The authors describe six central characteristics of “standards-based” mathematics curriculum materials and discuss how these characteristics are related and how each one sets the stage for and supports the others. OVER THE past decade, many efforts have been made to reform school mathematics to reflect recommendations made by the National Council of Teachers of Mathematics (NCTM) in 1989 in the Curriculum and Evaluation Standards for School Mathematics. The release of updated standards, Principles and Standards for School Mathematics (hereafter referred to as the Standards), will doubtless prompt additional efforts to ensure that every student experiences a high-quality mathematics program.1 One consistent and very tangible focus of reform efforts is the adoption of new forms of curriculum materials. By curriculum “materials,” we mean those resources that serve as daily guides for students and teachers in directing activity related to math instruction and learning.
During the past decade, the phrase “standards-based” has been loosely used to describe a variety of materials ranging from individual units to collections of classroom activities, to pieces “added on” to traditional materials. In this article, we discuss comprehensive sets of curriculum materials that embody the ideas expressed in the Standards. These materials differ in substantive ways from traditional textbooks used in the U.S., which tend to focus on acquisition of skills, to cover many topics superficially, and to be highly repetitive.2 Prime examples of “standards-based” curriculum materials are programs developed with support from the National Science Foundation explicitly to reflect the Standards.3 (For a list of these NSF-funded programs see “NSF-Funded Standards-Based Curriculum Projects,” page 257.)
These are the materials that are at the center of recent controversy, drawing criticism from some research mathematicians and others. The controversy raises such questions as, What is meant by standards? What are standards-based materials? How are they different from traditional textbooks? In this article we describe six central characteristics of “standards-based” mathematics curriculum materials and discuss how these characteristics are related and how each one sets the stage for and supports the others. Standards-Based Materials Are CoMPREHENSIVE A primary concern in all curriculum reform is the inclusion of knowledge, understandings, processes, and skills that constitute competency in a field.
Most long-time observers of U.S. mathematics programs have been struck by their narrow focus on skills and procedures. In On the Shoulders of Giants: New Approaches to Numeracy, Lynn Steen notes that “school tradition has it that arithmetic, measurement, algebra, and a smattering of geometry represent the fundamentals of mathematics” – a limited framework that has produced programs dominated by a heavy emphasis on skills. “But there is much more,” Steen continues, “to the root system of mathematics – deep ideas that nourish the growing branches of mathematics.”4 Thus the first characteristic of standards-based materials is a focus on core mathematics for all students. This mathematical core must address the general literacy goals of school mathematics, the mathematics that is considered central to preparing America’s youth for the work force, as well as the mathematics necessary to provide a foundation for continued, advanced study of the subject. Within this framework, mathematics includes such familiar strands as arithmetic, algebra, geometry, statistics, and probability. It also addresses broad themes, such as dimension, quantity, uncertainty, shape, and change. The Standards lists five content standards for preschool through 12th- grade mathematics: 1) number and operations, 2) algebra, 3) geometry, 4) measurement, and 5) data analysis and probability. Under each standard are three or four statements describing what all students should know and be able to do across all grade levels.
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