Rowman & Littlefield Publishers

Pages: 158
•
Trim: 7¼ x 10½

978-1-4758-3422-2 • Hardback • October 2017 • $78.00 • (£60.00)

978-1-4758-3423-9 • Paperback • October 2017 • $39.00 • (£30.00)

978-1-4758-3424-6 • eBook • October 2017 • $37.00 • (£28.00)

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.

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 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.

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

How the Math Gets Done is not a quick fix to raise the child's math grade for tomorrow’s test, but about deciphering the child's thinking and establishing real math understanding for the long haul. Once a kid is in trouble, parents will not feel there is time to immediately get to the bottom of the issues, so they may want to skip around the book to locate the particular topic that is giving their child difficulty. This is the book that will wake parents (and teachers) up to the notion that multiple strategies are helpful and that opportunities for misunderstandings are lying in the path like so many land mines!

**— ****Ann Hammond McCamy, Parent and Assistant Director, Delmont Public Library. Former curriculum writer for Lambert Book House, Education Coordinator at The House of the Seven Gables, and public and private school teacher**

Oh my goodness, this book is brilliant and so helpful. As an educator and a mother, I can't help thinking that this is a book for everyone not just parents. How the Math Gets Done spotlights and breaks down into understandable nuggets the most intimate mathematical thinking of our children. While illuminating for us their understandings and misunderstandings, it pushes us -the adults- to think our very own understandings in the most non-threatening way, so that we can support our kids.

**— ****Regine Philippeaux-Pierre, Mother of Two Children, Director, Excellence for All, Boston Public Schools**