Clearly, many factors can affect math performance. Even though studies suggest that gender is not a big factor in determining number skills at an early age, girls remain underrepresented in higher-level math education, presumably due to social or cultural hurdles. Socioeconomic status can also play a role in how well children are prepared to learn math.
Yet beyond these external factors, and independent of overall intelligence and language skills, there appears to be a separate mental faculty for dealing with numbers that helps determine how well a child grasps math. Those with serious impairment to this faculty may account for the 5- to 7-per-cent of people who suffer from a condition called developmental dyscalculia, analogous to dyslexia in reading.
When it comes to the direct link between the brain and performance, the challenge for researchers is to pinpoint precisely which fundamental concepts are essential for children to be able to keep up in class. Just as many children with reading problems can be helped by the right teaching strategies at the right time, the hope is that those who struggle with numerical concepts can be similarly supported if identified soon enough.
Drawing from his own work, Prof. Geary says those fundamental concepts include a clear understanding of numbers and the quantities they represent, seeing how those quantities relate to one another, as on a number line, and being able to understand that larger numbers can be broken down into smaller ones, the way 7 can become 3 and 4, for example.
“We’re beginning to understand what kids need to know at the beginning of First Grade in order to be really ready to learn formal math,” he says.
Wired for numbers
The growing scientific interest in numerical ability is also motivated by a broader interest in how the human brain overlays a complex skill on top of what appears to be preexisting biological ability.
This idea that a rudimentary number sense is hardwired into our brains at birth has a long history, supported by decades of work with animals, and by some unusual instances of brain damage in humans.
In the 1990s, Stanislas Dehaene, a neuroscientist based at College de France in Paris and a pioneer in the study of numerical ability, documented a subject he dubbed the “Approximate Man.” The patient had lost much of his mathematical reasoning ability, among other cognitive skills, as the result of ruptured blood vessels in his brain.
Curiously, though, he was still able to approximate quantities. He could estimate that a year was about 350 days long and that a quarter of an hour lasted about 10 minutes. It was the exactness of calculation that eluded him. His case seems to suggest that humans possess an underlying ability to deal with quantity in an approximate form, just as animals have been shown to, and that this innate ability can still be glimpsed when higher order skills are cut off.
The question for researchers today is whether this innate sense, known as non-symbolic number processing, is relevant to the acquisition of more formal math skills. A study published this week by Elizabeth Brannon, a cognitive neuroscientist at Duke University, suggest there is a connection.
Prof. Brannon and her team had a group of six-month-old infants watch and react to a stream of changing dot patterns, noting how readily they spotted changes in the number of dots, in contrast to changes in dot size and arrangement. “There’s a lot of variability,” Prof. Brannon says. “Some babies show a really strong effect and some babies don’t seem to notice at all.”
Three years later, the same children, now preschoolers, were given standardized tests to probe their math ability. Those who were better at discriminating a change in the number of dots when they were babies also tended to score higher at age three-and-a-half.
“The possibility is that infants with good approximate number sense are finding it easier [three years later] to map number symbols onto these pre-verbal number concepts,” says Prof. Brannon.
Nevertheless, the role of non-symbolic number processing has lately become a subject of scientific debate.