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Symposium; Maths

Thursday stream 2 Session 11.35 - 12.50 Length 50 minutes

Dyslexia and problems with mathematics

Brian Butterworth

Institute of Cognitive Neuroscience and Department of Psychology, London ucjtsbb@ucl.ac.uk

Abstract

Difficulties with numbers and mathematics are far more likely to occur with dyslexics than with general population. There are three reasons why this may be so. 1. Dyslexia is going to affect all kinds of learning that depend on reading, including maths. 2. The dyslexia genotype includes deficits that could have a bearing on maths learning, such as working memory difficulties. In these two cases, dyscalculia would be secondary to other cognitive difficulties. 3. Although numerical abilities are independent of reading, and language skills more generally, people with the dyslexia genotype are more at risk of primary dyscalculia. I review the currently available evidence. New tests of primary dyscalculia are suggested.

Many children who have difficulties learning to read also have problems learning arithmetic. Some studies estimate that half of all poor readers (including dyslexics) are poor at arithmetic. It is worth pointing out, that the other side of this story is that half poor readers are good at arithmetic. One famous example of the other half is a distinguished mathematician here at UCL whose handicap is so severe that he needed someone to read his final exam papers to him. Even today, he cannot read the newspaper, or use notes for his lectures (beyond the formulae)!

The exact proportion of dyslexic children who are bad at maths is far from clear. It depends on definitions - of course. Is the child really dyslexic, or just late learning to read? And we all know that there are many reasons for being bad at sums: inappropriate teaching methods not least of them.

Nevertheless, whatever definitions are used, there is far higher proportion of bad arithmetic among dyslexics, than among matched controls. One large-scale study of children in Lancashire, found that 37% of "reading disabled" children were also "arithmetic disabled". Why should this be? The short answer is that we don't know. But we are trying to find out.

There are several possibilities. First and most obvious is that the child struggling to understand written words, is going to struggle to understand books about mathematics. A second possibility is that some of the dyslexic's other cognitive differences may have an impact on learning arithmetic. Sequencing difficulties may affect learning to count. Reduced short-term memory span could make mental arithmetic more difficult. Difficulties with spoken words could slow the learning of specialised mathematical vocabulary. This could also slow learning the kind of arithmetical facts that are learned "by heart", such as multiplication tables. It could also affect how well "word problems" are understood (e.g. It takes five people six days to dig one 50 metre ditch ….).

If the child has visual or spatial problems, this could affect aspects of written arithmetic where position is crucial. This would include learning the place value system of the numerals, and setting numerals in columns as part of a long sum or multiplication. Children who confuse b and d, or b and q. and get the order of letters wrong may show similar problems with numerals - confusing 6 and 9 for example. Of course, some dyslexic children are very good visualisers and they may show no problems in this area at all.

Maths, more than any other school subject, is vulnerable to falling behind. Once this happens, there is a real risk that the child will try to avoid doing maths because it's frustrating and embarrassing, and so will fall further behind. leading to more avoidance. A vicious circle of underachievement.

It should be pointed out that there are children who are arithmetic disabled with no reading problems, and indeed with good cognitive abilities in other areas. The Lancashire study suggested that these make up nearly 4% of the population - about one in every classroom, somewhat fewer than dyslexics, but a sizeable educational issue nonetheless. The children probably fall into the category of "dyscalculics" - a specific learning difficulty for maths. This is a condition with which a child is born. Dyscalculic learners may have difficulty understanding simple number concepts, lack an intuitive grasp of numbers and have problems learning number facts and procedures. Even if they produce a correct answer or use a correct method, they may do so mechanically and without confidence. Very little is known about the prevalence of dyscalculia, its causes, or treatment. Most dyscalculic learners will have cognitive and language abilities in the normal range, and may excel in non-mathematical subjects.

Sometimes slowness to learn arithmetic is taken as a sign of dyslexia. And, although there is an overlap of symptoms in many children, this is not helpful, since dyslexics need not be dyscalculic and dyscalculics need not be dyslexic.

Public recognition of dyscalculia as a specific learning deficit is patchy. Most teachers and educational psychologists have only the sketchiest idea that such a condition exists.. We are in the position dyslexia was in twenty years ago, with many people denying its existence. As you can imagine, many children are being classified by their teachers, by their parents, and even by themselves, as stupid, when in fact they have specific learning deficit that needs special treatment. Unfortunately, the National Numeracy Strategy, with its stress on whole class methods, doesn't help. "Pupils are expected to play an active part by answering questions …. and explaining their methods to the class" (p11). Asking a dyscalculic child to answer maths questions in public will inevitably lead to embarrassment and frustration, and probably to anxiety and avoidance. The BDA and its friends are beginning to persuade national and local government agencies to be more sensitive to this problem and to make special provision for these children, just as they now make special provision for children with reading problems.

Brian Butterworth is Professor of Cognitive Neuropsychology at University College London, and author of "The Mathematical Brain" published by Macmillan in 1999.