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 at the sixth-grade level 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 engagement, with tasks that reflect the latest brain science on learning. Open, creative, and visual math tasks have been shown to improve student test scores, 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 – anyone can learn mathematics to high levels.
* Mistakes, struggle and challenge are the most important times for brain growth.
* Speed is unimportant 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.
Зміст
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 10
Note on Materials 16
Manipulatives and Materials Used in This Book 17
Activities for Building Norms 19
Encouraging Good Group Work 19
Paper Folding: Learning to Reason, Convince, and Be Skeptical 21
Big Idea 1: Taking Apart Prisms and Polygons 24
Visualize: How Big Is the Footprint? 26
Play: Shards of a Shape 38
Investigate: Rising from the Footprint 46
Big Idea 2: Folding and Unfolding Objects 57
Visualize: Folding Cubes in Your Mind 60
Play: Folding Nets in Your Mind 70
Investigate: Filling Our Nets 85
Big Idea 3: Expanding the Number Line 92
Visualize: Folding around Zero 94
Play: Bouncing around the Number Line 101
Investigate: Going 2-D 107
Big Idea 4: Finding and Using Unit Rates 116
Visualize: Seeing Unit Rates 118
Play: Seeing the Best Deal 128
Investigate: How Fast Do You Walk? 136
Big Idea 5: Reasoning with Proportions 142
Visualize: Jump! Jump! 144
Play: Seeing Animals in a New Way 149
Investigate: A Seat at the Table 156
Big Idea 6: Visualizing the Center and Spread of Data 164
Visualize: The Shape of Data 167
Play: What Does Mean Mean? 178
Investigate: When Does Mean = Median = Mode = Range? 185
Big Idea 7: Using Symbols to Describe the World 192
Visualize: Cuisenaire Rod Equivalents 195
Play: Math Mobiles 204
Investigate: Radial Patterns 215
Big Idea 8: Generalizing 221
Visualize: Generalizing Number Patterns 223
Play: Generalizing Strategy 230
Investigate: Generalizing Visual Patterns 239
Appendix 246
Centimeter Grid Paper 247
Grid Paper 248
1′ Grid Paper 249
Isometric Dot Paper 250
Dot Paper 251
About the Authors 252
Acknowledgments 254
Index 255
Про автора
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 postdoctoral fellow 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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