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Helping Children Learn Mathematics

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Helping Children Learn Mathematics
Introduction
Today the United States has the challenge and the opportunity to provide all students with the mathematical knowledge, skills, and confidence they will need in a highly technical world. There is considerable nation-wide interest in improving students’ understanding of mathematics, combined with an emerging consensus about the essential elements of mathematics instruction; in addition, research has provided valuable insights into how children learn. Together these factors are opening the way to substantial and enduring progress in school mathematics.
Greater understanding of mathematics will be essential for today’s schoolchildren. Success in tomorrow’s job market will require more than computational competence. It will require the ability to apply mathematical knowledge to solve problems. If today’s students are to compete successfully in the world of tomorrow, they must be able to learn new concepts and skills. They need to view mathematics as a tool they can use every day. They need to have the mathematical sophistication that will enable them to take full advantage of the information and communication technologies that permeate our homes and workplaces. Students with a poor understanding of mathematics will have fewer opportunities to pursue higher levels of education and to compete for good jobs.
Despite the dramatically increased role of mathematics in our society, mathematics classrooms in the United States today too often resemble their counter-parts of a century ago.1 Many mathematics teachers still spend the bulk of their class time demonstrating procedures and supervising students while they practice those procedures. In numerous elementary and middle schools, time for learning mathematics is too brief. Textbooks are typically packed with an assortment of topics, so that the treatment of any one topic is often both shallow and

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Helping Children Learn Mathematics
repetitive. Key ideas can be difficult to pick out from among the many incidental details. This scattered and superficial curriculum means that students learn much less than they might. They then take standardized tests that often measure low-level skills rather than the kind of problem-solving abilities needed in modern life. All too often, mathematics instruction serves to alienate students rather than to reveal to them the beauty and usefulness of mathematics.
Despite its remarkable stability, school mathematics has changed somewhat in the United States over the past decade or so. Some districts are using instructional materials that are more likely to lead to mathematical proficiency, and some states have developed tests to measure more than low-level skills. More teachers are effectively engaging students with worthwhile mathematics. However, progress has been uneven and poorly documented.
Results from national and international assessments indicate that schoolchildren in the United States are not learning mathematics well enough. During the 1990s, performance on national assessments did improve in some areas of mathematics and for some groups of students. For example, fourth and eighth graders made significant gains. Performance also improved among black and Hispanic students, although the gap between the performance of these students and that of white students remains large. Even with these gains, however, performance is still below what is needed of U.S. students.2 Many students cannot use computations to solve problems. Their understanding and use of decimals and fractions are especially weak. In international comparisons, their mathematics performance is usually no better than average and sometimes below that.
Helping all children succeed in mathematics is an imperative national goal. Yet, although there is ample research on the learning of mathematics, there is a shortage of comprehensive and reliable information gleaned from that research to guide efforts to improve school mathematics.

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Helping Children Learn Mathematics
Frequently Asked Questions
Shaded boxes appearing throughout this book address the following questions, which arise in discussions of school mathematics:
Which side of the “math wars” is correct?
(page 12)
Do students still need to learn how to compute with paper and pencil now that calculators and computers are available?
(page 15)
What is wrong with the old ways of teaching math?
(page 22)
How can teachers develop all the strands of math proficiency when they already have so much to teach?
(page 22)
Does working in small groups help students to develop math proficiency?
(page 27)
Don’t students have to be grouped by ability to develop math proficiency?
(page 27)
Why are students playing with blocks, sticks, and beans in math classes?
(page 29)
Should all students study algebra?
(page 29)
Does improving students’ math proficiency require new types of tests?
(page 32)

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Helping Children Learn Mathematics
This short book is based on Adding It Up: Helping Children Learn Mathematics. Both are products of the National Research Council’s Mathematics Learning Study Committee, a multidisciplinary group of scholars, educators, researchers, and administrators with differing perspectives on school mathematics but a shared commitment to making it as effective as possible. Our committee has sought to move the discussion beyond the narrow views that have characterized past debates about how to improve student learning. We have not focused on a particular aspect of school mathematics, such as the curriculum or textbooks. Instead, we have taken a comprehensive view of what it means to be successful in mathematics. By examining, debating, and synthesizing the available research evidence, we have come to a consensus about how school mathematics needs to change to prepare students for life in the 21st century.
This book examines school mathematics during a critical period in a child’s education—from pre-kindergarten (pre-K) through eighth grade. During these years, students need to become proficient in mathematics if they are to be successful at higher levels of education and in the workplace. This book focuses on the domain of number, which is at the heart of preschool, elementary school, and middle school mathematics. Many of the controversies about school mathematics concern the learning of number, and it is the most thoroughly investigated part of the curriculum. But our concentration on number is not meant to imply that school mathematics from pre-K through eighth grade should be limited to arithmetic. On the contrary, school mathematics in the early grades needs to give significant attention to additional mathematical domains, such as algebra, geometry, probability, and statistics. We use the domain of number to illustrate what might be done throughout the curriculum.
This book, Helping Children Learn Mathematics, is addressed to parents and caregivers, teachers, administrators, and policy makers, all of whom must work together to improve mathematics learning. The book concludes with lists of recommended actions for each of these groups. Many other groups also must contribute, including textbook publishers, the creators of state and national learning standards and assessments, and education researchers. For those groups, Adding It Up provides more detailed guidance.

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Helping Children Learn Mathematics
The Origins of This Book
In 1998 the National Science Foundation and the U.S. Department of Education asked the National Research Council to conduct a study of what research says about successful mathematics learning from the preschool years through eighth grade. The National Research Council, which is the principal operating agency of the National Academy of Sciences, established a committee of 16 people to carry out this task. The charge to the committee had three parts:
to synthesize the rich and diverse research on pre-kindergarten through eighth-grade mathematics learning;
to provide research-based recommendations for teaching, teacher education, and curriculum for improving student learning and to identify areas where research is needed;
to give advice and guidance to educators, researchers, publishers, policy makers, and parents.
The Mathematics Learning Study Committee included school practitioners, research mathematicians, educational researchers, and a retired business executive. Committee members differed not only in expertise but in viewpoint—at the beginning of the committee’s work its members had many different and contrasting ideas about how mathematics learning can and should be improved. Over the course of eighteen months and eight meetings, the committee reviewed and synthesized the relevant research, gathered materials from commissioned papers and presentations, and discussed mathematics learning in light of the many and varied experiences of its members. In the process, the committee members gradually arrived at a consensus about the changes needed in mathematics teaching, teacher education, and the mathematics curriculum.
The committee’s final book benefited from the efforts of many different people concerned with improving mathematics education. The book Adding It Up: Helping Children Learn Mathematics can be purchased from the National Academy Press at 800–624–6242; it is also available on the World Wide Web at http://www.nap.edu/catalog/9822.html.
To disseminate the major conclusions of Adding It Up to a broader audience, a subcommittee of the Mathematics Learning Study Committee has overseen the production of this short book.