Featured Research

from universities, journals, and other organizations

Intuitions regarding geometry are universal, study suggests

Date:
May 26, 2011
Source:
CNRS (Délégation Paris Michel-Ange)
Summary:
All human beings may have the ability to understand elementary geometry, independently of their culture or their level of education. In a spherical universe, researchers found that Amazonian Indians gave better answers than French or North American participants who, by virtue of learning geometry at school, acquire greater familiarity with planar geometry than with spherical geometry.

A Mundurucu participant measuring an angle using a goniometer laid on a table.
Credit: © Pierre Pica / CNRS

All human beings may have the ability to understand elementary geometry, independently of their culture or their level of education.

Related Articles


This is the conclusion of a study carried out by CNRS, Inserm, CEA, the Collège de France, Harvard University and Paris Descartes, Paris-Sud 11 and Paris 8 universities (1). It was conducted on Amazonian Indians living in an isolated area, who had not studied geometry at school and whose language contains little geometric vocabulary. Their intuitive understanding of elementary geometric concepts was compared with that of populations who, on the contrary, had been taught geometry at school. The researchers were able to demonstrate that all human beings may have the ability of demonstrating geometric intuition. This ability may however only emerge from the age of 6-7 years. It could be innate or instead acquired at an early age when children become aware of the space that surrounds them. This work is published in the PNAS.

Euclidean geometry makes it possible to describe space using planes, spheres, straight lines, points, etc. Can geometric intuitions emerge in all human beings, even in the absence of geometric training?

To answer this question, the team of cognitive science researchers elaborated two experiments aimed at evaluating geometric performance, whatever the level of education. The first test consisted in answering questions on the abstract properties of straight lines, in particular their infinite character and their parallelism properties. The second test involved completing a triangle by indicating the position of its apex as well as the angle at this apex.

To carry out this study correctly, it was necessary to have participants that had never studied geometry at school, the objective being to compare their ability in these tests with others who had received training in this discipline. The researchers focused their study on Mundurucu Indians, living in an isolated part of the Amazon Basin: 22 adults and 8 children aged between 7 and 13. Some of the participants had never attended school, while others had been to school for several years, but none had received any training in geometry. In order to introduce geometry to the Mundurucu participants, the scientists asked them to imagine two worlds, one flat (plane) and the second round (sphere), on which were dotted villages (corresponding to the points in Euclidean geometry) and paths (straight lines). They then asked them a series of questions illustrated by geometric figures displayed on a computer screen.

Around thirty adults and children from France and the United States, who, unlike the Mundurucu, had studied geometry at school, were also subjected to the same tests.

The result was that the Mundurucu Indians proved to be fully capable of resolving geometric problems, particularly in terms of planar geometry. For example, to the question Can two paths never cross?, a very large majority answered Yes. Their responses to the second test, that of the triangle, highlight the intuitive character of an essential property in planar geometry, namely the fact that the sum of the angles of the apexes of a triangle is constant (equal to 180°).

And, in a spherical universe, it turns out that the Amazonian Indians gave better answers than the French or North American participants who, by virtue of learning geometry at school, acquire greater familiarity with planar geometry than with spherical geometry. Another interesting finding was that young North American children between 5 and 6 years old (who had not yet been taught geometry at school) had mixed test results, which could signify that a grasp of geometric notions is acquired from the age of 6-7 years.

The researchers thus suggest that all human beings have an ability to understand Euclidean geometry, whatever their culture or level of education. People who have received no, or little, training could thus grasp notions of geometry such as points and parallel lines. These intuitions could be innate (they may then emerge from a certain age, as it happens 6-7 years). If, on the other hand, these intuitions derive from learning (between birth and 6-7 years of age), they must be based on experiences common to all human beings.

(1) The two CNRS researchers involved in this study are Véronique Izard of the Laboratoire Psychologie de la Perception (CNRS / Université Paris Descartes) and Pierre Pica of the Unité ?Structures Formelles du Langage? (CNRS / Université Paris 8). They conducted it in collaboration with Stanislas Dehaene, professor at the Collège de France and director of the Unité de Neuroimagerie Cognitive à NeuroSpin (Inserm / CEA / Université Paris-Sud 11) and Elizabeth Spelke, professor at Harvard University.


