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 centred on focus of this programme on set theory (influenced ultimately by Nicolas Bourbaki and his works), functions and diagram drawings. It was stressed that these subjects should be introduced early. Some of this focus was exaggerated, or dogmatic. For example, first-graders were taught axiomatic set theory in some cases. The idea behind this was that if the axiomatic foundations of mathematics was introduced to children, they could "easily" cope with the theorems of the mathematical system later.

In the USA, many parents and teachers complained that the new curriculum was too far outside of students' ordinary experience and was not worth taking time away from fundamentals (namely, arithmetic). The material also put new demands on teachers. In the end it was concluded that the experiment was not working, and New Math eventually fell out of favor before the end of the decade.

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. 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 facility 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 US experience does seem in retrospect to have the hallmarks of a moral panic.