Teaching Student-Centered Mathematics: Developmentally Appropriate Instruction for Grades 3-5, 3rd edition
Published by Pearson (January 9, 2017) © 2018
- John A. Van de Walle Virginia Commonwealth University
- Karen S. Karp Johns Hopkins University
- LouAnn H. Lovin James Madison University
- Jennifer M. Bay-Williams University of Louisville
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- NEW! Embedded videos throughout provide examples of students' misconceptions, expand on key concepts, and demonstrate how to implement strategies and techniques in real classrooms.
- NEW! Downloadable Teacher Resource and Activity Pages support teaching activities such as formative assessment and team-building are now available in the Enhanced Pearson eText at the point of use.
- NEW! Downloadable Blackline Masters in Part 2 Chapters. Readers may download Blackline Masters that support the activities and Expanded Lessons by clicking on hyperlinks embedded in the Enhanced Pearson eText. Appendix E includes a list of the Blackline Masters and a thumbnail version of each.
Students can experience the advantages of the Enhanced Pearson eText along with all the benefits of print for 40% to 50% less than a print bound book! Students, register for or purchase your eText at pearsonhighered.com/etextbooks/ted. Instructors, visit pearsonhighered.com/etextbooks/ted to register for your digital examination copy.
- NEW! The use of color in the figures, tables, and text helps to enhance and clarify the concepts presented.
- Teaching Tips. These brief tips offer practical takeaway ideas and instructional suggestions that support teaching and learning.
- Stop and Reflect sections. With an eye to reflective thinking as the key to effective learning, these sections ask readers to pause to consider a problem or reflect on what they have read. As these features appear at the end of every chapter in Part 1, they are ideal for use as discussion prompts in professional learning communities.
- Big Ideas. Lists of key mathematical ideas appear at the beginning of each chapter and provide a snapshot of the math being presented.
- NEW! Activities corresponding to the CCSS have been added. Numerous problem-based tasks, designed to engage students in doing mathematics, are presented in the activities and now connect to the appropriate CCSSs. Most include adaptation and accommodation suggestions for English Learners and students with special needs. Appendix D includes a table listing all of the activities at a glance.
- NEW! Tables of Common Errors and Misconceptions help readers avoid or move beyond common problems in learning mathematics. Each chapter in Part 2 includes a new table addressing chapter-related mathematical topics. The tables often include examples of student work or responses that reflect the common errors.
- Formative Assessment Notes. These notes describe ways to assess students’ developing knowledge and understanding, and can also help teachers improve their understanding of how to best help students through targeted instruction.
- Technology Notes. These notes provide practical information about how technology can be used to help students learn the content in the section.
- Standards for Mathematical Practice Notes. Connections to the eight Standards for Mathematical Practice from the CCSS are highlighted in the margins.
- Expanded Lessons. The activities in the book are written in a brief format to avoid detracting from the flow of ideas. But in each chapter, one or more activities have been expanded it into a complete lesson plan, following the before, during, after structure described in Chapter 2.
- Common Core State Standards Appendices. The mathematical practices outlined in the CCSSs are described in Chapter 1; examples are highlighted throughout the content chapters in Part 2 through margin notes; and Appendix A outlines the eight Standards for Mathematical Practice.
Invigorate learning with the Enhanced Pearson eTextThe Enhanced Pearson eText provides a rich, interactive learning environment designed to improve student mastery of content with the following multimedia features:
- NEW! Embedded videos throughout provide examples of students' misconceptions, expand on key concepts, and demonstrate how to implement strategies and techniques in real classrooms.
- NEW! Downloadable Teacher Resource and Activity Pages support teaching activities such as formative assessment and team-building are now available in the Enhanced Pearson eText at the point of use.
- NEW! Downloadable Blackline Masters in Part 2 Chapters. Readers may download Blackline Masters that support the activities and Expanded Lessons by clicking on hyperlinks embedded in the Enhanced Pearson eText. Appendix E includes a list of the Blackline Masters and a thumbnail version of each.
Students can experience the advantages of the Enhanced Pearson eText along with all the benefits of print for 40% to 50% less than a print bound book! Students, register for or purchase your eText at pearsonhighered.com/etextbooks/ted. Instructors, visit pearsonhighered.com/etextbooks/ted to register for your digital examination copy.
