Teaching Student-Centered Mathematics Series: Developmentally Appropriate Instruction, 3rd Ed
Imprint
Pearson Canada
Author(s)
John Van De Walle, Jennifer M. Bay-Williams, LouAnn H. Lovin, Karen S. Karp
Helping students make connections between mathematics and their worlds–and helping them feel empowered to use math in their lives–is the focus of this widely popular guide. Designed for classroom teachers, the book focuses on specific grade bands and includes information on creating an effective classroom environment, aligning teaching to various standards and practices, such as the Common Core State Standards and NCTM’s teaching practices, and engaging families. The first portion of the book addresses how to build a student-centered environment in which children can become mathematically proficient, while the second portion focuses on practical ways to teach important concepts in a student-centered fashion. The new edition features a corresponding Enhanced Pearson eText version with links to embedded videos, blackline masters, downloadable teacher resource and activity pages, lesson plans, activities correlated to the CCSS, and tables of common errors and misconceptions.
These books are part of the Student-Centered Mathematics Series, which are designed with three objectives: to illustrate what it means to teach student-centered, problem-based mathematics, to serve as a reference for the mathematics content and research-based instructional strategies suggested for the specific grade levels, and to present a large collection of high quality tasks and activities that can engage students in the mathematics that is important for them to learn.
Features and Benefits
- 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.
Authors
John A. Van de Walle
The late John 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.
Jennifer M. Bay Williams
Jennifer 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: Tools and Resources for Coaches and Leaders, K-12;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. 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 the Association of Mathematics Teacher Educators (AMTE), and editor for the 2012 NCTM Yearbook.
LouAnn Lovin
LouAnn Lovin is a professor of mathematics education at James Madison University (Virginia). She co-authored the First Edition of the Teaching Student-Centered Mathematics Professional Development Series with John A. VandeWalle as well as Teaching Mathematics Meaningfully: Solutions for Reaching Struggling Learners with special educators David Allsopp and Maggie Kyger. LouAnn taught mathematics to middle and high school students before transitioning to PreK-8. Over the last 15 years, she has worked in K-8 classrooms and engaged with teachers in professional development as they implement a student-centered approach to teaching mathematics. She has published articles in NCTM’s Teaching Children Mathematics and Mathematics Teaching in the Middle School and has served on NCTM’s Educational Materials Committee.LouAnn’s research interest is on ways to develop teachers’ mathematical knowledge needed to teach for understanding.
Karen Karp
Karen S. Karpis a professor of mathematics education at the University of Louisville (Kentucky). Prior to entering the field of teacher education she was an elementary school teacher in New York. Karen’s research interests is on teaching mathematics to diverse populations. She is also co-author of Elementary and Middle School Mathematics: Teaching Developmentally, Growing Professionally: Readings from NCTM Publications for Grades K-8, Developing Essential Understanding of Addition and Subtraction for Teaching Mathematics in Pre-K-Grade 2 and numerous book chapters and articles. 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 to support teachers of students with disabilities in their mathematics instruction.
Grades Pre-K-2 (Volume I)
A practical, comprehensive, student-centered approach to effective mathematical instruction for grades Pre-K-2.
New to This Edition
Key content changes include:
- The use of color in the figures, tables, and text helps to enhance and clarify the concepts presented.
- NCTM Teaching Practices Appendix. The Principles to Actions (NCTM, 2014) eight teaching practices are provided in Appendix C. These describe the actions that teachers do to support student thinking and provide guidance on how to enact student-centered mathematics.
- 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.
- 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 chapters in Part 1 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”; 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: A more detailed discussion about assessment for learning (AFL) on 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; and an expanded section on using writing to learn mathematics.
- Chapter 4: This chapter was revised to better highlight differentiated tasks for whole-classroom instruction. New team-building activities for working in groups are also included.
- Chapter 5: Twenty-two new references reflect research in the field, including increased attention to Culturally Responsive Mathematics Instruction (CRMI), developed around four key aspects and an expanded section on nurturing students’ mathematical identities.
- Chapter 6: Features several new tools, including: a printable set of cards, each with a Strategy for Making Math Accessible for learners who struggle, which can be used when planning core instruction modifications or interventions for students with special needs; and 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.
