Enlarge

APPROXIMATE THE DOTSIn a new study, 14-year-olds had a fraction of a second to identify the more numerous of two sets of colored dots, such as those in the images shown here. Teens who performed this task especially well had also achieved high scores on standardized math tests throughout grade school.Halberda

Count on evolution to play favorites. When it comes to math achievement, some kids may start out with an inherent advantage.

A portion of 14-year-olds deftly estimate approximate quantities of items without counting, whereas others do so with either moderate or limited success, a new study finds. The ability is evolutionarily ancient and cannot be taught, but tends to get better with age. Large variations in this number sense closely parallel youngsters’ mathematics achievement scores from kindergarten to sixth grade, concludes a team reporting in the Sept. 7 Nature and led by psychologist Justin Halberda of Johns Hopkins University in Baltimore.

Earlier studies indicated that a faculty for rapidly estimating approximate quantities appears by age 4 months, long before any math instruction. How precisely a child can estimate amounts may influence math learning and achievement, Halberda proposes. He and his colleagues are now assessing this ability in 3-year-olds whose math achievement in elementary school will be tracked.

It’s also possible that high-quality or intensive math instruction may increase the accuracy of a person’s number estimates. Halberda suspects that if such effects exist, they’re relatively small.

“Our results suggest that there is a strong and significant relationship between the acuity of a student’s approximate number system and his or her performance in school mathematics,” the Hopkins researcher says.

Until now, he adds, researchers have ignored individual differences in people’s ability to estimate quantities quickly and without counting. “We found much greater variability from one person to another than we would have predicted,” Halberda says.

“Halberda’s group provides a beautiful demonstration of a link between a measure of number sense and classical measures of math achievement,” comments cognitive neuroscientist Stanislas Dehaene of the INSERM-CEA Cognitive Neuroimaging Unit in Gif-sur-Yvette, France. Unlike Halberda, Dehaene considers it likely that higher degrees of mathematical training markedly boost the precision of rapid quantity estimates.

In Halberda’s study, 64 healthy 14-year-olds attending regular classes in public schools viewed arrays of blue and yellow dots on a computer screen. Each array appeared for a fraction of a second, making it impossible to count dots. The number of dots of each color varied from five to 16. Dots also varied in size to ensure that greater numbers of one color did not cover a larger total area than smaller numbers of the other color, thus giving away the more numerous set of dots.

Top-performing teens estimated quantities as well as mathematically astute adults have in earlier studies. The teens discriminated between numerical ratios of blue and yellow dots as close as 9 to 10. Low-performing volunteers, who estimated quantities at about the level of 2-year-olds, had difficulty discriminating between numerical ratios higher than 2 to 3.

Individual performance on the approximation task corresponded closely with scores on two standard math achievement tests the participants had taken from kindergarten through sixth grade. This finding held after statistically accounting for IQ, spatial reasoning ability, working memory capacity and more than a dozen other cognitive measures.

It’s not clear how a faculty for estimating approximate amounts would aid in learning arithmetic operations consisting of exact numbers, as suggested in the new study, remarks psychologist Brian Butterworth of University College London.

“Arithmetic requires a sense of exact number — approximate numbers just won’t do,” Butterworth asserts. In other words, formal math learning may depend on an inherent ability to recognize anywhere from exactly one to perhaps six or seven items, but not on the ability to estimate the number of items.

In the Sept. 2 Proceedings of the National Academy of Sciences, Butterworth and his coworkers report that 4- to 7-year-olds who speak either of two languages that have few number words identify and remember small quantities of items as well as English-speakers of the same age. Number words in those two languages roughly correspond to one, few and many.

Another study, led by Michael Frank, a psychology graduate student at the Massachusetts Institute of Technology, suggests that an Amazonian tribe has no number words but can still count small quantities (7/19/08, p. 5).

“These new results are surprising and the study is well-conducted,” Frank says of Halberda’s work.

In other work, Butterworth has found no relationship between several measures of approximate number estimation and tests of various math skills among 23 healthy 8- and 9-year-olds. He and his colleagues present their findings in the September Developmental Science.

A handful of recent studies have reached the same conclusion, Halberda notes. But all of them, including Butterworth’s, examine the performance of groups of children rather than probing for individual differences in the precision of estimates, he says. Statistical links to math achievement only emerge when researchers account for those individual disparities, in his view.

An inborn ability to track precise numbers of items may be crucial for grasping math concepts, as Butterworth argues, or it might only assist in learning number words, Frank adds.

• Print
• |
• Comment