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WE'RE HARD-WIRED FOR GEOMETRY

Tests with Amazon villagers hint at innate geometrical sense.

By Daniel B. Kane

Science, January 19, 2006

WASHINGTON - Even if you never learned the difference between a triangle, a rectangle and a trapezoid, and you never used a ruler, a compass or a map, you would still do well on some basic geometry tests, according to a new study.

Using a series of nonverbal tests, scientists claim to have uncovered core knowledge of geometry in villagers from a remote region of the Amazon who have little schooling or experience with maps and speak a language without the mathematical language of geometry.

For thousands of years, people have wondered if the basics of geometry came naturally to all humans or if they something you had to learn through instruction or cultural experiences. According to Plato's writings, Socrates attempted to determine how well an uneducated slave in a Greek household understood geometry, and eventually concluded that the slave's soul "must have always possessed this knowledge".

While a slave in a Greek household would have been introduced to aspects of geometry through the Greek language and culture, the Munduruku villagers who participated in the new study did not have this head start. Nevertheless, the 14 Munduruku children, as young as 6 years old, and the 30 adults who were quizzed by anthropologist Pierre Pica from Paris VIII University did well on the basic geometry test.

During the test, each participant was shown 43 sets of six images - and asked to choose the one "weird" or "odd" image out of each set of six. A correct answer required the person to choose the image that did not follow the same basic aspect of geometry illustrated in the other five images. The image sets used in the test are illustrated here.

In the first set, the bottom right box does not belong because the lines do not intersect at a 90-degree or right angle. Ninety three percent of the villagers picked out the non-right angle in this exercise.

The next set of images includes five closed shapes and one open shape. 77 percent of the Munduruku participants picked out the open shape as the "weird" or "odd" image.

The images used in the tests are supposed to examine your sensitivity to differences in geometrical figures, despite the fact that you may not know the textbook difference between an equilateral and an isosceles triangle. Sixty-six percent of the villagers correctly chose the top right images as the odd one.

Finding the one "left-Handed" image from five "right-handed" images below proved difficult, and the Munduruku study participants did not do much better than chance. Only 23 percent chose the bottom right as the weird or strange image.

Considering the 43 sets of images together, the Munduruku villagers got about two-thirds of the answers right. Munduruku children and adults did about as well as the 26 U.S. children the researchers tested. A group of 28 U.S. adults did better than any of the other groups. Nevertheless, the Munduruku and U.S. participants had the most trouble with the same questions, which adds further evidence for the presence of core knowledge of geometry among the Munduruku, according to the team led by cognitive scientist Stanislas Dehaene from the College de France and INSERM in Paris.

The word "geometry" comes from the Greek words for "Earth" and "measure". Geometry was first used to measure and chart the length, area and shape of land surfaces.

Tests with Amazon villagers hint at innate geometrical sense.

By Daniel B. Kane

Science, January 19, 2006

WASHINGTON - Even if you never learned the difference between a triangle, a rectangle and a trapezoid, and you never used a ruler, a compass or a map, you would still do well on some basic geometry tests, according to a new study.

Using a series of nonverbal tests, scientists claim to have uncovered core knowledge of geometry in villagers from a remote region of the Amazon who have little schooling or experience with maps and speak a language without the mathematical language of geometry.

For thousands of years, people have wondered if the basics of geometry came naturally to all humans or if they something you had to learn through instruction or cultural experiences. According to Plato's writings, Socrates attempted to determine how well an uneducated slave in a Greek household understood geometry, and eventually concluded that the slave's soul "must have always possessed this knowledge".

While a slave in a Greek household would have been introduced to aspects of geometry through the Greek language and culture, the Munduruku villagers who participated in the new study did not have this head start. Nevertheless, the 14 Munduruku children, as young as 6 years old, and the 30 adults who were quizzed by anthropologist Pierre Pica from Paris VIII University did well on the basic geometry test.

During the test, each participant was shown 43 sets of six images - and asked to choose the one "weird" or "odd" image out of each set of six. A correct answer required the person to choose the image that did not follow the same basic aspect of geometry illustrated in the other five images. The image sets used in the test are illustrated here.

In the first set, the bottom right box does not belong because the lines do not intersect at a 90-degree or right angle. Ninety three percent of the villagers picked out the non-right angle in this exercise.

The next set of images includes five closed shapes and one open shape. 77 percent of the Munduruku participants picked out the open shape as the "weird" or "odd" image.

The images used in the tests are supposed to examine your sensitivity to differences in geometrical figures, despite the fact that you may not know the textbook difference between an equilateral and an isosceles triangle. Sixty-six percent of the villagers correctly chose the top right images as the odd one.

Finding the one "left-Handed" image from five "right-handed" images below proved difficult, and the Munduruku study participants did not do much better than chance. Only 23 percent chose the bottom right as the weird or strange image.

Considering the 43 sets of images together, the Munduruku villagers got about two-thirds of the answers right. Munduruku children and adults did about as well as the 26 U.S. children the researchers tested. A group of 28 U.S. adults did better than any of the other groups. Nevertheless, the Munduruku and U.S. participants had the most trouble with the same questions, which adds further evidence for the presence of core knowledge of geometry among the Munduruku, according to the team led by cognitive scientist Stanislas Dehaene from the College de France and INSERM in Paris.

The word "geometry" comes from the Greek words for "Earth" and "measure". Geometry was first used to measure and chart the length, area and shape of land surfaces.

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