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
"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."
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.
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
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."
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
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."
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.
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
- Josh Schonwald