American Public Schools Begin Teaching New Math

views updated

American Public Schools Begin Teaching New Math

Overview

Since the end of World War II, methods for teaching mathematics in the United States have changed in style repeatedly, often with controversial results. The first major change, coined New Math, was launched into American schools in the early 1960s. New Math stressed conceptual understanding of the principles of mathematics and de-emphasized technical computing skills. With New Math, out went the rote drill and practice of math facts and formulas. Instead, along with a whole new vocabulary of terms related to mathematical operations, students were taught abstract concepts involving operations on sets of numbers grouped by their characteristics and properties. The intended focus of New Math was to teach children basic mathematical truths that they would then be able to apply to specific problems in a rapidly specializing scientific and technical world. New Math, however, stirred controversy among educators and students alike and brought into focus sharp divisions in opinions regarding the goals and objectives of math education.

Background

The cultural and political climate of World War II through the 1950s sparked the need for a new way to teach mathematics. During World War II the demands of understanding and operating new technologies such as radar highlighted the weakness of American soldiers' math skills. The immigration of eminent mathematicians and scientists, who played major roles in the development of theories and technologies vital to the Allied victory, brought home the need to improve math and science education in the U.S. Throughout the Korean conflict and start of the arms race with the Soviet Union in the 1950s, military technologies continued to develop rapidly. During these years mathematics students were educated in groups according to ability, and they learned mathematical concepts through repetition, memorization (multiplication tables, for example), and timed drills. Two thirds of students studied math only through the ninth grade.

In 1952 the National Science Foundation, in conjunction with a group of mathematicians at the University of Illinois and Yale University, began to develop a reformed method of teaching mathematics. By the mid-1950s a small number of schools were testing the group's recommended curriculum, which relied heavily on incorporating set theory and abstract mathematical laws. This curriculum served as the basis for the New Math movement.

The concepts and terminology of basic set theory were pillars of the New Math that introduced into American public school curricula during the 1960s. Instead of simply using standard arithmetic operations to solve relatively straightforward problems—where students were required to know which operations to perform and in what order to do them—an attempt was made to teach students to identify sets (groupings of numbers or objects) and elements of sets upon which operations were to be performed.

Prior to the introduction of New Math, for example, a typical student might be asked, given a sales price (e.g., $20) for a pair of widgets and a manufacturing cost of 3/5 the sales price (i.e., $12), to calculate the profit realized from the sale of the widgets. The same problem reworded according to the dictates of New Math might—in the extreme—assert:

A set of widgets (designated as set W) was exchanged for a set of money (designated as set M). The cardinality (the number of elements in a set) of set M was equal to 20—with each element (i.e., currency) being equal to one (e.g., a monetary denomination of $1). If x's are used to designate the elements of each set, then set P (representing manufacturing costs) has eight fewer x's than set M. Represent set P as a subset of set M and determine the cardinality of the elements to determine the profit realized from the sale of widgets.

Although the construction of such densely complex problems was, in scope, far from actual problems presented to students, it is illustrative of many of the conceptual challenges and obstacles facing students studying New Math.

The Soviet Union's launch of Sputnik 1 (the first satellite to successfully orbit the Earth) in October 1957 raised revision of math and science education in the U.S. to a strategic national crisis. Americans, seemingly behind the Soviets at every turn in the early space race, also perceived the U.S. as behind in mathematics and scientific achievement. Throughout the country school districts rushed to boost their mathematics curricula with New Math. Although primary education received its share of the blame, special emphasis was placed on high schools, as perception grew during the Cold War that the U.S. was not producing enough mathematicians and scientists.

The introduction of New Math forced educators to abandon many of the long-cherished institutions of mathematics with regard to rote practice of operational skills. Out went computational worksheets and memorization of tables, facts, and formulas. In many cases, parents were not only incapable of helping with homework, they were incapable of understanding what they often argued was a seemingly unnecessary complication of what had once been straightforward problem solving. To make matters worse for the proponents of New Math, its introduction came at a time of radical and sweeping change in American society that ultimately resulted in changes in the public education system. Opponents of New Math, fueled by fears of falling test scores and a perceived educational gap between the United States and other industrial powers, laid the blame for many ills at the doorstep of New Math.

Impact

New Math, swiftly implemented in high schools, was widely introduced in kindergarten through grade eight by the early 1960s. Despite initial enthusiasm from researchers and endorsement from the National Council of Teachers of Mathematics (NCTM), the New Math curriculum proved difficult to maintain in real-life classroom situations. Teachers, whose classrooms were bulging with baby-boom students, struggled to introduce New Math concepts, often with little training. Parents were doubly confused. They could not understand the New Math concepts themselves, and they became concerned that many of the fundamental concepts they had learned (multiplication tables, for example) were foreign to their children. Although many school districts attempted to allay parents' concerns by conducting classes in understanding New Math, both parents and students continued to struggle.

As early as 1962 academic journals began to publish articles opposing New Math. Publication of a five-year study in 1967, showing American students lagging in math skills among other Western nations, dealt the New Math curriculum a serious blow. By the early 1970s opinion polls indicated that Americans, concerned that students were not learning basic skills, favored a "Back to Basics" approach in their children's' mathematics education, emphasizing computation, formulas, and mathematical laws. When an indictment of New Math entitled Why Johnny Can't Add was published in the mid-1970s, two new but similar approaches to teaching mathematics—the back to basics movement and the reform movement—found their way into American mathematics curricula.

Historians and educators often argue that Americans did not embrace the New Math of the 1960s for several reasons. Most notably, any decline or stagnation in standardized test scores, which were increasingly the index of success or failure for schools, was often blamed on confusion caused by New Math. Additionally, some fundamental concepts taught in New Math did not translate as expected into understanding New Math based technologies. Teaching arithmetic using numbers written in bases other than the often-used base ten, for example, was intended to ready Americans for the dawning computer age. The ability to write assembly language computer programs in binary (base two) code was presumed to be an essential future task. That Americans would buy their computer software rather than write it, and would deal with computer language in a point-and-click environment was, at best, an unforeseen development.

By the 1980s educators re-evaluated the New Math movement. Some educators argued that New Math concepts were beneficial and that any fault lay in the implementation process. After studying how teachers prepared to teach New Math, educators and schools of education adjusted the classroom-teacher education process to include more training in the use of manipulatives (i.e., objects such as blocks and figures that could be used to build models of mathematical concepts, or to allow physical representation of mathematical formula).

A "newer" New Math was reintroduced in some states in the 1990s, partially funded by the U.S. Congress, and again supported by the National Council of Teachers of Mathematics. Coined "Fuzzy Math" by its critics, it also shuns rote computation while embracing "experiential learning" where students figure out answers for themselves through group learning and an increased use of manipulative tools and computer simulations designed to stimulate conceptual thinking.

Regardless of its actual merit or intents, New Math was alternatively lampooned and despised by the general public. The major impact of the controversy surrounding New Math, however, was that it became the focal point for passionate social and political debate regarding pedagogy (teaching methods) in American schools. As mathematical concepts became increasingly distant, the influence of scholars over the merits of curricula became increasingly obtuse to a general public and political process comfortable only with "bottom-line" analysis of test scores. As the twentieth century drew to a close, mathematics education remained in a controversial quest for solutions that might close the documented gap in mathematics education between trailing American students and students in the rest of the industrialized world.

BRENDA WILMOTH LERNER