For Elementary Mathematics Methods or Middle School Mathematics Methods Covers preK-8
Written by leaders in the field, this best-selling book will guide teachers as they help all PreK-8 learners make sense of math by supporting their own mathematical understanding and cultivating effective planning and instruction.
Elementary and Middle School Mathematics: Teaching Developmentally provides an unparalleled depth of ideas and discussion to help teachers develop a real understanding of the mathematics they will teach and the most effective methods of teaching the various mathematics topics. This text reflects the NCTM and Common Core State Standards and the benefits of problem-based mathematics instruction. It is structured for maximum flexibility, offering 23 chapters that may be mixed and matched to fit any course or teaching approach. This comprehensive, practical text offers readers a strong theoretical perspective reflecting the most current research on how students learn mathematics, ways to best teach it, and many problem-based activities to engage students. An important reference to consult throughout a teaching career, Van de Walle, Karp and Bay-William’s book helps teachers and their preK-8 students find the excitement that happens when mathematics makes sense.
Table of contents
Section 1: 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 Building Assessment into Instruction
Chapter 6 Teaching Mathematics Equitably to All Children
Chapter 7 Using Technological Tools to Teach Mathematics
Section 2: Development of Mathematical Concepts and Procedures
Chapter 8 Developing Early Number Concepts and Number Sense
Chapter 9 Developing Meanings for the Operations
Chapter 10 Helping Students Master the Basic Facts
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: Generalizations, Patterns, and Functions
Chapter 15 Developing Fraction Concepts
Chapter 16 Developing Strategies for Fraction Computation
Chapter 17 Developing Concepts of Decimals and Percents
Chapter 18 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
New to this edition
The Eighth Edition has been revised to better prepare teachers to teach mathematics to all learners.
· New adaptations and accommodations for English Language Learners and Students with Disabilities appear not only in the narrative in Section I but also in many activities through direct examples and descriptions for the various content areas in Section II.
· Revised Expanded Lessons, located in the book, the Field Experience Guide*, and on MyEducationLab* (www.myeducationlab.com)now include tips and strategies for English language learners and students with disabilities.
· Increased emphasis on student misconceptions and how to address them effectively will better support teachers in understanding what needs explicit attention in teaching.
· New samples of authentic student work illustrate student thinking. Responses to problem-based assignments present glimpses into how students think about problems and what students’ written work on mathematical tasks looks like increasing teachers’ awareness of how rich students’ mathematical thinking can be - and how high our expectations can be. Some student work also demonstrates naïve understandings.
· Increased early childhood coverage with attention to early numeracy showcased by extensive revision of Ch 8 to reflect National Research Council’s research and current publications addressing number core and relations core and the learning trajectory research published by Clements and Sarama.
· New Formative Assessment Notes in every chapter in Section II guide teachers’ use of various assessment methods to evaluate student progress and student thinking to inform instruction.
· NEW information is included on using NCTM and Common Core State Standards to inform instruction.
· Updated and Expanded! Learn how to effectively integrate new technological tools to support teaching and learning with updated technology integration content and strategies throughout the text and now also in select activities.
· 10 New Fraction Operation Activities will provide teachers more guidance on how to teach fraction operations for increased student learning.
· Chapters 12 and 13 have been reorganized and now focus on developing strategies for addition and subtraction and multiplication and division computation, respectively. Coverage of estimation is infused in both chapters.
· New! Discussion on engaging families in meaningful ways to help students learn mathematics appears in Ch 4.
· Expanded! Additional attention to discourse now appears in the Problem Solving chapter (Ch. 3). Coverage, illustrated with vignettes, now includes how to conduct productive discussion sessions and developing effective questioning
*Field Experience Guide and MyEducationLab (www.myeducationlab.com) are sold separately. Visit www.pearsonhighered.com or your contact your local Pearson Representative for more information.
Features & benefits
Takes a 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.
Updated! Provides the most complete coverage of the NCTM and Common Core State Standards in the market—Includes a textual discussion (Chapter 1) the actual Common Core State Standards for Mathematical Practices and NCTM Teaching standards (App. A, B), and numerous references throughout the text.
This book is uniquely designed to help teachers:
· Prepare for problem-based mathematics instruction:
o Big Ideas provide clear and succinct exploration of the most critical concepts in mathematics to help teachers plan instruction around “big ideas” rather than isolated skills or concepts
o Mathematics Content Connections help teachers be aware of the interaction of content as they plan lessons and diagnose student difficulties.
o Field Experience Guide Connections at the end of each chapter showcase specific classroom-based tasks, activities, and resources available to readers in the popular Field Experience Guide.
