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 A Common Core State Standards: Standards for Mathematical Practice Appendix B Common 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 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. Exploring Number and Operation Sense Developing Addition and Subtraction Operation Sense Developing Multiplication and Division Operation Sense Multiplication and Division Problem Structures Teaching Multiplication and Division Properties of Multiplication and Division Strategies for Solving Contextual Problems Multistep Word Problems 9. Developing Basic Fact Fluency Developmental Phases for Learning the Basic Fact Combinations Teaching and Assessing the Basic Fact Combinations Reasoning Strategies for Addition Facts Reasoning Strategies for Subtraction Facts Reasoning Strategies for Multiplication and Division Facts Reinforcing Basic Fact Mastery 10. Developing Whole-Number Place-Value Concepts Extending Number Relationships to Larger Numbers Important Place-Value Concepts Extending Base-Ten Concepts Oral and Written Names for Numbers Patterns and Relationships with Multidigit Numbers Numbers beyond 1000 11. Building Strategies for Whole-Number Computation Toward Computational Fluency Development of Invented Strategies in Addition and Subtraction Standard Algorithms for Addition and Subtraction Invented Strategies for Multiplication Standard Algorithms for Multiplication Invented Strategies for Division Standard Algorithms for Division Computational Estimation 12. Exploring Fraction Concepts Meanings of Fractions Models for Fractions Fractional Parts of a Whole Equivalent Fractions Comparing Fractions Teaching Considerations for Fraction Concepts 13. Building Strategies for Fraction Computation Understanding Fraction Operations Addition and Subtraction Multiplication Division 14. Developing Decimal and Percent Concepts and Decimal Computation Developing Concepts of Decimals Connecting Fractions and Decimals Developing Decimal Number Sense Computation with Decimals Introducing Percents 15. Promoting Algebraic Thinking Strands of Algebraic Thinking Generalized Arithmetic Meaningful Use of Symbols Making Structure in the Number System Explicit Patterns and Functional Thinking 16. Building Measurement Concepts The Meaning and Process of Measuring The Role of Estimation and Approximation Length Area Volume Weight and Mass Angles Time Money 17. Developing Geometric Thinking and Concepts Geometry Goals for Your Students Developing Geometric Thinking Shapes and Properties Learning about Transformations Learning about Location Learning about Visualizations 18. Representing and Interpreting Data What Does It Mean to Do Statistics? Formulating Questions Data Collection Data Analysis: Classification Data Analysis: Graphical Representations Interpreting Results Appendix A Common Core State Standards: Standards for Mathematical Practice Appendix B Common 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.