Professor, Student Study Children’s Ability to Count

In back, Hilary Barth, assistant professor of psychology, works with her student, Ariel Ballinger ’07, on data resulting from a study on children’s counting ability.
Posted 12/20/06
“So many people have had one of those moments, when a check comes after dinner and they’re having a problem adding it up, and they stop and say, ‘I’m just not any good at math!” says Hilary Barth, assistant professor of psychology. “But they are. We all are. We’re born with it.”

This isn’t just an opinion from an overly-optimistic academic. Barth is one of a growing number of researchers studying intuitive understanding of numbers. So far, they’ve established that human beings and even many other species are born with impressive mathematical abilities.

“Studies have shown that animals who have no language can think about quantities approximately – for example, rats can be trained to press a key about 40 times. And babies, who haven’t learned a language yet, can tell that adding 5 toys and 5 more toys gives you about 10 toys,” Barth says. “But animals and babies can’t count. Counting takes language.”

And counting isn’t as simple as you might think. Preschool children quickly learn to count to 10, but it takes them a while to figure out the purpose of counting.

“If I asked a child who has recently learned to count to 10 to go to the toy box and get four dinosaurs, the child will probably just give me a handful,” Barth says.

Most children learn the concept of “one” soon after learning to count. Typically, about six months after that, they comprehend the idea of “two” and about six months later they understand “three.”

“Studies have established that once children understand the concept of three it usually clicks for all the other numbers,” Barth says.

So, counting may be tougher than parents realize. But arithmetic, on the other hand, may be easier than you think! Barth confirmed this with a study published in 2005 based on work completed at Harvard University.

The study, titled “Abstract number and arithmetic in preschool children,” published in an issue of the Proceedings of the National Academy of Sciences, showed that preschoolers can add big sets approximately long before they learn how to add big numbers exactly in school.

In the study, Barth showed pre-school children graphics with blue colored dots, covered them for a few moments, then showed them an array of a similar number of red dots. Then Barth asked the children which set – blue or red – had more dots. She also showed them two successive arrays of dots and asked them if the aggregate number was larger or smaller than a third array of dots. In another permutation, the dots were replaced by sounds, to make sure children weren’t just using visual imagery to solve the problem.

“The children were consistently able to recognize the differences between the dot sets, even in the tasks that included adding the dots,” Barth says. “The sets were too big for these kids to count, yet they had no problems recognizing which sets, when combined, would be larger than the third set. And we didn’t find any differences in gender: girls were just as adept at this as boys.”

One of Barth’s students, Ariel Ballinger ’07, designed a separate study based on Barth’s work thanks to a Fellowship from the Hughes Program in the Life Sciences. The fellowship provides a stipend so students can undertake full-time research during the summer.

“There’s no way I could’ve done a study like this without help from the Hughes Program,” Ballinger says.

Her study, titled “Counting, Estimation and Approximate Nonverbal Addition in Young Children,” is a new examination of number approximation in children who’ve reached different levels of verbal counting ability.

“Some previous studies done by Jennifer Lipton and Elizabeth Spelke at Harvard showed that a child’s ability to estimate numbers is related to verbal counting range,” Ballinger says. “Children were shown pictures containing different numbers of dots and asked to quickly guess how many there were, without counting. These studies showed that kids who could count to 100 guessed pretty well. But kids who could only count to 30, for example, could only guess well for sets of up to 30 dots. For bigger sets, they had no idea – they didn’t even give bigger estimates for 100 dots than for 40 dots.”

“But these studies often averaged the performance of large groups of children with very different levels of counting skill. I wanted to test this relationship by looking at more specific groups.”

Ballinger divided her children into three groups based on counting ability. She found that although counting ability was related to the accuracy of the guesses, even children who could only count to 30 guessed bigger numbers for bigger sets of dots.

“This went against the previous findings,” Barth says. “Children do seem to understand the rough meanings of big number words like 80 or 90 even before they can count that high.”

Ballinger’s study has been accepted for a presentation at a professional meeting. She will present her research at the annual meeting of the Society for Research in Child Development, held in Boston in March. Barth will present another research project completed with Ballinger and AnjaLi Carrasco ‘07, Rachel Jacobson ‘08, and Jessica Tsai ‘07.

“It’s great to be at a place like Wesleyan where undergrads can get involved with ongoing faculty research,” Ballinger says.

Ballinger will continue to work with Barth in the next semester gathering more data for her thesis.

Barth has been working with local children – who are rewarded with stickers and prizes for participating, and their parents are compensated for travel expenses – and has recently entered into an arrangement with some local schools.

“We assure parents that we aren’t ‘testing’ the children to see how good they are at math, but rather, finding out how kids in general think about numbers,” Barth says. “There are educational implications as well. “Understanding these abilities better will help us figure out the most effective ways to teach kids.”

Barth’s Cognitive Development Lab is always looking for new participants. Interested people may visit the lab Web site at, call 860-685-3588, or email

By David Pesci, director of Media Relations. Photo by Olivia Drake, The Wesleyan Connection editor