Elementary and Middle School Mathematics : Teaching Developmentally

John A. Van de Walle

The late John A. Van de Walle was a professor emeritus at Virginia Commonwealth University. He was a mathematics education consultant who regularly gave professional development workshops for K-8 teachers in the United States and Canada. He visited and taught in elementary school classrooms and worked with teachers to implement student-centered math lessons. He co-authored the Scott Foresman-Addison Wesley Mathematics K-6 series and contributed to the Pearson School mathematics program, enVisionMATH. Additionally, he wrote numerous chapters and articles for the National Council of Teachers of Mathematics (NCTM) books and journals and was very active in NCTM, including serving on the Board of Directors, Chair of the Educational Materials Committee, and a frequent speaker at national and regional meetings.

Karen S. Karp

Karen S. Karp is a professor of mathematics education at the University of Louisville in Kentucky.  Prior to entering the field of teacher education she was an elementary school teacher in New York.  Karen is a co-author of Feisty Females: Inspiring Girls to Think Mathematically, which is aligned with her research interests on teaching mathematics to diverse populations. With Jennifer, Karen co-edited Growing Professionally: Readings from NCTM Publications for Grades K-8 and co-authored (along with Janet Caldwell) Developing Essential Understanding of Addition and Subtraction for Teaching Mathematics in Pre-K-Grade 2. She is a former member of the Board of Directors of the National Council of Teachers of Mathematics (NCTM) and a former president of the Association of Mathematics Teacher Educators (AMTE). She continues to work in classrooms with elementary and middle school students and with teachers at all levels who work with students with disabilities.

Jennifer M. Bay-Williams

Jennifer M. Bay-Williams is a professor of mathematics education at the University of Louisville (Kentucky). Jennifer has published many articles on teaching and learning in NCTM journals. She has also coauthored numerous books, including: Developing Essential Understanding of Addition and Subtraction for Teaching Mathematics in Pre-K-Grade 2, Math and Literature: Grades 6-8, Math and Nonfiction: Grades 6-8, and Navigating through Connections in Grades 6-8. She is the author of the Field Experience Guide for this book. Jennifer taught elementary, middle, and high school in Missouri and in Peru, and continues to work in classrooms at all levels with students and with teachers. Jennifer is on the Board of Directors for TODOS: Equity for All, Editor for the 2012 NCTM Yearbook, and past-president of the Association of Mathematics Teacher Educators (AMTE).

Jonathan Wray, technology contributor to Elementary and Middle School Mathematics, Teaching Developmentally (6th-8th editions).

Jonathan Wray is the Instructional Facilitator for Secondary Mathematics Curricular Programs in the Howard County Public School System. He is the president of the Association of Maryland Mathematics Teacher Educators (AMMTE) and past president of the Maryland Council of Teachers of Mathematics (MCTM). He has been recognized for his expertise in infusing technology in mathematics teaching receiving the Outstanding Technology Leader in Education by the Maryland Society for Educational Technology (MSET). Jon is also actively engaged in NCTM, serving on the editorial panels of Teaching Children Mathematics and ON-Math . Mr. Wray  has been a primary and intermediate grades classroom teacher, gifted/talented resource teacher, elementary mathematics specialist, curriculum and assessment developer, grant project manager, and educational consultant.

Section 1: Teaching Mathematics: Foundations and Perspectives

Chapter 1 Teaching Mathematics in the 21^st Century                

Chapter 2 Exploring What it Means to Know and Do Mathematics

Chapter 3 Teaching through Problem Solving

Chapter 4 Planning in the Problem-Based Classroom

Chapter 5 Building Assessment into Instruction

Chapter 6 Teaching Mathematics Equitably to All Children

Chapter 7 Using Technological Tools to Teach Mathematics

Section 2: Development of Mathematical Concepts and Procedures

Chapter 8 Developing Early Number Concepts and Number Sense

Chapter 9 Developing Meanings for the Operations

Chapter 10 Helping Students Master the Basic Facts

Chapter 11 Developing Whole-Number Place-Value Concepts

Chapter 12 Developing Strategies for Addition and Subtraction Computation

Chapter 13 Developing Strategies for Multiplication and Division Computation

Chapter 14 Algebraic Thinking: Generalizations, Patterns, and Functions

Chapter 15 Developing Fraction Concepts

Chapter 16 Developing Strategies for Fraction Computation

Chapter 17 Developing Concepts of Decimals and Percents

Chapter 18 Proportional Reasoning

Chapter 19 Developing Measurement Concepts

Chapter 20 Geometric Thinking and Geometric Concepts

Chapter 21 Developing Concepts of Data Analysis

Chapter 22 Exploring Concepts of Probability

Chapter 23 Developing Concepts of Exponents, Integers, and Real Numbers

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