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Teaching Student-Centered Mathematics: Developmentally Appropriate Instruction for Grades 3-5 (Volume II), 3rd edition

  • John A. Van de Walle
  • Karen S. Karp
  • LouAnn H. Lovin
  • Jennifer M. Bay-Williams

Published by Pearson (January 22nd 2017) - Copyright © 2018

3rd edition

Overview

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Helping students make connections between mathematics and their worlds—and helping them feel empowered to use math in their lives—is the focus of this widely popular guide. Designed for classroom teachers, the book focuses on specific grade bands and includes information on creating an effective classroom environment, aligning teaching to various standards and practices, such as the Common Core State Standards and NCTM’s teaching practices, and engaging families. The first portion of the book addresses how to build a student-centered environment in which children can become mathematically proficient, while the second portion focuses on practical ways to teach important concepts in a student-centered fashion. The new edition features a corresponding Enhanced Pearson eText version with links to embedded videos, blackline masters, downloadable teacher resource and activity pages, lesson plans, activities correlated to the CCSS, and tables of common errors and misconceptions.

 

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0134081412 / 9780134081410 Teaching Student-Centered Mathematics: Developmentally Appropriate Instruction for Grades 3-5, Enhanced Pearson eText -- Access Card Package, 3/e

Package consists of: 

  • 0134556402 / 9780134556406 Teaching Student-Centered Mathematics: Developmentally Appropriate Instruction for Grades 3-5, Enhanced Pearson eText -- Access Card
  • 0134556429 / 9780134556420 Teaching Student-Centered Mathematics: Developmentally Appropriate Instruction for Grades 3-5

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 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

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