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 coauthored 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 coauthored 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 ed.) 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 student-centered approach to teaching mathematics. She has published articles in Teaching Children Mathematics, Mathematics Teaching in the Middle School, Teaching Exceptional Children, and Journal of Mathematics Teacher Education  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 in Baltimore (Maryland). 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.

Jennifer M. Bay-Williams is a professor of mathematics education at the University of Louisville (Kentucky). Jennifer frequently offers professional development about effective mathematics teaching to K-12 teachers and leaders. She has coauthored numerous books, including On the Money: Math Activities to Build Financial Literacy ; 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;  and Navigating through Connections in Grades 6-8 . Additionally, she has written dozens of articles on teaching and learning in NCTM journals. Jennifer serves on the NCTM Board of Directors, and has served on the TODOS: Equity for All Board, and president of the Association of Mathematics Teacher Educators (AMTE). 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.

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

Part 2: Teaching Student-Centered Mathematics

8. Developing Early Number Concepts and Number Sense

9. Developing Meanings for the Operations

10. Helping Children Develop Fluency with Basic Facts

11. Developing Whole-Number Place-Value Concepts

12. Building Strategies for Whole-Number Computation

13. Promoting Algebraic Reasoning

14. Exploring Early Fraction Concepts

15. Building Measurement Concepts

16. Developing Geometric Reasoning and Concepts

17. Helping Children Use Data

Appendix A Common Core State Standards: Standards for Mathematical Practice 

Appendix B Common Core State Standards: Grades K-2 Critical Content Areas and Overviews 

Appendix C Mathematics Teaching Practices: NCTM Principles to Action (2014) 

Appendix D Activities at a Glance: Volume I 

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 Children Learn?

              Teaching for Understanding

              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

              Children's 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 Children

              Culturally and Linguistically Diverse Children

              Culturally Responsive Mathematics Instruction

              Teaching Strategies That Support Culturally and Linguistically Diverse Children

              Assessment Considerations for ELLs

6. Planning, Teaching, and Assessing Children with Exceptionalities

              Instructional Principles for Diverse Learners

              Implementing Interventions

              Teaching and Assessing Children with Learning Disabilities 

              Adapting for Children with Moderate/Severe Disabilities 

              Planning for Children 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. Developing Early Number Concepts and Number Sense

              The Number Core: Early Counting and Number Concepts

              The Relations Core: More Than, Less Than, and Equal To

              Developing Number Sense by Building Number Relationships

              Number Sense and the Real World

              Revisiting the Big Ideas for Number Concepts

9. Developing Meanings for the Operations

              Teaching Operations through Contextual Problems 

              Children’s Conceptions of Addition and Subtraction 

              Addition and Subtraction Problem Structures

              Teaching Addition and Subtraction

              Laying the Foundation for Multiplication and Division

              Teaching Multiplication and Division

              Supporting Children in Solving Contextual Problems

              Final Thoughts: Outcomes Related to Teaching and Learning Operations

10. Helping Children Develop Fluency with Basic Facts

              The Developmental Nature of Learning Basic Facts 

              Different Approaches to Teaching Basic Facts

              Teaching Basic Facts Effectively

              Assessing Basic Facts Effectively

              Reasoning Strategies for Addition Facts

              Reasoning Strategies for Subtraction Facts

              Reinforcing Reasoning Strategies

              Building a Foundation for Multiplication Facts

              Reinforcing Basic Fact Mastery

              Do’s and Don’ts for Teaching Basic Facts

11. Developing Whole-Number Place-Value Concepts

              Pre—Place-Value Understandings

              Developing Foundational Ideas in Whole-Number Place Value
              Base-Ten Models for Place Value

              Developing Base-Ten Concepts

              Oral and Written Names for Numbers

              Patterns and Relationships with Multidigit Numbers

              Connecting Place Value to Addition and Subtraction 

              Connections to Real-World Ideas

12. Building Strategies for Whole-Number Computation

              A Move to Computational Fluency 

              Connecting Addition and Subtraction to Place Value 

              Three Types of Computational Strategies

              Development of Invented Strategies

              Development of Invented Strategies for Addition and Subtraction

              Standard Algorithms for Addition and Subtraction

              Introducing Computational Estimation

              Computational Estimation Strategies

              Common Misconceptions with Whole-Number Computation

13. Promoting Algebraic Reasoning

              Strands of Algebraic Reasoning 

              Structure in the Number System: Connecting Number and Algebra

              Meaningful Use of Symbols

              Structure in the Number System: Properties

              Patterns and Functions

              Common Misconceptions with Algebraic Reasoning

14. Exploring Early Fraction Concepts

              Meanings of Fractions for PreK—2 Children

              Introducing Fraction Language 

              Models for Fractions

              Building Fractional Parts through Partitioning and Iterating

              Fraction Equivalence and Comparison 

              From Fraction Words to Symbols 

              Teaching Considerations for Fraction Concepts

15. Building Measurement Concepts

              The Meaning and Process of Measuring

              Length

              Time

              Money

              Other Measurable Attributes

              Common Misconceptions with Measurement

16. Developing Geometric Reasoning and Concepts

              Geometry Goals for Young Children 

              Developing Geometric Reasoning

              Shapes and Properties

              Transformations

              Location 

              Visualization

17. Helping Children Use 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 K-2 Critical Content Areas and Overviews 

Appendix C Mathematics Teaching Practices: NCTM Principles to Action (2014) 

Appendix D Activities at a Glance: Volume I 

Appendix E Guide to Blackline Masters 

References 

Index 

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