The New New Math

Focus on Algebra: An Integrated Approach

by Randall I. Charles and Alba González Thompson
Addison-Wesley, 843 pp., $56.00

Life by the Numbers: Math As You've Never Seen It Before

narrated by Danny Glover. Seven boxed videotapes produced by WQED, Pittsburgh


Surveys have shown for many decades that the mathematical skills of American high school students lag far behind those of their counterparts in Japan, Korea, Singapore, and many European countries. In the United States whites do better than blacks, Hispanics, and Native Americans. Males outscore females. Students from high socioeconomic backgrounds do better than those from lower strata.

These are troubling statistics because, in an advanced technological society such as ours, a firm grasp of basic mathematics is increasingly essential for better-paying jobs. Something clearly is wrong with how math is being taught in pre-college grades, but what?

In the late 1960s the National Council of Teachers of Mathematics (NCTM) began to promote a reform movement called the New Math. In an effort to give students insight into why arithmetic works, it placed a heavy emphasis on set theory, congruence arithmetic, and the use of number bases other than ten. Children were forbidden to call, say, 7 a “number.” It was a “numeral” that symbolized a number. The result was enormous confusion on the part of pupils, teachers, and parents. The New Math fad faded after strong attacks by the physicist Richard Feynman and others. The final blow was administered by the mathematician Morris Kline’s 1973 best seller Why Johnny Can’t Add: The Failure of the New Math.

Recently, the NCTM, having learned little from its New Math fiasco, has once more been backing another reform movement that goes by such names as the new new math, whole math, fuzzy math, standards math, and rain forest math. Like the old New Math, it is creating a ferment among teachers and parents, especially in California, where it first caught on. It is estimated that about half of all pre-college mathematics in the United States is now being taught by teachers trained in fuzzy math. The new fad is heavily influenced by multiculturalism, environmentalism, and feminism. These trends get much attention in the twenty-eight papers contributed to the NCTM’s 1997 yearbook, Multicultural and Gender Equity in the Mathematics Classroom: The Gift of Diversity.

It is hard to fault most of this book’s advice, even though most of the teachers who wrote its chapters express themselves in mind-numbing jargon. “Multiculturalism” and “equity” are the book’s most-used buzzwords. The word “equity,” which simply means treating all ethnic groups equally, and not favoring one gender over another, must appear in the book a thousand times. A typical sentence opens Chapter Eleven: “Feminist pedagogy can be an important part of building a gender-equitable multicultural classroom environment.” Over and over again teachers are reminded that if they suspect blacks and females are less capable of understanding math than Caucasian males, their behavior is sure to subtly reinforce such beliefs among the students themselves, or what one teacher calls, in the prescribed jargon, a student’s “internalized self-image.”

“Ethnomathematics” is another popular word. It refers to math as practiced by cultures other than Western, especially among primitive African tribes. A book much admired by fuzzy-math teachers is Marcia…

This is exclusive content for subscribers only.
Get unlimited access to The New York Review for just $1 an issue!

View Offer

Continue reading this article, and thousands more from our archive, for the low introductory rate of just $1 an issue. Choose a Print, Digital, or All Access subscription.

If you are already a subscriber, please be sure you are logged in to your account.