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Teaching Student-Centered Mathematics
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Table of Contents

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

About the Author

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.

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