"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 structure described in Chapter 4 and include mathematical goals, notes on preparation, specific student expectations, notes for assessment, and Blackline Masters when needed. These Lessons have been updated and reformatted for the new edition. The lessons provide a model for conveying an activity description into a real lesson plan and indicate the kind of thinking that is required in doing so. An example of an Expanded Lesson is found at the end of Chapter 4. In addition, one activity or concept in seven of the content chapters has been converted to a similar Expanded Lesson found on MyEducationLab. NEW! Developing as a Professional. There is a new emphasis on your long-term professional growth, from keeping you abreast of the most current documents in mathematics education to a whole new section in Chapter 1 that invites you to grow and learn as you become a teacher of mathematics. In Chapter 1, you will be introduced to the Curriculum Focal Points, and the newest version of the NCTM Professional Teaching Standards called Teaching Mathematics Today (these professional teaching standards are also found in Appendix B). You will also be made aware of all new NCTM position statements, thinking on Grade Level Expectations, and the results of major national and international assessments. In addition, there is a specific section in Chapter 1 that emphasizes your responsibility to develop your personal knowledge of mathematics, persistence, positive attitude, readiness for change, and reflective disposition. These are the elements of becoming a life-long learner. NEW! Algebraic Thinking. One of themost important changes in this edition is the treatment of algebraic thinking in Chapter 14 Algebraic Thinking: Generalizations, Patterns, and Functions. Although recently revised in the sixth edition, this new version reorganizes the chapter around five critical themes of algebraic thinking: generalization from arithmetic and from patterns in all of mathematics, meaningful use of symbols, study of structure in the number system, study of patterns and functions, and the process of mathematical modeling, which integrates the first four. In addition, there is increased attention to developing meaningful contexts for algebraic thinking across grades Pre-K-8, including connections to other subject areas. NEW! Doing and Understanding Mathematics. You will immediately note that there is one fewer chapter. Chapters 2 and 3 in the sixth edition separated the doing and understanding of mathematics. Now Chapter 2 connects the theories of learning "why do" to the implementation of "doing" mathematics. The theories of constructivism and socio-cultural theory are concisely and clearly described, followed by implications for teaching. Many sixth edition users requested this melding of the two chapters, and the resulting chapter should point to the need to tie theory to practice. NEW! Problem Solving. Although problem solving is integrated throughout the book, in Section I chapters you will find a new emphasis on teaching problem solving with a focus on the work of George Polya. Since we recognize that many teachers are using a curriculum that may not include the same focus on problem solving as espoused in the book, there is an excellent section in Chapter 3 on how to adapt textbooks to promote problem solving. NEW! Diversity. The emphasis on diversity will be obvious to those who have used the book in the past. This appears in many chapters, including how to differentiate instruction (including tiered lessons) and the advantages of flexible grouping (in Chapter 4), a new component of the lesson planning process (Chapter 3), and working with families who have diverse linguistic and cultural backgrounds (Chapters 4 and 6). Teaching Mathematics Equitably to all Children (Chapter 6) contains several new features including an expanded section for working with students with special needs covering the Response to Intervention (RTI) Model adapted for use with students in the mathematics classroom and a revised section offering research-based strategies for students with mild and significant disabilities. Finally, in Part II there is an intentional effort to weave considerations for working with students from diverse backgrounds into the discussions of concepts and methods. NEW! Technology. Not surprisingly there are many changes in the world of technology since the last edition and it will be challenging to keep up even as this edition is published. There is a more inclusive definition of technologies including digital tools, collaborative authoring tools, podcasts and dynamic software. This is in light of the thinking about Technological Pedagogical Content Knowledge, which reflects the need to infuse technology in every lesson. In Chapter 7, there is also a new rubric on how to select and evaluate internet resources, something that previous readers and reviewers requested. With that in mind, there is a distinct effort throughout the book to focus on software you do not need to buy, but can instead access online. NEW! Statistics and Data Analysis. Since the sixth edition, the American Statistical Association published the Guidelines for Assessment and Instruction in Statistics Education (GAISE) K-12 Report. This important document outlines a process for doing statistics that provides the foundation for Chapter 21. While data analysis remains an essential focus of this chapter, there are now added sections on posing questions, data collection and drawing inferences. Other Changes. Here are some other highlights new to the seventh edition: Chapter 5 Building Assessment into Instruction now includes definitions of formative and summative assessment, rubrics that are clearly focused on the collection of evidence, and a section on diagnostic interviews to support you when working with students who are struggling. Chapter 15 Developing Fraction Concepts now includes a section on the meaning of fractions and gives a list of ten strategies to remember when teaching fractions Chapter 19 Developing Measurement Concepts, now includes the topic of money that was previously discussed in the chapter on place value. Chapter 22 Exploring...