Set Theory for Six-Year-Olds Alex Bellos Savours a History of the ‘New Math’ That Swept US Schools in the 1960S

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US maths education was kicked into space-age overdrive by the launch of the Soviet Sputnik satellite.

MATHEMATICS Set theory for six-year-olds Alex Bellos savours a history of the ‘new math’ that swept US schools in the 1960s.

t was hailed as a revolutionary math- not for the last time) introduced, as the property shared by equiv- ematics curriculum that prioritized the by the risk of falling alent sets, represented by a symbol called a concept of a set over the concept of a behind in science, numeral. The number 1, for example, was Inumber. ‘New math’ was introduced to mil- leading to a political precisely that which all sets with a single lions of US schoolchildren in the 1960s. Yet consensus that maths member had in common. in less than a decade it was being lampooned teaching needed to be The New Math charts the method’s rise unforgettably by the mathematician and sati- reformed to produce and fall through the story of the School rist Tom Lehrer. The refrain of his song ‘New students with sharper Mathematics Study Group (SMSG), an Math’ is: “It’s so simple, so very simple, that cognitive skills. association of mathematicians and teachers only a child can do it!” As Phillips explains, The New Math: A formed in early 1958 and funded by the US Teaching set theory to six-year-olds as a rather than starting a Political History National Science Foundation. Awash with way into mathematics, from arithmetic on, maths class by learn- CHRISTOPHER J. money, the SMSG came up with progres- would come to be considered misguided, ing to count, children PHILLIPS sive new ideas for “how mathematics could overcomplicating the basics and introduc- were asked to think University of Chicago and should cultivate mental habits”; this, ing jargon. Yet however radical a shift it about sets of objects, Press: 2014. Phillips writes, is “the only reform effort that represented, the new math was not a liberal such as the set of ani- rooted federal money directly and explic- experiment. It was, writes science historian mals on a farm and the set of sweets in a itly in claims about how students should Christopher Phillips in The New Math, an jar. If you paired each animal with a sweet, learn to think”. The SMSG concluded that essentially conservative cold-war initia- and there were sweets left over, that set was maths lessons should be less about number tive. In 1957, the Soviet Union launched greater than the set of animals — and vice crunching and more about abstract think- Sputnik, the first Earth-orbiting satel- versa. Perfectly paired-up sets were ‘equiva- ing. A tension between rote learning and lite. The United States was spooked (and lent’. Only now was the concept of number puzzle-solving lies at the heart of maths