- A shift in topics to correspond to the Common Core State Standards (CCSS) and other new state standards, among them: a considerable emphasis on multiplicative thinking, rational numbers, and the development of the mathematical practices. This includes:
- Basic Facts: Chapter 9 includes an increased focus on assessing basic facts, presenting the risks of using timed tests and presenting a collection of alternative assessment ideas.
- Whole Number Computation: Chapter 11 includes an expanded discussion of the written records of computing multiplication and division problems including lattice multiplication, open arrays, and partial quotients.
- Fraction Operations: Chapter 11 uses a developmental approach capitalizing on learning trajectories ad expands the discussion of developing meaning for each operation with more examples and activities.
- Algebra: Chapter 15 carefully bridges the connection between arithmetic and algebra with increased attention to relational thinking and the structure of equations. Significant attention is paid to content described in the CCSS, including generalizing arithmetic, use of symbols, structure in the number system, and functional thinking.
- Measurement: Includes an increased emphasis on converting units in the same measurement system, a new section on perimeter, which focuses on the third grade, and new activities and additional activity sheets across all measurement topics.
- Activities corresponding to the CCSS have been added. Numerous problem-based tasks, designed to engage students in doing mathematics, are presented in the activities and now connect to the appropriate CCSSs. Most include adaptation and accommodation suggestions for English language learners and students with special needs. Appendix D includes a table listing all of the activities at a glance.
- Tables of Common Errors and Misconceptions help readers avoid or move beyond common problems in learning mathematics. Each chapter in Part 2 includes a new table addressing chapter-related mathematical topics. The tables often include examples of student work or responses that reflect the common errors.
Major changes to specific chapters include:
- Chapter 1: A new table that relates NCTM’s process standards (2000) and CCSS-M’s mathematical practices (CCSSO, 2010), clarification about the difference between modeling mathematics and modeling with mathematics, and an additional emphasis on the characteristics of productive classrooms that promote student understanding.
- Chapter 2: A new section on the eight mathematics teaching practices from Principles to Actions (NCTM, 2014); a new section on “Evaluating and Adapting Tasks” that includes suggestions for adapting tasks to increase their potential for learning; a new section on growth versus fixed mindsets and their relationship to productive struggle and learning from mistakes; a new section on aspects of questioning that helps teachers think, in particular, about the level of questions asked and the pattern of questions used; and more detail pertaining to the three-phases (before, during, and after) to better highlight that these phases occur during (not after) the lesson.
- Chapter 3: Supported by the recent position statement from professional organizations (NCSM and AMTE) about assessment for learning (AFL), this chapter was revised to be more explicit about how to collect evidence from students on their progress, interpret that evidence, make informed decisions about the next instructional steps and provide actionable feedback to students. There is also an expanded section on using writing to learn mathematics.
- Chapter 4: This chapter was revised to better highlight differentiated tasks for whole-classroom instruction. You will also find new team-building activities to enhance your children’s interactions with each other when working in groups.
- Chapter 6: Chapter 6 has several new features including a printable set of cards, each with a Strategy for Making Math Accessible for learners who struggle. This resource can be used when planning core instruction modifications or interventions for students with special needs. There is also a Mathematics Integration Plan Template to support planning for gifted students or students with a high interest in exploring mathematical topics in relation to other subject areas or perspectives.
