The test results are in: America’s children are flunking math. In 1996 American high school seniors finished close to the bottom on an international mathematics test. At the end of last year, American eighth-graders ranked below those of Malaysia, Bulgaria, and Latvia.
As educators scramble to explain America’s math meltdown–as the Bush administration urges more “accountability” and a National Research Council study recommends better “training”–few are willing to look at the fundamental cause: the new, “whole-math” method for teaching.
Inspired by a strain of progressive-education theory called “constructivism,” whole-math proponents claim that all knowledge–including mathematical knowledge–is arbitrarily constructed. They reject the idea that there are objectively demonstrable right and wrong answers, and that, consequently, there are basic skills that students must be taught. Instead, the advocates of whole math believe that each student should invent his or her own math “strategies” by using a “guess-and-check” approach. They create an inability to think beyond immediate concretes.
In a typical whole-math classroom, children do multiplication not by learning the abstract multiplication table, but by using piles of marshmallows. They count a million birdseeds in order to understand the concept “million.” They measure angles by stretching rubber bands across pegged boards. One whole-math program preposterously claims to foster a “conceptual understanding” of math by asking fifth-graders the following stumper: “If math were a color, it would be ______ , because ______.” Surely such exercises foster in children only conceptual stultification–along with a bewildered sense of frustration and disgust.
Another whole-math program asks sixth-graders to address the following problem: “I’ve just checked out a library book that is 1,344 pages long! The book is due in three weeks. How many pages will I need to read a day to finish the book in time?” The proper way to solve the problem would be to use the method for long division: 1,344 divided by 21. By contrast, the whole-math approach assigns students to a group, requires them to design their own problem-solving rules, and urges them to guess if all else fails. In other words, children are told that their random “strategies” are just as good as the logically proven principles of long division. They are taught that the vote of the group, rather than the reasoning of the individual mind, is the means of arriving at the truth.
Now imagine flying on a plane designed by aeronautical engineers who have been trained to concoct their own math schemes and to use a “guess-and-check” method.
Whole math must lead to a miasma of confusion, boredom, and despair. Rather than encouraging independent, conceptual-level thinking, it is thoroughly anti-conceptual. It dooms children to function on a primitive, perceptual level–i.e., to flounder in a chaotic sea of concretes with no objective principles to guide them. This is cognitive child abuse. Whole-math defenders are shrinking the cognitive capacities of their students to those of infants or even animals.
Is it any wonder that most college freshman take remedial math courses, that American universities award more than half of their mathematics Ph.D.s to foreign nationals, that for-profit math remediation companies are booming, and that 200 of the nation’s leading mathematicians and scientists signed a public letter denouncing whole math?
Mathematics is like any other field. To master it, one must acquire basic knowledge before proceeding to more advanced stages. Proficiency in math requires that grade-school children learn the standard algorithms (i.e., the methods for addition, subtraction, multiplication, and division) and the four forms of numbers (i.e., integers, fractions, decimals, and percents). This forms the foundation upon which higher and higher levels of knowledge can then be built.
The controversy surrounding whole math is not simply about how children are taught to deal with numbers. If we undermine the capacity of our children to learn mathematics, we undercut their ability to think. More and more, our schools are turning out students whose capacity to reason has atrophied. Students who have not learned how to add and divide are also unable to perform the more demanding cognitive tasks of understanding concepts like “justice” or “truth” or “logic.” America’s children are being turned into mindless drones, who will soon be unable to distinguish freedom from tyranny.
Today’s “math wars,” like the controversy over how to teach reading, are at root philosophic battles that will have enormous implications for the future of America. If the advocates of whole math are allowed to win, they will be taking us a huge step away from the values of reason and science that once made America great.
Made available through the Ayn Rand Institute.