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.
Professor, Student Study Children's Ability to Count
“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
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
“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,”
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
“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
www.wesleyan.edu/cdl, call 860-685-3588, or email
By David Pesci, director of Media Relations.
Photo by Olivia Bartlett, The Wesleyan Connection