Numbers and the Mind
Broadcast beginning the week of March 06, 2007

Why are some people math whizzes while others are scared to do simple arithmetic without a calculator? This week we explore differences in math ability; new and old debates on math education (remember "The New Math?"); the link between autism and skills in rapid-fire calculation; and Hollywood's fascination with brilliant, troubled mathematicians. Plus a trip to AT&T's research labs and some of the best minds working in mathematics today. Guests include Brian Butterworth, Professor of Cognitive Neuropsychology in the Institute of Cognitive Neuroscience at University College in London; Keith Devlin, executive director of The Center for the Study of Language and Information at Stanford University; Jeremy Kilpatrick, professor of mathematics education at the University of Georgia; Gary Mesibov, professor of psychology at The University of North Carolina; Jerry Newport; and AT&T mathematics researchers David Applegate and Jeff Lagarius.

In an introductory essay, host Dr. Fred Goodwin recalls his attempt to devise a theorem that would trisect an angle, one of geometry's long-standing problems. The attempt failed to yield a workable theorem, but it did teach him the joy and discipline of sustained scientific effort. As a research scientist investigating the human mind, Dr. Goodwin relied on the same sense of passionate investigation that he'd unleashed in high school geometry. "For that," he concludes, "I'll always thank my high school math teacher... and that stubborn theorem."

Love math? Hate math? As Dr. Goodwin's essay suggests, math is a subject that seems to arouse strong passions in high school. Our first guests today are two students in the thick of it…Marla Slussky in New Jersey and Brian Ware in North Carolina. While Marla Slussky loves math, and scored 800 on the math portion of the SATs, Brian Ware says he usually gets Cs in math. "I don't like math," he says. "More specifically, I hate it." Marla loves math because it's so logical. Brian says he can't figure out the point of finding the function of P... "It just seems like something the teacher's giving me to do to aggravate me."

Next, Dr. Fred Goodwin interviews Dr. Brian Butterworth, Professor of Psychology at University College, London. His books include What Counts: How Every Brain is Hardwired for Math. Dr. Butterworth contends that the vast majority of human beings are born with an innate concept of numbers, but that about one in twenty people seem to lack basic math abilities. These basic abilities include an intuitive understanding of numbers and counting, and they are controlled by the brain's parietal lobes. Physicist Albert Einstein had abnormally shaped, unusually large parietal lobes. The site of the brain that controls number processing is adjacent to a circuit that controls finger movement, says Dr. Butterworth, and he points out that our ability to calculate is intimately related to fingers. Most children learn to count on their fingers and we refer to numbers as "digits," after the Latin word for finger. Evidence for the development of the human capacity for counting goes back over thirty thousand years, says Dr. Butterworth, to signs of tallying on bone and on the walls of upper Paleolithic caves.

For more information about Dr. Brian Butterworth or to email him, visit the web site for The Institute of Cognitive Neuroscience; University College, London. Or you can write to him at Institute of Cognitive Neuroscience, University College London, Alexandra House, 17 Queen Square London WC1N 3AR

Rods, sets, blocks, and subsets. If you were a student in the sixties or early seventies - or the parent of one - you might remember the "New Math." But whatever happened to the "New Math?" Phillip Martin reports. The Russian launching of Sputnik in 1957 stirred American fears that the United States was being left behind in the technological revolution of the space race. In response, American educators devised a new school mathematics curriculum that soon became known as "New Math." It was easy to satirize, says songwriter Tom Lehrer. "It just seemed like a desperate attempt to keep up with the Russians." Dr. Jeremy Kilpatrick, professor of mathematics education at the University of Georgia, says the "New Math" curriculum focused less on procedural-oriented mathematics, like adding, subtracting and multiplying, and more on the language of sets, relations, and functions. The new math also made use of manipulatives -- things like beads and blocks that young children can handle, sort and count.

But many people just didn't get it, including some teachers and many parents. Research suggested that children who were taught according to the new math grew up to have difficulty with the simple arithmetic involved in balancing a checkbook. Critics pressured textbook publishers to drop elements of the new math from their materials in the 1970s. But elements of "New Math," such as the use of manipulatives to teach young children math, remain in the curriculum standards that the National Council of Teachers of Mathematics (NCTM) promotes today. That's a problem, say critics, some of whom call the NCTM's standards "The New New Math." A 2001 National Research Council report, called "Adding It Up" doesn't endorse any one approach to teaching mathematics. But in an echo of the warning precipitated by Sputnik forty-five years ago, Jeremy Kilpatrick and the other authors concluded that too few students are leaving schools with adequate mathematical skills "for the nation to be satisfied with the condition of school mathematics, today."

