Posted on 01/20/2006 3:11:23 AM PST by Pharmboy
Amazonian hunter-gatherers who lack written language and who have never seen a math book score highly on basic tests of geometric concepts, researchers said on Thursday in a study that suggests geometry may be hard-wired into the brain.
Adults and children alike showed a clear grasp of concepts such as where the center of a circle is and the logical extension of a straight line, the researchers report in this week's issue of the journal Science.
Stanislas Dehaene of the College de France in Paris and colleagues tested 14 children and 30 adults of an Amazonian group called the Munduruku, and compared their findings to tests of U.S. adults and children.
"Munduruku children and adults spontaneously made use of basic geometric concepts such as points, lines, parallelism, or right angles to detect intruders in simple pictures, and they used distance, angle, and sense relationships in geometrical maps to locate hidden objects," they wrote.
"Our results provide evidence for geometrical intuitions in the absence of schooling, experience with graphic symbols or maps, or a rich language of geometrical terms."
Geometry is an ancient field and Dehaene's team postulated that it may spring from innate abilities.
"Many of its propositions -- that two points determine a line, or that three orthogonal axes localize a point -- are judged to be self-evident and yet have been questioned on the basis of logical argument, physical theory, or experiment," the researchers wrote.
There was no way the Munduruku could have learned these ideas, they added.
"Most of the children and adults who took part in our experiments inhabit scattered, isolated villages and have little or no schooling, rulers, compasses, or maps," they wrote.
"Furthermore, the Munduruku language has few words dedicated to arithmetical, geometrical, or spatial concepts, although a variety of metaphors are spontaneously used."
They designed arrays of six images, each of which contained five conforming to a geometric concept and one that violated it.
"The participants were asked, in their language, to point to the weird or ugly one," the researchers wrote.
"All participants, even those aged 6, performed well above the chance level of 16.6 percent," they found. The average score was nearly 67 percent correct -- identical to the score for U.S. children.
"The 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," they concluded.
Our public schools are not teaching our children....they are indoctrinating them.
But of a truth, I don't see where Euclidean or Riemannian or whatever makes any difference. IMHO, the point is the unreasonable effectiveness of mathematics and man's astonishing ability to notice it and make use of it.
Thank you for thinking of me. :)
Is that an actual answer? (As a geometry teacher, I've seen worse!) <^..^>
Actually, the mind is programmed by heredity toward survival skills. The world hunter-gatherers knew was involved with the dimensions and experiences they encountered. That would make things that surround them inherently obvious, while stuff like programming the TiVo or figuring out the remote control lighting's 60 zillion steps totally incomprehensible to sensible people. <^..^>
What Kant says has validity. I've really had very good luck teaching Geometry when I filled in those "a priori" deficits, and built logically from there.
Hint....at the start of Geometry, hand a child a piece of paper and a pencil, and ask him/her to draw a map from home to school. It's the best diagnostic test there is for Geometry preparation.
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