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 change involved new curriculum topics and 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 technological threat of Soviet engineers, reputedly highly skilled mathematicians, could be met.
Topics introduced in the New Math include modular arithmetic, algebraic inequalities, bases other than 10, matrices, symbolic logic, Boolean algebra, and abstract algebra. In elementary school, in addition to bases other than 10, students were taught basic set theory and made to distinguish "numerals" from "numbers." 
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 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."
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.":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.":98
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.[clarification needed] 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]
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 [sic] presented in the textbook produced by Vladimir Boltyansky and Isaak Yaglom."
In Japan, the New Math was supported by the Ministry of Education, Culture, Sports, Science and Technology (MEXT), but not without encountering problems, leading to student-centred approaches.
- 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."
- New Math was the name of a 1970s punk rock band from Rochester, New York.
- 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 Pixar animated film Incredibles 2 (which is set approximately in the 1960s or 1970s), Bob Parr (Mr. Incredible) can be seen wrangling with New Math in his son's homework, and promptly describes it as making no sense at all, and then to ridicule "I don't know that way! Why would they change Math? Math is Math! MATH IS MATH!"
- André Lichnerowicz – Created 1967 French Lichnerowicz Commission
- Comprehensive School Mathematics Program (CSMP)
- Secondary School Mathematics Curriculum Improvement Study (SSMCIS)
- List of abandoned education methods
- School Mathematics Study Group (SMSG)
- Kline, Morris (1973). Why Johnny Can't Add: The Failure of the New Math. New York: St. Martin's Press. ISBN 0-394-71981-6.
- Raimi, Ralph (May 6, 2004). "Chapter 1: Max". Retrieved April 24, 2018.
- Simmons, George F. (2003). "Algebra – Introduction". Precalculus Mathematics in a Nutshell: Geometry, Algebra, Trigonometry: Geometry, Algebra, Trigonometry. Wipf and Stock Publishers. p. 33. ISBN 9781592441303.
- Feynman, Richard P. (1965). "New Textbooks for the 'New' Mathematics" (PDF). Engineering and Science. XXVIII (6): 9–15. ISSN 0013-7812.
- Malaty, George (1999). "The Third World Mathematics Education is a Hope for the World Mathematics Education Development in the 21st Century" (PDF). Proceedings of the International Conference Mathematics Education into the 21st Century: Societal Challenges, Issues and Approaches. Mathematics Education into the 21st Century: Societal Challenges, Issues and Approaches. Cairo, Egypt. pp. 231–240.
- Lehrer, Tom (2019). "New Math Lyrics". Genius Media Group. Retrieved May 19, 2019.
- Weld, Henry (May 14, 2014). "Discography of American Punk in Upstate New York". Retrieved May 19, 2019.
- Schulz, Charles (October 2, 1965). "Peanuts by Charles Schulz for October 02, 2012". GoComics. Universal Uclick. Retrieved May 19, 2019.
- Schulz, Charles. "Charlie Brown Poster (1970s) – Peanuts – How Can You do "New Math" Problems with an "Old Math" Mind?". Retrieved May 19, 2019 – via Chisholm Larsson Gallery.
- Allain, Rhett (April 16, 2018). "Incredibles 2 Asks: What's the Right Way to Solve a Math Problem?". Wired. Retrieved May 19, 2019.
- 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.