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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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