Elementary and Middle School Mathematics: Teaching Developmentally, 10th edition

Published by Pearson (January 23, 2018) © 2019

  • John A. Van de Walle Virginia Commonwealth University
  • Karen S. Karp Johns Hopkins University
  • Jennifer M. Bay-Williams University of Louisville


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For courses in teaching math methods (preK-8).

Guide teachers to help all PreK to 8th grade learners make sense of math

Elementary and Middle School Mathematics illustrates how children in PreK to 8th grade learn math, and then supplies concrete, effective methods of teaching math using problem-based activities. Examples of real student work, new common challenges, and hundreds of classroom-ready hands-on tasks help readers visualize developmentally appropriate mathematics instruction and assessment that supports and challenges all learners.

The 10th Edition reflects the Common Core State Standards and NCTM's Principles to Actions, as well as current research and the latest teaching technology.

Hallmark features of this title

  • Samples of real student work show children's mathematical reasoning in context.
  • Adaptations to Challenge and Support Students offer practical strategies to make activities accessible to all students.
  • Formative Assessment Notes help educators evaluate students' understanding of content areas and offer the best methods to assist struggling students.
  • Big Ideas lists help readers envision how to form their lesson plans around major themes rather than isolated skills or concepts.
  • Hundreds of problem-based activities model specific ways to engage students in doing mathematics.
  • Research-based strategies, NCTM Teaching Standards, and Standards for Mathematical Practice Margin Notes provide a thorough reference for all of the math content suggested for grades PreK-8.

New and updated features of this title

  • NEW: Common Challenges tables outline a student challenge and what it looks like, with tips on how to help.
  • NEW: Routines, including innovative lesson designs and short discussion starters, help students develop number sense, flexibility and mathematical practices.
  • UPDATED: Mathematical modeling discussions now reflect the Guidelines for Assessment and Instruction in Mathematical Modeling Education (GAIMME) Report (COMAP & Siam, 2016), as well as findings from recent books and articles.
  • UPDATED: Technology Notes, discussions, tools and ideas reflect the pervasiveness of technology used in teaching today.
  • UPDATED: Nearly 300 new references reflect the most current research, standards and exemplars.

Features of Pearson eText for the 10th Edition

  • Video Examples use authentic classroom videos and clips of children solving math problems to expand on key concepts and instructional strategies in each chapter. Additional videos feature the authors and experts in the field explaining strategies for teaching important topics.
  • Blackline masters, activity pages, teacher resources and expanded lessons are linked throughout each chapter. These classroom-ready documents are easy to download and print for use in a methods class or school settings.

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

  1. Developing Early Number Concepts and Number Sense
  2. Developing Meanings for the Operations
  3. Developing Basic Fact Fluency
  4. Developing Whole-Number Place-Value Concepts
  5. Developing Strategies for Addition and Subtraction Computation
  6. Developing Strategies for Multiplication and Division Computation
  7. Algebraic Thinking, Equations, and Functions
  8. Developing Fraction Concepts
  9. Developing Fraction Operations
  10. Developing Decimal and Percent Concepts and Decimal Computation
  11. Ratios, Proportions, and Proportional Reasoning
  12. Developing Measurement Concepts
  13. Geometric Thinking and Geometric Concepts
  14. Developing Concepts of Data Analysis
  15. Exploring Concepts of Probability
  16. Developing Concepts of Exponents, Integers, and Real Numbers


  1. Standards for Mathematical Practice
  2. NCTM Mathematics Teaching Practices: from Principles to Actions
  3. Guide to Blackline Masters
  4. Activities at a Glance

About our authors

Dr. John A. Van de Walle (1943-2006) 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.

Dr. 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 20 years. Prior to entering the field of teacher education, she was an elementary school teacher in New York. She is the coauthor of Strengths-Based Teaching and Learning in Mathematics: 5 Teaching Turnarounds for grades K-6, the three-book series The Math Pact: Achieving Instructional Cohesion within and Across Grades, and the What Works Clearinghouse Practice Guide on Assisting Students Struggling with Mathematics: Intervention in the Elementary Grades. 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. In 2020, she received the NCTM Lifetime Achievement Award and in 2021 became a member of the United States National Committee on Mathematics Instruction. She continues to work in classrooms to support teachers in ways to instruct students with special needs in math.

Dr. Jennifer Bay-Williams is a professor at the University of Louisville. She is a leader in mathematics education, continually working to support mathematics instruction. Beyond her work on this book and the related Teaching Student Centered Mathematics book series, Jennifer has most recently authored a book series called Figuring out Fluency in Mathematics K-12 and Math Fact Fluency: 60+ Games and Assessment Tools to Help Learning and Retention. For teacher leaders, she has authored Everything You Need for Mathematics Coaching. In the area of financial literacy, she authored a three-book series titled On the Money. Over the years, Jennifer has taught elementary, middle, and high school in the U.S. and in Peru. She continues to work with teachers around the world and in her local school districts to support their work. Jennifer has been actively involved in NCTM, NCSM, AMTE, and TODOS: Mathematics for All. Currently she is serving as an associate editor for Mathematics Teacher: Learning and Teaching in preK-12.

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