how children learn mathematics and the kinds of teaching that supports that learning. Research continues to expand our understanding of the teaching-learning process. All of this taken together makes us believe that our goal is in large measure achievable.

Mathematics and Reading

A comparison of mathematics with reading leads to several important observations. First, competence in both domains is important in determining children’s later educational and occupational prospects. Children who fail to develop a high level of skill in either one are precluded from the most interesting and rewarding careers. As a recent report on reading from the National Research Council put it, “To be employable in the modern economy, high school graduates need to be more than merely literate. They must be able to read challenging material, to perform sophisticated computations, and to solve problems independently.”2

Second, there are important similarities as well as differences in the problems children face in developing competence in reading and mathematics. Understanding the common features of reading development and mathematical development is as important as understanding the special characteristics of learning in each domain.

Finally, international comparisons suggest that U.S. schools have been relatively successful in developing skilled reading, with improvements in both instruction and achievement occurring in a large number of schools.3 Unfortunately, the same cannot be said of mathematics. International comparisons discussed in the next chapter suggest that by eighth grade the mathematics performance of U.S. children is well below that of other industrialized countries. Furthermore, this performance has been relatively low in a variety of comparisons conducted at intervals over several decades. The organizational and instructional factors that U.S. schools have used in developing skilled reading performance may be equally important in improving the learning of mathematics. Learning to read and developing mathematical proficiency both rest on a foundation of concepts and skills that are acquired by many children before they leave kindergarten. In the case of reading, children are expected to enter school with a basic understanding of the sound structure of their native language, a conscious awareness of the units (phonemes) that are represented by an alphabetic writing system, and skill in handling basic language concepts. Likewise in mathematics, students should possess a toolkit of basic mathematical concepts and skills when they enter first grade. (These

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