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.
Nope, which is why I said never mind............
AG, you ole salty dog, you.
You called this ahead of time.
"The unreasonable effectiveness of math." (or something like that.)
HA! Designer indeed!
Definitely not for me. Attending to one ping list is already more than I can properly handle!
However, it was the environment that was just not acceptable for younger child. We always had to supplement the education she got in private school but the learning environment and the social norms were world's better than in public school
All in all, we wouldn't have done it any differently.
Every parent needs to take responsibility for their child's education and make sure it's not left to the school!
LOL! Me, too. My own first thought on seeing the title was that, in my HS geometry class, it seemed clear that those of us who were good at geometry got at sight and just had to learn the vocabulary, and those who weren't good, well, just would never get it (I got the same feeling about logic in college!).
Hadn't thought about it from this angle before.
These self-evident truths are interrogated not for their confessions but for their universality.
Imaginatively, we speak of extra dimensions but logically we can only account for three.
What is better displayed here is the seeming fact that not all children come equipped with the same ability to intuit the obvious and that is a phenomenon for social study, not the science of mathematics, per se.
"points, lines, parallelism, right angles simple pictures, distance, angle, relationships"
All of these exist in the Amazon and tribe. All are used in hunting, farming, cooking and taking care of the tribe.
Look at what has been built over 1,000 years where modern math did not exist - we cannot duplicate today - maybe modern math is incorrect.
This whole article is based on a completely faulty premise. The whole point of High School Geometry is not to teach people how to compute areas of rectangles or know that two points make a straight line. Students are expected to intuitively know that coming in.
High School Geometry is meant to introduce axiomatic thinking and theorem proving.
All this proves is that the hunters know geometry and the guys who designed the study do not!
Hmmm.
Cordially,
Good one...
I only wish that there was such as thing as Angle-Side-Side congruence. It would have made Geometry class a little more fun. :)
You rang?
Sounds more like plain old spatial relations.
I recall that Kant said the same thing more than 200 years ago.
Well, at least you narrow it down to two solutions. With angle-angle-angle, you have an infinite number.
That's because their instruction never goes much beyond this intuitive level. Many educators--many math teachers--do not know that Euclidiean geometry is an application of logic, that it is the only opportunity for the school to teach formal logic to ordinary students.
Well, Kant said that there were three dimensions of space, and that that was all there could be, since it was clearly the case that there couldn't be any others.
Special Relativity blew a hole in that. General Relativity nailed the coffin shut. Quantum Field Theory and String Theory are currently dancing on the grave.
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