34 | NATURE | VOL 516 | 4 DECEMBER 2014 © 2014 Macmillan Publishers Limited. All rights reserved BOOKS & ARTS COMMENT pedagogy, but never has practice swung so far from arithmetic drills as during the new- math era. The SMSG’s textbook for junior Books in brief high schools began, for example, with the story of a mathematician on a plane telling Raw Data: Infographic Designers’ Sketchbooks his neighbour that counting with numbers Steven Heller and Rick Landers Thames and Hudson (2014) is best done by machines and that his job is An artist’s sketchbook is a peek at cognition’s wilder shores: the “logical reasoning”. on-the-fly observations and dogged experimentation that feed the One reason for the SMSG favouring final picture. In this splendid compilation, Steven Heller and Rick abstraction over calculation was that it was Landers riffle through the pages of 73 infographic artists — the led by professional mathematicians, not wizards who translate numbers into graphics. Juxtaposing doodles teachers. Many were deeply influenced by with smooth finales, the book explores the work of stars such as Nicolas Bourbaki, the pseudonym for a Nigel Holmes, whose ‘meat and two veg’ head reworks the food group of ideological French mathematicians pyramid in wacky homage to the ‘cornucopia’ portraits of sixteenth- of the 1930s who argued that mathematics century artist Giuseppe Arcimboldo. was about structure, and that set theory underlay the structure of numbers. ‘Mod- ern’ maths, argued the SMSG, was needed Fred Sanger — Double Nobel Laureate: A Biography for space-age science. George G. Brownlee Cambridge University Press (2014) New math was a voluntary programme, The biochemist Frederick Sanger, whose DNA sequencing method and in terms of take-up it was a huge success. made the Human Genome Project possible, died last year. One of By 1965, it was estimated, nearly 75% of US only four scientists to win two Nobel prizes, Sanger is revealed in high-school pupils and 40% of elementary- this slim biography by George Brownlee (who studied under him) school pupils were studying a version of it; as inherently modest about his landmark achievements in protein a decade later, it was still taught in an esti- and DNA sequencing. Included are a revealing and fascinating 1992 mated 85% of schools. Major educational interview with Sanger that elucidates how he hit on his discoveries, publishers sold millions of books influenced and encomia from the likes of fellow laureates Paul Berg, Elizabeth by the SMSG’s ideas. But the backlash, which Blackburn and Paul Nurse. had started in the early 1960s, had become fierce by the 1970s. And as Phillips points out, the reasons were as much to do with Animal Weapons: The Evolution of Battle politics as with pedagogy. Douglas J. Emlen Henry Holt (2014) Phillips notes the irony of a nationalis- It began with dung beetles. Evolutionary biologist Douglas Emlen’s tic, cold-war-inspired project introduced self-confessed fixation on ‘extreme’ animal weapons was first to promote rigorous thinking becoming channelled into research on these horned insects. In this original the target of conservatives less than two study, Emlen tours offensive and defensive anatomy and behaviours decades later, partly because they claimed across aeons and taxa, from Tyrannosaurus rex’s fearsome teeth to that it failed to impart mental rigour. The ibex horns and amphibian poisons. He sharpens the discussion 1970s ‘back to basics’ movement — a by interweaving parallels with humanity’s own evolving arsenal, decentralized collection of vocal parents including weapons of mass destruction — the most extreme of all horrified at the lack of memorization drills arms, which if deployed cancel out the very concept of battle. — echoed broader political shifts. People were less inclined to accept diktats from elite authorities such as Washington DC Banned: A History of Pesticides and the Science of Toxicology politicians and Ivy League academics. The Frederick Rowe Davis Yale University Press (2014) new math was criticized, possibly unfairly, Historian Frederick Davis takes on the ambitious task of writing for declining test scores, rowdy classrooms the history of pesticides before and in the wake of Rachel Carson’s and children’s poor computational skills, iconic 1962 book Silent Spring. In a treatment dense with references, and its name became a byword for crazy acronyms, chemical names and technical discussions of lethal progressive reforms. The SMSG shut down doses, Davis offers a keen historical perspective on the compounds in 1972, although many schools that had that big agriculture has used to keep bugs at bay. He forms a invested in new math had to keep using the scholarly indictment of a system that heeded Carson’s superficial same textbooks until the end of the 1970s message in banning DDT, but ignored her underlying warning that and beyond. (By then, the method had existing systems for managing pesticides are often inadequate. spread around the world. I was taught set theory at primary school in Scotland in the late 1970s.) Life on Display: Revolutionizing U.S. Museums of Science and Phillips reminds us in his fascinating Natural History in the Twentieth Century book that even though mathematics is sup- Karen A. Rader and Victoria E. M. Cain University of Chicago Press (2014) posed to be apolitical, the teaching of it is The exquisite dioramas in New York’s American Museum of Natural anything but. ■ History have wowed crowds since the early twentieth century. But as historians Karen Rader and Victoria Cain reveal in this cogent study, Alex Bellos is the author of Alex Through they were part of a broader revolution: the “New Museum Idea”, which the Looking-Glass (US title: The Grapes of saw “smell machines” and dynamic models supersede dusty cases. Math). He is based in London. The behind-the-scene struggles between ‘edutainers’ and serious e-mail: [email protected] museum researchers were, they show, no less dynamic. Barbara Kiser

4 DECEMBER 2014 | VOL 516 | NATURE | 35 © 2014 Macmillan Publishers Limited. All rights reserved