Visible Thinking in the K-8 Mathematics Classroom

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