New Math: revisionist narrative watch

I've been doing some posts for the Monkey Cage. The first was a historical perspective piece on our last big educational reform initiative, the now anachronistically named 'New Math,' a post-Sputnik push for axiomatic rigor in primary and secondary mathematics education. Much of the feedback I got on the post indicated that I had gotten too deep in the weeds and spent too much time on the history lesson and not enough making my points. I'm inclined to agree.

One point I wish in retrospect I would have hammered harder was the way supporters of Common Core are pushing a convenient but false narrative about the initiative, namely that it was a noble effort that failed because most teachers lacked the training and mathematical sophistication to handle the new material. Recently, Elizabeth Green,* the chief executive of Chalkbeat (an organization that receives funding from both Bill Gates and the Walton Family), published a long piece in the New York Times that contains a perfect example.

The trouble always starts when teachers are told to put innovative ideas into practice without much guidance on how to do it. In the hands of unprepared teachers, the reforms turn to nonsense, perplexing students more than helping them. One 1965 Peanuts cartoon depicts the young blond-haired Sally struggling to understand her new-math assignment: “Sets . . . one to one matching . . . equivalent sets . . . sets of one . . . sets of two . . . renaming two. . . .” After persisting for three valiant frames, she throws back her head and bursts into tears: “All I want to know is, how much is two and two?”

Before we go on, you'll notice that the actual cartoon has nothing to do with how the material was taught. Schulz was satirizing bringing in arcane and needlessly complex methods to do simple tasks. In other words, his point was pretty much the opposite of Green's.

It is easy to see the appeal of the "unprepared teacher" narrative for many movement reformers. The reformers were the heroes here, visionary innovators who came up with great ideas but were stymied by the incompetence of the rank and file. As mentioned before, the tension between teachers and reformers is longstanding and can be traced to, among other things, a strong pro-privatization/anti-union faction in the movement and to teachers' understandable reluctance to try unproven approaches like 29-page scripted close readings of the Gettysburg Address.

Of course, the whole narrative falls apart if those 'innovative ideas' of New Math weren't actually that good or well executed to begin with (from the Monkey Cage post):

[George] Pólya was only one of many mathematicians and scientists who publicly criticized the new curriculum. Despite the common perception that “new math” failed because it was too advanced for general consumption, it was often those who understood the mathematics best who had the harshest comments.

Most notable of these may have been the physicist Richard Feynman, who eviscerated reform-era math and science texts in his essay “Judging Books by Their Covers.” Feynman mocked the confusing and overly technical language and complained about the emphasis on obscure mathematical topics, such as doing basic arithmetic in base five or seven (it is worth noting that songwriter and mathematician Tom Lehrer satirized the same topic in his song “New Math”).

Perhaps Feynman’s most cutting criticism was that, after dragging students through painfully rigorous presentations, the textbooks did not get the rigor correct:

The reason was that the books were so lousy. They were false. They were hurried. They would try to be rigorous, but they would use examples (like automobiles in the street for ‘sets’) which were almost OK, but in which there were always some subtleties. The definitions weren’t accurate. Everything was a little bit ambiguous — they weren’t smart enough to understand what was meant by ‘rigor.’ They were faking it. They were teaching something they didn’t understand, and which was, in fact, useless, at that time, for the child.

One of the best summaries of these criticisms came from Pólya, who alluded to the famous, though probably apocryphal, story of Isadora Duncan suggesting to George Bernard Shaw that they should have a child because it would have her beauty and his brains, to which Shaw is supposed to have replied that it could well have her brains and his beauty.

Pólya suggested that new math was somewhat analogous to Duncan’s proposal. The intention had been to bring mathematical researchers and high school teachers together so that the new curriculum would combine the mathematical understanding of the former and the teaching skills of the latter, but the final product got it the other way around.

We could could go back and forth on the place of axiomatic rigor in mathematics education (my position is a firm "it depends"), but in the case of New Math, it is difficult to argue that the initiative was not seriously flawed before it ever got to the teachers, and the last thing reformers like David Coleman want people thinking about is a narrative that includes that inconvenient fact.

* I contacted Ms. Green shortly after the piece ran. I have yet to hear back.