Dyscalculia: more than just a block

The door of a converted church in the back streets of Hammersmith opens slowly, and I find myself looking down at the upturned face of a shy, small girl. “Can you remember the guest’s name?” says Jane Emerson, the teacher standing by her side, and the child manages, very softly, to say my name, to great applause. Later, Emerson explains that the girl, who is seven, has a particularly poor memory, and that is one reason—of many—why children may struggle with numbers.

In the previous articles, Mark Feltham and David McConnell have argued that it should be possible greatly to improve someone’s facility at least with basic arithmetic, whether adult or child, despite what may have been an entrenched phobia of sums. But a small group of people appear to have difficulty in building up even a basic sense of what numbers are, to an altogether different degree.

“Dyscalculia” is the awkward name given to this phenomenon. Recognition of it and techniques for handling it “are where dyslexia was 30 years ago,” says Emerson, who founded a specialist centre in 1991 to help primary school children tackle both conditions. It is an umbrella term, though, and while some studies estimate that 5 per cent of British primary school children suffer from it, roughly the same as dyslexia, others dispute the incidence. Neuroscience, as so often, has observed correlations between the condition and apparent differences in some children’s brains, but has not much precise yet to say about the nature or cause of these.

Researchers have observed, however, that the crucial ability to judge the quantity of objects differs even among babies of four or five months old. Many, if presented with a game of peekaboo, in which one toy is hidden and brought out repeatedly, will laugh or pay special attention if suddenly two are revealed. But a few infants appear to make no distinction. Babies who find it unusually hard to pay attention will absorb fewer of these early “lessons” in differences between numbers of things, says Emerson.

In an older child, problems may show up not just as difficulties in counting or doing sums, but as a lack of any sense of what we mean by numbers. Trying to tackle that takes you instantly to the heart of profound concepts we generally take for granted. Watching a young child struggle to understand what is meant by saying that eight is one more than seven can give you a sense of vertigo. You might not have thought, say, about your facility to know instantly that one plus two equals three, but for some people, that feels like a black hole. The symbols from 0 to 9 might seem to them to have no relation to physical objects, nor might it be clear they can be combined to make all possible numbers.

Problems show up in different ways, says Emerson. They might have difficulty in counting, which is, of course, a first necessary step. But they might well have mastered that, and then get stuck in the “counting trap,” as experts in the condition call it, approaching any sum by counting from one. Even if they knew that two plus two was four, they might approach a request for two plus three as an entirely new operation, not seeing that it was simply one more. They find it hard to see that a number is made up of other numbers, and can be combined with others, which is the start of mathematics. They find it very hard to work out which two numbers “make ten.”

“Place value”—the modern school jargon for the different values that a digit will have depending on whether it falls in the hundreds, tens or units column and so on—can present a further obstacle, and “teen” numbers between 12 and 20 present special problems. The English language doesn’t help, Emerson points out, because although 18 is written with the “teen” numeral first, and then the unit, we say it “eight-teen,” where French, for example, is more logical in naming it dix-huit. Some children count to 19 and then on to what they call “twenteen,” she says.

What can be done to help? The techniques for helping someone get a sense of what numbers mean are very visual, based on objects of graded sizes that can be put next to each other or stacked. Many ordinary classrooms move too quickly to abstract sums, Emerson suggests, where even children who do not struggle with numbers could do with more time handling physical shapes which represent quantity.

One exercise, to help explain the idea of the difference between two numbers, is to represent each by a series of flat glass pebbles in a line—say, one line of three and one of six. The bigger number will stretch out further, and the teacher can make the difference clearer by using another colour of pebbles for the difference—that is, the last three of the line of six, in the example above. One 11-year-old girl, who had been working in the mornings at Emerson House, confidently explained to me the technique, noting that “eleven is three more than eight.” On that point she was clearly right, but Emerson and I paused for a second before replying; on the table was one line which was indeed three pebbles longer than the other, but it was nine pebbles long, not eleven, as she had said. People with these kinds of difficulties find it particularly hard to judge the number of objects in front of them without counting, says Emerson, who is also the co-author of a book, The Dyscalculia Assessment.

Teachers do much work in grouping objects into the patterns on the faces of dice, to try to bring some easily recognisable form to the apparent jumbles of units. Parents can help by simple board games, such as snakes and ladders, which use dice and practice counting.

What progress is it reasonable to hope for from a primary school child who does get some systematic help with such difficulties? To cope with numbers in adult life, ideally, you would have mastered adding, subtracting, multiplying, dividing, fractions, decimals and percentages, says Emerson. Dyscalculic people have a tendency, if they have not reached some confidence in the techniques by adult life, to resort, say, to handing over notes rather than change to pay for things (and to find it hard to work out if they have been given the right change). But with sustained help, many should be able to master these basic manipulations of numbers, and many should be able to pass the GCSE in maths, she says.