New math
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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.
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The new mathematical pedagogy
New Math emphasized more abstract concepts like set theory and number bases other than 10, rather than strictly being concerned with mathematical concepts traditionally taught to those age groups. 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 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 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.
Across the developed world
In the broader context, reform of school mathematics curricula was also pursued in European countries such as the UK (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 probably never experienced such upheavals, being kept in tune both with the applications and academic trends.
In Japan and Asian countries generally, the emphasis on basic numeracy has traditionally been high. The U.S. experience does seem in retrospect to have the hallmarks of a moral panic.
Popular culture
Tom Lehrer wrote a satirical song named New Math, making fun of the more absurd aspects of the subject. 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."
In modern culture (specifically within the geek community), the term is often used sarcastically to instances where people base analyses upon incorrect calculations. An example would be "She justified that expenditure with that New MathTM."