How the Math Gets Done (eBook)

Catheryne Draper 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.Winning the Math Homework Challenge: Insights for Parents To See Math Differently and User-Friendly Math for Parents: Learning and Understanding the Language of Numbers is Key.

PrefaceIntroductionPart I. Definition 1. Math According to Jen, Bobby, and OthersBobby’s Experience with Multiplication and Number ArrangementsTrevor and Jim Invent Their Own Multiplication MethodsKeep in Mind2. 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 SignWord Problems Put Math Verbs in Stories Keep in Mind3. A Choice between Two Rs – Rote Memorization or ReasoningSound Bites That Bite Back Memorization vs. Organization Acronyms - Sense or NonsenseKeep in MindAdding PercentagesA Note About Multiplication and Division Keep in Mind5. Artful Assembly of Operations Facts, Frogs, and FormatsJackie’s Thinking About Number OperationsJames, Janie, and Napier’s Lattice MultiplicationDivision Interpretations That Made Sense Keep in Mind6. Same Math, Same Meaning, Different Organization – New vs. Old“If It Ain’t Broke, Don’t Fix It.” Digit Alignment ContinuesZeke, Jake, and Long DivisionKeep in MindPart III. Relationships and Patterns7. “Seeing” Math Patterns with ViewfindersMultiplication Table Patterns Addition Table PatternsKathy’s and Rudy’s Fraction ViewfindersKeep in Mind8. Spelunking for Patterns with More ViewfindersReflections on Addition and Multiplication Subtraction, Division, and Missy’s “Different Family”A Few Rules of Engagement for Working with NumbersKeep in MindPredictability and FunctionsOne Answer or Many Answers, Same Balance Keep in MindPart IV. Connections10. A Multiplication Area Image for the AgesSame Design for Mixed Numbers, Fractions and DecimalsKeep in Mind11. Ratios, Proportions, and Rate of ChangeFractions as GatekeepersChanging Numbers, Changing Locations, and Moving Targets in ProportionsKeep in Mind12. Algebraic ThinkingThe Shapes for an Algebra TransitionFrom Multiplication Tables to Coordinate TablesJill’s Graphic SolutionsF.O.I.L.’ed AgainKeep in MindConclusion: What Parents Can DoProblem Solving Beyond Word ProblemsRight Tool for the Right Job - A Hard Look At TechnologyKeep in MindGlossaryReferencesAbout the Author