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. This book helps students understand mathematics and become confident in their ability to teach the subject to children in pre-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.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 MyEducationLab icons in every chapter connect topics and ideas from chapter content to related videos, Expanded Lessons, simulations and other activities found on the MyEducationLab website at www.myeducationlab.com. NEW Field Experience Guide Connections is a new box at the end of each chapter that connects content and topics from the chapter with related experiences and activities from the Field Experience Guide. NEW Blackline Masters are updated and revised. Specific, numbered references are provided within each chapter. The full set of Blackline Masters is found in Appendix C and full-size copies of each Blackline Master are available both on MyEducationLab and also within the Field Experience Guide. NEW End-of-Chapter pedagogy is reorganized to include: Reflections On and Resources For. The Reflections On section contains Writing to Learn and For Discussion and Exploration.The Resources For section contains Literature Connections (in Chapters 8-23), Field Experience Guide Connections, Recommended Readings (including books and articles), and Online Resources. NEW Curriculum Focal Points are introduced in Chapter 1 and coverage and connections to chapter content are provided throughout the text. NEW Appendix B: Mathematics Teaching Today (Second Edition of Professional Standards for Teaching Mathematics: Teaching Standards). The second edition of the teaching standards (released in 2007) provide a guide to mathematics educators on the knowledge, skills, and dispositions required for effective mathematics teaching. NEW Expanded Lessons follow the lesson struc