The late John A. Van de Walle was a professor emeritus at Virginia Commonwealth University. He was a leader in mathematics education who regularly gave professional development workshops for K—8 teachers in the United States and Canada focused on mathematics instruction that engaged students in mathematical reasoning and problem solving. He visited and taught in many classrooms and worked with teachers to implement student-centered mathematics lessons. He co-authored the Scott Foresman-Addison Wesley Mathematics K—6 series and contributed to the original Pearson School mathematics program enVisionMATH. Additionally, John was very active in the National Council of Teachers of Mathematics (NCTM), writing book chapters and journal articles, serving on the board of directors, chairing the educational materials committee, and speaking at national and regional meetings.

Karen S. Karp is a professor at Johns Hopkins University (Maryland). Previously, she was a professor of mathematics education at the University of Louisville for more than twenty years. Prior to entering the field of teacher education she was an elementary school teacher in New York. Karen is the volume editor of Annual Perspectives in Mathematics Education: Using Research to Improve Instruction and is the co-author of Developing Essential Understanding of Addition and Subtraction for Teaching Mathematics in PreK—Grade 2, Discovering Lessons for the Common Core State Standards in Grades K—5, and Putting Essential Understanding of Addition and Subtraction into Practice PreK—Grade 2. She is a former member of the board of directors for the National Council of Teachers of Mathematics (NCTM) and a former president of the Association of Mathematics Teacher Educators. She continues to work in classrooms to support teachers in ways to instruct students with disabilities.

Dr. Jennifer Bay-Williams is a mathematics teacher educator, author, and life-long learner with a passion for making mathematics meaningful for all students. She has written many articles and books around K-12 mathematics education, including the three book series related to this book, Teaching Student Centered Mathematics (with John Van de Walle, LouAnn Lovin, and Karen Karp), and various other books including Mathematics Coaching: Resources and Tools for Coaches and Other Leaders, Developing Essential Understanding of Addition and Subtraction in Prekindergarten—Grade 2, On the Money (financial literacy book series), Math and Literature: Grades 6—8, and Math and Nonfiction: Grades 6—8. Jennifer is a professor at the University of Louisville (Kentucky) and previously taught elementary, middle, and high school in Missouri and in Peru. She continues to learn and work in K-8 classrooms in rural and urban settings. Jennifer is very active in national mathematics organizations, having served is on the NCTM board of directors, AMTE secretary, president, and lead writer for Standards for the Preparation of Teachers of Mathematics (AMTE, 2017), and currently serving on the TODOS: Mathematics for All Board of Directors as Chair of the Advocacy Committee.

Brief Contents

Section I: Teaching Mathematics: Foundations and Perspectives

1. Teaching Mathematics in the 21st Century

2. Exploring What It Means to Know and Do Mathematics

3. Teaching through Problem Solving

4. Planning in the Problem-Based Classroom

5. Creating Assessments for Learning

6. Teaching Mathematics Equitably to All Students

Section II: Development of Mathematical Concepts and Procedures

7. Developing Early Number Concepts and Number Sense

8. Developing Meanings for the Operations

9. Developing Basic Fact Fluency

10. Developing Whole-Number Place-Value Concepts

11. Developing Strategies for Addition and Subtraction Computation

12. Developing Strategies for Multiplication and Division Computation

13. Algebraic Thinking, Equations, and Functions

14. Developing Fraction Concepts

15. Developing Fraction Operations

16. Developing Decimal and Percent Concepts and Decimal Computation

17. Ratios, Proportions, and Proportional Reasoning

18. Developing Measurement Concepts

19. Geometric Thinking and Geometric Concepts

20. Developing Concepts of Data Analysis

21. Exploring Concepts of Probability

22. Developing Concepts of Exponents, Integers, and Real Numbers

Appendix A. Standards for Mathematical Practice A-1

Appendix B. NCTM Mathematics Teaching Practices: from Principles to Actions A-5

Appendix C. Guide to Blackline Masters A-7

Appendix D. Activities at a Glance A-13

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Elementary and Middle School Mathematics Teaching Developmentally

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