By developing treatments for dyscalculia, Butterworth hoped to test competing theories about the cognitive basis of numeracy. If, as he believes, dyscalculia is at heart a deficiency of basic number sense and not of memory, attention or language, as others have proposed, then nurturing the roots of number sense should help dyscalculics such as Christopher. “It may be the case that what these kids need is just much more practice than the rest of us,” Butterworth says. Christopher's school is one of several in London working with the software, and students in Cuba, Singapore and elsewhere will also soon start using it.
Christopher starts with a game involving a number line — a spatial representation that scientists believe is key to number sense. “What is the number that is right in the middle between 200 and 800? Do you know it?” Babtie asks. Christopher shrugs. “Think of any number that is bigger than 200 and smaller than 800 and put it in this box. It could be 201,” she says. He enters 200, and Babtie reminds him that the number needs to be greater than 200. He selects 210, probably mistaking it for 201. A classic sign of dyscalculia is difficulty in grasping the place-value system, according to Babtie. “That will do fine,” she says. A soft computer voice tells Christopher to “find the number and click it”. The game involves zooming in and zooming out to rescale the number line, and Christopher talks through each move — a strategy that Babtie encourages — but it takes him more than a minute to locate 210. His classmates, meanwhile, are learning to multiply two-digit numbers.
Some children at Christopher's school have more profound numeracy problems. One nine-year-old classmate says that she doesn't know if 50 is greater or less than 100; another the same age confuses four dots for five and routinely tots up small sums on his fingers, a common strategy for dyscalculics.
“OK, time to stop. We'll do some more of this another day,” Babtie says to Christopher, after 20 frustrating minutes. It is clear he would rather be back in class than here in this room practicing a skill his classmates learned years ago.
How many are there?
Butterworth, now 69, straddles the academic and public spheres. A fellow of the British Academy, the United Kingdom's national body for the humanities and social sciences, he made his name probing obscure speech and language disorders and has appeared in the British media for many years. In a Sunday Times article in 1984, for example, Butterworth claimed that the speech patterns of former US president Ronald Reagan indicated Alzheimer's disease. Reagan was diagnosed with the condition a decade later.
In the late 1980s Butterworth studied a stroke patient who would change the course of his professional life. The woman, a 59-year-old former hotel manager from Italy, fared about average on verbal IQ tests and had a good memory, but when Butterworth's Italian colleagues asked her to count, she would start, “uno, due, tre, quattro,” and then stall. “Miei matematica finisce alle quattro” — my mathematics stops at four — the woman, known as CG, would tell them.
Neurologists had presented case studies of 'acalculic' patients such as CG from the early twentieth century onwards, if not before, but “people hadn't thought a lot about the specific brain areas involved in calculation”, says Butterworth. Brain scans of CG revealed a lesion in the parietal lobe, a part of the brain just above the ears. Later, Butterworth found another patient with the opposite pattern of disability: neurodegeneration had robbed him of speech, language and much of his knowledge, save for the ability to do intricate calculations. Butterworth grew more certain that numerical abilities relied on specialized brain networks, and not only on those supporting general intelligence, as many scientists believed at the time.
Genetics and the vagaries of brain development disrupted these networks in dyscalculics, Butterworth proposed. And Moorcraft was one of Butterworth's most revelatory subjects because of the great disparity in his abilities in different domains. Butterworth and his colleagues also tested 31 eight- and nine-year-old children who were near the bottom of their class in mathematics but did well enough in other subjects. Compared with normal children and those with dyslexia, the dyscalculic children struggled on almost every numerical task, yet were average on tests of reading comprehension, memory and IQ.