One of the defining events in the history of mathematics education was the launching of Sputnik 1 by the Soviet Union in 1957. This marked the start of the space age and the space race between the United States and the Soviet Union. Concern that the United States was falling behind in the areas of math and science triggered major national reforms in these areas. These reforms brought about the “New Math” of the 1960s and 1970s. The emphasis of this New Math was on set language and properties, proof, and abstraction. However, the New Math curriculum failed to meet the challenge of increasing the nation’s mathematical prowess as a whole. Some would even say that the New Math created more math confusion than it eliminated, which brought about the trend of Back to Basics in the late 1970s and early 1980s. Back to Basics emphasized arithmetic computation and rote memorization of algorithms and basic arithmetic facts.

### The 1989 NCTM Standards

In the later 1980s the focus shifted to critical thinking. In 1989 the National Council of Teachers of Mathematics (NCTM) released a groundbreaking document, Curriculum and Evaluation Standards for School Mathematics. This publication, sometimes referred to as the “NCTM Standards,” stresses problem solving, communication, connections, and reasoning. The key assumptions underlying the 1989 NCTM curriculum standards for Grades K–4, listed below, are addressed throughout this textbook.

The 1989 NCTM Standards include 13 curriculum standards addressing both content and emphasis. One theme common to the NCTM Standards and to the recent changes in mathematics education is that “the study of mathematics should emphasize reasoning so that students can believe that mathematics makes sense” (NCTM, 1989, p. 29). Although not discussed here, this document also includes similar sets of assumptions and standards for Grades 5 through 8 and for Grades 9 through 12.

The 1989 NCTM Standards list five goals for students. Although these are goals stated for elementary students, it is especially important that teachers of elementary students have attained them.

### Professional and Assessment Standards for Teaching Mathematics

A second groundbreaking document released by the National Council of Teachers of Mathematics was Professional Standards for Teaching Mathematics. This set of standards “present[s] a vision of what teaching should entail to support the changes in curriculum set out in the Curriculum and Evaluation Standards. This document spells out what teachers need to know to teach toward new goals for mathematics education and how teaching should be evaluated for the purpose of improvement” (NCTM, 1991, p. vii). NCTM followed with the 1995 release of Assessment Standards for Teaching Mathematics. NCTM produced this important document because “new assessment strategies and practices need to be developed that will enable teachers and others to assess students’ performance in a manner that reflects the NCTM’s reform vision for school mathematics” (NCTM, 1995, p. 1).

In the 1990s the major focus of reform in mathematics education was directed toward teaching pedagogy. Numerous studies and articles promoted the use of manipulatives and technology in the classroom (Burns, 1996; Hatfield, 1994; National Association for the Education of Young Children [NAEYC], 1996; Roth, 1992). Key ideas of this era included the use of developmentally appropriate activities and the constructivist approach to teaching. The NCTM Standards continued to gain support and popularity among mathematics educators, and many states developed grade-level scope and sequences and competency-based model programs that reflected these standards. Proficiency testing became more widespread, with some states requiring a certain level of competency in subject areas such as mathematics for grade promotion.

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