Knowing how precisely a high school freshman can
estimate the number of objects in a group
gives you a good idea how well he has done in math as far
back as kindergarten, researchers at Johns
Hopkins have found.
Good "number sense" at age 14 correlates with higher
scores on standardized math tests
throughout a child's life up to that point and weaker
number sense at 14 predicts lower scores on
those standardized tests, said Justin Halberda, assistant
psychological and brain
sciences in the Krieger School of Arts and Sciences.
"We discovered that a child's ability to quickly
estimate how many things are in a group
significantly correlates with that child's performance in
school math for every single year, reaching all
the way back to when he or she was in kindergarten,"
Halberda teamed up on the research with colleagues
Michele Mazzocco, professor of psychiatry
and behavioral sciences in the School of Medicine and
researcher at the
Kennedy Krieger Institute,
and Lisa Feigenson, an assistant professor of psychological
and brain sciences in the Krieger School.
The results of their investigation were published online on
Sept. 7 by the journal Nature.
Though people often think of mathematics as a pinnacle
of intellectual achievement, research
reveals that some intuition about numbers, counting and
mathematical ability is basic to almost all
animals. For example, creatures that gather or hunt for
food keep track of the approximate number
of food items they procure in order to return to the places
where they get the most sustenance.
Humans share this very basic number sense, allowing them,
at a glance, to estimate the number of
people in a subway car or bus, Halberda says.
The Johns Hopkins team wondered whether this basic,
seemingly innate number sense had any
bearing on the formal mathematics that people learn in
school. So the researchers asked 64
14-year-olds to look at flashing groups of yellow and blue
dots on a computer screen and estimate which dots
were more numerous. Though most of the subjects easily
arrived at the correct answer when there
were, for example, only 10 blue dots and 25 yellow ones,
some had difficulty when the number of dots
in each set was more nearly equal. Those results helped the
researchers ascertain the accuracy of
each child's individual number sense.
They then examined the teenagers' record of
performance in school math all the way back
through kindergarten, and found that students who exhibited
more acute number sense had
performed at a higher level in mathematics than those who
showed weaker number sense, even
controlling for general intelligence and other factors.
"What this seems to mean is that the very basic number
sense that we humans share with
animals is related to the formal mathematics that we learn
in school," Halberda concluded. "The
number sense we share with the animals and the formal math
we learn in school may interact and
inform each other throughout our lives."
Though the team found this strong correlation between
number sense and scholastic math
achievement, Halberda cautions against concluding that
success or failure in mathematics is
genetically determined and, therefore, immutable.
"There are many factors that might affect a person's
performance in school mathematics,"
Halberda said. "What is exciting in our result is that
success in formal mathematics and simple math
intuitions appear to be related."
Future directions for research include investigating
the trainability of one's number sense and
seeing whether early help in number sense could affect
later formal math learning.
Funding for this research was provided by the National
Institutes of Health.