"New Math"

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.