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Natural Born Mathematicians
October
2002
by Bruce Fellman
One of
the longest running debates among philosophers and cognitive scientists
alike concerns
the nature of the human mind. Are we, echoing Aristotle and John
Locke, born with a blank slate on which everything must be written,
or do we, shades of Kant and Noam Chomsky, enter this life with
our brains "hard-wired" with certain capabilities?
After watching nearly
5,000 babies, Karen
Wynn, a professor of psychology, has moved away from the tabula
rasa notion. "I guess I'm a closet Kantian," says Wynn. For
the past ten years, she has been asking infants, many of them between
the ages of four and six months old, to tell her what they know
about that most abstract endeavor, mathematics. The surprising answer
is "plenty."
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"The
ability to do math might be as much a part of our birthright
as the sucking reflex."
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In numerous studies,
Wynn has demonstrated that well before babies can talk or, for that
matter, sit up by themselves, they understand the concepts of addition
and subtraction, the foundation on which more sophisticated mathematical
notions, from balancing a checkbook to tackling topology, will be
built.
Researchers have shown
that what Wynn calls a "pretty impressive sensitivity to numbers"
is present in creatures as diverse as honeybees and chimps. But
until the psychologist published a controversial paper titled "Addition
and Subtraction by Human Infants" in the journal Nature in
1992, few would have suspected that the ability to do math might
be as much a part of our birthright as the sucking reflex.
To uncover these capabilities,
Wynn, who came to Yale in 1999 after nine years on the psychology
faculty at the University of Arizona, used a technique employed
by other researchers examining infant cognition. "Babies tend to
look longer at things that are new, unexpected, or surprising to
them," she says. "So we present infants with various situations
and record their looking times."
A
typical scenario involves puppets. (Mickey Mouse is a favorite.)
On a little stage, a baby sees one puppet. A curtain is drawn, hiding
it, while another puppet appears and goes behind the curtain, which
is then opened. Sometimes, there are two puppets on stage, but other
times, it's a different number.
"There's a secret trap
door in the stage, so without the baby knowing it, we may insert
a third puppet, or take one away," says Wynn. "We've shown that
the infants look longer at what they see as an incorrect outcome."
Researchers call this
the "violation of expectations technique," and for it to work, a
baby must come prepackaged with the ability to expect that one and
one will be two. "This also works with subtraction," says Wynn.
So
far, the researcher has not uncovered any budding Einsteins. "We're
getting at the fundamental structure of the human mind," she says.
"Science used to think that babies were passive blobs, but we feel
our research shows that we're all born with the innate ability to
recognize numbers in our environment and to reason about numbers
in certain ways."
A facility for calculus
is, however, a different story.  |
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