Why Students Can't Add or Subtract
By Andrew Bernstein (Miami Herald, July 21, 2000; Buffalo News, August 13, 2000; Charlotte Observer, July 23, 2000; San Jose Mercury News; July 18, 2000; Las Vegas Review-Journal, July 24, 2000; Spokesman-Review, July 19, 2000)
Imagine that your child comes home from school one day and announces that in his math course there are no textbooks, no teaching--and no right answers. Instead, students form groups to construct their own math "strategies." They add fractions by folding paper strips, without ever learning how to convert to common denominators. They measure angles not with protractors but by means of bent straws. They are not taught to multiply or divide; rather, they are told to rely on calculators.
Your child further tells you that even the idea that a math problem has an objectively right answer has now been discarded. On tests, students receive high grades if they "wrestle diligently" with the problems, even if their answers are wrong.
Most parents would be horrified at such "dumbing down" of math instruction. Yet this is what constitutes the new math education in our public schools today. The new math guidelines explicitly disparage rigorous "paper and pencil computation" as an outdated attempt to find correct answers. Students are encouraged to "explore and conjecture," to "guess and check"--rather than to use strict rules of multiplication or division to figure out the answers precisely. Not surprisingly, many parents claim that children are now confused. Tutoring services report an epidemic of students coming to them to learn arithmetic.
Professional mathematicians are alarmed over declining U.S. math scores and point out that students in European and Asian countries--where they still teach basic math content--tend to score significantly higher than Americans on standardized tests. One recent test in mathematics literacy showed American high school seniors ranking 18th out of 21 nations.
The new math is sadly similar to the "look-say" method widely used in the attempt to teach reading. In that method, children are not taught to sound out a word phonetically. Rather, they look at its shape and guess its identity by means of the surrounding context. So if a sentence states, "The dog ate from his bowl," and the student guesses "dish" instead of "bowl," the student is praised for making a "good guess."
Similarly, the new math neither teaches nor permits the student to perform rigorous calculation. He must work with his classmates to devise techniques that will help them guess at the answer. If the answer is wrong, he is taught neither the correct answer nor a proper method of understanding it. Rather, he is praised for devising a "viable" mathematical strategy.
Students will be complimented for collecting thirteen piles of thirteen objects (more or less) in an attempt to answer the problem of 13x13--even if they arrive at an answer other than 169. Since the students don't learn the multiplication tables, they are lost when working with large numbers. Given these "educational" methods, it is clear why many American students never learn to read, write or understand arithmetic.
But there is a still more tragic result. The student's cognitive capacity has been stunted. Unable to deal with words or with numbers--having no means of knowing, but only of guessing--the child loses confidence in his mind. He loses confidence in his ability to deal rationally with reality. Unable to think, he is not qualified for college, for a demanding career--or even to make change at a check-out counter. With his mind crippled, the abysmally low self-esteem he experiences is inevitable. Rage, violence and widespread drug use are anticipatable consequences.
Today's educators are creating individuals who cannot think independently. They cannot question authority. They can only mindlessly obey. They can only melt into groups and subordinate themselves to the consensus. They are ripe for political indoctrination. The chilling truth is that this assault on our children's minds is characteristic of a totalitarian state, not a free society. Parents don't realize it, but this brain-mangling method of teaching has consequences far beyond mathematics.
The solution to this disaster is for the schools to emphasize that there are right and wrong answers--and to teach the student the precise means of arriving at them. Students need to be taught that there are objective methods for acquiring knowledge, in math as in all other fields. Learning this will enable students to gain genuine confidence in their cognitive abilities.
Our educators must recognize that they are entrusted with the sacred responsibility of training the mind. If they understand, and discharge, that responsibility, our high school graduates will be easily able to master mathematics--but even more important, they will be able to think.
Andrew Bernstein, author of The Capitalist Manifesto, is a senior writer for the Ayn Rand Institute in Irvine, Calif. The Institute promotes Objectivism, the philosophy of Ayn Rand--author of Atlas Shrugged and The Fountainhead.
For more articles by Andrew Bernstein, and his bio, click here.