The new math was widely praised at first as a model bipartisan reform effort. It was developed in the 1950s as part of the “Cold War of the classrooms,” and the resulting textbooks were most widely disseminated in the 1960s, with liberals and academic elites promoting it as a central component of education for the modern world. The United States Chamber of Commerce and political conservatives also praised federal support of curriculum reforms like the new math, in part because these reforms were led by mathematicians, not so-called progressive educators.I suspect Phillips is right about the politics, but I think that debates about teaching math are about more than right vs. left or elites vs. populists. Mathematicians find math beautiful and fascinating and it bothers them that most Americans hate it. They keep searching for ways to convey the power and fascination of math, to make it interesting, to create a world in which Barbie dolls don't say "Algebra is soooooo hard." Approaches like New Math and some of the recent Common Core math are supposed to show students that math isn't just the multiplication table and the quadratic formula, but something flexible and powerful, and that understanding math at a more fundamental level opens up a world of both practical uses and amazing discoveries. But most Americans, including most middle school math teachers, don't care enough to bother.
By the 1970s, however, conservative critics claimed the reforms had replaced rigorous mathematics with useless abstractions, a curriculum of “frills,” in the words of Congressman John M. Ashbrook, Republican of Ohio. States quickly beat a retreat from new math in the mid-1970s and though the material never totally disappeared from the curriculum, by the end of the decade the label “new math” had become toxic to many publishers and districts.
Though critics of the new math often used reports of declining test scores to justify their stance, studies routinely showed mixed test score trends. What had really changed were attitudes toward elite knowledge, as well as levels of trust in federal initiatives that reached into traditionally local domains. That is, the politics had changed.
Whereas many conservatives in 1958 felt that the sensible thing to do was to put elite academic mathematicians in charge of the school curriculum, by 1978 the conservative thing to do was to restore the math curriculum to local control and emphasize tradition — to go “back to basics.”
Most people just aren't interested in abstract thought, and they never will be.