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New Mathematics or New Math was a brief, dramatic change in the way mathematics was taught in American grade schools, and to a lesser extent in European countries, during the 1960s. The name is commonly given to a set of teaching practices introduced in the U.S. shortly after the Sputnik crisis in order to boost science education and mathematical skill in the population so that the perceived intellectual threat of Soviet engineers, reputedly highly skilled mathematicians, could be met.
Mathematicians describe interesting objects with set-builder notation. Under the stress of Russian engineering competition, American schools began to use textbooks based on set theory. For example, the process of solving an algebraic equation required a parallel account of axioms in use for equation transformation. To develop the concept of number, non-standard numeral systems were used in exercises. Binary numbers and duodecimals were new math to the students and their parents. Teachers returning from summer school could introduce students to transformation geometry. If the school had been teaching Cramer's rule for solving linear equations, then new math may include matrix multiplication to introduce linear algebra. In any case, teachers used the function concept as a thread common to the new materials.
Philosopher and mathematician W.V. Quine wrote that the "rarefied air" of Cantorian set theory was not to be associated with the New Math. According to Quine, the New Math involved merely..."the Boolean algebra of classes, hence really the simple logic of general terms."
It was stressed that these subjects should be introduced early. The idea behind this was that if the axiomatic foundations of mathematics were introduced to children, they could easily cope with the theorems of the mathematical system later.
Other topics introduced in the New Math include modular arithmetic, algebraic inequalities, matrices, symbolic logic, Boolean algebra, and abstract algebra. Most of these topics (except algebraic inequalities) have been greatly de-emphasized or eliminated in elementary school and high school since the 1960s.
Parents and teachers who opposed the New Math in the U.S. complained that the new curriculum was too far outside of students' ordinary experience and was not worth taking time away from more traditional topics, such as arithmetic. The material also put new demands on teachers, many of whom were required to teach material they did not fully understand. Parents were concerned that they did not understand what their children were learning and could not help them with their studies. Many of the parents took time out to try to understand the new math by attending their children's classes. In the end it was concluded that the experiment was not working, and New Math fell out of favor before the end of the decade, though it continued to be taught for years thereafter in some school districts. New Math found some later success in the form of enrichment programs for gifted students from the 1980s onward in Project MEGSSS.
In the Algebra preface of his book Precalculus Mathematics in a Nutshell, Professor George F. Simmons wrote that the New Math produced students who had "heard of the commutative law, but did not know the multiplication table."
In 1973, Morris Kline published his critical book Why Johnny Can't Add: the Failure of the New Math. It explains the desire to be relevant with mathematics representing something more modern than traditional topics. He says certain advocates of the new topics "ignored completely the fact that mathematics is a cumulative development and that it is practically impossible to learn the newer creations if one does not know the older ones" (p. 17). Furthermore, noting the trend to abstraction in New Math, Kline says "abstraction is not the first stage but the last stage in a mathematical development" (p. 98).
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In the broader context, reform of school mathematics curricula was also pursued in European countries such as the United Kingdom (particularly by the School Mathematics Project), and France, where the extremely high prestige of mathematical qualifications was not matched by teaching that connected with contemporary research and university topics.[clarification needed] In West Germany the changes were seen as part of a larger process of Bildungsreform. Beyond the use of set theory and different approach to arithmetic, characteristic changes were transformation geometry in place of the traditional deductive Euclidean geometry, and an approach to calculus that was based on greater insight, rather than emphasis on facility[clarification needed].
Again the changes met with a mixed reception, but for different reasons. For example, the end-users of mathematics studies were at that time mostly in the physical sciences and engineering; and they expected manipulative skill in calculus, rather than more abstract ideas. Some compromises have since been required, given that discrete mathematics is the basic language of computing.
Teaching in the USSR did not experience such extreme upheavals, while being kept in tune both with the applications and academic trends.