SAN FRANCISCO -- Some people don't mind math, and some people don't mind root canals; there's no accounting for taste, perhaps.
But however much you may dislike mathematics, and however much you think you differ from the monkish number mavens who scratch away at theorems all day long, your brain is really no different from a world-class mathematician's, says Keith Devlin, a mathematician and the dean of science at Saint Mary's College of California.
Devlin, whose recent book The Math Gene covers the largely unstudied topic of how humans developed sophisticated mathematical abilities, was one of several scientists who held forth on the origins of mathematical thinking at the American Advancement for the Association of Science conference held here this weekend.
The message of the day was, "All brains are created equal" -- i.e., the guy who needs his PDA to help him calculate a waiter's tip was born with essentially the same mathematical ability as Andrew Wiles, the fellow who solved Fermat's Last Theorem.
And it has been this way for a very long time -- at least 200,000 years or so, Devlin said.
"Most math is two or three thousand years old at most, and the vast majority of what we teach in college is less than 300 years old," Devlin said. "But we have no evidence that the human brain underwent any sophisticated, major change a couple thousand years ago."
Consequently, Devlin posits that "Mathematical thinking is an amalgam of nine basic mental abilities that every one of us has," as he wrote in a paper to accompany his talk. "(They are) abilities that our ancestors acquired hundreds of thousands of years ago in order to survive in the world."
The most basic of these abilities is "number sense," or the capacity of humans (and many other animals) to "know" the number of objects in very small collections, without counting.
This is not a learned ability; it is "hard wired," the scientists said, and can be seen in infants immediately after birth. Prentice Starkey, a cognitive scientist at the University of California-Berkeley, described an experiment in which suckling babies are shown puppets, and their "excitement" is measured in the number of sucks on the mother's nipple.
"When we show the baby four puppets, it gets excited," Starkey said. "But when we repeat it many times, the baby starts to get bored. Then when we change it to three, the baby gets excited again."
The ability to know how many objects there are in a collection was an invaluable evolutionary trait, Devlin said. People had to know whether their group was larger or smaller than an opposing group, or whether this tree or that had more fruit in it.
A few other human traits that contribute to our math shrewdness include spatial reasoning ability -- which was necessary, Devlin writes, for "all that swinging to tree" of our ape-like ancestors -- and relational reasoning ability, which allowed humans to keep track of all the members of a society and how they are interconnected to each other.
More advanced mathematics, including the ability to count, are learned behaviors, Devlin said. Indeed, there's great evidence that human numerical ability is intimately entwined with human language ability, which humans acquired between 75,000 and 200,000 years ago.
But if all humans are blessed with the same basic abilities, why aren't we all Alan Turing? Because some people are better at abstraction, or the ability to think about theory with the same facility as with reality, Devlin said.
"In any episode of TV soap opera, the relationships and the logic are more complex than on any page of a math text book," he said. But we can all follow the soaps while not making heads or tails of the text book because we have become accustomed to the show's human relationships: If the father double-crosses the step-son by eloping with his favorite mistress, who is the show's fur-wearing, longtime villain, we don't need to stop and ask, "Now, 'father' and 'son' -- what does that mean, again?"
Not so with numbers. Most people who find math problems difficult, Devlin said, haven't mastered the ability to trick their minds into thinking of math as TV, to fool their brains into making abstract objects seem real.
How does one master the ability to do this? The same way you get to Carnegie Hall -- practice, practice, practice.
In fact, if children practice math from a very young age, they are put on a track to do well in math for the rest of their lives, said Starkey.
His tests show that there is marked difference in the mathematical abilities of four-year-olds from different parts of society, which is due to the different levels of math practice the kids have had. For example, four-year-olds from American low-income households have markedly less math ability than those from high-income households, and American four-year-olds have less ability than those from China.
Improving the situation in the United States involves reforming math teaching at the pre-school level, Starkey said, and possibly putting stronger cultural emphasis on the virtue of being good at math.
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