Visible Thinking in the K–8 Mathematics Classroom

Ted H. Hull - Educational Consultant, Texas
Don S. Balka - Saint Mary's College, Notre Dame, IN
Ruth Harbin Miles - Mary Baldwin College, VA
Visible Thinking in the K–8 Mathematics Classroom
January 2011 | 184 pages | Corwin
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eBook
ISBN: 9781452269405
Available from January 0001
Paperback
ISBN: 9781412992053
Available from January 0001

Description

"This book is a crucial tool for meeting NCTM mathematical content and process standards. Through the useful problems and strategies presented within, teachers will definitely know how well their students will comprehend. If comprehension is an issue in your class, this book is a must have!"
—Therese Gessler Rodammer, Math Coach
Thomas W. Dixon Elementary School, Staunton, VA

Seeing is believing with this interactive approach to math instruction

Do you ever wish your students could read each other's thoughts? Now they can—and so can you! Veteran mathematics educators Ted Hull, Don Balka, and Ruth Harbin Miles explain why making students' thought processes visible is the key to effective mathematics instruction. Their newest book contains numerous grade-specific sample problems and instructional strategies for teaching essential concepts such as number sense, fractions, and estimation. Among the many benefits of visible thinking are:

  • Interactive student-to-student learning
  • Increased class participation
  • Development of metacognitive thinking and problem-solving skills

Helpful features include vignettes, relevant word problems, classroom scenarios, sample problems, lesson adaptations, and easy-to-follow examples of each strategy in action. The authors also explain how students can demonstrate their thinking using calculators and online tools. The final chapter outlines steps math leaders can take to implement visible thinking and maximize mathematics comprehension for all students.


 

Contents

Preface

Preface

Acknowledgments

Acknowledgments

About the Authors

About the Authors

Part I. Preparing the Foundation

  • 1. What Is Visible Thinking?
  • Understanding Mathematical Concepts
  • Thinking as a Mathematical Premise
  • Visible Thinking in Classrooms
  • Visible Thinking Scenario 1: Area and Perimeter
  • Summary
  • 2. How Do Students Learn Mathematics?
  • What Is Thinking?
  • What Does Brain Research Indicate About Thinking and Learning?
  • What Is Mathematical Learning?
  • What Are Thinking and Learning Themes From Research?
  • Example Problems Revisited
  • Visible Thinking Scenario 2: Addition of Fractions
  • Summary
  • 3. What Is Happening to Thinking in Mathematics Classrooms?
  • Improvement Initiatives and Visible Thinking
  • Visible Thinking Scenario 3: Subtraction With Regrouping
  • Summary
  • Part II. Promoting Visible Thinking With an Alternative Instructional Model
  • 4. How Do Effective Classrooms Depend on Visible Thinking?
  • What Are Strategies, Conditions, and Actions?
  • Practice Into Action
  • Technology as Visible Thinking
  • Visible Thinking Scenario 4: Division
  • Summary
  • 5. How Are Long-Term Changes Made?
  • Enhancing Student Learning
  • Teaching Approaches
  • Visible Thinking Scenario 5: Mixed Numerals
  • Visible Thinking Scenario 6: Place Value
  • Summary
  • 6. How Are Short-Term Changes Made?
  • Pitfalls and Traps
  • Strategy Sequence
  • The Relationships Among the Strategy Sequence, Conditions, and Goals
  • Visible Thinking Scenario 7: Basic Addition and Subtraction Facts
  • Visible Thinking Scenario 8: Exponents
  • Summary
  • 7. How Are Lessons Designed to Achieve Short-Term and Long-Term Changes?
  • The Current Approach to Teaching Mathematics
  • Elements of an Alternative Instructional Model
  • Types of Problems
  • Summary

Part III. Implementing the Alternative Model at Different Grade Levels

  • 8. How Is Thinking Made Visible in Grades K–2 Mathematics?
  • Brainteaser Problem Example
  • Group-Worthy Problem Example
  • Transforming Problem Example
  • Summary
  • 9. How Is Thinking Made Visible in Grades 3–5 Mathematics?
  • Brainteaser Problem Example
  • Group-Worthy Problem Example
  • Transforming Problem Example
  • Summary
  • 10. How Is Thinking Made Visible in Grades 6–8 Mathematics?
  • Brainteaser Problem Example
  • Group-Worthy Problem Example
  • Transforming Problem Example
  • Summary

Part IV. Continuing the Work

  • 11. How Do Teachers, Leaders, and Administrators Coordinate Their Efforts to Improve Mathematics Teaching and Learning?
  • Working With Administrators
  • Embedding Lessons Into the Curriculum
  • Providing Professional Development
  • Co-planning and Co-teaching
  • Summary

Appendix A: Research Support for Visible Thinking Strategies, Conditions, and Actions

Appendix A: Research Support for Visible Thinking Strategies, Conditions, and Actions

