Rowman & Littlefield Publishers

Pages: 170
•
Trim: 7¼ x 10⅜

978-1-4758-3428-4 • Hardback • December 2017 • $87.00 • (£67.00)

978-1-4758-3429-1 • Paperback • December 2017 • $44.00 • (£35.00)

978-1-4758-3430-7 • eBook • December 2017 • $41.50 • (£35.00)

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. 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,User-Friendly Math for Parents: Learning and Understanding the Language of Numbers is Key, and How the Math Gets Done: Why Parents Don’t Need to Worry About New vs. Old Math.

ForewordPrefaceAcknowledgementsIntroductionPart I. Definition 1. A Perspective on Spatial Sense

Permission to Move Freely

Compositions and Decompositions of Shapes

Symmetry Is Spatial, Not One-Half

Keep in Mind

2. The Vocabulary Clues Are in the Words

Prefix Power for Polygons and Polyhedra

Vocabulary Ancestry

Keep in Mind

3. Sorting and Classifying the Symbols of Space

Arrangement-Driven Vocabulary

Measurement-Driven Vocabulary

Mixing the Arrangements and Measurements for Names

Keep in Mind

Part II. Organization 4. Ribbons, Rolls, and Rulers for the First Dimension

Transitioning from Zero Dimension to One Dimension

The Rolls of Circumferences and Perimeters

Diagonals, Diameters, Radii (Radians), and More Straight PiecesHeights, Altitudes, Apothems, and Legs

Keep in Mind

5. Angle Swings and Area Squares in Flatland

Angles Are at the Entry Gate to Flatland

Areas as Spatial Arrangements

Permission to Surround and Rearrange Shapes to Find Areas

Keep in Mind

6. Stack and Pour to Fill Volume in Spaceland

Polyhedra Nets Make Three Dimensions From Two Dimensions

Surface Areas, Polyhedra Nets, and Orange Peels

Fill ‘er Up for Volume

Keep in Mind

Part III. Relationships and Patterns7. Similarity and CongruenceSimilarity Allows Stretching and ShrinkingCongruence, Transformations, and TessellationsSymmetry as a Matter of Congruence

Keep in Mind

8. Special Spatial, Yet Irrational, Patterns

Pi , π, and 3.141592654… - From Archimedes to Supercomputers Phi , f, and 1.618… - Beauty in the Golden RatioThe Limit of e and 2.71826… - A Curious Number with Curious CousinsEccentricity e - A Circle Decider Keep in Mind

9. Shape Changes and Patterns

Same Perimeters, Same Areas, Different Polygons

Similar Shapes and Side Changes Predict Areas and Perimeters

Dots, Vertices, Spaces, and Faces

Keep in Mind

Part IV. Connections10. The Influential Right Triangle

Shadows, Right Triangles, and Proportions

The Pythagorean Theorem: A Relationship of Sides

Trigonometry: A Relationship Between Sides and Angles

Keep in Mind

11. A Circle’s NobilityAngles and Triangles Under Circle ControlCircle Relationships and Algebra TransformationsReturn of the Apothems for Polygon Areas

Diameters, Diagonals, and Ratios Revisited

Keep in Mind

12. From Figures to Scale Models, Then on to Calculus Connections

Shapes As Figured Numbers and Algebra

Written Geometry Through Keeping Records

Triangulation, Scale Models, and Similar Triangles

A Gentle Connection to Calculus

Keep in Mind

Conclusion: What Parents Can Do

The Best Strategy is a Team Strategy

A Visual-Spatial Parent and Child Story

Support Your Child’s Strengths

Four Possible Math Profiles to Consider

Keep in Mind

Glossary

References

About the Author

Spatial Sense Makes Math Sense makes math sound like fun, even though "math" and "fun" have been mutually exclusive categories for my entire life. I clearly recall my frustration as a child, attempting to master multiplication and not getting it. That experience left a life-long negative attitude about math and my ability to master it.

I dearly wish Cathy Draper, her skills, her passion, and her determination that all students love, value, and enjoy math, had been part of my math education! Buy this book for a child you love!

**— ****Rita H. Losee R.N., author of “Overcoming Trigeminal Neuralgia, The Waist Management Playbook"**

Cathy Draper’s passion to fight innumeracy is evident in Spatial Sense Makes Math Sense. The book is personable, conversational, and makes sense. It provides a great refresher of geometry and shows how parents can make sense of it to help their children. Each chapter is introduced with a quote that frames the theme of the passage and weaves history with foundational facts to make sense of mathematical theory. Draper has undertaken a remarkable goal by focusing on the support of parents to support the student learner.

**— ****Rudolph Weekes, principal, West Roxbury Academy, Boston Public Schools, father, former headmaster of Academy of Public Service and high school mathematics teacher**

Designed to help parents help their children with the content and psychology of math, this book focuses on visual models that support “Math Avoiders,” and can help them become "Math Aficionados." Catheryne Draper "has been learning from her students for more than half a century" and she shares wisdom and advice for families to rock math homework! The top to-dos include accepting mistakes, trusting your child, and being willing to learn along with them, rather than you learning it first.

**— ****Robin Schwartz, founder, Math Confidence, adjunct professor, Math and Education, College of Mount Saint Vincent**