New math

New math is a term referring to a brief dramatic change in the way mathematics was taught in American grade schools 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 scientific education and mathematical skill in the population; so that the supposed intellectual threat of the Soviet engineers, reputedly highly skilled mathematicians, could be met. In the consciousness of many Americans in the late 20th and early 21st century, New Math is reputed to have been a relatively ineffective approach, sometimes the object of mockery.

The new mathematical pedagogy
New Math emphasized mathematical structure through abstract concepts like set theory and number bases other than 10. Beginning in the early 1960s the new educational doctrine was installed, not only in the USA, but all over the western hemisphere.

Much of the publicity centered on the focus of this program on set theory (influenced ultimately by the Nicolas Bourbaki group and their work), functions, and diagram drawings. It was stressed that these subjects should be introduced early. Some of this focus was seen as exaggerated, even dogmatic. For example, in some cases first-graders were taught axiomatic set theory. 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.

Resistance to curriculum change
Many parents and teachers 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. 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.

Across the developed world
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 most 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.


 * 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 Boltyansky and Yaglom.

In Japan and Asian countries generally, the emphasis on basic numeracy has traditionally been high.

Popular culture
Tom Lehrer wrote a satirical song named New Math which centered around the process of subtracting 173 from 342 in decimal and octal. The song is in the style of a lecture about the general concept of subtraction in arbitrary number systems, illustrated by two simple calculations, and highlights the emphasis on insight and abstract concepts of the New Math approach. Lehrer's explanation of the two calculations is entirely correct, but presented in such a way (at rapid speed, with minimal visual aids, and with snide remarks thrown in) as to make it difficult for most audience members to follow the rather simple calculations being performed. This is intended to poke fun at the kind of bafflement the New Math approach often evoked when apparently simple calculations were presented in a very general manner which, while mathematically correct and arguably trivial for mathematicians, was likely very confusing to absolute beginners and even contemporary adult audiences. Summing up his opinion of New Math is the final sentence from his introductory remarks to the song: "...in the new approach, as you know, the important thing is to understand what you're doing, rather than to get the right answer."