To achieve the coherence and focus observed in the Japanese materials, the Curriculum and Evaluation Standards for School Mathematics need to be further extended to provide grade level guidance about focus and primary activities for given years. This step to achievement and delivery standards for school mathematics is curricularly achievable within the framework outlined by the NCTM content standards. Whether it is politically acceptable or systematically implementable are larger and more volatile questions.17

On balance, we see the efforts made since 1989 to develop standards for teaching and learning mathematics as worthwhile. Many schools have been led to rethink their mathematics programs, and many teachers to reflect on their practice. Nonetheless, the fragmentation of these standards, their multiple sources, and the limited conceptual frameworks on which they rest have not resulted in a coherent, well-articulated, widely accepted set of learning goals for U.S. school mathematics that would detail what students at each grade should know and be able to do. Part of our purpose in this report is to present a conceptual framework for school mathematics that could be used to move the goal-setting process forward.

Instructional Programs and Materials

Learning goals are inert until they are translated into specific programs and materials for instruction. What is actually taught in classrooms is strongly influenced by the available textbooks because most teachers use textbooks as their primary instructional materials.18 As of 1998, 12 states—including the very large markets of California and Texas—had policies in which the state either chose the materials that students would use or drew up a list of textbooks and materials from which districts had to choose, though sometimes only if they wanted to use state funds for the purchase. Another seven states recommended materials for use.19

Surveys of U.S. teachers have consistently shown that nearly all their instructional time is structured around textbooks or other commercially produced materials, even though teachers vary substantially in the extent to which they follow a book’s organization and suggested activities.20 In 1980 one researcher maintained that the chalkboard and printed textbooks were the predominant instructional media in mathematics classes,21 a verdict substantiated by recent data from the National Assessment of Educational Progress (NAEP). Responding to a questionnaire in 1996, teachers of three fifths of the fourth graders and of almost three fourths of the eighth graders in the



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