- Chapter 7: This chapter was significantly revised to focus on advocacy across stakeholders, including creased attention to communicating about CCSS Mathematics. The homework section was expanded, including new activities and games for families.
Major changes in the chapters in Part 2 include:
- Chapter 8: Includes a new learning progression for counting that identifies increasingly sophisticated levels of reasoning and includes:
- Several new activities focusing on developing early counting skills, and
- A new section on thinking about zero.
- Chapter 9: Features an increased focus on helping children write equations from word problems, using both computational and semantic forms. Also included are:
- An improved section on helping children analyze contextual problems by detailing strategies that can help children prepare to solve problems, and
- A new section about helping children solve multistep problems, including the use of hidden questions to help children progress from one-step to multistep problems.
- Chapter 10: Includes an increased focus on assessing basic facts, presents the risks of using timed tests, and offers a collection of alternative assessment ideas.
- Chapter 12: Includes an expanded discussion of the written records of computing multiplication and division problems including lattice multiplication, open arrays, and partial quotients.
- Chapter 16: The geometry chapter is now reorganized around the four geometry strands (shapes and properties, location, transformations, visualization) to provide more cohesiveness. Examples of appropriate activities help clarify each level as it’s introduced.
- Chapter 17: The new addition of driving questions (Hourigan and Leavy) is introduced as a way to motivate involvement in the processes of doing statistics. There is an increased emphasis on helping children consider the shape of the data as they engage in the analysis and interpretation phases of doing statistics.
Grades 3-5 (Volume II)
A practical, comprehensive, developmentally appropriate approach to effective mathematical instruction in grades 3 to 5.
New to This Edition
Key content changes include:
- 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:
- 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.
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- 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.
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.
Grades 6-8 (Volume III)
A practical, comprehensive, developmentally appropriate approach to effective mathematical instruction in grades 6 to 8.
New to This Edition
Key content changes include:
- The use of color in the figures, tables, and text helps to enhance and clarify the concepts presented.
- 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.
- Part 1 focuses on important “hot” topics that address ideas for creating a classroom environment in which all children succeed. By design, the chapters are shorter in length than the content chapters in Part 2, but are full of effective strategies and ideas. These chapters are ideal for use in professional development workshops, book study, or professional learning community (PLC) discussions.
Major changes to chapters in Part 1 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”; 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 4: This chapter was revised to better highlight differentiated tasks for whole-classroom instruction. New team-building activities for working in groups are also included.
Major changes in the chapters in Part 2 include:
- Chapter 8: Includes a new learning progression for counting that identifies increasingly sophisticated levels of reasoning and includes:
- Several new activities focusing on developing early counting skills, and
- A new section on thinking about zero.
- Chapter 9: Features an increased focus on helping children write equations from word problems, using both computational and semantic forms. Also included are:
- An improved section on helping children analyze contextual problems by detailing strategies that can help children prepare to solve problems, and
- A new section about helping children solve multistep problems, including the use of hidden questions to help children progress from one-step to multistep problems.
- Chapter 10: Includes an increased focus on assessing basic facts, presents the risks of using timed tests, and offers a collection of alternative assessment ideas.
- Chapter 12: Includes an expanded discussion of the written records of computing multiplication and division problems including lattice multiplication, open arrays, and partial quotients.
- Chapter 13: Features more focused sections on generalization with number, place value, and algorithms to better illustrate how to connect arithmetic to algebra. Included is an enhanced section on repeating patterns.
- Chapter 14: Looks at an increased focus on moving from the part-whole meaning of fractions to an iterative notation of fractions. Included are new activities and references to technology, and a new table providing a quick overview of three types of models—area, length, and set—defining the wholes and their related parts for each model.
- Chapter 16: The Geometry chapter is now reorganized around the four geometry strands (shapes and properties, location, transformations, visualization) to provide more cohesiveness. Examples of appropriate activities help clarify each level as it’s introduced.
- Chapter 17: In the chapter on Data, the new addition of driving questions (Hourigan and Leavy, 2015/2016) is introduced as a way to motivate involvement in the processes of doing statistics. There is an increased emphasis on helping children consider the shape of the data as they engage in the analysis and interpretation phases of doing statistics.