To Conquer Fear of Counting

By Stefan Kanfer

The fight against illiteracy has become such a crusade in the U.S. that another enemy seems to have slipped past the ramparts while everyone has been learning to read. Bruce R. Vogeli, chairman of the department of mathematics and science education at Columbia University Teachers College, calls this foe the "major untouched educational issue of the decade." Science writer Martin Gardner (The Relativity Explosion) finds it a "problem that is getting worse and worse." Its name: innumeracy, or the inability to understand numbers and their meaning.

Now John Allen Paulos, professor of mathematics at Temple University, has written a book about mathematical illiteracy. Titled Innumeracy (Hill & Wang; $16.95), it seeks to explain why so many people are numerically inept and shows how they can learn to work and play with figures. Paulos, 43, has no patience with mathematical dumbos who almost boastfully claim, "I can't even balance my checkbook," or "I'm a people person, not a numbers person." "I'm pained," he says, "at the belief that mathematics is an esoteric discipline with little relation or connection to the 'real' world."

Paulos swiftly explodes that notion by discussing stock-market scams, batting averages, newspaper psychics, fraudulent medical treatments, election polls and the reasons why blackjack is a better gambler's game than dice. Those who break into a sweat at the mention of calculus or plane geometry can relax. This elegant little survival manual is brief, witty and full of practical applications. Best of all, it has no quiz at the end, and as Paulos generously admits, the "occasional difficult passage can be ignored with impunity."

Using easy-to-follow formulas, the author demonstrates that the chance of falling victim to terrorists is less than 1 in 1.5 million (compared with, for example, 1 chance in 68,000 of choking to death or 1 in only 5,300 of dying in a car crash), that the number of possible five-card poker hands is 2,598,960 and that the size of a human cell is to that of a person as that of a person is to the size of Rhode Island. Paulos also notes that 367 people have to be gathered to ensure that two of them share the same birthday. How many must be in a group to guarantee a fifty-fifty chance that two have a birthday in common? "The surprising answer," he says, "is that there need be only 23." Doubters can find the proof in a section called "Probability and Coincidence."

Other entertaining and illuminating chapters include "Examples and ! Principles," in which Paulos shows why the giant Gargantua would be a physical impossibility; "Pseudo-science," a saline, agnostic examination of parapsychology and astrology; and "Statistics, Trade-Offs and Society," in which some astonishing questions arise. Among them: What percentage of college women enjoy watching the Three Stooges? (According to his personal survey, 8%.)

Another question: Why are so many people innumerate? Adults who fumble with numbers have been "intimidated by officious and sometimes sexist teachers," says Paulos, himself a victim of inept instruction. "They feel that there are mathematical minds and nonmathematical minds." The result of that misconception is a "gap that threatens eventually to lead either to unfounded and crippling anxieties or to impossible and economically paralyzing demands for risk-free guarantees."

Gardner, an author of books and essays on math, also puts much of the blame on teachers -- particularly at the elementary level, where many classrooms are run by people with little or no math training. "When a class is taught by a teacher not interested in the subject," he notes, "then the class is bored also." Another setback for numbers proficiency, Gardner argues, was infatuation with the new math that emerged during the 1950s. Says he: "Youngsters were learning all kinds of advanced things, but not basic math."

Still, America's number may not be up. According to Vogeli, curriculum materials that emphasize practical application have been emerging. "Change is on the way," he says. "Books like Innumeracy and Allan Bloom's The Closing of the American Mind articulate dissatisfactions present and already known to the teaching community." By so doing, they may greatly reduce the odds that Americans will continue to wallow in innumeracy.