Teaching Student-Centered Mathematics

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**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.

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