# Math For Babies

Doing math is thought to be a uniquely human skill. We can learn the abstract concept of a number: two things or three things or four things; we can represent that concept symbolically (2, 3, 4); and we can use those symbols to understand more complex abstractions (2*3^4).

We’re not born with these abilities, but we do seem to be born with a general sense of number. A few years ago, researchers played newborn infants — as young as seven hours! — recordings of spoken syllables repeated a fixed number of times. In one trial, babies would hear “tuuuuu” four times, for example, whereas in another they’d hear “tu” twelve times. At the same time, the babies were shown pictures of geometric shapes, such as four squares or twelve circles. Somewhat amazingly (at this age, after all, they’re basically blind, sucking potato sacks), the babies matched the number of sounds they heard with the number of shapes they saw. On the trials where they had heard four syllables, they would look longer at pictures of four shapes, and on those with 12 syllables, they’d look longer at pictures of 12 shapes.

Those findings suggested that people have an innate sense of number — or, as cognitive scientists call it, an “approximate number system,” or ANS. Many researchers have argued that the ANS serves as a foundation for learning how to count and do more complicated math later on. That idea makes intuitive sense, but it has been challenging to prove because so many things influence math skills, including general intelligence, language ability, and educational experiences.

“Because children learn number words and symbols so early, it was always hard to say whether symbolic number knowledge was influencing ANS precision or vice-versa,” notes Gavin Price, a cognitive neuroscientist at Vanderbilt University.

That tricky issue is clearer now, experts say, thanks to a study out yesterday in the Proceedings of the National Academy of Sciences. The researchers found that the better a baby’s number sense at 6 months old, the stronger her mathematical abilities three years later. What’s more, the relationship held after controlling for general intelligence. “It’s a huge contribution to the literature,” says Price, who was not involved in the work.

The study hinges on a method in which researchers track babies’ eye movements as they watch two video screens at the same time. One screen always shows the same number of dots, but the dots change in size and location. The other screen shows the same thing, except that the number of dots changes as well. Here’s a short video of one of the trials; the screen on the right always shows 10 dots whereas the one on the left toggles between 10 and 20 dots (warning: utterly adorable baby coming):

Babies like novelty. In an earlier study using this method, the researchers showed that 6-month-old babies tend to look longer at the screen in which the number of dots changes (the left side of the video above) than the other screen, presumably because they notice the difference in the number of dots and like watching it change. “In the video, you can see the baby at the beginning really testing it out, looking back and forth at both of the screens to figure out what’s going on. Then he hones in on the one that’s changing,” says Ariel Starr, a graduate student in Elizabeth Brannon’s lab at Duke University, who carried out the new work.

Three years after the babies watched the videos, Starr’s team brought 48 of them back in the lab for a series of tests measuring their math skills (including their ability to count, identify numbers, compare the size of numbers, and do basic calculations) and general verbal and non-verbal intelligence. Babies who had strongly preferred to look at the changing number of dots at 6 months tended to have higher math scores at 3 years than did babies who had a weaker number sense. That was true even after the researchers corrected for intelligence scores.

“To me this is interesting because it suggests that this pre-verbal, primitive, quantitative ability seems to be foundational for acquiring more uniquely human symbolic math capabilities,” Starr says. “It really seems to be a building block.”

Still, she adds, the correlation was modest: “I can’t tell you what your baby’s SAT scores are going to be.” It’s also clear from past work that other cognitive skills, notably working memory and attention, influence math ability. How our early sense of number may interact with those abilities across development is still a mystery.

The connection between early number sense and later math skill seems to be strongest for infants that have either extremely high or extremely low scores in the dot test, notes Daniel Hyde, assistant professor of psychology at the University of Illinois at Urbana Champaign. “This method may be best suited for identifying early propensities to excel or struggle in math class and less predictive for those that fall in the middle.”

More provocatively, the study also suggests that boosting babies’ number sense could influence their math development, Hyde says. In line with that idea, this past weekend, at the meeting of the Cognitive Development Society in Memphis, Brannon’s group reported that training first and second graders on non-symbolic approximation tasks ups their scores on symbolic arithmetic tests. “This might be a way to help boost numerical competence in young children who are struggling at math, or even preschool children before they have a chance to fall behind,” Starr says.