For younger readers, let me start by explaining that the “new math” was a K–12 mathematics curriculum reform movement in roughly the years 1955–1965. I volunteered to review this book because my dissertation was a history of that movement.

The relevance of the “new math” today is that there are striking similarities between the politics and controversy over new math and the current politics and controversy over Common Core. The book at hand is particularly relevant because of its subtitle: *A Political History*. The emphasis on politics is also its principal weakness. Sometimes crucial bits of the new math get lost in the politics. But then the same is true of current discussions of Common Core.

A welcome aspect of this book is that it is thoroughly researched with many references to primary sources. A point that is missed nonetheless is the discontinuity created by the creation of the School Mathematics Study Group (SMSG). There had been (generally glowing) reports on a number of new math projects in the media for some years prior. SMSG represented such a drastic change in direction that one earlier pioneer felt that the movement had been hijacked.

Unfortunately, Phillips takes SMSG as the paradigm of new math and does not say much about the creators of the movement. What SMSG did do was to spread vaguely related reforms to a much larger audience than had the pioneers. SMSG perhaps also gets too much emphasis in this book because it was influential mainly in the high schools. New math became famous for what it did in the elementary schools, and that was the source of its becoming a hotly debated political issue. “Had the reform efforts ended after SMSG finished writing high school textbooks, the new math might now be remembered as an overwhelmingly successful reform of secondary school mathematics.” (p.98) Phillips does devote a fair amount of space to what happened in the elementary schools, but the emphasis on SMSG still seems overdone considering their slight contribution to the political controversy.

Despite any faults this book may have, it is still a much better guide than the folklore that exists about new math. For example, to the public, the story of the new math is confined to the problems with commercial textbooks for the elementary schools. In contrast, many college mathematics faculty have told me that the new math years brought them the best prepared high school students they ever saw, before or since, and that a record number of those students were interested in further study of mathematics. Part of the folklore is that the new math was a failure, when in fact it was a failure at some levels and a success at others.

Another bit of folklore is that new math was abandoned because of falling test scores. That might be true in terms of the reasons given in political discourse, but in fact verbal test scores declined more, and math scores continued to decline after the back-to-basics movement replaced new math. Today, controversy about Common Core is driven more by perceptions and the symbolic meanings people attach to it than by the actual content of the standards. As another morbidly amusing example, SMSG began as something of a revolt against progressive education, and a response to the military implications of Sputnik, issues usually considered right wing, but at its demise it was considered a failed liberal attempt at general social reform.

I can recommend this book for its timeliness in connection with debates over Common Core. It is not a good guide to the content and pedagogy issues that gave rise to the new math in the first place. In essence, this book begins with the formation of SMSG, and the marginalization of those issues. The original new math can’t be said to have failed because it was never widely implemented. Its ideas are still worthy of consideration today.

After a few years in industry, Robert W. Hayden (bob@statland.org) taught mathematics at colleges and universities for 32 years and statistics for 20 years. In 2005 he retired from full-time classroom work. He now teaches statistics online at statistics.com and does summer workshops for high school teachers of Advanced Placement Statistics. He contributed the chapter on evaluating introductory statistics textbooks to the MAA's Teaching Statistics.