- In section II, four chapters include features that describe an activity from the standards-based curriculum Investigations in Number, Data, and Space (an elementary curriculum) or Connected Mathematics Project (CMP II) (a middle school curriculum) to demonstrate how the spirit of professional standards and problem-based mathematics instruction presented in this book can be translated to existing commercial curricula.
o New! Additional samples of real student work are included to illustrate student thinking and responses to problem-based assignments. Teachers can see direct examples of the ideas suggested - glimpsing how students think about problems and how students’ written work on mathematical tasks looks. This increases prospective teachers’ awareness of how smart students are - and how high our expectations can be. Some student work demonstrates naïve understandings.
· Plan for all learners:
o New! Strategies for English language learners and students with disabilities are interwoven in the text in Section I (highlighted in Chapter 6). In Section II many Activities in each chapter now contain specific tips for accommodations.
- New! Increased early childhood coverage with attention to early numeracy showcased by extensive revision of Ch 8 to reflect National Research Council’s research and current publications addressing number core and relations core and the learning trajectory research published by Clements and Sarama.
o Revised! Expanded Lessons now include tips and strategies for English language learners and students with disabilities
o New! Formative Assessment Notes in every chapter in Section II help teachers understand how to best help their students.
· Become advocates for NCTM and reform-based curricula:
- Information on how to communicate with administrators and parents is included.
- NEW! Information is included on using NCTM and Common Core State Standards to inform instruction
· Updated and Expanded! Effectively integrate technological tools to support teaching and learning with comprehensive coverage of new technologies and teaching strategies. Many of the Activities in the book include a technological component.
· Practice doing the mathematics that they will teach through numerous activities in each of the 16 content chapters and on MyEducationLab*.
*Field Experience Guide and MyEducationLab (www.myeducationlab.com) are sold separately. Visit www.pearsonhighered.com or your contact your local Pearson Representative for more information
John A. Van de Walle
The late John A. Van de Walle was a professor emeritus at Virginia Commonwealth University. He was a mathematics education consultant who regularly gave professional development workshops for K-8 teachers in the United States and Canada. He visited and taught in elementary school classrooms and worked with teachers to implement student-centered math lessons. He co-authored the Scott Foresman-Addison Wesley Mathematics K-6 series and contributed to the Pearson School mathematics program, enVisionMATH. Additionally, he wrote numerous chapters and articles for the National Council of Teachers of Mathematics (NCTM) books and journals and was very active in NCTM, including serving on the Board of Directors, Chair of the Educational Materials Committee, and a frequent speaker at national and regional meetings.
Karen S. Karp
Karen S. Karp is a professor of mathematics education at the University of Louisville in Kentucky. Prior to entering the field of teacher education she was an elementary school teacher in New York. Karen is a co-author of Feisty Females: Inspiring Girls to Think Mathematically, which is aligned with her research interests on teaching mathematics to diverse populations. With Jennifer, Karen co-edited Growing Professionally: Readings from NCTM Publications for Grades K-8 and co-authored (along with Janet Caldwell) Developing Essential Understanding of Addition and Subtraction for Teaching Mathematics in Pre-K-Grade 2. She is a former member of the Board of Directors of the National Council of Teachers of Mathematics (NCTM) and a former president of the Association of Mathematics Teacher Educators (AMTE). She continues to work in classrooms with elementary and middle school students and with teachers at all levels who work with students with disabilities.
Jennifer M. Bay-Williams
Jennifer M. Bay-Williams is a professor of mathematics education at the University of Louisville (Kentucky). Jennifer has published many articles on teaching and learning in NCTM journals. She has also coauthored numerous books, including: Developing Essential Understanding of Addition and Subtraction for Teaching Mathematics in Pre-K-Grade 2, Math and Literature: Grades 6-8, Math and Nonfiction: Grades 6-8, and Navigating through Connections in Grades 6-8. She is the author of the Field Experience Guide for this book. Jennifer taught elementary, middle, and high school in Missouri and in Peru, and continues to work in classrooms at all levels with students and with teachers. Jennifer is on the Board of Directors for TODOS: Equity for All, Editor for the 2012 NCTM Yearbook, and past-president of the Association of Mathematics Teacher Educators (AMTE).
Jonathan Wray, technology contributor to Elementary and Middle School Mathematics, Teaching Developmentally (6th-8th editions).
Jonathan Wray is the Instructional Facilitator for Secondary Mathematics Curricular Programs in the Howard County Public School System. He is the president of the Association of Maryland Mathematics Teacher Educators (AMMTE) and past president of the Maryland Council of Teachers of Mathematics (MCTM). He has been recognized for his expertise in infusing technology in mathematics teaching receiving the Outstanding Technology Leader in Education by the Maryland Society for Educational Technology (MSET). Jon is also actively engaged in NCTM, serving on the editorial panels of Teaching Children Mathematics and ON-Math. Mr. Wray has been a primary and intermediate grades classroom teacher, gifted/talented resource teacher, elementary mathematics specialist, curriculum and assessment developer, grant project manager, and educational consultant.