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Visible Thinking in the K–8 Mathematics Classroom
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Visible Thinking in the K–8 Mathematics Classroom



January 2011 | 184 pages | Corwin
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 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 maths leaders can take to implement visible thinking and maximize mathematics comprehension for all students.

 
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

"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

"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

Sample Materials & Chapters

Preface

Chapter 1: What is Visible Thinking?


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ISBN: 9781412992053

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