Let Me Count the Ways
Imagine that you’re in the grocery store, full cart in tow. It’s a busy Saturday night, and the checkout lanes are teeming with other customers. But each lane is slightly different—not only do they have different numbers of customers, but each customer’s cart has a different number of items. How do you know which lane to choose?
The answer, says Justin Halberda, an associate professor in the Department of Psychological and Brain Sciences, lies in your number sense—an intuitive understanding of quantities, how they relate to each other, and how they can change with various mathematical operations. It’s the sense that allows you to estimate how many items are in an individual customer’s cart, tells you whether one cart has more or fewer items than another, and tells you that because the lead cart’s items are being steadily laid on the checkout counter’s belt, that cart’s numbers are decreasing.
Halberda and his colleagues have discovered that this “number sense” is universal among cultures across the world and even different species. Studies have shown that humans, nonhuman primates, and even rats have the ability to compare quantities, even if they don’t have the language to tell you that there are five pieces of cheese in a pile.
Even though we all have number sense, when in the life span did we acquire it? And how will it change throughout our lives? Over the past several years, Halberda and his colleagues at Hopkins’ Laboratory for Child Development have taken on these questions, developing a timeline of when number sense starts and how it tracks with age.
Researchers have long known that babies get bored looking at the same thing. Consequently, Halberda and his colleagues tested whether babies could distinguish between numerical quantities by showing them different representations of the number 8, such as colored dots on a screen, and then switching it up by changing the number. Tests showed that babies as young as 4 months old looked longer when there were big differences between quantities—say, between 8 and 16—but didn’t register a change when quantities were closer, as between 8 and 12.
Until last year, the group’s research revealed that number sense sharpened at least until age 10—the oldest age that the researchers had been able to gather enough subjects to make findings statistically significant. Getting a large number of children and adults to come to the lab was challenging.
“Tracking cognitive abilities in general across the entire life span has been a nearly impossible challenge for scientists to overcome because you can’t get all those people to come into the lab,” Halberda explains. But he and his colleagues had an idea: Why not present their study over the Internet?
The researchers devised a web page where people could test their number sense with a simple game, choosing whether there were more blue or yellow dots on a page over several trials. In some trials, the difference was obvious, but in others, the numbers were much closer, making the relative quantities much harder to gauge.
Since posting their web page in 2011, the researchers have attracted more than 20,000 respondents, ranging in age from 11 to 85. Last year, they published data from 13,000 of these study participants. After crunching the numbers, the researchers discovered that number sense steadily improves until the age of 30. But while a lucky few keep excellent number sense until old age, the majority of us begin to decline.
Given the findings of Halberda and his colleagues linking good number sense to better formal math abilities, there’s good reason to try to strengthen and maintain number sense with age. One of his studies shows that number sense precision can be improved with practice. Right now, he and his colleagues are formulating ways to integrate that sort of practice into various school curricula.
“We’ve also begun to explore how to teach both teachers and students about the number sense, what it is, what it does for us, and how we can use it more effectively,” he says.