New Math

thumb|right|Paperback introductions to the New Math in the United StatesNew Mathematics or New Math was a dramatic but temporary change in the way mathematics was taught in grade schools which started in France and spread to many other countries between 1950s and 1970s.

Overview

Following World War II, the Western world underwent substantial economic and technological transformations and the training of scientists and engineers was seen as crucial for further economic growth. Furthermore, in the context of the Cold War, the launch of the world's first artificial satellite Sputnik by the Soviet Union in 1957 raised concerns that the West was falling behind. To this end, educational reforms—including in mathematics, which underlies the natural sciences and engineering—were considered necessary. In Europe, reform of school mathematical curricula was pursued by multiple countries, including the United Kingdom (particularly by the School Mathematics Project), and West Germany, where the changes were seen as part of a larger process of Bildungsreform. In the United States, the educational status quo was severely criticized as sorely lacking on substance and as a source of national humiliation, prompting Congress to introduce the National Defense Education Act of 1958, pouring enormous sums of money into not just research and development but also STEM education.

Indeed, during the postwar era, the importance of modern mathematics—especially mathematical logic, optimization, and numerical analysis—was acknowledged for its usefulness during the war. From this sprang proposals for reforms in mathematics education. The international movement to bring about such reforms was launched in the late 1950s, with heavy French influence. In France, they also grew out of a desire to bring the subject as it was taught in schools closer to the research done by pure mathematicians, particularly the Nicholas Bourbaki school, which emphasized an austere and abstract style of doing mathematics, axiomatization. Up until the 1950s, the purpose of primary education was to prepare students for life and future careers. This changed in the 1960s. A commission headed by André Lichnerowicz was established to work out the details of the desired reforms in mathematical education. At the same time, the French government mandated that the same courses be taught to all schoolchildren, regardless of their career prospects and aspirations. Thus the same highly abstract courses in mathematics were taught not only to those willing and able to pursue university studies, but also to those leaving school early to join the workforce.

thumb|In the New Math curriculum for traditional topics such as geometry, geometric intuition and diagrams, like this illustration of the [[law of sines, were eschewed in favor of an austere and abstract presentation in terms of linear algebra.]]

In France, from elementary school to the French Baccalaureate, traditional topics such as Euclidean geometry and calculus were de-emphasized in favor of mathematical and formal logic;); and bases other than 10. In the case of Euclidean geometry, the use of intuition and diagrams was replaced by a formal approach using linear algebra (linear transformations and vector spaces). were given with no diagrams at all while complex numbers were defined in terms of matrices and fields. This conception of mass public education was inherited from the interwar period and was taken for granted; the model for the elites was to be applied to all segments of society. 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 provide instructional scaffolding, that is, to move from table to table assessing the theory that each group of students had developed and "torpedo" 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.

In Japan, New Math was supported by the Ministry of Education, Culture, Sports, Science and Technology (MEXT), but not without encountering problems, leading to student-centered approaches.

Reception

But by the early 1970s, the New Math initiative ran into problems. Mathematicians, physicists, members of professional societies, economists, and industrial leaders criticized the reforms as being suitable for neither schoolteachers nor students. In particular, the abandonment of classical geometry and an emphasis on formalism and abstraction were the main target of complaints. In a 1971 article, mathematician René Thom rejected the New Math as "a test of memory that poisons intelligence" because of its complete neglect of intuition. Mathematician and author George F. Simmons wrote in the algebra section of his textbook Precalculus Mathematics in a Nutshell (1981) that by focusing on form rather than substance, the New Math produced students who had "heard of the commutative law, but did not know the multiplication table." Mathematician Laurent Schwartz described the new reforms as "very poor" pedagogy. For him, "The goal of mathematics is not to prove rigorously things that everyone knows. Instead, the goal is to find rich results and then, in order to make sure they are true, to prove them."

Legacy

By the end of the 1970s, the New Math was all but abandoned. Subsequent curricula were less ambitious and carried less content. Traditional topics were reinstated. Abstraction and rigorous proofs were supplanted by intuition and calculations. Teaching in the USSR did not experience the extreme upheavals as seen in other countries, while being kept in tune, both with the applications and academic trends:

In the United States, an enduring contribution of the New Math initiative was the addition of calculus in high school. (See Advanced Placement Calculus.)

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 that the introduction of New Math wrought between families, friends, and neighbors and its impact on the then ever-widening generation gap.

Overview

Reception

Legacy

See also

Notes