Research in mathematics education has consistently found that understanding and skills are best developed when students are allowed to wrestle with new ideas, to create and defend solutions to problems, and to participate in a mathematical community of learners. This student-centered, problem-based approach to learning is a central theme of this book. Learning how best to help children believe that mathematics makes sense and that they themselves can make sense of mathematics is an exciting endeavor and a lifelong process. It requires the knowledge gained from research, the wisdom shared by professional colleagues, and the insightful ideas that come from your own daily experiences with students. I hope that this book will assist you on this fantastic journey.

Praise for Elementary and Middle School Mathematics

This is absolutely the best book on the market. No other book comes close.

I particularly like the emphasis on doing math more than one way (invented math) and the emphasis on problem solving. There is a wealth of resources and children’s books for students to use in their development of concepts.

This text is not only a valuable tool in making sense of and encouraging the use of mathematics by preservice teachers, but also for those educators already in the field.

About the Author

John A. Van de Walle is Professor Emeritus, Virginia Commonwealth University. As a mathematics education consultant, he regularly works with K—8 teachers and in elementary school classrooms and has taught mathematics to children at all levels, K—8. He is also a coauthor of the Scott Foresman, Addison Wesley Mathematics K,6 series.

Jennifer M. Bay-Williams has written a Field Experience Guide to accompany the text." Organized to cover all NCATE and NCTM standards and correlated to all chapters of the text, the Field Experience Guide is packed with field-based assignments and reproducible forms to record your experiences." The guide also includes additional activities for students, full-size versions of the Blackline Masters in the text, and 16 extended lesson plans written by John Van de Walle. For more information or to purchase a copy, visit www.ablongman.com and search for the ISBN (0-205-49314-9.

Section I

Teaching Mathematics:

Foundations and

Perspectives 

chapter 1

Teaching Mathematics in the Era of the NCTM Standards 

chapter 2

Exploring What It Means to Do Mathematics 

chapter 3

Developing Understanding in Mathematics 

chapter 4

Teaching Through Problem Solving 

chapter 5

Planning in the Problem-Based Classroom 

chapter 6

Building Assessment into Instruction 

chapter 7

Teaching Mathematics Equitably to All Children 

chapter 8

Technology and School Mathematics 

Section II

Development of

Mathematical Concepts

and Procedures 

chapter 9

Developing Early Number Concepts

and Number Sense 

chapter 10

Developing Meanings for the Operations 

chapter 11

Helping Children Master the Basic Facts 

chapter 12

Whole-Number Place-Value Development 

chapter 13

Strategies for Whole-Number Computation 

chapter 14

Computational Estimation with Whole Numbers 

chapter 15

Algebraic Thinking: Generalizations, Patterns, and Functions 

chapter 16

Developing Fraction Concepts 

chapter 17

Computation with Fractions 

chapter 18

Decimal and Percent Concepts and Decimal Computation 

chapter 19

Proportional Reasoning 

chapter 20

Developing Measurement Concepts 

chapter 21

Geometric Thinking and Geometric Concepts 

chapter 22

Concepts of Data Analysis 

chapter 23

Exploring Concepts of Probability 

chapter 24

Developing Concepts of Exponents,

Integers, and Real Numbers 

appendix A

Principles and Standards for School Mathematics: Content Standards and Grade Level Expectations 

appendix B

Professional Standards for Teaching Mathematics: Teaching Standards 

appendix C

Guide to Blackline Masters 

References