Investigations

Babies can't count
Although many people would like to think that their babies are bright enough to count before their first birthdays-and some child psychologists have suggested they can-that possibility is in dispute as the results of a ten-year evaluation by University of Chicago scholars are released.

"Earlier claims of infants' quantitative skill are greatly exaggerated," says Janellen Huttenlocher, the William S. Gray professor of psychology and an author of Quantitative Development in Infancy and Early Childhood (Oxford University Press, 2002). "Infants start with only a crude awareness of amount, which slowly evolves into an ability to distinguish between numbers of discrete objects."

Coauthors Huttenlocher and psychology professor Susan Levine, researchers with the Center for Early Childhood Research, and Indiana University assistant professor Kelly S. Mix, AM'93, PhD'95, carried out several studies that found flaws in the so-called "nativist" view, which has gained wide acceptance among developmental psychologists. They also refute French psychologist Jean Piaget's (1896-1980) view that children do not develop a quantitative competence until much later than infancy-after age 5.

"Neither the nativists nor Piaget were right," Levine says.

Infants, contrary to nativist claims, do not have an innate ability to discriminate the number of discrete objects, nor can they recognize numerical equivalents. During the first months of life, they can, however, distinguish "amount of stuff," Levine says. "An infant can recognize quantity based on amount, but not on number." For instance, an infant can distinguish between six elephants and six ants-because the size of six elephants is vastly different from the size of six ants. But an infant could not distinguish quantities that are the same in total mass but not in number. For instance, Levine explains, an infant could not distinguish between one full chocolate bar and the 12 pieces into which it could be divided.

Toddlers and preschoolers also have far more advanced skills than Piaget believed. Between 2 1/2 to 3 1/2 years old, toddlers begin distinguishing between amount and numbers of discrete objects. As early as age 3, some children exhibit nonverbal math skills, comprehending quantity and performing simple addition and subtraction using groups of objects. "Children bring far more mathematical understanding to preschool than parents and teachers realize," Levine says. "Because preschoolers' verbal understanding of conventional math terms is limited, their ability to comprehend quantitative concepts is often overlooked."

Though the researchers' book is aimed at an academic audience, it has important lessons for parents preparing their children for kindergarten, Huttenlocher says, because it "demonstrates that preschoolers have an abstract understanding of numerical knowledge before they develop the language skills necessary to articulate that knowledge."

Huttenlocher urges parents to "teach children to label quantity." She explains, "When you're setting the table, count out the number of forks: one, two, three. Children may understand quantity, but they need the language to begin conventional math learning."

The impetus for Quantitative Development, Huttenlocher says, was a general skepticism about nativist claims-particularly a finding that 7-month-old infants could distinguish numerical equivalence. Infants, it was claimed, could recognize that a set of two apples was equivalent to a set of two horn honks because both contained the same quantity.

"It just didn't make sense," Huttenlocher says. When the "honking" experiment was replicated at Chicago, the researchers found that even 3-year-olds had trouble recognizing numerical equivalence between objects and sounds.

Identifying this possible flaw in earlier claims spurred Huttenlocher, Levine, and Mix to revisit findings of number awareness in infants and, ultimately, to demonstrate that early quantitative sensitivity consists of an understanding of amount and not number.
- Josh Schonwald