Developing Mathematical Reasoning: The Strategies, Models, and Lessons to Teach the Big Ideas in Grades K-2(Corwin Mathematics Series)

Math is not rote-memorizable. Math is not random-guessable. Math is figure-out-able. Author Pam Harris argues that teaching real math—math that is free of distortions—will reach more students more effectively and result in deeper understanding and longer retention. This book is about teaching undistorted math using the kinds of mental reasoning that mathematicians do. Memorization tricks and algorithms meant to make math "easier" are full of traps that sacrifice long-term student growth for short-lived gains. Students and teachers alike have been led to believe that they’ve learned more and more math, but in reality their brains never get any stronger. Using these tricks may make facts easier to memorize in isolation, but that very disconnect distorts the reality of math. In her landmark book Developing Mathematical Reasoning: Avoiding the Trap of Algorithms, Pam emphasizes the importance of teaching students increasingly sophisticated mathematical reasoning and understanding underlying concepts rather than relying on a set rule for solving problems. Now, in this first companion volume, Developing Mathematical Reasoning: The Strategies, Models, and Lessons to Teach the Big Ideas in Grades K-2, she demonstrates how counting and additive strategies serve as the foundation for creating efficient, accurate, and flexible thinkers. Everyone is capable of understanding and doing real math. This book: Gives step-by-step guidance on how to teach the strategies, models, and big ideas that foster confidence and long-term success, preparing students for increasingly complex mathematical challenges Offers the "what to do" to teach counting, addition, and subtraction in ways that promote reasoning over rote memorization Provides practical tools such as problem strings, models, classroom routines, and discussion questions designed to implement reasoning-based practices Includes supporting resources for creating a classroom culture where students see math as figure-out-able and gain confidence as mathematical thinkers By addressing common misconceptions about math and providing practical strategies for teaching real math, this book shows that everyone can use the mathematical relationships they already know to reason about new relationships. In other words, everyone can math-even the very youngest students!

Table of Contents:
Preface About This Book Language Use in This Book Acknowledgments About the Author PART I: SETTING THE STAGE Chapter 1: MATHEMATICS FOR TEACHING What’s the Purpose of Learning Math? The Development of Mathematical Reasoning Major Strategies Conclusion Discussion Questions PART II: DEVELOPING COUNTING AND COUNTING STRATEGIES Chapter 2: ALL ABOUT COUNTING The Difference Between Counting and Counting Strategies Foundations of Number How to Develop Counting The Number Sequence in the Teens The Number Sequence After the Teens Meaning of Decades Student Interview Conclusion Discussion Questions Chapter 3: COUNTING STRATEGIES About Counting Strategies Early Counting Strategies The Counting On, Counting Back Strategy Problem Types Developing Counting Strategies Conclusion Discussion Questions PART III: DEVELOPING ADDITIVE REASONING Chapter 4: THE MAJOR STRATEGIES FOR ADDITION WITHIN 20 Additive Reasoning Additive Strategies Developing Addition Within 20 The Get to 10 Strategy The Next Two Major Strategies The Using Doubles to Add Strategy The Add 10 and Adjust Strategy Comparing the Single-Digit Addition Strategies Conclusion Discussion Questions Chapter 5: THE MAJOR STRATEGIES FOR SUBTRACTION WITHIN 20 Developing Subtraction Within 20 The Remove to 10 Strategy The Next Two Major Strategies The Using Doubles to Subtract Strategy The Remove 10 and Adjust Strategy Finding the Distance/Difference Strategy Comparing the Single-Digit Subtraction Strategies Conclusion Discussion Questions Chapter 6: THE MAJOR STRATEGIES FOR DOUBLE-DIGIT ADDITION Developing Multi-Digit Addition Strategies The Splitting by Place Value Strategy The Next Two Major Strategies The Add a Friendly Number Strategy The Get to a Friendly Number Strategy The Add a Friendly Number Over Strategy The Give and Take Strategy Comparing the Major Addition Strategies Conclusion Discussion Questions Chapter 7: THE MAJOR STRATEGIES FOR MULTI-DIGIT SUBTRACTION Developing Multi-Digit Subtraction Strategies The Remove by Place Value Strategy The Next Two Major Strategies The Remove a Friendly Number Strategy The Remove to a Friendly Number Strategy The Remove a Friendly Number Over Strategy Finding the Distance/Difference Strategy The Constant Difference Strategy Comparing the Major Strategies for Multi-Digit Subtraction Conclusion Discussion Questions PART IV: PUTTING IT ALL TOGETHER Chapter 8: TASKS TO DEVELOP MATHEMATICAL REASONING Sequencing Tasks Problem Strings Other Instructional Routines Games Hint Cards Conclusion Discussion Questions Chapter 9: MODELING AND MODELS Strategies Versus Models The Many Meanings of Model Exploring Models by Their Best Uses Our Modeling Framework Conclusion Discussion Questions Chapter 10: MOVING FORWARD Mentor Mathematicians Where to Start Conclusion Discussion Questions References Index

About the Author :
Pamela Weber Harris is changing the way we view and teach mathematics. Pam is the author of several books, including the Numeracy Problems Strings K-5 series, Building Powerful Numeracy, and the series Foundations for Strategies. As a mom, a former high school math teacher, a university lecturer, and an author, she believes everyone can do more math when it is based in reasoning rather than rote-memorizing or mimicking. Pam has created online Building Powerful Mathematics workshops and presents frequently at national and international conferences.  Her particular interests include teaching real math, building powerful numeracy, sequencing rich tasks to construct mathematics, using technology appropriately, and facilitating smart assessment and vertical connectivity in curricula in schools PK-12. Pam helps leaders and teachers to make the shift that supports students to learn real math because math is figureoutable!