Story Source:

The above story is based on materials provided by CNRS (Délégation Paris Michel-Ange). Note: Materials may be edited for content and length.


Journal Reference:

  1. Véronique Izard, Pierre Pica, Elizabeth S. Spelke, and Stanislas Dehaene. Flexible intuitions of Euclidean geometry in an Amazonian indigene group. Proceedings of the National Academy of Sciences, 23 May 2011 DOI: 10.1073/pnas.1016686108

Cite This Page:

CNRS (Délégation Paris Michel-Ange). "Intuitions regarding geometry are universal, study suggests." ScienceDaily. ScienceDaily, 26 May 2011. <www.sciencedaily.com/releases/2011/05/110525115902.htm>.
CNRS (Délégation Paris Michel-Ange). (2011, May 26). Intuitions regarding geometry are universal, study suggests. ScienceDaily. Retrieved October 30, 2014 from www.sciencedaily.com/releases/2011/05/110525115902.htm
CNRS (Délégation Paris Michel-Ange). "Intuitions regarding geometry are universal, study suggests." ScienceDaily. www.sciencedaily.com/releases/2011/05/110525115902.htm (accessed October 30, 2014).

Share This



More Computers & Math News

Thursday, October 30, 2014

Featured Research

from universities, journals, and other organizations


Featured Videos

from AP, Reuters, AFP, and other news services

Samsung's Incredible Shrinking Smartphone Profits

Samsung's Incredible Shrinking Smartphone Profits

Reuters - Business Video Online (Oct. 30, 2014) — The world's top mobile maker is under severe pressure, delivering a 60 percent drop in Q3 profit as its handset business struggles. Turning it around may not prove easy, says Reuters' Jon Gordon. Video provided by Reuters
Powered by NewsLook.com
Ban On Wearable Cameras In Movie Theaters Surprises No One

Ban On Wearable Cameras In Movie Theaters Surprises No One

Newsy (Oct. 30, 2014) — The Motion Picture Association of America and the National Association of Theatre Owners now prohibit wearable cameras such as Google Glass. Video provided by Newsy
Powered by NewsLook.com
Microsoft Launches Fitness Band After Accidental Reveal

Microsoft Launches Fitness Band After Accidental Reveal

Newsy (Oct. 30, 2014) — Microsoft accidentally revealed its upcoming fitness band on Wednesday, so the company went ahead and announced it. Video provided by Newsy
Powered by NewsLook.com
Mind-Controlled Prosthetic Arm Restores Amputee Dexterity

Mind-Controlled Prosthetic Arm Restores Amputee Dexterity

Reuters - Innovations Video Online (Oct. 29, 2014) — A Swedish amputee who became the first person to ever receive a brain controlled prosthetic arm is able to manipulate and handle delicate objects with an unprecedented level of dexterity. The device is connected directly to his bone, nerves and muscles, giving him the ability to control it with his thoughts. Matthew Stock reports. Video provided by Reuters
Powered by NewsLook.com

Search ScienceDaily

Number of stories in archives: 140,361

Find with keyword(s):
 
Enter a keyword or phrase to search ScienceDaily for related topics and research stories.

Save/Print:
Share:  

Breaking News:

Strange & Offbeat Stories

 

Space & Time

Matter & Energy

Computers & Math

In Other News

... from NewsDaily.com

Science News

Health News

    Environment News

    Technology News



    Save/Print:
    Share:  

    Free Subscriptions


    Get the latest science news with ScienceDaily's free email newsletters, updated daily and weekly. Or view hourly updated newsfeeds in your RSS reader:

    Get Social & Mobile


    Keep up to date with the latest news from ScienceDaily via social networks and mobile apps:

    Have Feedback?


    Tell us what you think of ScienceDaily -- we welcome both positive and negative comments. Have any problems using the site? Questions?
    Mobile iPhone Android Web
    Follow Facebook Twitter Google+
    Subscribe RSS Feeds Email Newsletters
    Latest Headlines Health & Medicine Mind & Brain Space & Time Matter & Energy Computers & Math Plants & Animals Earth & Climate Fossils & Ruins