Next up, a trip to the highly mathematical world of Florham Park, New Jersey. Here, in the research laboratories of telecommunications giant AT&T, some of the world's best mathematicians spend their days probing the mysteries of algorithms, combinotorics, quantum computers, and number theory. Dr. David Applegate is an expert in mathematical optimization. He creates mathematical models that apply to AT&T's business, such as the routing of calls and the creation of software that would allow computers to process customer service calls. He's a self-described "puzzle freak," who once wrote a computer program that predicts the lowest number of moves needed to solve a Rubik's cube-like puzzle called "Square One."

Dr. Jeff Lagarius, another mathematics researcher at AT&T Labs, made headlines in mathematics journals last year when he untied a complicated problem in "knot theory." When he's working on a problem, he says, "I think about it all the time. My shoulder muscles are tense... it's slightly uncomfortable." The relief comes in solving the problem, or recognizing that it's not soluble and moving on. A long-standing interest of his is an infamous problem in mathematics called "The 3x plus one problem." He wants to prove something that mathematicians almost know to be true. Here's how it works: You pick ANY positive integer. If it's even, you divide it by two. If it's odd, you multiply the number by three and add one. You keep repeating that process over and over again and the belief is that you'll always get to one. For example - say you start out with five. Five times three plus one is sixteen. That's an even number, so you divide that by two. You get eight. Divide that by two and you get four. Divide four by two and you get two. Divide two by two and you get one. Computers have checked this recipe for a million, billion numbers and it always yields a one. Mathematicians conjecture that it always works but they haven't been able to figure out exactly WHY.

For more information about AT&T Labs or to contact Jeff Lagarius or David Applegate, log on to the Mathematics Research web site for AT&T Labs. Or write to AT&T Labs - Research, Shannon Laboratory 180 Park Ave, Bldg 103, Room C223 Florham Park, NJ 07932.

Next, Dr. Fred Goodwin interviews Dr. Keith Devlin, executive director of The Center for the Study of Language and Information at Stanford University and a consulting professor in Stanford's department of Mathematics. Movie makers have released a number of movies in recent years that focus on troubled mathematical geniuses, including Academy Award winners "A Beautiful Mind" and "Good Will Hunting" and art house hit "Pi." And there are more on the way - Miramax has optioned the rights to the Tony and Pulitzer Prize winning play "Proof." Dr. Devlin says that the math in "Pi" was a bit too elementary for the character, who is meant to be an expert mathematician. "A Beautiful Mind" offers several apt cinematic renditions of complex mathematical ideas, he says. While a fear of math, dubbed "math anxiety" by many, is widespread, he says that a typical math problem is actually a lot less complicated in its web of relations than the plot of a typical soap opera episode.

To learn more about Keith Devlin visit The Center for the Study of Language and Information at Stanford University. Or you can write to him at CSLI, Ventura Hall, 220 Panama Street, Stanford, CA 94305-4115.

Next, Devorah Klahr reports on the link between autism, a neurological developmental disorder, and super-quick mathematical calculation. Soon after seeing the movie "Rain Man," which featured Dustin Hoffman in the role of an autistic man, Jerry Newport was diagnosed with Asperger's syndrome, a mild form of autism. Like the character Hoffman played, Newport can multiply four digit numbers very rapidly. About one in twenty people with Asperger's syndrome develop such splinter skills in one of several fields, including music, art, and high speed mathematical calculation. Dr. Gary Mesibov, professor of psychology at The University of North Carolina suggests that autistic people's tendency to develop a very narrow focus may be behind these abilities. That same narrow focus, he says, can also be an obstacle. "Things like algebra and trigonometry cause them difficulty because those require sequential processing of information which they’re not as strong at. And also it requires holding several concepts in their head at the same time." Jerry Newport has learned to improve many of his social skills, a big challenge for people with autism. He says his calculating abilities made him feel like "the town freak" when he was growing up but that today he feels good about himself and his work in educating others about autism.

For more information about autism, you can visit the website of the Autism Society of America, at http://www.autism-society.org/. You can call Dr. Gary Mesibov at (919) 966-8189, or email him at gmesibov@email.unc.edu. Or, you can email Jerry Newport at wholphin48@hotmail.com.

In a concluding commentary, John Hockenberry recalls how he fell in love with math. It wasn't the arithmetic or the industrial processing problems like figuring out how many donuts a baker can make out of a given amount of flour. (Why shouldn't the baker figure it out for himself and leave the third grade math class out of his industrial processing problems?) No. It was algebra. Hockenberry fell in love with "X" in math class. She was next to the letter "M." "M" described a slope but the siren appeal of "X" was that "X" could be .... anything.

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