The monkeys were taught that if the second set was equal to the first set, then pressing a lever would earn them a reward of a sip of apple juice. If the second set was not equal to the first, then there was no apple juice. After about a year, the monkeys learned to press the lever only when the number of dots on the first and second screens was equal. Nieder and his colleagues reasoned that during the one-second interval between screens the monkeys were thinking