Rowman & Littlefield Publishers
Pages: 170
•
Trim: 7¼ x 10⅜
978-1-4758-3428-4 • Hardback • December 2017 • $92.00 • (£71.00)
978-1-4758-3429-1 • Paperback • December 2017 • $47.00 • (£36.00)
978-1-4758-3430-7 • eBook • December 2017 • $44.50 • (£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 and2.71826… - A Curious Number with Curious CousinsEccentricitye - 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