New Math

Part of a convergent series on Mathematics

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Alan Sokal JBS Haldane Roger Penrose Albert Einstein v - t - e

“”But in the new approach, as you know, the important thing is to understand what you're doing, rather than to get the right answer.

—Tom Lehrer

“”Why would they change math? Math is math!

—Mr. Incredible

"New Math" or reform mathematics was a series of modified mathematics curricula introduced into American schools from the 1960s onward. The first round of modifications was made for political purposes, as the U.S. government, having witnessed the launch of Sputnik in 1957, was trying desperately to farm more mathematicians for the purpose of one-upping the Soviets in space technology.

Similar programs were pursued in the UK (School Mathematics Project) and Europe. In common with many educational approaches associated with the 1960s (although it actually began in the late 50s), New Math aimed to minimize rote and promote a deeper understanding through exploration and play. However New Math was much more rigorous than some caricatures. It proved short-lived, and by 1976 only 9% of schools were still using the National Science Foundation (NSF)'s program.

But another round, still ongoing, came in the 1990s after the publication of Principles and Standards for School Mathematics, which expresses similar motives, though shorn of the "one-upping the Reds" veneer. At least one cycle of textbooks has been made as a specific repudiation of it.

Starting point

New Math is based on the premise that "all children can learn mathematics." This contrasted with a view in progressive education that math was useless for most people and in the words of William Heard Kilpatrick, "we have in the past taught algebra and geometry to too many, not too few" and the subjects were "an intellectual luxury" of no more value than Latin or ancient Greek.

If taking the view that maths is for all, it being observed that there are people who cannot put two and two together without making less than six thousand, one of two courses of action must be taken in order to make the premise jive with reality: one must either (1) transform the understanding of a considerable number of students who hitherto appeared thick, or (2) evacuate the definition of "mathematics" so that even the chumps can be hot-shots at it. We will let the reader decide which of these courses of action New Math takes.

Content

As the name suggests, the New Math curricula are quite different from the traditional sort, primarily in that they put a greater emphasis on grasping abstract mathematical concepts than on solving numerical problems in math. Despite many people's assumption that anything new must be dumbing down, New Math was not a trendy anti-intellectual, child-centred activity: it drew on the knowledge of mathematicians and offered a more rigorous program that what came before it, introducing high school students to topics such as calculus and set theory, and it attempted to promote deep understanding rather than just teaching how to do the basics. This was in contrast to a practical tendency going back to John Dewey that held education should teach practical skills not abstract concepts.

• The nursery-school pupil, instead of being taught such archaic nonsense as how to wipe his nose and say the ABCs, will learn how to "represent and analyze mathematical situations and structures using algebraic symbols." He will be taught the commutative law, geometric transformations, and analytic geometry.
• The elementary-school pupil, instead of working through big complicated computations that are best left to calculators, such as dividing 36 by 6, will play with exciting toys such as Snap^TM cubes and power polygons, which unlike most toys will be paid for by the State, to the tune of over $1,000.
• The middle-school pupil, instead of having to trudge through endless columns of fractions (boring!), will be introduced to such stimulating mathematical conundrums as the social role of zoos and how pollution threatens the planet.
• The high-school pupil will get to think just like mathematicians and scientists, who (contrary to the popular myth that they are engaged in high-level thinking for which the prerequisite is 20 years of education) actually sit around all day yanking conjectures from where the sun don't shine.

Influence

“”So which book requires students to think? It is not the American one.

—Richard Askey

By the time the first generation of children educated on New Math were reaching adulthood, instead of a new wave of mathematicians racing to solve complex engineering problems and shoot colonists off to Mars one step ahead of the communists, the U.S. had a moribund space program and mathematics departments that were beginning to fill with immigrants from certain communist countries, who (unlike their American counterparts) actually knew how to count to ten.

Historical context

"New Math" has become a byword for short-lived fads, particularly in education, and considered an example of trendy teachers rejecting what works. However, the reality was more complex, as was its place in a long struggle over the nature and purpose of education. In the first half of the 20th century, progressivists who wanted student-centred learning fought against traditionalists who wanted kids to learn facts. By the early 1950s, there was a sense that people didn't really need to know mathematics and the number of students studying math was falling. New Math recognised the importance of math and sought to introduce logical rigor and deep understanding. However there was a feeling among many mathematicians that New Math went too far in its abstraction, and it certainly alienated parents and some mathematicians, as well as confusing a lot of children.

Horror over innovations like New Math is interspersed by equally regular horror that traditional learning (working through long lists of sums) is failing to provide students with a genuine understanding of the subject and an inability to innovate: rote learning let them regurgitate 2+2 or the integral of log(x) but they were unable to apply skills to anything they'd not already encountered. The history of education is largely a history of panics that kids today know nothing and the education system is shit. The National Council of Teachers of Mathematics (NCTM) released An Agenda for Action in 1980 which recommended using calculators and focusing on team activities. However it was ignored. In 1983 the US Department of Education produced A Nation At Risk which again found that Americans knew nothing about math. This led to the introduction of the 1989 NCTM Standards which again rejected paper-and-pencil skills in favour of teamwork and technology.

In the 2000s there was another round of panic. This led to the Common Core State Standards Initiative which attempted to use actual evidence to improve educational methodology. The result was something of a soft return to New Math, with a focus on methods rather than results - and again it was met with fear and contempt. Whether American kids will ever be able to add is an open question. Although it's possible that the low attainment of many students isn't due to the pedagogical method, but has other causes such as poverty and lack of resources.