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# "New Math"

By L. Huetinck|S.N. Munshin
Pearson Allyn Bacon Prentice Hall

The impetus for the "new math" was the successful launch of Sputnik, the Soviet Earth-orbiting satellite, in 1957. In the United States, there was concern that we were so far behind the Soviet Union, our cold war foe, that our national security was in danger. In response, a spate of federal funds became available to improve the mathematics, science, and foreign language competence of our school children. University mathematicians saw the necessity of having some students understand the structural underpinnings of mathematics as the basis for their future work in mathematics. These mathematicians intended to "jump-start" young people who demonstrated a talent for mathematics and better prepare them for the rigors of university mathematics programs. Their strategy was to introduce topics into the school mathematics curriculum that aided the development of mathematical reasoning and proof.

Two components of the "new math" that appeared in elementary and secondary textbooks at the time were set theory (including set notation) and the structural properties of mathematics (commutative, associative, closure, etc.). Sometimes structural properties were developed through the study of number systems other than our Hindu-Arabic base-lO system. These topics often were presented abstractly in textbooks, not connected to any practical applications. For example, in typical eighth-grade texts of that era, integer addition was introduced by giving a set of principles, such as the commutative, associative, and distributive principles, that could be extended from the whole number system to prove relationships on the set of integers, and later to verify operations on rational numbers. Algebra texts continued this approach with particular emphasis on additive and multiplicative inverses and their applications to equation solving. Justification by deductive reasoning was the intent.

### Society's Concerns with "New Math"

Many elementary teachers, already insecure in their own mathematical knowledge, failed to fully understand or appreciate the mathematical implications of "new math's" structural approach. Indeed, many had difficulty connecting their familiar calculation skills with the abstract underpinnings promoted in materials grounded in the new approach. Exacerbating their lack of content knowledge was the fact that insufficient professional development was provided to support the change.

Likewise, support materials for teachers and students did not account for parents' needs and reactions. Worksheets on abstract reasoning were sent home, instead of worksheets on calculations. The result was considerable parental confusion and consternation. In short, most parents had no understanding of what their children were learning and its relationship to their conception of arithmetic. Parents complained, for example, that students could identify the associative property underlying multiplication and addition but were not able to get correct answers on standard arithmetic exercises. Most elementary programs based on the "new math" were soon discontinued.

The overall response in the mathematics community, however, was not to do away with "new math" altogether. Most current textbooks continue to include lessons emphasizing fundamental concepts important to student understanding and appreciation of mathematics. For example, various sorting activities still appear in elementary textbooks, with or without set notation. Sets are used in algebra (solution sets, for example) and in probability (sample space). Learning multiplication facts is made simpler by knowing that the operation is commutative, whether the term is introduced or not. In fact, students working with matrices, a topic now occurring in some ninth-grade materials, are astonished to realize that some mathematical systems are not commutative under multiplication.

### Continuing Influence of "New Math"

At the high school level, one of the most popular series of algebra textbooks, commonly known as Dolciani in reference to one of the major authors, was published in 1970 with the title Modern Algebra: Structure and Method, Books 1 and 2. The two major authors of these books, as well as the editorial adviser, were involved with the School Mathematics Study Group (SMSG), an outgrowth of the reform movement of the 1960s. Sets and mathematical structure play a major role throughout this algebra curriculum. Many iterations later, long after the death of Mary Dolciani, those textbooks remain among the most widely used in the United States. The "new math" did not go away. Rather, it was adapted to enhance and extend the skills-based algebra textbooks that were commonly used in the 1950s.

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