Teaching Student-Centered Mathematics Developmentally Appropriate Instruction for Grades 3-5 (Volume II)

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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.

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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.

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.

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.

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 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

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