Basic understanding of geometry not dependent on education: study

by Deborah Braconnier report
Mundurucu chief. Image: Fabio Rodrigues Pozzebom/ABr, via Wikipedia.

(PhysOrg.com) -- In a recent study published in the Proceedings of the National Academy of Sciences, psychologist Veronique Izard from the Universite Paris Descartes and her colleagues show how abstract geometric principles are understood despite a lack of formal education.

Izard and her team administered geometry-based tests to an Amazonian group known as the Mundurucu. They tested 22 adults and 8 children (ages 7 - 13) and then compared their results with adults and children from France and America (French children ages 7 - 13 and American children ages 5 - 7). One test focused on the geometrical properties of lines, while the other test asked participants to estimate the angle and location of an incomplete ’s apex.

Results showed that the Amazonian group, who had no formal education in , had results comparable to their French and American counterparts, with the exception of the American children. American children in the 5 - 7 age group were able to somewhat understand geometric space, but not to the level of the others tested, including those from the Amazon with no .

This leads researchers to believe that geometric knowledge is obtained through two possible routes. Either it is innate but not fully developed until around the age of seven or it is learned by experience with space, such as how our bodies move.

More information: Flexible intuitions of Euclidean geometry in an Amazonian indigene group, PNAS, Published online before print May 23, 2011, doi: 10.1073/pnas.1016686108

Abstract
Kant argued that Euclidean geometry is synthesized on the basis of an a priori intuition of space. This proposal inspired much behavioral research probing whether spatial navigation in humans and animals conforms to the predictions of Euclidean geometry. However, Euclidean geometry also includes concepts that transcend the perceptible, such as objects that are infinitely small or infinitely large, or statements of necessity and impossibility. We tested the hypothesis that certain aspects of nonperceptible Euclidian geometry map onto intuitions of space that are present in all humans, even in the absence of formal mathematical education. Our tests probed intuitions of points, lines, and surfaces in participants from an indigene group in the Amazon, the Mundurucu, as well as adults and age-matched children controls from the United States and France and younger US children without education in geometry. The responses of Mundurucu adults and children converged with that of mathematically educated adults and children and revealed an intuitive understanding of essential properties of Euclidean geometry. For instance, on a surface described to them as perfectly planar, the Mundurucu's estimations of the internal angles of triangles added up to ∼180 degrees, and when asked explicitly, they stated that there exists one single parallel line to any given line through a given point. These intuitions were also partially in place in the group of younger US participants. We conclude that, during childhood, humans develop geometrical intuitions that spontaneously accord with the principles of Euclidean geometry, even in the absence of training in mathematics.

Related Stories

Study: Preschool kids have math skills

Sep 20, 2005

Harvard psychologists in Cambridge, Mass., say 5-year-olds are able to grasp numeric abstractions and arithmetic concepts even without formal education.

Children in formal child care have better language skills

Jan 05, 2011

Fewer children who attend regular formal centre- and family-based child care at 1.5 years and 3 years of age were late talkers compared with children who are looked after at home by a parent, child-carer or in an outdoor ...

Can children outgrow chronic daily headache?

Jul 15, 2009

Most children who suffer from chronic daily headache may outgrow the disabling condition, according to research published in the July 15, 2009, online issue of Neurology, the medical journal of the American Academy of Neu ...

Infantile amnesia: Gauging children's earliest memories

May 11, 2011

The inability of individuals to remember the very earliest years of their lives, called infantile amnesia, has been studied for many years in adults, who seem to recall very little before ages 3 or 4. But children also experience ...

Recommended for you

Brains transform remote threats into anxiety

Nov 21, 2014

Modern life can feel defined by low-level anxiety swirling through society. Continual reports about terrorism and war. A struggle to stay on top of family finances and hold onto jobs. An onslaught of news ...

Mental disorders due to permanent stress

Nov 21, 2014

Activated through permanent stress, immune cells will have a damaging effect on and cause changes to the brain. This may result in mental disorders. The effects of permanent stress on the immune system are studied by the ...

Could there be a bright side to depression?

Nov 21, 2014

(Medical Xpress)—A group of researchers studying the roots of depression has developed a test that leads them closer to the idea that depression may actually be an adaptation meant to help people cope with ...

User comments

Adjust slider to filter visible comments by rank

Display comments: newest first

hermano
not rated yet May 31, 2011
we were born to speak and practice geometry

Please sign in to add a comment. Registration is free, and takes less than a minute. Read more

Click here to reset your password.
Sign in to get notified via email when new comments are made.