Teaching Student-Centered Mathematics: Developmentally Appropriate Instruction for Grades Pre-K-2 (Volume 1), 3rd edition

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

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
Teachinghrough 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 nstruction
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