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Elementary and Middle School Mathematics (9e)

By John A. Van De Walle, Karen Karp, Jennifer M. Bay-Williams
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For use in Elementary Mathematics Methods or Middle School Mathematics Methods courses (covers Pre-K-8)

Guide teachers to help all Pre-K-8 learners make sense of math

Written by leaders in the field, Elementary and Middle School Mathematics: Teaching Developmentally helps teacher candidates develop a real understanding of the mathematics they will teach and the most effective methods of teaching Pre-K-8 math topics. This text reflects the Common Core State Standards and NCTM’s Principles to Actions, as well as current research. Emphasis is placed on teaching math conceptually, in a problem-based, developmentally appropriate manner that supports the learning needs of all students. Pause and Reflect prompts and Activities engage pre-service teachers as they bolster their own knowledge of the math. Classroom videos and examples of real student work allow teacher candidates to visualise good mathematics instruction and assessment. An important reference to consult throughout a teaching career, this book helps teachers and their students experience the excitement that happens when math makes sense.

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Table of contents
  • SECTION I Teaching Mathematics: Foundations and Perspectives
  • CHAPTER 1 Teaching Mathematics in the 21st 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 Creating Assessments for Learning
  • CHAPTER 6 Teaching Mathematics Equitably to All Children
  • CHAPTER 7 Using Technological Tools to Teach Mathematics
  • SECTION II Development of Mathematical Concepts and Procedures
  • CHAPTER 8 Developing Early Number Concepts and Number Sense
  • CHAPTER 9 Developing Meanings for the Operations
  • CHAPTER 10 Developing Basic Fact Fluency
  • 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, Equations, and Functions
  • CHAPTER 15 Developing Fraction Concepts
  • CHAPTER 16 Developing Fraction Operations
  • CHAPTER 17 Developing Concepts of Decimals and Percents
  • CHAPTER 18 Ratios, Proportions, and 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
  • 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
Features & benefits


  • A textual discussion (Chapter 1) of the actual Common Core State Standards for Mathematical Practices (CCSS-M) and NCTM Teaching standards (App. A, B) is included.
  • Help teachers become advocates for NCTM and reform-based curricula:
    • Information on how to communicate with administrators and parents is included.
    • Information is included on using NCTM and Common Core State Standards to inform instruction.
  • Emphasise fluency. Developing Fluency topics are critical to students as they develop a strong understanding of different operation situations.
  • Develop conceptual knowledge with problem-based tasks. The problem-based approach to the teaching of mathematics espouses the theory of Hiebert et al. that the best approach to teaching mathematics is to teach with problem-based tasks.
  • Plan lessons around ‘big ideas’. Rather than using isolated skills or concepts, Big Ideas provide clear and succinct exploration of the most critical concepts in mathematics to help teachers plan their instruction.
  • View real student work. Samples of real student work illustrate student thinking and responses to problem-based assignments. Pre-service teachers see direct examples of the ideas suggested—providing a window into children’s mathematical reasoning. This increases prospective teachers’ awareness of how capable students are—and how high our expectations can be.
  • Support teaching, and learning, mathematics conceptually. The authors provide comprehensive coverage of new technologies, teaching strategies, and recommended web sites and tools for teaching conceptually.
  • Address classroom diversity and individual student needs. To help teachers make tasks and activities accessible for all students in all content areas, adaptations and accommodations for English Language Learners (ELL) and Students with Disabilities are included not only in the narrative, but also in Activities that contain direct examples and descriptions in the various content areas. Lessons include tips and strategies for ELLs and students with disabilities.
  • Identify student misconceptions and the best way to address them effectively. A focus on misconceptions will better support teachers in understanding what needs explicit attention in teaching specific mathematics topics.
  • Learn strategies to foster parental involvement. A discussion is included on parental involvement. The opportunity to engage families in meaningful ways is critical to helping students learn mathematic
  • Evaluate student progress and student thinking to inform instruction. Formative Assessment Notes in every chapter in Section II help teachers understand how to best help their students.
  • Engage students with conversation and discussion to enhance the learning of mathematics. Strategies for facilitating discourse include how to conduct productive discussion sessions, developing effective questioning strategies, and vignettes that can be used as illustrative examples.  
Educator downloads

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Instructor's Manual

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