Adults and school-age children may understand some basic principles of geometry even without formal math training at all, according to a study published online yesterday by the Proceedings of the National Academy of Sciences. Thirty members of the Mundurucú, an indigenous Amazonian group, could intuitively grasp geometric concepts about angles, lines, and points, the researchers found. How the Heck:
What's the News:
The researchers asked eight Mundurucú children ages 7 to 13 and twenty-two Mundurucú adults to answer 21 questions about the geometry of a plane or a sphere, such as “Can a line be made to cross two other parallel-looking lines?” They also had the participants estimate angles that would complete an unfinished triangle, using their hands or a measuring tool.
The Mundurucú children and adults performed far better than would be expected by chance, if they were randomly answering "yes" or "no" to the questions. They answered 90% of questions about planar geometry---an imaginary, totally flat world---correctly, and 70% of questions about a spherical world correctly. When estimating angles, their answers tended to be within about 5 degrees of the correct answer.
In fact, the Mundurucú did about as well as French children of the same age and American adults who had had formal math education. Younger American children, however, ages 5 to 7, did poorly by comparison, answering more questions correctly than they would by chance but not as many as older children or adults.
These findings suggest two possible explanations: Either understanding of geometry is innate, but for some unknown reason doesn't emerge until about age 7, or it's acquired through "general experiences with space, such as the ways our bodies move,” says psychologist Véronique Izard, lead author of the study.
What's the Context:
Nature versus nurture is a longstanding debate in psychology (and many other fields of science): what are we born with, and what do we glean from experience? Much recent research has eroded the divide between the two: it turns out that many human traits are defined by the interaction of nature and nurture.
As far back as the 18th century, philosopher Immanuel Kant argued that people have in-born intuitions about geometry.
Other research has suggested that humans have innate number sense and math aptitude.
Not So Fast:
This is a small study, looking mainly at one isolated group. While the comparison with French people and Americans suggested a broad human facility, it remains to be seen whether people in other groups would grasp geometry the same way, or whether a different sort of assessment would produce the same results.
Reference: Véronique Izard, Pierre Pica, Elizabeth S. Spelke, & Stanislas Dehaene. "Flexible intuitions of Euclidean geometry in an Amazonian indigene group." Proceedings of the National Academy of Sciences online before print, May 23, 2011. DOI: 10.1073/pnas.1016686108
Image: Wikimedia Commons / HAHA VENOM