Do not think about, write about or deal with human behavior without determining the effects of incentives.
The following is a rundown on the “New Math” which came about as a reaction to the Soviet Union’s supposed “win” in the Space Race. Man in orbit, but no good automobiles or toilet paper. The New Math tried to teach number theory to grade schoolers and left millions of students with few math skills and an abiding hatred of mathematics.
The quotes are from: A Math Warrior’s Almanac, by Nakonia (Niki) Hayes and available at nakonia69@saxonmathwarrior.com
“With Sputnik’s launch in 1957, Russia had beaten the U.S. in the space race. Bruised egos and even panic ensued as government leaders set up four major committees to bring math education into “modern times.” The most famous of these groups was the School Mathematics Study Group (SMSG), a think tank composed mostly of theoretical mathematicians and directed by Yale University mathematician Edward G. Begle. It had about 36 college mathematicians, 15 high school teachers, and one physicist as members.”
……
“He wrote that college professors as theoretical mathematicians “knew little or nothing of what high-school students know, how they think, and how they learn. They
also were uninformed about what topics should be taught at what level.” That was why high school teachers were asked to join the SMSG meetings, but most of them were overshadowed by the college contingent, John said.
He told how he had talked to several participants in the SMSG, and they stated that it operated like all too many committees: There was little agreement as to what should be done, prima donnas got mad and stalked out of meetings, cliques formed, and on occasion arbitrary decisions were made. While their goal was to bring “math education into modern times, there was a paucity of new ideas, and much time as spent rummaging through existing textbooks. There was no consensus on much of what was discussed; but after meeting for three or four summers, they printed what they had come up with, to be used as a guide by the major book companies.” He summarized their work as “groping in the dark,” which euphemistically represented “catching up with the Russians.”
The SMSG committee basically got the idea that teaching math could be improved somehow by concentrating on more recently developed concepts in mathematics. John wrote, “They were not definite in their criticism of what was wrong and did not know what should be changed and set no goals for these changes.” He concluded that topics were chosen under the assumption that all the children were being trained to be theoretical mathematicians. “Topics of interest in physics and chemistry were ignored,” he said, “and it was the imbalance that gave the new math a bad name, not the new ideas themselves.”
The committee also chose to join the negative reaction held by Progressive educators against Edward L. Thorndike, whose book, The Psychology of Arithmetic, in 1924 had dominated much of the thinking in education. He had held that “Learning is essentially the formation of connections or bonds between situations and responses…and that habit [repetition and practice] rules in the realm of thought as truly and as fully as in the realm of action.”
Prof. Begle’s group would follow, instead, the 1935 response begun by mathematics educators W. A. Brownell and C.B. Chazal who denigrated the emphasis on drill and who advocated a meaning theory. The meaning theory emphasized the inner relationships of the number system as well as social uses of arithmetic. Their theory was incorporated with John Dewey’s Progressive ideology and the “modern math” movement was born—in the 1930’s.
The major book companies got into the act by hiring “experts” to write books that followed the SMSG recommendations. Although schools were expected to use these new texts, the emphasis on the esoteric and the neglect of fundamentals made them unworkable, John said, “but most people went along with them under the impression that everyone else was pleased.”
Disbanding in 1977, the SMSG committee left an indelible mark on math education with books that were poorly conceived and abominably executed, according not only to John but too many parents and colleges as students were being graduated from high school severely deficient in math skills. Worse, a generation of students had learned to hate mathematics because they felt they couldn’t learn it. John said, “Math teachers and parents should have raised hell the first time a ninth-grader brought home an the first time a ninth-grader brought home an algebra book that his college-graduate mother and father could not decipher. The idea that children can be taught from books that are unintelligible to adults is absurd. This should be our first check from now on: If we can’t read and understand the book, then the book is unsatisfactory.”
Further, in the ‘Progressives’ giant leap of teaching abstractions over concrete skills, John said the “new mathers” decided being able to work the problem did not suffice if the student didn’t understand the bigger picture in which the problem might be found. The “doing” (small steps) and “practice” were ridiculed. It was acceptable, in fact, for a student not to be able to work a problem if he understood the concept. A student might understand the concept of paying interest on a loan, for example, but not know how to set up a problem to find that interest. He was amazed by their idea of teaching children “to think and to understand, and from that understanding, then children would be able to do.” Using this approach, he insisted, was analogous to trying to teach the piano by giving lessons in music theory, demonstrating the major and minor chords and fingering techniques and then asking the student to put it all together and play a sonata. “It just can’t be done that way,” he said. “The student must learn to play simple pieces before more difficult pieces are attempted.”“
Unfortunately, this scenario is played over and over again. The theory dictates everything, children fail to learn, the theory is changed, etc.
Saxon makes an interesting point about textbooks being incomprehensible. This is supposed to lead to “advanced thinking”, but it only leads to frustration and waste. This is what happens when no one is accountable.
Cheerio and ttfn,
Grant Coulson
Cui Bono–Cherchez les Contingencies
