New Math

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New Math was a brief dramatic change in the way mathematics was taught in American grade schools during the 1960s. The name is commonly given to a set of teaching practices introduced in the U.S. shortly after the Sputnik crisis in order to boost scientific education and mathematical skill in the population so that the supposed intellectual threat of the Soviet engineers, reputedly highly skilled mathematicians, could be met.

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[edit] The new mathematical pedagogy

New Math emphasized mathematical structure through abstract concepts like set theory and number bases other than 10. Beginning in the early 1960s the new educational doctrine was installed, not only in the USA, but all over the developed world.

Much of the publicity centered on the focus of this program on set theory (influenced ultimately by the Nicolas Bourbaki group and their work), functions, and diagram drawings. It was stressed that these subjects should be introduced early. Some of this focus was seen as exaggerated, even dogmatic. For example, in some cases pupils were taught axiomatic set theory at an early age.[1] The idea behind this was that if the axiomatic foundations of mathematics were introduced to children, they could easily cope with the theorems of the mathematical system later.

[edit] Resistance to curriculum change

Parents and teachers who opposed the New Math in the U.S. complained that the new curriculum was too far outside of students' ordinary experience and was not worth taking time away from more traditional topics, such as arithmetic. The material also put new demands on teachers. In the end it was concluded that the experiment was not working, and New Math fell out of favor before the end of the decade, though it continued to be taught for years thereafter in some school districts.

In the Algebra preface of his book "Precalculus Mathematics in a Nutshell," Professor George F. Simmons wrote that the New Math produced students who had "heard of the commutative law, but did not know the multiplication table."

[edit] Across the developed world

In the broader context, reform of school mathematics curricula was also pursued in European countries such as the United Kingdom (particularly by the School Mathematics Project), and France, where the extremely high prestige of mathematical qualifications was not matched by teaching that connected with contemporary research and university topics. In West Germany the changes were seen as part of a larger process of Bildungsreform. Beyond the use of set theory and different approach to arithmetic, characteristic changes were transformation geometry in place of the traditional deductive Euclidean geometry, and an approach to calculus that was based on greater insight, rather than emphasis on facility.

Again the changes met with a mixed reception, but for different reasons. For example, the end-users of mathematics studies were at that time mostly in the physical sciences and engineering; and they expected manipulative skill in calculus, rather than more abstract ideas. Some compromises have since been required, given that discrete mathematics is the basic language of computing.

Teaching in the USSR did not experience such extreme upheavals, while being kept in tune both with the applications and academic trends.

Under A. N. Kolmogorov, the mathematics committee declared a reform of the curricula of grades 4-10, at the time when the school system consisted of 10 grades. The committee found the type of reform in progress in Western countries to be unacceptable; for example, no special topic for sets was accepted for inclusion in school textbooks. Transformation approaches were accepted in teaching geometry, but not to such sophisticated level presented in the textbook produced by Boltyansky and Yaglom.[2]

In Japan and Asian countries generally, the emphasis on basic numeracy has traditionally been high.

[edit] The New New Math

In 1989, the National Council of Teachers of Mathematics (NCTM), an organization made up of mathematics teachers and mathematics educators, published the Curriculum and Evaluation Standards for School Mathematics, a set of national standards for K-12 mathematics. An updated version was published in 2000 as the Principles and Standards for School Mathematics. The National Science Foundation funded the development and adoption of several curricula, which were placed on the list of U.S. Department of Education exemplary mathematics programs. As a key component of standards based education reform, it was to increase mathematical power for all students by creating frameworks which set world class standards of what all students must know and be able to do.

As landmark publications in an era during which the debate over philosophies of classroom mathematics instruction was highly contested, both standards publications attracted controversy. Groups such as Mathematically Correct, which purports to be made largely of parents whose careers involve regular use of mathematics, issued severe criticism of the Standards; a primary claim has been that they eliminate instruction of traditional arithmetic methods, and focus more on process and explanations than upon answers. Such groups instituted the label of "New New Math" to decry the irrelevance of Standards-based approaches, although in fact Standards-based reform is independent of the original New Math program. Researchers in mathematics education, as well as some mathematics researchers, however, continue to support the goals of the Standards.

[edit] Popular culture

Tom Lehrer wrote a satirical song named "New Math" which centered around the process of subtracting 173 from 342 in decimal and octal. The song is in the style of a lecture about the general concept of subtraction in arbitrary number systems, illustrated by two simple calculations, and highlights the emphasis on insight and abstract concepts of the New Math approach. Lehrer's explanation of the two calculations is entirely correct, but presented in such a way (at rapid speed, with minimal visual aids, and with snide remarks thrown in) as to make it difficult for most audience members to follow the rather simple calculations being performed. This is intended to poke fun at the kind of bafflement the New Math approach often evoked when apparently simple calculations were presented in a very general manner which, while mathematically correct and arguably trivial for mathematicians, was likely very confusing to absolute beginners and even contemporary adult audiences. Summing up his opinion of New Math is the final sentence from his introductory remarks to the song: "...in the new approach, as you know, the important thing is to understand what you're doing, rather than to get the right answer."

Excerpt:

So you've got thirteen 10s and you take away seven
And that leaves five ... well, six, actually.
But the idea is the important thing.

Chorus:

Hooray for new math,
New-hoo-hoo-math,
It won't do you a bit of good to review math.
It's so simple,
So very simple,
That only a child can do it!

New Math was also the name of a '70s punk rock band from Rochester, NY[3].

New Math was a confounding concept to Cliff Huxtable on The Cosby Show episode 85 "Dance Mania".[4]

The episode "Dog of Death" of The Simpsons makes an indirect reference to the New Math, when Principal Skinner describes the new textbooks he'd like to use: "History books that know how the Korean War came out… math books that don't have that base six crap in them…"

A federal jury awarded a photographer $0.20 after Bill Cosby allegedly assaulted him. In an interview later Cosby said: "Ten percent is my fault and 90 percent is their fault, and they win? What is that ...the New Math?"[5]

New Math was the subject of a short story arc in Peanuts.

[edit] See also

[edit] Further reading

  1. ^ A Brief History of American K-12 Mathematics Education in the 20th Century (David Klein)
  2. ^ http://math.unipa.it/~grim/EMALATY231-240.PDF
  3. ^ Punk Rock In Upstate New York By Henry Weld
  4. ^ The Cosby Show: Dance Mania - TV.com
  5. ^ Bill Cosby ordered to pay photographer 20 cents in battery suit - photographer Dick Corkery - Brief Article | Jet | Find Articles at BNET.com

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