New Math

New Mathematics or New Math was a change in the way mathematics was taught in schools. It happened between the 1950s, and 1970s. In the United States, it happened shortly after the Sputnik crisis. The goal was to boost students' science education and mathematical skill to meet the technological threat of Soviet engineers. These engineers were said to be very skilled mathematicians.

Topics introduced in the New Math include set theory, modular arithmetic, algebraic inequalities, bases other than 10, matrices, symbolic logic, Boolean algebra, and abstract algebra.

All of the New Math projects emphasized some form of discovery learning. Students worked in groups to invent theories about problems posed in the textbooks. Materials for teachers described the classroom as "noisy." Part of the job of the teacher was to move from table to table assessing the theory that each group of students had developed and "torpedoing" wrong theories by providing counterexamples. For that style of teaching to be tolerable for students, they had to experience the teacher as a colleague rather than as an adversary or as someone concerned mainly with grading. New Math workshops for teachers, therefore, spent as much effort on the pedagogy as on the mathematics.

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. In an effort to learn the material, many parents attended their children's classes. In the end, it was concluded that the experiment was not working, and New Math fell out of favor before the end of the 1960s, 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".

In 1965, physicist Richard Feynman wrote in the essay, New Textbooks for the "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 are 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 worthwhile teaching such material.

In his book, Why Johnny Can't Add: The Failure of the New Math, Morris Kline says that 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". He also noted the trend to abstraction in New Math. Kline says "abstraction is not the first stage, but the last stage, in a mathematical development".

As a result of this controversy, and despite the ongoing influence of the New Math, the phrase "new math" is often used now to describe any short-lived fad that quickly becomes discredited. In 1999, Time placed it on a list of the 100 worst ideas of the 20th century.

In popular culture

• Musician and university mathematics lecturer Tom Lehrer wrote a satirical song named "New Math" (from his 1965 album That Was the Year That Was), which revolved 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 New Math's emphasis on insight and abstract concepts – as Lehrer put it with an indeterminable amount of seriousness, "In the new approach ... the important thing is to understand what you're doing, rather than to get the right answer." At one point in the song, he notes that "you've got thirteen and you take away seven, and that leaves five... well, six, actually, but the idea is the important thing." The chorus pokes fun at parents' frustration and confusion over the entire method: "Hooray for New Math, New 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."
• In 1965, cartoonist Charles Schulz authored a series of Peanuts strips, which detailed kindergartener Sally's frustrations with New Math. In the first strip, she is depicted puzzling over "sets, one-to-one matching, equivalent sets, non-equivalent sets, sets of one, sets of two, renaming two, subsets, joining sets, number sentences, placeholders." Eventually, she bursts into tears and exclaims, "All I want to know is, how much is two and two?" This series of strips was later adapted for the 1973 Peanuts animated special There's No Time for Love, Charlie Brown. Schulz also drew a one panel illustration of Charlie Brown at his school desk exclaiming, "How can you do 'New Math' problems with an 'Old Math' mind?"
• In the 1966 Hazel episode, "A Little Bit of Genius", the show tackles the division New Math’s introduction wrought between families, friends, and neighbors, as well as its impact on the then ever-widening generation gap.
• The 2018 film Incredibles 2 shows Bob Parr/Mr. Incredible struggling to teach his son math, frustrated by the new methods students are expected to use.

Further reading

• Ralph A. Raimi (1995). Whatever Happened to the New Math? Archived 2020-12-10 at the Wayback Machine
• Adler, Irving (1972). The New Mathematics (revised ed.). New York: John Day Company. ISBN 0-381-98002-2.
• Mashaal, Maurice (2006). "New Math in the Classroom". Bourbaki: A Secret Society of Mathematicians. American Mathematical Society. pp. 134–145. ISBN 9780821839676. This work was originally published as Bourbaki: une société secrète de mathématiciens (2002, ISBN 2842450469, in French) and the 2006 English-language version was translated by Anna Pierrehumbert.
• Phillips, Christopher J. (2014). The New Math: A Political History. University of Chicago Press. ISBN 9780226185019.

Other websites

• Why Johnny Can’t Add: The Failure of the New Math by Morris Kline
• Richard P. Feynman: NEW TEXTBOOKS FOR THE "NEW" MATHEMATICS by Richard P. Feynman
• Tom Lehrer Deposit #10