New Math

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 change involved new curriculum topics and 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 technological threat of Soviet engineers, reputedly highly skilled mathematicians, could be met.If we would like to, we can and do say, 'The answer is a whole number less than 9 and bigger than 6,' but we do not have to say, 'The answer is a member of the set which is the intersection of the set of those numbers which are larger than 6 and the set of numbers which are smaller than 9' ... In the 'new' mathematics, then, first there must be freedom of thought; second, we do not want to teach just words; and third, subjects should not be introduced without explaining the purpose or reason, or without giving any way in which the material could be really used to discover something interesting. I don't think it is worthwhile teaching such material.'Under A. N. Kolmogorov, the mathematics committee declared a reform of the curricula of grades 4–10, at the time when the school system consisted of 10 grades. The committee found the type of reform in progress in Western countries to be unacceptable; for example, no special topic for sets was accepted for inclusion in school textbooks. Transformation approaches were accepted in teaching geometry, but not to such sophisticated level presented in the textbook produced by Vladimir Boltyansky and Isaak Yaglom.' 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 change involved new curriculum topics and 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 technological threat of Soviet engineers, reputedly highly skilled mathematicians, could be met. The phrase is often used now to describe any short-lived fad which quickly becomes highly discredited. Topics introduced in the New Math include modular arithmetic, algebraic inequalities, bases other than 10, matrices, symbolic logic, Boolean algebra, and abstract algebra. In elementary school, in addition to bases other than 10, students were taught basic set theory and made to distinguish 'numerals' from 'numbers.' 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. In an effort to learn the material, many parents attended 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. 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 1965, physicist Richard Feynman wrote in the essay New Textbooks for the 'New' Mathematics: In his book Why Johnny Can't Add: the Failure of the New Math, Morris Kline says that 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.':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.':98 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. 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. 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.