Three months on, Christopher seems to be faring better at the number-line game, going so quickly that Babtie asks him to slow down and explain his reasoning for each move. Babtie says that dyscalculic children tend to learn much more quickly when they talk through what they do. She also believes that Christopher's maths anxiety, a near-universal trait of child and adult dyscalculics, is fading.
He moves on to a Tetris-like game called Numberbonds, in which bars of different lengths fall down the screen, and he is asked to select a block of the correct size to fill out a row. This emphasizes spatial relationships, which some dyscalculics also struggle with. The blocks move too quickly at first, frustrating Christopher, but he soon gets the hang of it, and when Babtie suggests he stop for the day, he begs for ten more minutes.
The Number Sense games, including a snazzy-looking iPhone version of Numberbonds, are intended to nurture the abilities that, Butterworth contends, are the root of numerical cognition and the core deficit of dyscalculia — manipulating precise quantities. In a game called Dots to Track, for example, children must ascribe an Arabic numeral to a pattern of dots, similar to those on dice. When they enter the wrong value — and they often do — the game asks the children to add or remove dots to achieve the correct answer.
As the summer holidays approach, Babtie is worried that Christopher and the other students she has been working with won't practice the games at home, returning in the autumn the worse for it. But in early October when school is back, Christopher announces that he will challenge himself with a number line that stretches from 950 to 9,000, “if you'll allow me”, he adds. At first he flounders, but quickly starts to understand the game and locates a string of four-digit numbers, beaming with each correct response.
Other students are improving more slowly, but it is not easy to say why. Dyslexia, attention deficit hyperactivity disorder and autism spectrum disorder are common among dyscalculics, and it can be difficult to untangle these problems, says Babtie. The nine-year-old who counted on his fingers nine months ago can now deal with numbers below 6, but still struggles to distinguish 9 from 10. Yet with the right practice and attention from teachers and parents, dyscalculic children can thrive, says Babtie, who emphasizes that computer games are a supplement, not a replacement, for one-on-one tutoring.
Butterworth knows that it will take a controlled evaluation of Number Sense before he can say if the game genuinely improves numeracy in dyscalculic children. Small studies of other computer-based interventions hint that they might help. Dehaene reported in 2009 that Number Race, a game his group developed, modestly improved the ability of 15 dyscalculic kindergarten children to discern the larger of two numbers, but that it had no effect on their arithmetic or counting. Meanwhile, a Swiss team reported in 2011 that a game that involves placing a spaceship on a number line helped eight- to ten-year-old dyscalculics with arithmetic. The researchers also studied the children in an fMRI scanner during a task that involved arranging numbers. They found that one month after training, the children showed increased activation in the intraparietal sulcus and reduced neural activation elsewhere in the parietal lobes — a hint that their improvements in arithmetic were related to changes involving brain areas that respond to number.
Butterworth hopes to monitor the brains of students such as Christopher as they practice Number Sense, to see if their parietal lobes are indeed changing. But he has been turned down by every funding source he has applied to. Although dyscalculia, like other learning disabilities, takes a toll on productivity (one report estimated that low numeracy costs the United Kingdom £2.4 billion (US$4 billion) per year, mostly in lost wages) it doesn't attract much attention or money. In the United States, for example, the National Institutes of Health spent $2 million studying dyscalculia between 2000 and 2011, compared with more than $107 million on dyslexia.