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<span><span>How the Math Gets Done: Why Parents Don't Need to Worry About New vs. Old Math</span><span> provides a roadmap to understanding what the symbols for math operations (add, subtract, multiply, and divide) </span><span>really</span><span> mean, what the clues are to interpret these symbols, and a kind of short story of how they evolved over time.</span></span>

<span><span>Foreword</span></span>
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<span>Preface</span>
<span>Introduction</span>
<span>Part I. Definition </span>
<span><span>1. Math According to Jen, Bobby, and Others</span></span>
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<span><span>Jen’s Deductions </span></span>
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<span><span>Bobby’s Experience with Multiplication and Number Arrangements</span></span>
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<span><span>Children’s Descriptions About Making Sense</span></span>
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<span><span>Trevor and Jim Invent Their Own Multiplication Methods</span></span>
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<span><span>Keep in Mind</span></span>
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<span><span>2. Math Grammar of Nouns, Verbs, and Stories </span></span>
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<span><span>“Putting Together” Verbs for Addition and Multiplication </span></span>
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<span><span>“Taking Apart” Verbs for Subtraction and Division </span></span>
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<span><span>A Short Interlude About the Use of that Negative Sign</span></span>
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<span>Word Problems Put Math Verbs in Stories </span>
<span><span>Keep in Mind</span></span>
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<span><span>3. A Choice between Two Rs – Rote Memorization or Reasoning</span></span>
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<span><span>Sound Bites That Bite Back </span></span>
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<span><span>Memorization vs. Organization </span></span>
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<span><span>Acronyms - Sense or Nonsense</span></span>
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<span><span>Keep in Mind</span></span>
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<span><span>Part II. Organization </span></span>
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<span><span>4. In Search of Like Terms, Classification Revisited</span></span>
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<span>Like Terms, Common Denominators, and Same Units </span>
<span>Place Value Columns Have Like Terms Categories </span>
<span>What’s Wrong with this Picture?</span>
<span>Adding Percentages</span>
<span>A Note About Multiplication and Division </span>
<span><span> Keep in Mind</span></span>
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<span>5. Artful Assembly of Operations </span>
<span><span>Facts, Frogs, and Formats</span></span>
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<span><span>Jackie’s Thinking About Number Operations</span></span>
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<span><span>James, Janie, and Napier’s Lattice Multiplication</span></span>
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<span><span>Division Interpretations That Made Sense </span></span>
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<span><span>Keep in Mind</span></span>
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<span><span>6. Same Math, Same Meaning, Different Organization – New vs. Old</span></span>
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<span><span>“If It Ain’t Broke, Don’t Fix It.” </span></span>
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<span><span>Multiplication Organization Sense</span></span>
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<span><span>Digit Alignment Continues</span></span>
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<span><span>Zeke, Jake, and Long Division</span></span>
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<span><span>Keep in Mind</span></span>
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<span>Part III. Relationships and Patterns</span>
<span><span>7. “Seeing” Math Patterns with Viewfinders</span></span>
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<span><span>Multiplication Table Patterns </span></span>
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<span><span>Addition Table Patterns</span></span>
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<span><span>Kathy’s and Rudy’s Fraction Viewfinders</span></span>
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<span><span>Keep in Mind</span></span>
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<span><span>8. Spelunking for Patterns with More Viewfinders</span></span>
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<span><span>Reflections on Addition and Multiplication </span></span>
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<span><span>Subtraction, Division, and Missy’s “Different Family”</span></span>
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<span><span>A Few Rules of Engagement for Working with Numbers</span></span>
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<span><span>Keep in Mind</span></span>
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<span><span>9. Functions, Predictability, and Balance </span></span>
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<span>Predictability and Functions</span>
<span>One Answer or Many Answers, Same Balance</span>
<span><span> Keep in Mind</span></span>
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<span>Part IV. Connections</span>
<span><span>10. A Multiplication Area Image for the Ages</span></span>
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<span><span>From Theon to Dienes – A Bridge Across the Centuries</span></span>
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<span><span>Same Design for Mixed Numbers, Fractions and Decimals</span></span>
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<span><span>Visual-Spatial Multi-Digit Multiplication</span></span>
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<span><span>Keep in Mind</span></span>
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<span><span>11. Ratios, Proportions, and Rate of Change</span></span>
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<span><span>Fractions as Gatekeepers</span></span>
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<span><span>David’s Decluttering Fractions</span></span>
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<span><span>Changing Numbers, Changing Locations, and Moving Targets in Proportions</span></span>
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<span><span>Slope as a Rate of Change</span></span>
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<span><span>Keep in Mind</span></span>
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<span><span>12. Algebraic Thinking</span></span>
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<span><span>The Shapes for an Algebra Transition</span></span>
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<span><span>From Multiplication Tables to Coordinate Tables</span></span>
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<span><span>Jill’s Graphic Solutions</span></span>
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<span><span>F.O.I.L.’ed Again</span></span>
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<span><span>Keep in Mind</span></span>
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<span><span>Conclusion: What Parents Can Do</span></span>
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<span><span>Problem Solving Beyond Word Problems</span></span>
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<span><span>Right Tool for the Right Job - A Hard Look At Technology</span></span>
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<span><span>Keep in Mind</span></span>
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<span><span>Glossary</span></span>
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<span><span>References</span></span>
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<span><span>About the Author</span></span>

<span><span>Catheryne Draper</span><span> has been learning from her students for over half a century of teaching, supervising the math program in a school district, advising math education at the state level, coaching math in schools, and presenting math workshops for teachers.</span></span>
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<span><span>She is the author of The Algebra Game, a hands-on multi-deck algebra program in four topics covering Linear Graphs, Quadratic Equations, Conic Sections, and Trig Functions that allows students to work together in cooperative groups, or individually, to identify the algebra relationships and patterns in the each topic and in the organization across the topics. In addition to contributing many published articles, Draper is also the author of </span><span>Winning the Math Homework Challenge: Insights for Parents To See Math Differently </span><span>and </span><span>User-Friendly Math for Parents</span><span>: </span><span>Learning and Understanding the Language of Numbers is Key.</span></span>