Appendix B: Lessons Using Technology: Additional Materials

Appendix B: Lessons Using Technology: Additional Materials

References

References

Index

Index

Description

"This book is a crucial tool for meeting NCTM mathematical content and process standards. Through the useful problems and strategies presented within, teachers will definitely know how well their students will comprehend. If comprehension is an issue in your class, this book is a must have!"
—Therese Gessler Rodammer, Math Coach
Thomas W. Dixon Elementary School, Staunton, VA

Seeing is believing with this interactive approach to math instruction

Do you ever wish your students could read each other's thoughts? Now they can—and so can you! Veteran mathematics educators Ted Hull, Don Balka, and Ruth Harbin Miles explain why making students' thought processes visible is the key to effective mathematics instruction. Their newest book contains numerous grade-specific sample problems and instructional strategies for teaching essential concepts such as number sense, fractions, and estimation. Among the many benefits of visible thinking are:

  • Interactive student-to-student learning
  • Increased class participation
  • Development of metacognitive thinking and problem-solving skills

Helpful features include vignettes, relevant word problems, classroom scenarios, sample problems, lesson adaptations, and easy-to-follow examples of each strategy in action. The authors also explain how students can demonstrate their thinking using calculators and online tools. The final chapter outlines steps math leaders can take to implement visible thinking and maximize mathematics comprehension for all students.


 

Contents

Preface

Preface

Acknowledgments

Acknowledgments

About the Authors

About the Authors

Part I. Preparing the Foundation

  • 1. What Is Visible Thinking?
  • Understanding Mathematical Concepts
  • Thinking as a Mathematical Premise
  • Visible Thinking in Classrooms
  • Visible Thinking Scenario 1: Area and Perimeter
  • Summary
  • 2. How Do Students Learn Mathematics?
  • What Is Thinking?
  • What Does Brain Research Indicate About Thinking and Learning?
  • What Is Mathematical Learning?
  • What Are Thinking and Learning Themes From Research?
  • Example Problems Revisited
  • Visible Thinking Scenario 2: Addition of Fractions
  • Summary
  • 3. What Is Happening to Thinking in Mathematics Classrooms?
  • Improvement Initiatives and Visible Thinking
  • Visible Thinking Scenario 3: Subtraction With Regrouping
  • Summary
  • Part II. Promoting Visible Thinking With an Alternative Instructional Model
  • 4. How Do Effective Classrooms Depend on Visible Thinking?
  • What Are Strategies, Conditions, and Actions?
  • Practice Into Action
  • Technology as Visible Thinking
  • Visible Thinking Scenario 4: Division
  • Summary
  • 5. How Are Long-Term Changes Made?
  • Enhancing Student Learning
  • Teaching Approaches
  • Visible Thinking Scenario 5: Mixed Numerals
  • Visible Thinking Scenario 6: Place Value
  • Summary
  • 6. How Are Short-Term Changes Made?
  • Pitfalls and Traps
  • Strategy Sequence
  • The Relationships Among the Strategy Sequence, Conditions, and Goals
  • Visible Thinking Scenario 7: Basic Addition and Subtraction Facts
  • Visible Thinking Scenario 8: Exponents
  • Summary
  • 7. How Are Lessons Designed to Achieve Short-Term and Long-Term Changes?
  • The Current Approach to Teaching Mathematics
  • Elements of an Alternative Instructional Model
  • Types of Problems
  • Summary

Part III. Implementing the Alternative Model at Different Grade Levels

  • 8. How Is Thinking Made Visible in Grades K–2 Mathematics?
  • Brainteaser Problem Example
  • Group-Worthy Problem Example
  • Transforming Problem Example
  • Summary
  • 9. How Is Thinking Made Visible in Grades 3–5 Mathematics?
  • Brainteaser Problem Example
  • Group-Worthy Problem Example
  • Transforming Problem Example
  • Summary
  • 10. How Is Thinking Made Visible in Grades 6–8 Mathematics?
  • Brainteaser Problem Example
  • Group-Worthy Problem Example
  • Transforming Problem Example
  • Summary

Part IV. Continuing the Work

  • 11. How Do Teachers, Leaders, and Administrators Coordinate Their Efforts to Improve Mathematics Teaching and Learning?
  • Working With Administrators
  • Embedding Lessons Into the Curriculum
  • Providing Professional Development
  • Co-planning and Co-teaching
  • Summary

Appendix A: Research Support for Visible Thinking Strategies, Conditions, and Actions

Appendix A: Research Support for Visible Thinking Strategies, Conditions, and Actions

Appendix B: Lessons Using Technology: Additional Materials

Appendix B: Lessons Using Technology: Additional Materials

References

References

Index

Index

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Visible Thinking in the K–8 Mathematics Classroom

Ted H. Hull , Don S. Balka , Ruth Harbin Miles
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January 2011 | 184 pages | Corwin

Format Published Date ISBN Price
Paperback 28/04/2023 9781412992053 $39.95
Lifetime 28/04/2023 9781452269405 $36.00

"This book is a crucial tool for meeting NCTM mathematical content and process standards. Through the useful problems and strategies presented within, teachers will definitely know how well their students will comprehend. If comprehension is an issue in your class, this book is a must have!"
—Therese Gessler Rodammer, Math Coach
Thomas W. Dixon Elementary School, Staunton, VA

