Can infants count? Some researchers say yes

By Beth Azar
Monitor staff

Parents cheer when their 2-and-a-half year old begins reciting a string of number words in some semblance of counting. But do those first struggled proclamations of "one, two, three" indicate the child's understanding of numbers, or merely a parroting of words?

A whole branch of cognitive psychology has sprung up around that question. And over the past decade, a large and vocal group of researchers have held the belief that some aspects of a child's "number sense" are innate--hard-wired into the human brain.

Infants, they contend, can tell if they're looking at one, two or three objects and can base their judgment on the number of items, not on the size, shape or mass of the objects. For higher numbers, infants can see that one group of objects has fewer discrete members than another group.

But over the past several years another cadre of researchers has risen to challenge the assertions that infants know their numbers. They believe the studies that support an innate number sense suffer from a basic flaw: Instead of measuring number competency, they're gauging infants' remarkable ability to sense changes in what they see and hear.

It may be that, instead of measuring infants' ability to notice the number of objects they see, studies have been measuring their ability to register a change in the general amount of object they're seeing, say researchers, including Indiana University's Kelly Mix, PhD.

Others land in the middle. It may be that infants use many skills to process a scene, including number and overall "amount."

"There are a lot of studies that have to be done before we can nail down one account of what infants are doing," says Rochel Gelman, PhD, of the University of California, Los Angeles.

"The situation is confused," agrees Stanislas Dehaene, PhD, a research affiliate at the Institute de la Santé et de la Recherche Médicale in Paris.

No single study proves that infants can tell the difference between discrete numbers of items. But, he contends, taking the research as a whole--including studies of visual as well as auditory stimuli--supports the idea that infants have some general understanding of number.

Knowing their numbers?

All researchers agree that studying infants' understanding of simple numbers is anything but easy. The standard approach uses a habituation paradigm, a technique that takes advantage of the fact that babies tend to look longer at new or surprising visual stimuli.

To test a hypothesis, researchers show infants the same visual stimulus--say, a Mickey Mouse doll--over and over until they get bored and stop paying attention to it. Then they show the babies something new--maybe Donald Duck--and see if babies look longer, indicating that they recognize the difference between Mickey and Donald.

The trick for number researchers is to design stimuli so that the only thing different between the habituation stimuli and the test stimuli is the number of objects the babies see. For example, a researcher might habituate a baby to pictures of two random items--a car and a glass, then an apple and a telephone--in varying shapes, sizes, colors and positions so that the only aspect of the visual scene that stays the same is the number of items.

Over the years, hundreds of studies have found that after infants habituate to, say, two objects, they look longer if they then see three objects than if they again see two objects. Many researchers interpret the findings to mean that infants understand discrete numbers, at least up to three or four.

"It's hard to ignore the findings," says UCLA's Gelman. "It's been done in too many different ways in too many different labs."

Or just amounts?

Indiana University's Mix disagrees. Infants' abilities "could be inexact and have nothing to do with number," she says.

Indeed, she has a new study in press in Psychological Science that calls into question much of the work that's come before it.

"What everyone has thought for a long time may be untrue," she says.

Mix's study, co-authored with graduate student Melissa Clearfield, finds that instead of a change in number, infants may be responding to a change in contour length--the "amount" of a material visible. Although many studies have systematically controlled the objects that the infants habituate to, none have systematically controlled for the size of the objects, says Mix.

"When you add a third duck to two ducks, you're adding a proportionally greater amount of duck," explains Mix. "To test whether infants use number instead of amount of duck, you would have to make the two ducks big enough so that they have the same overall amount as three small ducks. No one has controlled for that."

She and Clearfield did. They habituated infants to two squares. Then they showed them three small squares equivalent in contour length to the first two squares. Or they showed them two big squares that were equivalent in contour length to three squares the size of the original squares. Instead of looking longer at the three small squares, the babies looked longer at the two big squares. This finding implies that the babies were more focused on the overall amount of square than on the number of objects.

"The conservative interpretation is that infants prefer to use contour length over number, but if you push them far enough you might be able to get them to use number," says Mix. "The more radical interpretation is that in all the other habituation studies, the infants were really attending to contour length rather than number." At best, infants have an awareness of quantity and are sensitive to the fact that one quantity is different from another, Mix argues.

Maybe both

But few researchers are willing to dismiss the idea that infants can tell the difference between two and three. UCLA's Gelman, for example, believes that infants have many ways to analyze a scene. They can distinguish stimuli by area, mass, tone, resonance, color, shape and number. They use the method that's easiest for any particular task.

To make her case, she points to research by University of Arizona psychologist Karen Wynn, PhD--a study several researchers contend is one of the most convincing that infants understand the concept of discrete number.

In the study, published in Psychological Science (Vol. 7, No. 3, p. 164­169), Wynn challenged the infants to distinguish how many times a puppet jumped in the air--three versus two times. Taking steps to ensure that the only consistent difference between the study's habituation phase and its test phase was number, she varied the duration and speed of the puppet's jumps. As predicted, if the infants habituated to three jumps, they looked longer when the puppet jumped two times.

"It's the best evidence to date that infants can pay attention to number," concedes Mix.

But she's not convinced it means infants can discriminate discrete rather than approximate number. Mix subscribes to a theory put forth by her mentor Janellen Huttenlocher, PhD, a developmental psychologist at the University of Chicago: Because it's so hard to collect data from infants, researchers must average results across trials and babies to get significant results. So if a study examines the behavior of 20 babies, any one baby may not show significant awareness of number. But, on average, the babies show a trend toward recognizing number. That, Huttenlocher argues, makes it impossible to say that infants understand two is two and that three is not only more than two, it's one more than two. Instead, the findings point more toward the idea that infants have a general sense of quantity.

"The idea that babies have an inexact representation of quantity--a general sense of mass and approximate number--can deal with the existing data with infants," says Huttenlocher.

Arizona's Wynn disagrees.

"The evidence is clear that infants are not operating in terms of overall amountness," she says. "People have controlled for volume and mass by varying everything on every trial but number. To try to think that babies were being habituated to some particular visual area is extremely difficult to believe."

Debates such as these are the nature of science, says Gelman. Each study adds an incremental piece to the overall picture of exactly how infants decipher their environment. "Right now, the best thing to say is that there are enough data to encourage some people to want to get more data," she says.

* Dehaene, S. "The Number Sense." (Oxford, 1997).

* Haith, M. Infant cognition. In: D. Kuhn & R. Siegler (Eds.), "Handbook of Child Psychology, 5th Edition, Vol. 2, Cognition, Perception and Language." (Wiley, 1998).

* Wynn, K. Psychological foundations of number: numerical competence in human infants. Trends in Cognitive Sciences, Vol. 2, p. 296­303, 1998.

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