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Elementary and Middle School Mathematics: Teaching Developmentally, 7th Edition

By John A. Van de Walle, Jennifer M. Bay-Williams

Published by Pearson

Published Date: Jan 15, 2009


“It is fun to figure out the puzzle of how children go about making sense of mathematics and then how to help teachers help kids.”  John A. Van de Walle, Late of Virginia Commonwealth University


This is the philosophy behind Elementary and Middle School Mathematics:  Teaching Developmentally.  John A. Van de Walle wrote this book to help students understand mathematics and become confident in their ability to teach the subject to children in kindergarten through eighth grade.  Although he could not have foreseen the changes in mathematics teaching over the last three decades, he was at the forefront of the movement towards a constructivist view of teaching, or teaching developmentally.  Constructivism says that children construct their own knowledge.  They are not blank slates waiting to absorb whatever the teacher tells them.  Teachers must understand both mathematics itself and how students learn mathematics in order to teach it effectively. 


Learning through problem solving is another major theme of this book.  Students solve problems not just to apply mathematics, but also to learn new mathematics.  Effective problems will take into account where students are, the problematic or engaging aspect of the problem must be due to the mathematics that the students are to learn and not be diluted by non-mathematical activities such as cutting or pasting, and the problem must require justifications and explanations for answers and methods.  Learning then becomes an outcome of the problem solving process. 


The book also addresses in more detail than any other book on the market the effect that the trends of standards-based education, increased pressure to test, and increased teacher accountability have had on teaching mathematics.  He addresses the 2000 NCTM Standards in depth, in Chapter 1 on Teaching Mathematics in the Era of the NCTM Standards, through the NCTM icon that appears in the margins throughout the text, and in two appendices in the back of the book.  Chapter 5 on Building Assessment into Instruction has also been heavily revised to focus on increased testing pressure, creating more explicit links between objectives and assessment, and including assessments for students with special needs. Additionally, samples of Pearson's reformed-based curricula, Connnected Math Project  (5-8) as well as Investigations (K-4),  are featured in the text and on the myeducationlab site.


Elementary and Middle School Mathematics:  Teaching Developmentally is a book for doing math today–for both students who want to become teachers, and the students they will eventually teach. 


New To This Edition:


NEW!  Revises Chapter 5 on assessment--Discusses increased testing pressure and accountability, adds more information on equitable assessments, creates more explicit links between objectives and assessment, and includes assessments for students with special needs.


NEW!  Updates the Literature Connections feature to remove all out of print children’s literature and include more non-fiction, poetry, and other types of readings.


NEW!  Weaves the Focal Points throughout the chapters as well as links them with the Big Ideas featureFocal Points have also been added to the Appendix. 


NEW!  Includes expanded coverage of working with diverse learners. 


NEW!  Gives greater emphasis on dealing with math anxiety.

Table of Contents

  1. Teaching Mathematics in the Era of the NCTM Standards
  2. Exploring What it Means to Do Mathematics and Developing Understanding in Mathematics
  3. Teaching Through Problem Solving
  4. Planning in the Problem-Based Classroom
  5. Building Assessment Into Instruction
  6. Teaching Mathematics Equitably to All children
  7. Technology and School Mathematics
  8. Developing Early Number Concepts and Number Sense
  9. Developing Meanings for the Operations
  10. Helping Children Master the Basic Facts
  11. Whole-Number Place-Value Development
  12. Strategies for Whole-Number Computation
  13. Computational Estimation with Whole Numbers
  14. Algebraic Thinking: Generalizations, Patterns, and Functions
  15. Developing Fraction Concepts
  16. Computation with Fractions
  17. Decimal and Percentage Concepts and Decimal Computation
  18. Proportional Reasoning
  19. Developing Measurement Concepts
  20. Geometric Thinking and Geometric Concepts
  21. Concepts of Data Analysis
  22. Exploring Concepts of Probability
  23. Developing Concepts of Exponents, Integers, and Real Numbers