Engage students in mathematics using growth mindset techniques
The most challenging parts of teaching mathematics are engaging students and helping them understand the connections between mathematics concepts. In this volume, you’ll find a collection of low-floor, high-ceiling tasks that will help you do just that, by looking at the big ideas in second grade through visualization, play, and investigation.
During their work with tens of thousands of teachers, authors Jo Boaler, Jen Munson, and Cathy Williams heard the same message–that they want to incorporate more brain science into their math instruction, but they need guidance in the techniques that work best to get across the concepts they needed to teach. So, the authors designed Mindset Mathematics around the principle of active student inquiry, with tasks that reflect the latest brain science on learning. Open, creative, and visual math tasks have been shown to support student learning, and more importantly change their relationship with mathematics and start believing in their own potential. The tasks in Mindset Mathematics reflect the lessons from brain science that:
* There is no such thing as a math person and anyone can learn mathematics to high levels.
* Mistakes, struggle, and challenge are opportunities for brain growth.
* Speed is unimportant, and even counterproductive, in mathematics.
* Mathematics is a visual and beautiful subject, and our brains want to think visually about mathematics.
With engaging questions, open-ended tasks, and four-color visuals that will help kids get excited about mathematics, Mindset Mathematics is organized around nine big ideas which emphasize the connections within the Common Core State Standards (CCSS) and can be used with any current curriculum.
Tabela de Conteúdo
Introduction 1
Low-Floor, High-Ceiling Tasks 2
Youcubed Summer Camp 3
Memorization versus Conceptual Engagement 4
Mathematical Thinking, Reasoning, and Convincing 5
Big Ideas 9
Structure of the Book 9
Note on Materials 17
Manipulatives and Materials Used in This Book 18
Activities for Building Norms 21
Encouraging Good Group Work 21
How Many Do You See? Learning to Reason, Convince, and Pose Questions 23
Big Idea 1: Partitioning Shapes into Equal Parts 31
Visualize: Equal or Same? 33
Play: Four Fourths 39
Investigate: Rows and Columns 44
Big Idea 2: Making and Using Equal Groups 53
Visualize: The Groups Inside 55
Play: Skipping down the Hall 61
Investigate: Array Museum 67
Big Idea 3: What Is 100? 73
Visualize: The Many Ways to See 100 75
Play: Scoop and Count 82
Investigate: Making a Dollar, Revisited 86
Big Idea 4: Composing and Decomposing Numbers 91
Visualize: Array Talks 93
Play: Which Is More? 103
Investigate: Coin Grab 114
Big Idea 5: Using Patterns in Place Value 119
Visualize: What’s in Your 12? 121
Play: Reach for It! 126
Investigate: Window Mysteries 136
Big Idea 6: Thinking on the Number Line 145
Visualize: Long Lives 148
Play: Life- Span Puzzles 157
Investigate: Living on the Number Line 166
Big Idea 7: Rulers and Clocks Are Number Lines 173
Visualize: Noticing the Ruler and Clock 175
Play: Walking the Clock 181
Investigate: A Sea of Sharks 187
Big Idea 8: Using Units to Estimate 205
Visualize: Foot by Foot 207
Play: Length Scavenger Hunt 216
Investigate: School- Day Walkabout 222
Big Idea 9: Using Data to Visualize and Wonder about Our World 229
Visualize: Fruit around the World 231
Play: Eat Your Roots 238
Investigate: Dear Data 243
Appendix 253
Grid Paper 254
About the Authors 255
Acknowledgments 257
Index 259
Sobre o autor
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 an assistant professor of learning sciences at Northwestern University, a professional developer, and a former classroom teacher. She received her Ph D in mathematics education from Stanford University. Her research focuses on 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.
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