Mindset Mathematics

JO BOALER is a professor of mathematics education at Stanford University and co-founder and faculty director of youcubed. She serves as an advisor to several Silicon Valley companies and is a White House presenter on girls and STEM (Science, Technology, Engineering, and Math). The author of seven books, including Mathematical Mindsets, and numerous research articles, she is a regular contributor to news and radio in the United States and England. JEN MUNSON is a doctoral candidate at Stanford University, a professional developer, and a former classroom teacher. She works with teachers and school leaders across the United States to develop responsive, equitable mathematics instruction. CATHY WILLIAMS is the co-founder and the executive director of youcubed at Stanford University. Before working at youcubed, she was a high school math teacher and worked in mathematics curriculum and administration at the county and district levels in California.

• Introduction 1Low-Floor, High-Ceiling Tasks 2Youcubed Summer Camp 3Memorization versus Conceptual Engagement 4Mathematical Thinking, Reasoning, and Convincing 5Big Ideas 9Structure of the Book 10Activities for Building Norms 17Encouraging Good Group Work 17Paper Folding: Learning to Reason, Convince, and Be a Skeptic 21Big Idea 1: Thinking in Cubes 23Visualize: Solids, Inside and Out 25Play: City of Cubes 33Investigate: A Box of Boxes 44Big Idea 2: Estimating with Fractions 53Visualize: Making Snowflakes 55Play: Fraction Blizzard 61Investigate: Wondering with Fractions 67Big Idea 3: Using Fraction Equivalence 81Visualize: Picking Paintings Apart 83Play: Make a Fake 94Investigate: Squares with a Difference 101Big Idea 4: Exploring the Coordinate Plane 115Visualize: Getting around the Plane 118Play: Ship Shape 124Investigate: Table Patterns 133Big Idea 5: Seeing and Connecting Patterns across Representations 143Visualize: Two-Pattern Tango 145Play: Pattern Carnival 153Investigate: Seeing Growth on a Graph 159Big Idea 6: Understanding Fraction Multiplication Visually 169Visualize: Fractions in a Pan 172Play: Pieces and Parts 180Investigate: The Sum of the Parts 187Big Idea 7: What Does It Mean to Divide Fractions? 199Visualize: Creating Cards 201Play: Cuisenaire Trains 209Investigate: Fraction Division Conundrum 217Big Idea 8: Thinking in Powers of 10 223Visualize: The Unit You 225Play: Filling Small and Large 233Investigate: Museum of the Very Large and Small 239Big Idea 9: Using Numbers and Symbols Flexibly 247Visualize: Seeing Expressions 250Play: Inside Pascal’s Triangle 261Investigate: The 1492 Problem 268Appendix 279Centimeter Dot Paper 280Isometric Dot Paper 281About the Authors 283Acknowledgments 285Index 287

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