Teaching Student-Centered Mathematics

Description

A practical, comprehensive, developmentally appropriate approach to effective mathematical instruction in grades 6 to 8.

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.

This book is part of the Teaching Student-Centered Mathematics series, which is designed with three objectives: 1) To illustrate what it means to teach student-centered, problem-based mathematics, 2) to serve as a reference for the mathematics content and research-based instructional strategies suggested for the specific grade levels, and 3) 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. 

Invigorate learning with the Enhanced Pearson eText
The Enhanced Pearson eText provides a rich, interactive learning environment designed to improve student mastery of content 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. The Enhanced Pearson eText is also available without a print version of the book.

Instructors, visit pearsonhighered.com/etextbooks/ted to register for your digital examination copy. Students, register for or purchase your eText at pearsonhighered.com/etextbooks/ted.
 

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. 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.

LouAnn H. 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. 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 pre-K—grade 8. For almost twenty years, she has worked in pre-K 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.

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 co-author of Elementary and Middle School Mathematics: Teaching Developmentally, 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 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.

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 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 AMTE, and as editor for the 2012 NCTM Yearbook.

Invigorate learning with the Enhanced Pearson eText
The Enhanced Pearson eText provides a rich, interactive learning environment designed to improve student mastery of content with the following multimedia features:

• NEW! Embedded videos. The Enhanced Pearson eText now includes links to videos throughout the text that 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 that 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.

• 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.
   

Note: This is the bound book only and does not include access to the Enhanced Pearson eText. To order the Enhanced Pearson eText packaged with a bound book, use ISBN 0134090691.

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.

Invigorate learning with the Enhanced Pearson eText
The Enhanced Pearson eText provides a rich, interactive learning environment designed to improve student mastery of content with the following multimedia features:

• NEW! Embedded videos. The Enhanced Pearson eText now includes links to videos throughout the text that 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 that 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.

A practical, comprehensive, developmentally appropriate approach to effective mathematical instruction in grades 6 to 8.

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.

Invigorate learning with the Enhanced Pearson eText
The Enhanced Pearson eText provides a rich, interactive learning environment designed to improve student mastery of content with the following multimedia features:

• NEW! Embedded videos. The Enhanced Pearson eText now includes links to videos throughout the text that 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 that 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 C includes a list of the Blackline Masters and a thumbnail version of each.

• 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 Children 
• 6 Planning, Teaching, and Assessing Children with Exceptionalities 
• 7 Collaborating with Families and Other Stakeholders

• Part 2: Teaching Student-Centered Mathematics

• 8 Fraction Concepts and Computation
• 9 Decimal Concepts and Computation
• 10 The Number System 
• 11 Ratios and Proportional Relationships 
• 12 Algebraic Thinking: Expressions, Equations, and Functions 
• 13 Developing Geometry Concepts 
• 14 Exploring Measurement Concepts 
• 15 Working with Data and Doing Statistics 
• 16 Investigating Concepts of Probability
• Appendix A Common Core State Standards: Standards for Mathematical Practice
• Appendix B Common Core State Standards: Grades 6—8 Critical Content Areas and Overviews 
• Appendix C Mathematics Teaching Practices: NCTM Principles to Actions (2014) 
• Appendix D Activities at a Glance: Volume III 
• Appendix E Guide to Blackline Masters 
• References 
• Index 

Invigorate learning with the Enhanced Pearson eText
The Enhanced Pearson eText provides a rich, interactive learning environment designed to improve student mastery of content with the following multimedia features:

• NEW! Embedded videos. The Enhanced Pearson eText now includes links to videos throughout the text that 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 that 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. 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 language 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 of 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.

Additional information