# New Math

**New Mathematics** or **New Math** was a dramatic but temporary change in the way mathematics was taught in American grade schools, and to a lesser extent in European countries and elsewhere, during the 1950s–1970s. Curriculum topics and teaching practices were changed in the U.S. shortly after the Sputnik crisis. The goal was to boost students' science education and mathematical skill to meet the technological threat of Soviet engineers, reputedly highly skilled mathematicians.

After the Sputnik launch in 1957, the U.S. National Science Foundation funded the development of several new curricula in the sciences, such as the Physical Science Study Committee high school physics curriculum, Biological Sciences Curriculum Study in biology, and in chemistry. Several mathematics curriculum development efforts were also funded as part of the same initiative, such as the , School Mathematics Study Group, and .

These curricula were quite different from one another, yet shared the idea that children's learning of arithmetic algorithms would last past the exam only if memorization and practice were paired with teaching for *understanding.* More specifically, elementary school arithmetic beyond single digits makes sense only on the basis of understanding place value. This goal was the reason for teaching arithmetic in bases other than ten in the New Math, despite critics' derision: In that unfamiliar context, students couldn't just mindlessly follow an algorithm, but had to think why the place value of the "hundreds" digit in base seven is 49. Keeping track of non-decimal notation also explains the need to distinguish *numbers* (values) from the *numerals* that represent them,^{[1]} a distinction some critics considered fetishistic.

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.^{[2]}

All of the New Math projects emphasized some form of *discovery learning.*^{[3]} 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.^{[4]}

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".^{[5]}

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.^{[6]}

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".^{[2]}^{: 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".^{[2]}^{: 98 }

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.^{[7]}^{[8]}

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 due to concerns that mathematics as taught in schools was becoming too disconnected from mathematics research, in particular that of the Bourbaki group.^{[9]} 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 were 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 [*sic*] presented in the textbook produced by Vladimir Boltyansky and Isaak Yaglom."^{[10]}

In Japan, New Math was supported by the (MEXT), but not without encountering problems, leading to student-centred approaches.^{[11]}