Mathematician Knocks School

From GWS 52

This is another article in the “more things change the more they stay the same” mold. This one features an expert mathematician from 40 years ago making a similar critique Holt first made in the sixties and that some researchers and teachers are making today: “… very young children learn in manifold ways, at a rate that will never be equaled in later life, and with no formal teaching. Yet the same children find much simpler things far more difficult as soon as they are formally taught in school.”

From the article “Learning Math By Thinking” by Fred M. Hechinger, the New York Times, 6/10/86:

… Dr. Hassler Whitney, a distinguished mathematician at the Institute for Advanced Study in Princeton, says that for several decades mathematics teaching has largely failed. He predicts that the current round of tougher standards and longer hours threatens to “throw great numbers, already with great math anxiety, into severe crisis.”

Dr. Whitney has spent many years in classrooms, both teaching mathematics and observing how it is taught, and he calls for an end to what he considers wrongheaded ways.

Long before school, he says, very young children “learn in manifold ways, at a rate that will never be equaled in later life, and with no formal teaching.” For example, they learn to speak and communicate, and to deal with their environment. Yet the same children find much simpler things far more difficult as soon as they are formally taught in school.

Learning mathematics, Dr. Whitney says, should mean “finding one’s way through problems of new sorts, and taking responsibility for the results.”

“This has been completely forgotten” in most schools, he finds. “The pressure is now to pass standardized tests. This means simply to remember the rules for a certain number of standard exercises at the moment of the test and thus ‘show achievement.’ This is the lowest form of learning, of no use in the outside world.”

Dr. Whitney, in a recent report in the Journal of Mathematical Behavior recalled an experiment begun in 1929 by L.P. Benezet, then superintendent of schools in Manchester, N.H. Mr. Benezet was distressed over eighth graders’ poor command of English and their inability to communicate ideas.

“In the fall of 1929,” he wrote in 1935, “I made up my mind to try an experiment of abandoning all formal instruction in arithmetic below the seventh grade and concentrate instead on teaching the children to read, to reason. and recite” by reporting on books they had read and incidents they had seen. The children were no longer made to struggle with long division. “For some years,” Mr. Benezet went on, “I had noticed that the effect of early introduction of arithmetic had been too dull and almost chloroform the child’s reasoning faculties.”

Over the years numbers crept into children’s experience, Mr Benezet said. They learned to deal with “halves” and “doubles,” with estimates of size, with a natural development of multiplication tables and slowly, with formal arithmetic.

Mr. Benezet concluded that children who had not been dragged into early but only dimly understood mathematics eventually outdistanced those who had. Literacy in English and a capacity to think independently and to speak and write clearly helped many to do well in mathematics, too.

In the traditional school climate, Dr. Whitney writes, children’s natural thinking “becomes gradually replaced by attempts at rote learning, with disaster as a result.” In high school, students increasingly say, “Just tell me which formula to use,” a way of saying “Don’t ask me to think.”

Because teachers must “cover the material,” Dr. Whitney adds, there is less time to think. When students are called on, they must answer instantly. Wrong answers are not discussed.

“Students and teachers are all victims” as national commissions clamor for more mathematics without realizing, Dr. Whitney warns, that they may create less knowledge and more anxiety. He says it is crucial to stop just learning the rules.