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 ACommon Core State Standards: Standards for Mathematical
Practice
Appendix BCommon 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 ACommon Core State Standards: Standards for Mathematical
Practice
Appendix BCommon 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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