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#### 1 Looking at Mathematics and Learning Pages 15-30

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 From page 15...... Many educational opportunities and good jobs require high levels of mathematical expertise. Mathematical topics arise in newspaper and magazine articles, popular entertainment, and everyday conversation. Read the entire page → From page 16...... For the United States to continue its technological leadership as a nation requires that more students pursue educational paths that enable them to become . Read the entire page → From page 17...... 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. Read the entire page → From page 18...... To ensure that students having reading difficulties get prompt and effective assistance outside the regular school program, the reading community has developed a variety of intervention programs designed to address the problems students are having and to bring them back rapidly into the regular Read the entire page → From page 19...... Children at the 80th percentile in reading level were estimated to average more than 20 times as much reading per day as children at the 20th percentile.7 Similar data are not available for mathematics, but differences in the amount of time spent doing mathematics are likely to be less than for reading. This suggests that direct school-based instruction may play a larger part in most children's mathematical experience than it does in their reading experience. Read the entire page → From page 20...... However, at the heart of preschool, elementary school, and middle school mathematics is the set of concepts associated with the term number.8 Children learn to count, and they learn to keep track of their counting by writing numerals for the natural numbers. They learn to add, subtract, multiply, and divide whole numbers, and later in elementary school they learn to perform these same operations with common fractions and decimal fractions. Read the entire page → From page 21...... Further, our review does not capture the many connections both between various topics in mathematics and between mathematics and its uses in the world around us. Hence, in describing what is known about how children learn mathematics, we are not indirectly prescribing what mathematics children should learn. Read the entire page → From page 22...... The experience that people know and understand best is their own. To establish policies for school mathematics, however, it is essential to look beyond one's own experience to the evidence obtained through a systematic examination of what others have seen and reported. Read the entire page → From page 23...... It might reveal features of good practice or evaluate tradeoffs among various educational alternatives. Soundness The soundness of a research study concerns the extent to which the study supplied the data needed to address the research question. Read the entire page → From page 24...... Yet research cannot be the only basis for making instructional decisions in mathematics. First, as we stated earlier, research, by itself, cannot tell educators which of their learning goals are most important or how they should set priorities. Read the entire page → From page 25...... Second, decisions about how to help students reach learning goals can never be made with absolute certainty. As the famous American psychologist William lames noted at the end of the nineteenth century, psychology's description of "the elements of the mental machine . Read the entire page → From page 26...... That research can never provide prescrip tions, but it can be used to help guide skilled teachers in crafting methods that will work in their particular circumstances. For many important issues in mathematics education, the body of evidence is simply too thin at present to warrant a comprehensive synthesis. Read the entire page → From page 27...... In response to the charge to describe what areas of mathematics are important, chapter 3 outlines the domain of number and discusses what it means to learn about number in the pre-kindergarten to eighth-grade years. Chapter 4 details the strands of what we refer to as "mathematical proficiency," which we have established as what is meant by successful mathematics learning in the elementary school and middle school years. Read the entire page → From page 28...... In that program, the teacher, who has received extensive instruction in the reading process and its implications for teaching, notes an individual child's literacy strategies and knowledge and then engages the child in a structured series of activities. Each child is tutored individually for a half hour a day for up to 20 weeks. Read the entire page → From page 29...... (1999~. Adolescent literacy: A position statement for the Commission on Adolescent Literacy of the International Reading Association. Read the entire page → From page 30...... In response to the charge to describe what areas of mathematics are important, chapter 3 outlines the domain of number and discusses what it means to learn about number in the pre-kindergarten to eighth-grade years. Chapter 4 details the strands of what we refer to as "mathematical proficiency," which we have established as what is meant by successful mathematics learning in the elementary school and middle school years. Read the entire page →

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