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03 Jul 2005 - 13:28 What Counts: How Every Brain is Hardwired for Math. The idea that math is language comes from Jean Piaget. (Surprise!) Noam Chomsky's in there, too. Chomsky believes, or once believed, that 'number was just a special aspect of language.' 'Special aspect' is the critical modifier here. The question of whether math is a language the way English is a language does not appear to have adherents outside ed schools. Neither Piaget nor Chomsky appears to have argued that math is a language per se. Their idea is that math depends on the same core logical-reasoning capacity language depends upon. (As I say, I've been skimming.)
off-topic: Of course, this leaves out hyperlexic kids and kids like me. I 'taught myself to read,' which is probably why I was always confused by the reading-isn't-natural idea. Christopher 'taught himself to read,' too. Two weeks after his Kindergarten teacher told us he was at risk for dyslexia, because of his very poor handwriting, he burst into literacy. He just took off. Then there's Andrew, who, back during the days of 9/11, was spelling out words like 'interpol warning' on the floor with his alphabet blocks. Once he spelled 'Osamy' and 'Somaly' on the refrigerator. Somebody should probably come study my kids....
Back on topic, here is a nice summation of the distinction between primary & secondary skills:
Even though many of the neurobiological systems that support language also support reading (Luria, 1980), these systems have not evolved to automatically acquire reading skills.
Stanislas Dehaene, one of the major researchers in the field:
[The] human capacity for arithmetic finds its ultimate roots in a basic cerebral system for perception and mental manipulation of approximate numbers, very ancient in evolution. According to this theory, we share this system with many animal species, and it appears very early in human development, independently of language. Of course, it is a primitive system, capable only of basic computations such as estimation, comparison, addition and subtraction of approximate numbers. On this shared basis, various human cultures invent increasingly elaborate cultural tools such as Arabic symbols, counting routines, algorithms for exact addition, multiplication etc. Thus, the origins of human arithmetic lie in both a universal core system of approximate quantity, and on various cultural tools for exact arithmetic.
converging lines of evidence, and it's important. Researchers have studied people who, because of brain injury, have lost only their ability to do math. Language is intact, memory is intact, logical reasoning is intact. But math is gone. There are also one or two cases of people who have lost everything but math. Here's one:
Mr. Bell's language had almost completely disappeared. He was left being able to utter just a few stereotyped phrases, such as 'I don't know' and, curiously, 'Millionaire bub.' His understanding of speech or of written language was almost nonexistent. Nevertheless he was still pretty good at calculation, and could accurately add and subtract . . . He could also select the larger of two-and three-digit numbers, showing that he still understood about numbers as being ordered by size, and the way the Arabic numeral system worked.
Millionaire bub. I'm going to remember that.
math and language again thread. I'm pretty sure that the (apparent) fact that math and language are two different things inside the brain does not mean they are necessarily two different things in philosophical or even linguistic terms. But if you're coming at the question from a neuroscientific or cognitive science point of view, math is not a language. (It's not dead, either!)
What Counts: How Every Brain is Hardwired for Math, by Brian Butterworth
The Number Sense: How the Mind Creates Mathematics by Stanislas Dehaene
Children's Mathematical Development: Research and Practical Applications by David C. Geary
(fyi: It is possible to buy Geary's book for far less than the $124 Amazon wants for it, or the $55 I paid for a used & extensively highlighted copy...)
Dehaene on high quality neuro-gear
Carolyn on math and language 7-2-05
Carolyn on math and language again 7-3-05
"the language of numbers is not language" 7-3-05
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Fascinating, Catherine. I've always been meaning to pick up a copy of Butterworth's book. Perhaps now I have a reason. From your evidence, it seems that brain researchers have reached a nearly unanimous conclusion that mathematics is not language. But I wonder if that conclusion is different from the conclusion that mathematics is not 'a' language. Anyway, Mr. Bell sounds like an interesting fellow. If mathematics can truly be seen as "a" language, then the only things that could explain Mr. Bell's peculiar abilities would be either (a) that they are not representative of the larger population or (b) he is not a female. Female brains are often lateralized--linguistic ability (and perhaps other abilities) are stored on both sides of the brain. Males brains tend to be more specialized. This makes women often more capable of recovering from a stroke. Did Mr. Bell suffer damage to the Broca's or Wernicke's area? -- JdFisher - 05 Jul 2005
Sounds like both, probably more to the Wernicke's area since he could come out with a little speech. -- CarolynJohnston - 05 Jul 2005
From your evidence, it seems that brain researchers have reached a nearly unanimous conclusion that mathematics is not language. But I wonder if that conclusion is different from the conclusion that mathematics is not 'a' language. My grasp of logic starts to fail me here (too many balls to keep in the air at once!) but I think, logically speaking, that the consensus of brain researchers does not (necessarily) tell us that math is not a language in the terms of other professionals who study language. OTOH, I personally am happiest, and feel most confident about what I'm doing, when different fields start coming to the same conclusions. I should say, too, that I've done some extremely quick skimming. So I wouldn't take it as gospel that the subject is settled for neuroscience & neuropsychology. Assuming that the issue is more or less settled in those fields, my questions have to do with the expressive & communicative functions of language. Obviously, people use mathematics to describe & explain things to each other; we use it to communicate. So is math a 'signal'? A 'sign'? A proto-language? In linguistic terms, what is it? -- CatherineJohnson - 05 Jul 2005
Did Mr. Bell suffer damage to the Broca's or Wernicke's area? I'll check-- -- CatherineJohnson - 05 Jul 2005
This is not on point, but relates to the use of symbolism as an aid to solving problems. Alfred North Whitehead in his "Introuction to Logic" states: "By the aid of symbolism, we an make transitions in reasoning almost mechanically, by the eye, which otherwise would call into play the higher faculties of the brain." In a book on symbolic logic by Irving M. Copi, the author refers to the Whitehead quote and states: "From this point of view, paradoxially enough, logic is not concerned with developing our powers of thought, but with developing techniques that enable us to get along without thinking!" One can substitute the word "math" for logic in the above sentence and it would still be true, I believe. In fact, this argument has been used in arguing for the use of algorithms. No, we don't want kids to stop thinking, we just want to make automatic some processes so they can think at a higher level. If you had to think about each step to take in order to walk, you literally could not think other thoughts and walk at the same time. Similarly, students subjected to the "reform math" follies of NCTM and others who are not properly taught algorithms for math operations are operating at a severe handicap. It always amazes me, however, to see many otherwise intelligent people arguing for NCTM's way of teaching math. -- BarryGarelick - 06 Jul 2005
No, we don't want kids to stop thinking, we just want to make automatic some processes so they can think at a higher level. This is the essence of developing expertise, as I understand research in cognitive science and in neuroscience. And these are fields I do understand reasonably well, from a sceince writer perspective. -- CatherineJohnson - 06 Jul 2005
I also have the perspective of being the mother of a child who can't talk. Andrew has to have a machine talk for him. It works on exactly the same principal as a calulator: he searches for the words he wants to say, presses the button, and the machine speaks. And it is a horrific handicap. Far, far, far better he should simply open his mouth and produce words. Spend five minutes at my house and you see, so very clearly, that the idea of turning simple arithmetic over to a machine is insane. Constructivist math curricula that do not teach the algorithms to automaticity are giving children handicaps. -- CatherineJohnson - 06 Jul 2005