How One's 'Number Sense' Helps With Mathematics

"That was very surprising to us," Halberda said. "The assumption was any variation wasn't going to be that large. This is very old cognitive machinery, so it was surprising there is such wide variation."

The researchers then examined whether there was any relationship to how well the students did in math class. They were surprised again.

"To me, it's mind-blowing," Halberda said. "While both abilities deal with numbers, they deal with numbers in two very different ways. Before this, all indications were they were separate systems."

The findings illustrate once again how many fundamental characteristics humans share with other species, Halberda said.

"We think of mathematics as the pinnacle achievement of humankind. It's something different and special that only humans have. We use mathematics to send a man to the moon. The idea that it relates in any way to what happens when a rat is looking for food is very surprising. It's moving to see a connection between ourselves and a human infant and another animal."

Moreover, the researchers found, the relationship between number sense and math ability appears to be independent of other factors that typically play a role in higher cognitive functions, including IQ, working memory, visual-spatial skills and verbal ability.

"Our data suggests there is a very specific relationship between the approximate number system and formal mathematics that is not dependent on any other ability," Halberda said.

Stanislas Dehaene, a French neuroscientist who has pioneered research in the field, praised the new work in an e-mail as a "beautiful demonstration" of the link to higher mathematical ability.

"We long suspected that symbolic mathematics was linked to the sense of numerosity or 'numerousness' of sets of concrete objects," wrote Dehaene, noting that while the cause-and-effect relationship between number sense and math remains to be proved, his team has unpublished data suggesting that some children are born with a deficit in this ability. "Again, however, longitudinal studies would be needed to establish a genuine causality."

If it does, the work could lead to ways to identify students who may have trouble with math, Halberda and others said.

"We could pick up early on those kids who might be having difficulty and develop interventions that we think might work for them," McCardle said.

Halberda said he has already begun studying whether testing a child's number sense at age 3 predicts his performance in math class, whether there may be a way to boost a child's number sense, and whether doing so might help him learn math.

"It's an exciting possibility," he said.