January 19, 2006. Copyright, 2006, Graphic News. All rights reserved

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ÒGut feelingÓ understanding of geometry 

LONDON, January 19, Graphic News: Children and adults who have probably never seen a ruler or talked about triangles, rectangles or parallel lines have a reliable Ògut feelingÓ about geometry, according to a new study.

Among people with such intuition are Mundurukœ Indians, a group of people who live in scattered, isolated villages deep in the Amazon.

Even though most of the Mundurukœ who participated in the study had little or no formal education in schools, and had not used rulers, compasses or maps, they grasped many different concepts of geometry as well as American children, according to research published in the January 20 issue of the journal Science.

The study by Stanislas Dehaene from INSERM-CEAÕs Cognitive Neuroimaging Unit in Orsay, France, and his colleagues VŽronique Izard, Pierre Pica, and Cathy Lemer, brings new evidence to bear on a much-discussed and debated question among psychologists and philosophers alike: how does language influence thought?

The work suggests that conceptual principles of geometry are inherently present in the minds of the Mundurukœ, even though they lack the words and language to express geometrical terms and concepts.

To investigate their grasp of geometry, 14 children and 30 adults were asked, in the Mundurukœ language, to point to the ÒweirdÓ or ÒuglyÓ image from a series of six images. Within each of 45 different sets of six images, five of the images all contained the same geometrical concept, and one image did not.

Even six-year-old children did a good job picking out the image that did not fit. American children who took the same tests did about as well as the Mundurukœ participants, and while well educated American adults did better, everyone had a tough time with the same kinds of questions.

The word ÒgeometryÓ comes from the words ÒEarthÓ and Òmeasure,Ó and geometry was first used to measure and chart the length, area and shape of land surfaces. To try to see if Mundurukœ could use geometry for useful tasks, the researchers also set up an abstract Òmap test.Ó

Three boxes or cans were arranged in a triangle, and an object was hidden in one of them. With his or her back to this array, each participant was presented with a sheet of paper upon which square and circular symbols represented the three containers and a star marked the location of the hidden object.

By recording where each participant first searched for the object the team evaluated whether participants could relate the map -- a two-dimensional geometrical relationship between the objects as viewed from above -- to the three dimensions of the environment.

Overall, the participantsÕ success rate averaged 71%, well above the chance level of 33.3%. Performance hardly differed between children (73.3% correct) and adults (70.4% correct).

ÒThe results provide evidence for geometrical intuitions in the absence of schooling, experience with graphic symbols or maps, or a rich language of geometrical terms,Ó concluded Dehaene.

ÒThe spontaneous understanding of geometrical concepts and maps by this remote human community provides evidence that core geometrical knowledge, like basic arithmetic, is a universal constituent of the human mind.Ó
/ENDS