Brief Table of Contents
Part 1: Establishing a Student-Centered Environment
1. Setting a Vision for Learning High-Quality Mathematics
2. Teaching Mathematics through Problem Solving
3. Creating Assessments for Learning
4. Differentiating Instruction
5. Teaching Culturally and Linguistically Diverse Students
6. Teaching and Assessing Students with Exceptionalities
7. Collaborating with Families and Other Stakeholders
Part 2: Teaching Student-Centered Mathematics
8. Exploring Number and Operation Sense
9. Developing Basic Fact Fluency
10. Developing Whole-Number Place-Value Concepts
11. Building Strategies for Whole-Number Computation
12. Exploring Fraction Concepts
13. Building Strategies for Fraction Computation
14. Developing Decimal and Percent Concepts and Decimal Computation
15. Promoting Algebraic Thinking
16. Building Measurement Concepts
17. Developing Geometric Thinking and Concepts
18. Representing and Interpreting Data
Appendix ACommon Core State Standards: Standards for Mathematical Practice
Appendix BCommon Core State Standards: Grades 3-5 Critical Content Areas and Overviews
Appendix C Mathematics Teaching Practices: NCTM Principles to Action (2014)
Appendix D Activities at a Glance: Volume II
Appendix E Guide to Blackline Masters
References
Index
Detailed Table of Contents
Part 1: Establishing a Student-Centered Environment
1. Setting a Vision for Learning High-Quality Mathematics
2. Teaching Mathematics through Problem Solving
3. Creating Assessments for Learning
4. Differentiating Instruction
5. Teaching Culturally and Linguistically Diverse Students
6. Planning, Teaching, and Assessing Students with Exceptionalities
7. Collaborating with Families and Other Stakeholders
Part 2: Teaching Student-Centered Mathematics
8. Exploring Number and Operation Sense
9. Developing Basic Fact Fluency
10. Developing Whole-Number Place-Value Concepts
11. Building Strategies for Whole-Number Computation
12. Exploring Fraction Concepts
13. Building Strategies for Fraction Computation
14. Developing Decimal and Percent Concepts and Decimal Computation
15. Promoting Algebraic Thinking
16. Building Measurement Concepts
17. Developing Geometric Thinking and Concepts
18. Representing and Interpreting Data
Appendix ACommon Core State Standards: Standards for Mathematical Practice
Appendix BCommon Core State Standards: Grades 3-5 Critical Content Areas and Overviews
Appendix C Mathematics Teaching Practices: NCTM Principles to Action (2014)
Appendix D Activities at a Glance: Volume II
Appendix E Guide to Blackline Masters
References
Index
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 studentcentered math lessons. He coauthored the Scott ForesmanAddison Wesley Mathematics K–6 series and contributed to the Pearson School mathematics program, enVisionMATH. In addition, 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, as the chair of the Educational Materials Committee, and as a frequent speaker at national and regional meetings.
Karen S. Karp is at the School of Education at Johns Hopkins University-Baltimore, MD. Previously, she was a professor of mathematics education at the University of Louisville for more than twenty years. Prior to entering the field of teacher education she was an elementary school teacher in New York. She is also coauthor of Elementary and Middle School Mathematics: Teaching Developmentally, Developing Essential Understanding of Addition and Subtraction for Teaching Mathematics in PreK–Grade 2, and numerous book chapters and articles. She is a former member of the Board of Directors of NCTM and a former president of the Association of Mathematics Teacher Educators (AMTE). She continues to work in classrooms to support teachers of students with disabilities in their mathematics instruction.
LouAnn H. Lovin is a professor of mathematics education at James Madison University (Virginia). She coauthored the first edition of the Teaching StudentCentered Mathematics Professional Development Series with John A. Van de Walle as well as Teaching Mathematics Meaningfully: Solutions for Reaching Struggling Learners, 2nd Edition with David Allsopp and Sarah Vaningen. LouAnn taught mathematics to middle and high school students before transitioning to preK–grade 8. For almost twenty years, she has worked in preK through grade 8 classrooms and engaged with teachers in professional development as they implement a studentcentered approach to teaching mathematics. She has published articles in Teaching Children Mathematics, Mathematics Teaching in the Middle School, and Teaching Exceptional Children and has served on NCTM’s Educational Materials Committee. LouAnn’s research on teachers’ mathematical knowledge for teaching has focused most recently on the developmental nature of prospective teachers’ fraction knowledge.
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 Mathematics Coaching: Resources and Tools for Coaches and Leaders, K–12; Developing Essential Understanding of Addition and Subtraction for Teaching Mathematics in PreK–Grade 2; Math and Literature: Grades 6–8; Math and Nonfiction: Grades 6–8; and Navigating through Connections in Grades 6–8. 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 served as member of Board of Directors for TODOS: Equity for All, as president of AMTE, and as editor for the 2012 NCTM Yearbook.
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