An article on math instruction appears in the current issue of Education Next. Education Next is a level-headed nondoctrinaire journal published by the Hoover Institute at Stanford University. The article, “An A-Maze-ing Approach to Math,” is by Barry Garelick, who works as an analyst for a federal agency. The article can be found on the Internet at www.educationnext.org/20052/28.html.

Mr. Garelick is not a math teacher. But he is a person who needs to use math for his work and is a parent of school-age children. He has dreams of becoming a math teacher as his second career. This led to volunteer work as a tutor in a local high school.

What he has discovered will come as no surprise to those of you who have been following my columns. Many, if not most American children are no longer being taught anything that most adults would consider mathematics. This is a result of the introduction of constructivist or “fuzzy” math to American classrooms during the past 15 years.

The results bode ill for our national interests. Of 41 countries participating in the Third International Mathematics and Science Study, American eighth-graders scored in the 28th position, below the international average. Twelfth graders finished 18th out of 21 countries participating. In the recently released results of the Program for International Student Assessment, American 15-year-olds ranked 24th out of 29 countries.

This should be considered a national crisis deserving of government attention. But it is in large part the government that has funded the tinkering with what was by-and-large the world’s most successful effort to teach math. After all, this country sent men to the moon and developed most of the technology in the personal computer, a revolutionary invention that almost defines our age. All of this was dependent on mastery of math. So we were doing just fine.

Mr. Garelick was tutoring a ninth-grader who was learning geometry. He needed help with proofs, which to Mr. Garelick was no surprise. For millennia, students have needed help with geometry proofs. In years past, the answer was usually found in the student’s textbook. Mr. Garelick was horrified to learn that what he called a “mainstay of mathematics” was largely missing from his student’s geometry text.

Geometry instruction is based on learning the concept of proofs. Absorbing this material was not pleasant, but students of my generation understood that we didn’t have to like it, we just had to do it. Why are proofs important? Aside from the use of proofs in higher math, there are lessons in logical progression that can be applied to nearly every discipline.

So Mr. Garelick began looking at other textbooks and found the same truncated instruction. Students were being given a Reader’s Digest version of math. Mr, Garelick’s daughter, then a student in the second grade, was not being taught the addition and subtraction facts. He discovered that none of this was an accident. He had encountered the new, new math. His daughter in Fairfax County, Va., was being taught with the same “fuzzy” program Chancellor Klein has mandated for all elementary schools here in New York.

Now some may argue that it really isn’t important to learn the algorithms, the formulas, and methods to solve common problems. After all, anyone with two or three dollars in his wallet can buy a pocket calculator that can solve 99% of the problems most of us face in real life, things like balancing a checkbook, or figuring out how much that 15% off coupon will save us at the sale at Macy’s.

This may be true. But many have to do more. One cannot learn algebra unless you know your basic arithmetic. And if one doesn’t master algebra, one is unlikely to learn calculus. And if one doesn’t know calculus, forget a career in a technical field.

As a nation we are falling behind. But what is worse, our best and brightest students are falling behind — and by the design of well-meaning, sensitive educrats. This was the nature of last year’s Senate testimony by the chairman of the Federal Reserve, Alan Greenspan.

Mr. Garelick tried to influence public policy on mathematics instruction through an internship he was given with a Democratic senator, identified only as “Senator X,” in the best mathematical tradition. The solon was interested in encouraging technology industry in his state. Improving math instruction seemed like a perfect remedy.

It is here that Mr. Garelick met the politics of American education. Somehow, the ideas that we hold on schooling have gotten confused with other political differences. When Democratic staffers of the Hill learned that one of the leading critics of “fuzzy” math was Lynne Cheney, the wife of the vice president, they backed away from advocating for the reforms they knew were called for. If Mrs. Cheney was involved, after all, it must be a right-wing plot.

Our politics have become so divisive that even the commonsense interests of children can no longer be common ground for our elected officials. Mr. Garelick is sadder and wiser, and now tells the students he tutors, “Don’t worry, it isn’t you.”