Seeing is believing with this interactive approach to math instruction

Do you ever wish your students could read each other's thoughts? Now they can—and so can you! Veteran mathematics educators Ted Hull, Don Balka, and Ruth Harbin Miles explain why making students' thought processes visible is the key to effective mathematics instruction. Their newest book contains numerous grade-specific sample problems and instructional strategies for teaching essential concepts such as number sense, fractions, and estimation. Among the many benefits of visible thinking are:

  • Interactive student-to-student learning
  • Increased class participation
  • Development of metacognitive thinking and problem-solving skills

Helpful features include vignettes, relevant word problems, classroom scenarios, sample problems, lesson adaptations, and easy-to-follow examples of each strategy in action. The authors also explain how students can demonstrate their thinking using calculators and online tools. The final chapter outlines steps math leaders can take to implement visible thinking and maximize mathematics comprehension for all students.


 


Table Of Contents:

  • Preface
  • Acknowledgments
  • About the Authors
  • Part I. Preparing the Foundation
  • 1. What Is Visible Thinking?
  • Understanding Mathematical Concepts
  • Thinking as a Mathematical Premise
  • Visible Thinking in Classrooms
  • Visible Thinking Scenario 1: Area and Perimeter
  • Summary
  • 2. How Do Students Learn Mathematics?
  • What Is Thinking?
  • What Does Brain Research Indicate About Thinking and Learning?
  • What Is Mathematical Learning?
  • What Are Thinking and Learning Themes From Research?
  • Example Problems Revisited
  • Visible Thinking Scenario 2: Addition of Fractions
  • Summary
  • 3. What Is Happening to Thinking in Mathematics Classrooms?
  • Improvement Initiatives and Visible Thinking
  • Visible Thinking Scenario 3: Subtraction With Regrouping
  • Summary
  • Part II. Promoting Visible Thinking With an Alternative Instructional Model
  • 4. How Do Effective Classrooms Depend on Visible Thinking?
  • What Are Strategies, Conditions, and Actions?
  • Practice Into Action
  • Technology as Visible Thinking
  • Visible Thinking Scenario 4: Division
  • Summary
  • 5. How Are Long-Term Changes Made?
  • Enhancing Student Learning
  • Teaching Approaches
  • Visible Thinking Scenario 5: Mixed Numerals
  • Visible Thinking Scenario 6: Place Value
  • Summary
  • 6. How Are Short-Term Changes Made?
  • Pitfalls and Traps
  • Strategy Sequence
  • The Relationships Among the Strategy Sequence, Conditions, and Goals
  • Visible Thinking Scenario 7: Basic Addition and Subtraction Facts
  • Visible Thinking Scenario 8: Exponents
  • Summary
  • 7. How Are Lessons Designed to Achieve Short-Term and Long-Term Changes?
  • The Current Approach to Teaching Mathematics
  • Elements of an Alternative Instructional Model
  • Types of Problems
  • Summary
  • Part III. Implementing the Alternative Model at Different Grade Levels
  • 8. How Is Thinking Made Visible in Grades K–2 Mathematics?
  • Brainteaser Problem Example
  • Group-Worthy Problem Example
  • Transforming Problem Example
  • Summary
  • 9. How Is Thinking Made Visible in Grades 3–5 Mathematics?
  • Brainteaser Problem Example
  • Group-Worthy Problem Example
  • Transforming Problem Example
  • Summary
  • 10. How Is Thinking Made Visible in Grades 6–8 Mathematics?
  • Brainteaser Problem Example
  • Group-Worthy Problem Example
  • Transforming Problem Example
  • Summary
  • Part IV. Continuing the Work
  • 11. How Do Teachers, Leaders, and Administrators Coordinate Their Efforts to Improve Mathematics Teaching and Learning?
  • Working With Administrators
  • Embedding Lessons Into the Curriculum
  • Providing Professional Development
  • Co-planning and Co-teaching
  • Summary
  • Appendix A: Research Support for Visible Thinking Strategies, Conditions, and Actions
  • Appendix B: Lessons Using Technology: Additional Materials
  • References
  • Index

Recent Product Reviews:

"This book will help you, your students and your school. The author merges what we know works in mathematical problem solving, metacognition, social learning theory, and formative assessment. The examples display grade-specific ways to help individual students tackle brainteasers, whole-class concepts, and adaptations of traditional textbook exercises."
Alan Zollman, President of School Science and Mathematics Association, Northern Illinois University
"The author gives an excellent overview of what visual thinking is, why it is important, and how to implement it in the classroom. The text offers great advice for addressing many of the Common Core State Standards for Mathematics Habits of Mind, including making sense of problems and communicating mathematical reasoning."
Frederick L. Dillon, Mathematics Teacher, Strongsville City Schools, OH
"This book is a crucial tool for meeting NCTM mathematical content and process standards. Through the useful problems and strategies presented within, teachers will definitely know how well their students will comprehend. If comprehension is an issue in your class, this book is a must have!"
Therese Gessler Rodammer, Math Coach, Thomas W. Dixon Elementary School, Staunton, VA

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