Education Reform is the new New Math

June 16
peanuts

As a former math teacher, I’ll admit that I never expected math homework to be a sexy topic . . .

Strange as it may seem, there is currently a heated national debate over what kind of math problems primary and secondary school students should be given. The politics of the debate are extraordinarily complex and are a subject for other posts to explain. Suffice to say, this may be the only time you will have a debate with Barack Obama and Jeb Bush on one side and Michelle Malkin and Louis CK on the other. This debate calls to mind another major education initiative that peaked about 50 years ago and was best known by the now-dated name New Math.

Both our current set of education reforms and those of the late ’50s and ’60s were pushed through in large part because of concerns over America falling behind the rest of the world in what we now call STEM (Science, Technology, Engineering and Mathematics). The recent cause of this concern is the Program for International Student Assessment (better known as PISA), an international triennial test coordinated by the Organization for Economic Cooperation and Development (OECD) and first administered in 2000. The PISA scores seemed to show the United States falling behind the rest of the world in math, science and reading.

The general reaction was best captured by U.S. Education Secretary Arne Duncan, who said in 2009, “This is an absolute wake-up call for America. The results are extraordinarily challenging to us and we have to deal with the brutal truth. We have to get much more serious about investing in education.”

Further scrutiny revealed a somewhat murkier picture. Among other criticisms, it was pointed out by Tom Loveless, a senior fellow with the Brown Center on Education Policy at the Brookings Institution, that the top-ranked “country” (Shanghai) maintained its position largely, if not entirely, because China had systematically made sure to test only its most elite students. Despite these revelations, the idea of the United States falling behind China has become firmly entrenched in the standard op-ed narrative.

The impetus for New Math was also the fear that we were falling behind other countries, though back then the anxiety was triggered by a much more dramatic event. On Oct. 4, 1957, the Soviet Union had launched Sputnik. Having a Soviet satellite flying overhead at the height of the Cold War had a strong and immediate effect. The response included the creation of NASA and the Advanced Research Projects Agency (soon to be renamed DARPA) and a radical change in the way we taught math and science.

The ’50s had already been a period of great concern about the quality of education in what we now call STEM. It almost seems a little quaint now — the postwar era is considered a period of remarkable scientific progress — but these fears had been building for a long time, and they were supported by what seemed at the time to be some deeply troubling numbers.

From A History of Mathematics Education in the United States and Canada, National Council of Teachers of Mathematics, 1970, via “A Brief History of American K-12 Mathematics Education in the 20th Century” by David Klein:

Percentages of U.S. High School Students Enrolled in Various Courses

School Year

Algebra

Geometry

Trigonometry

1909 to 1910

56.9%

30.9%

1.9%

1914 to 1915

48.8%

26.5%

1.5%

1921 to 1922

40.2%

22.7%

1.5%

1927 to 1928

35.2%

19.8%

1.3%

1933 to 1934

30.4%

17.1%

1.3%

1948 to 1949

26.8%

12.8%

2.0%

1952 to 1953

24.6%

11.6%

1.7%

1954 to 1955

24.8%

11.4%

2.6%

For the education reformers of the ’50s, Sputnik was both a confirmation of their fears and a powerful tool for advancing their agenda. Their proposals were big and far-reaching, but for most people, they came down to one thing: New Math.

Of the various elements of New Math, the best known and most controversial was the decision that primary and secondary school students should learn advanced mathematical concepts and, what’s more, should learn them the way they were taught in upper-level mathematics courses. It seemed at first glance an entirely admirable, if perhaps overly ambitious, plan. But even at the proposal stage, there were concerns.

Upper-level math courses were and are generally built around the idea that every theorem must be rigorously proven before one proceeds to the next idea. Unfortunately, many of the basic, largely self-evident theorems that students encounter in algebra and geometry require a surprising level of sophistication to prove. George Pólya, one of the small set of major mathematicians to dig seriously into the subject of math education, pointed out the following example:

[T]he School Mathematics Study Group (SMSG) … geometry text that gave a theorem with proof — taking up half a page — stating that with three points on a line, one point must lie between the other two. [Pólya] argued that though this is a necessary theorem for a foundations course in geometry, it has no place in an elementary text. He said that had he been asked to study the proof of such a theorem in high school, he would almost certainly have given up on mathematics.

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.

While we can argue that New Math doesn’t quite deserve its reputation as a total failure, it is almost impossible to call it a policy success. Its reputation in the math and science communities was decidedly mixed, it showed little signs of having improved student performance, and it was a PR nightmare. Even now the topic is good for a punchline on shows such as “Community.”

New Math would seem to be an almost ideal starting point for a discussion of the current Common Core and Common Core-related education programs (the former being a relatively small part of the overall initiatives). It is perhaps the only precedent of similar scale. Its ties to concerns over Sputnik are analogous to today’s concerns over PISA. Its underlying assumptions about taking a more scientific approach to education are similar. Add to that New Math’s relatively high name recognition and generally agreed upon outcome (there’s not much point in bringing up something no one remembers).

And, yet, references to New Math are remarkably hard to find on either side of the current debate over education policy, even when the conversation seems to lead straight to the topic, such as when the following appeared in the Wall Street Journal. (A non-paywall version can be found at the site of the Thomas B. Fordham Institute, the education policy think tank where Chester E. Finn serves as president.)

A Sputnik moment for U.S. education by Chester E. Finn, Jr.
December 08, 2010

Fifty-three years after Sputnik caused an earthquake in American education by giving us reason to believe that the Soviet Union had surpassed us, China has delivered another shock. On math, reading, and science tests given to 15-year-olds in sixty-five countries last year, Shanghai’s teenagers topped every other jurisdiction in all three subjects — by a sweeping margin. What’s more, Hong Kong ranked in the top four on all three assessments.

Finn, who received his EdD in 1970, was certainly aware of the controversy over the education reforms that followed Sputnik, but after the title and opening paragraph, the subject is not broached again. New Math is not mentioned at all.
All of this begs some bigger questions about the way we discuss public policy. The New Math precedent would certainly seem to be relevant to the conversation, and we generally work under the assumption that a vigorous discussion will bring all relevant and available information to the surface. Is there something special about this example that keeps it off the table? Are we not very good at handling historical precedents? What other topics are being left out of other discussions?

Mark Palko is a statistician and blogger based in Los Angeles.

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