How the Math Gets Done: Why Parents Don't Need to Worry About New vs. Old Math provides a roadmap to understanding what the symbols for math operations (add, subtract, multiply, and divide) really mean, what the clues are to interpret these symbols, and a kind of short story of how they evolved over time.
How the Math Gets Done: Why Parents Don't Need to Worry About New vs. Old Math provides a roadmap to understanding what the symbols for math operations (add, subtract, multiply, and divide) really mean, what the clues are to interpret these symbols, and a kind of short story of how they evolved over time.
Foreword PrefaceIntroductionPart I. Definition 1. Math According to Jen, Bobby, and Others Jen's Deductions Bobby's Experience with Multiplication and Number Arrangements Children's Descriptions About Making Sense Trevor and Jim Invent Their Own Multiplication Methods Keep in Mind 2. Math Grammar of Nouns, Verbs, and Stories "Putting Together" Verbs for Addition and Multiplication "Taking Apart" Verbs for Subtraction and Division A Short Interlude About the Use of that Negative Sign Word Problems Put Math Verbs in Stories Keep in Mind 3. A Choice between Two Rs - Rote Memorization or Reasoning Sound Bites That Bite Back Memorization vs. Organization Acronyms - Sense or Nonsense Keep in Mind Part II. Organization 4. In Search of Like Terms, Classification Revisited Like Terms, Common Denominators, and Same Units Place Value Columns Have Like Terms Categories What's Wrong with this Picture?Adding PercentagesA Note About Multiplication and Division Keep in Mind 5. Artful Assembly of Operations Facts, Frogs, and Formats Jackie's Thinking About Number Operations James, Janie, and Napier's Lattice Multiplication Division Interpretations That Made Sense Keep in Mind 6. Same Math, Same Meaning, Different Organization - New vs. Old "If It Ain't Broke, Don't Fix It." Multiplication Organization Sense Digit Alignment Continues Zeke, Jake, and Long Division Keep in Mind Part III. Relationships and Patterns7. "Seeing" Math Patterns with Viewfinders Multiplication Table Patterns Addition Table Patterns Kathy's and Rudy's Fraction Viewfinders Keep in Mind 8. Spelunking for Patterns with More Viewfinders Reflections on Addition and Multiplication Subtraction, Division, and Missy's "Different Family" A Few Rules of Engagement for Working with Numbers Keep in Mind 9. Functions, Predictability, and Balance Predictability and FunctionsOne Answer or Many Answers, Same Balance Keep in Mind Part IV. Connections10. A Multiplication Area Image for the Ages From Theon to Dienes - A Bridge Across the Centuries Same Design for Mixed Numbers, Fractions and Decimals Visual-Spatial Multi-Digit Multiplication Keep in Mind 11. Ratios, Proportions, and Rate of Change Fractions as Gatekeepers David's Decluttering Fractions Changing Numbers, Changing Locations, and Moving Targets in Proportions Slope as a Rate of Change Keep in Mind 12. Algebraic Thinking The Shapes for an Algebra Transition From Multiplication Tables to Coordinate Tables Jill's Graphic Solutions F.O.I.L.'ed Again Keep in Mind Conclusion: What Parents Can Do Problem Solving Beyond Word Problems Right Tool for the Right Job - A Hard Look At Technology Keep in Mind Glossary References About the Author
Foreword PrefaceIntroductionPart I. Definition 1. Math According to Jen, Bobby, and Others Jen's Deductions Bobby's Experience with Multiplication and Number Arrangements Children's Descriptions About Making Sense Trevor and Jim Invent Their Own Multiplication Methods Keep in Mind 2. Math Grammar of Nouns, Verbs, and Stories "Putting Together" Verbs for Addition and Multiplication "Taking Apart" Verbs for Subtraction and Division A Short Interlude About the Use of that Negative Sign Word Problems Put Math Verbs in Stories Keep in Mind 3. A Choice between Two Rs - Rote Memorization or Reasoning Sound Bites That Bite Back Memorization vs. Organization Acronyms - Sense or Nonsense Keep in Mind Part II. Organization 4. In Search of Like Terms, Classification Revisited Like Terms, Common Denominators, and Same Units Place Value Columns Have Like Terms Categories What's Wrong with this Picture?Adding PercentagesA Note About Multiplication and Division Keep in Mind 5. Artful Assembly of Operations Facts, Frogs, and Formats Jackie's Thinking About Number Operations James, Janie, and Napier's Lattice Multiplication Division Interpretations That Made Sense Keep in Mind 6. Same Math, Same Meaning, Different Organization - New vs. Old "If It Ain't Broke, Don't Fix It." Multiplication Organization Sense Digit Alignment Continues Zeke, Jake, and Long Division Keep in Mind Part III. Relationships and Patterns7. "Seeing" Math Patterns with Viewfinders Multiplication Table Patterns Addition Table Patterns Kathy's and Rudy's Fraction Viewfinders Keep in Mind 8. Spelunking for Patterns with More Viewfinders Reflections on Addition and Multiplication Subtraction, Division, and Missy's "Different Family" A Few Rules of Engagement for Working with Numbers Keep in Mind 9. Functions, Predictability, and Balance Predictability and FunctionsOne Answer or Many Answers, Same Balance Keep in Mind Part IV. Connections10. A Multiplication Area Image for the Ages From Theon to Dienes - A Bridge Across the Centuries Same Design for Mixed Numbers, Fractions and Decimals Visual-Spatial Multi-Digit Multiplication Keep in Mind 11. Ratios, Proportions, and Rate of Change Fractions as Gatekeepers David's Decluttering Fractions Changing Numbers, Changing Locations, and Moving Targets in Proportions Slope as a Rate of Change Keep in Mind 12. Algebraic Thinking The Shapes for an Algebra Transition From Multiplication Tables to Coordinate Tables Jill's Graphic Solutions F.O.I.L.'ed Again Keep in Mind Conclusion: What Parents Can Do Problem Solving Beyond Word Problems Right Tool for the Right Job - A Hard Look At Technology Keep in Mind Glossary References About the Author
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