Developing Mathematical Reasoning

Preface About This Book Language Use in This Book Acknowledgments About the Author PART I: SETTING THE STAGE Chapter 1: MATHEMATICS FOR TEACHING Whats 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