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Visible Thinking in the K–8 Mathematics Classroom

Visible Thinking in the K–8 Mathematics Classroom

August 2012 | 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.

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


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


3. What Is Happening to Thinking in Mathematics Classrooms?
Improvement Initiatives and Visible Thinking

Visible Thinking Scenario 3: Subtraction With Regrouping


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


5. How Are Long-Term Changes Made?
Enhancing Student Learning

Teaching Approaches

Visible Thinking Scenario 5: Mixed Numerals

Visible Thinking Scenario 6: Place Value


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


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


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


9. How Is Thinking Made Visible in Grades 3–5 Mathematics?
Brainteaser Problem Example

Group-Worthy Problem Example

Transforming Problem Example


10. How Is Thinking Made Visible in Grades 6–8 Mathematics?
Brainteaser Problem Example

Group-Worthy Problem Example

Transforming Problem Example


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


Appendix A: Research Support for Visible Thinking Strategies, Conditions, and Actions
Appendix B: Lessons Using Technology: Additional Materials

"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


Chapter 1: What is Visible Thinking?

Ted Henry Hull

Consulting DescriptionTed H. Hull completed 32 years of service in public education before retiring and opening Hull Educational Consulting. He served as a mathematics teacher, K-12 mathematics coordinator, middle school principal, director of curriculum and instruction, and a project director for the Charles A. Dana Center at the University of Texas in Austin. While at the University of Texas, 2001 to 2005, he directed the research project “Transforming Schools: Moving from Low-Achieving to High Performing Learning Communities.” As part of the project, Hull worked directly with district leaders, school administrators, and teachers in... More About Author

Don S. Balka

Consulting DescriptionDon S. Balka, Ph.D., is a noted mathematics educator who has presented more than 2,000 workshops on the use of math manipulatives with PK-12 students at national and regional conferences of the National Council of Teachers of Mathematics and at in-service trainings in school districts throughout the United States and the world.  He is Professor Emeritus in the Mathematics Department at Saint Mary’s College, Notre Dame, Indiana. He is the author or co-author of numerous books for K-12 teachers, including Developing Algebraic Thinking with Number Tiles, Hands-On Math and Literature with Math Start, Exploring... More About Author

Ruth Harbin Miles

Ruth Harbin Miles coaches rural, suburban, and inner-city school mathematics teachers.  Her professional experiences include coordinating the K-12 Mathematics Teaching and Learning Program for the Olathe, Kansas, Public Schools for more than 25 years; teaching mathematics methods courses at Virginia’s Mary Baldwin College; and serving on the Board of Directors for the National Council of Teachers of Mathematics, the National Council of Supervisors of Mathematic, and both the Virginia Council of Teachers of Mathematics and the Kansas Association of Teachers of Mathematics.  Ruth is a co-author of five Corwin books including A... More About Author

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ISBN: 9781412992053
$ 34.95