Teaching Student-Centered Mathematics Developmentally Appropriate Instruction for Grades 6-8 (Volume III)

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.

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 student centered 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.

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 Children 

6 Planning, Teaching, and Assessing Children with Exceptionalities 

7 Collaborating with Families and Other Stakeholders

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 

Detailed Table of Contents

Part 1: Establishing a Student-Centered Environment

    1 Setting a Vision for Learning High-Quality Mathematics 

              Understanding and Doing Mathematics 

              How Do Students Learn? 

              Teaching for Understanding 

              The Importance of Students’ Ideas 

              Mathematics Classrooms That Promote Understanding 

    2 Teaching Mathematics through Problem Solving 

              Teaching through Problem Solving: An Upside-Down Approach 

              Mathematics Teaching Practices for Teaching through Problem Solving 

              Using Worthwhile Tasks 

              Orchestrating Classroom Discourse 

              Representations: Tools for Problem Solving, Reasoning, and Communication 

              Lessons in the Problem-Based Classroom 

              Life-Long Learning: An Invitation to Learn and Grow 

    3 Creating Assessments for Learning 

              Assessment That Informs Instruction 

              Observations 

              Questions 

              Interviews 

              Tasks 

              Students’ Self-Assessment and Reflection 

              Rubrics and Their Uses 

    4 Differentiating Instruction 

              Differentiation and Teaching Mathematics through Problem Solving 

              The Nuts and Bolts of Differentiating Instruction 

              Differentiated Tasks for Whole-Class Instruction 

              Tiered Lessons 

              Flexible Grouping 

    5 Teaching Culturally and Linguistically Diverse Students 

              Culturally and Linguistically Diverse Students 

              Culturally Responsive Mathematics Instruction 

              Teaching Strategies that Support Culturally and Linguistically Diverse Students 

              Assessment Considerations for ELLs 

    6 Planning, Teaching, and Assessing Students with Exceptionalities 

              Instructional Principles for Diverse Learners 

              Implementing Interventions 

              Teaching and Assessing Students with Learning Disabilities 

             Adapting for Students with Moderate/Severe Disabilities 

             Planning for Students Who Are Mathematically Gifted 

    7 Collaborating with Families and Other Stakeholders 

              Sharing the Message with Stakeholders 

              Administrator Engagement and Support 

              Family Engagement 

              Homework Practices and Parent Coaching 

Part 2: Teaching Student-Centered Mathematics

    8 Fraction Concepts and Computation 

              Meanings of Fractions 

              Partitioning and Iterating 

              Fraction Equivalencies 

              Comparing Fractions 

              Understanding Fraction Operations 

              Addition and Subtraction 

              Multiplication 

              Division 

              Teaching Fractions Effectively 

              Literature Connections 

    9 Decimal Concepts and Computation 

              Extending the Place-Value System 

              Connecting Fractions and Decimals 

              Emphasizing Equivalence between Fractions and Decimals 

              Comparing and Ordering Decimal Fractions

              Addition and Subtraction 

              Multiplication 

              Division 

              Percents

    10 The Number System 

              Exponents 

              Positive and Negative Numbers 

              Operations with Positive and Negative Numbers 

              Real Numbers 

              Literature Connections 

    11 Ratios and Proportional Relationships 

              Ratios 

              Proportional Reasoning 

              Covariation in Algebra

              Strategies for Solving Proportional Situations 

              Teaching Proportional Reasoning 

              Literature Connections 

    12 Algebraic Thinking: Expressions, Equations, and Functions 

              Structure in the Number System: Connecting Number and Algebra 

              Structure in the Number System: Properties 

              Patterns and Functions 

              Meaningful Use of Symbols 

              Mathematical Modeling 

              Algebraic Thinking across the Curriculum 

              Literature Connections 

    13 Developing Geometry Concepts 

              Developing Geometric Thinking 

              Shapes and Properties 

              Transformations

              Location 

              Visualization 

              Literature Connections 

    14 Exploring Measurement Concepts 

              Foundations of Measuring 

              Angles 

              Area 

              Volume and Capacity 

              Literature Connections 

    15 Working with Data and Doing Statistics 

              What Does It Mean to Do Statistics? 

              Formulating Questions 

              Collecting Data 

              Analyzing Data: Graphs 

              Analyzing Data: Measures of Center and Variability 

              Interpreting Results 

              Literature Connections 

    16 Investigating Concepts of Probability 

              Introducing Probability 

              Theoretical Probability and Experiments 

              Sample Spaces and the Probability of Compound Events 

              Simulations 

              Common Misconceptions about Probability 

              Literature Connections

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

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