## Math: Old, New, and Equalitarian — A Review

I have a new paper out in Academic Questions, a review, “Math: Old, New, and Equalitarian.”

Springer is charging a mere pittance for viewing it. Only $39.95. But I think you can get a PDF from this link, through something Springer is called “SharedIt“. I’m not at all clear what it means, and I have no interest in discovering. As long as you can read the article, I’ll be happy.

*Here’s the start…*

There are three ways to teach math to the young. The old way forced rote memorization of basics and then, for most, stopped the lessons, continuing them only for those who had the inclination or ability to advance. The “new” way was to “expose” every student from the beginning, no matter their age or inexperience, to the highest, most difficult mathematical concepts, so that all might know how wondrous and astonishing math is.

The modern way, which may soon be upon us, is to let students define what math is to them or their culture, to let them discuss their feelings about what math means, and to work toward the goal of equality, that happy state when all are satisfied with their level of (self-defined) mathematical understanding. Two new books—*The New Math: A Political History*, by Christopher J.Phillips, and *Critical Math ematicsEducation: Theory, Praxis, and Reality*, edited by Paul Ernest, Bharath Sriraman, and Nuala Ernest—bring these distinctions to the fore.

People were long happy with the old way and for the happiest of reasons. It worked. Nearly every child eligible to attend school could be made to learn, or at least to memorize, that 8 x 7 = 56 and that triangles encompassed half as many degrees as circles and what simple consequences flowed from these facts. Not every child could advance beyond these basics, but few thought that all should.

That attitude began to change mid-twentieth century, a time in which greater proportions of children were enrolling in all levels of schooling.Because of the Cold War and the impression that America was falling behind, the concern was that kids weren’t learning enough and that they needed to be better thinkers. “New Math” was the result.

In *The New Math: A Political History*, Carnegie Mellon University assistant professor of history Christopher J. Phillips tells of its rise and fall, centering the tale on the School Mathematics Study Group (SMSG), an entity created in earnest by government money during the Sputnik era: “Although originally funded to work on textbooks for the ‘college capable’ students in secondary schools, SMSG gradually expanded its operation, producing textbooks for every grade and type of student, including material for elementary schools, ‘culturally disadvantaged’ children,” etc. The ascension of New Math was thus partly due to routine mission creep found in well-funded bureaucracies.

At its onset, parents were more or less happy with the status quo. But education theorists and others were not. Students taught in the old way could cipher to the rule of three, but they didn’t know the why behind the how: “[O]ne generally accepted axiom was that math textbooks’ and teachers’ traditional reliance on memorization and regurgitation gave students a misleading sense of what mathematicians do and what mathematics was about.”

Yet is it really of interest what professional mathematicians do? Filling out grant requests, for instance? At any rate, what mathematics is about is something argued over by mathematicians themselves. This was true during the time of New Math…

*Click the above link to get the PDF and read the rest (I think).*