New Math

For the Bo Burnham song, see Bo Burnham (album).

New Mathematics or New Math was a brief, dramatic change in the way mathematics was taught in American grade schools, and to a lesser extent in European countries, 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 science education and mathematical skill in the population so that the intellectual threat of Soviet engineers, reputedly highly skilled mathematicians, could be met.

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 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.

Other topics introduced in the New Math include modular arithmetic, algebraic inequalities, matrices, symbolic logic, Boolean algebra, and abstract algebra.^[2] Most of these topics (except algebraic inequalities) have been greatly de-emphasized or eliminated since the 1960s.

Criticism

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, many of whom were required to teach material they did not fully understand. Parents were concerned that they did not understand what their children were learning and could not help them with their studies. Many of the parents took time out to try to understand the new math by attending their children's classes.^[3] 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. New Math found some later success in the form of enrichment programs for gifted students from the 1980s onward in Project MEGSSS.^[4]

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."

In 1965, physicist Richard Feynman wrote in "New books for new mathematics":

"If we would like to, we can and do say, 'The answer is a whole number less than 9 and bigger than 6,' but we do not have to say, 'The answer is a member of the set which is the intersection of the set of those numbers which is larger than 6 and the set of numbers which are smaller than 9' ... In the 'new' mathematics, then, first there must be freedom of thought; second, we do not want to teach just words; and third, subjects should not be introduced without explaining the purpose or reason, or without giving any way in which the material could be really used to discover something interesting. I don't think it is worth while teaching such material.'

In 1973, Morris Kline published his critical book Why Johnny Can't Add: the Failure of the New Math. It explains the desire to be relevant with mathematics representing something more modern than traditional topics. He says certain advocates of the new topics "ignored completely the fact that mathematics is a cumulative development and that it is practically impossible to learn the newer creations if one does not know the older ones" (p. 17). Furthermore, noting the trend to abstraction in New Math, Kline says "abstraction is not the first stage but the last stage in a mathematical development" (p. 98).

Across other countries

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^{[clarification needed]}.^{[citation needed]}

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.^{[citation needed]}

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.^[5]

In Japan, the New Math was supported by MEXT, but not without problems, leading to child-centred approaches.^[6]

Example

A "New Math Way" is to not only learn how to accomplish subtraction by regrouping in the normal decimal system, but learn it in base 8 as well.

Base 8: regrouping the eights column means adding eight to the ones column and subtracting one from the eights column

i.e. 342 − 173 = 147.

This is the problem Tom Lehrer sings about in his song, “New Math” where he parodies overcomplexity in New Math.^[7]

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 side 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;" at one point in the song, he inserts the assertion that 13 – 7 = 5, which is (deliberately) incorrect.

Lehrer stated that "Base 8 is just like Base 10, if you're missing 2 Fingers."

Lehrer, at the end of the song, said that he often wanted to write a mathematics textbook someday that would be a million seller, entitled "Tropic of Calculus".

• "New Math" was also the name of a 1970s punk rock band from Rochester, NY.^[8]

• In the Simpsons episode "Dog of Death," Principal Skinner refers to the New Math:

Kent: But there's already one big winner: Our state school system, which gets fully half the profits from the lottery.
Skinner: [talking with his teachers] Just think what we can buy with that money... History books that know how the Korean War came out. Math books that don't have that base six crap in them!^[9]

See also

• André Lichnerowicz – Created 1967 French Lichnerowicz Commission
• Comprehensive School Mathematics Program (CSMP)
• List of abandoned education methods

References

1. ^ A Brief History of American K-12 Mathematics Education in the 20th Century (David Klein)
2. ^ Kline, Morris (1973). Why Johnny Can't Add: The Failure of the New Math. New York: St. Martin's Press. ISBN 0394719816. 
3. ^ Remillard, Janine T., and Kara Jackson. "Old Math, New Math: Parents' Experiences with Standards-Based Reform." Mathematical Thinking and Learning 8.3 (2006): 231-59. Print.
4. ^ http://megsss.org/
5. ^ http://math.unipa.it/~grim/EMALATY231-240.PDF
6. ^ http://www.researchgate.net/publication/37261895___
7. ^ http://curvebank.calstatela.edu/newmath/newmath.htm
8. ^ Punk Rock In Upstate New York By Henry Weld
9. ^ [1]Dog of Death on SNPP.com

Further reading

• Adler, Irving. The New Mathematics. New York: John Day and Co, 1972 (revised edition). ISBN 0-381-98002-2
• Maurice Mashaal (2006), Bourbaki: A Secret Society of Mathematicians, American Mathematical Society, ISBN 0-8218-3967-5, Chapter 10: New Math in the Classroom, pp 134–45.

External links

• A history of the New Math, including the UICSM and SMSG projects
• Tom Lehrer Deposit #10