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 third-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.
Innehållsförteckning
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
Activities for Building Norms 17
Encouraging Good Group Work 17
Paper Folding: Learning to Reason, Convince, and Be a Skeptic 21
Big Idea 1: Solving Problems with Data 23
Visualize: Tongues, Tails, and in Between 25
Play: Inspector Graph-It 36
Investigate: Data Tells Us about Ourselves 41
Big Idea 2: Thinking around Shapes 51
Visualize: Get Your Arms around It 53
Play: 36-Unit Walk 59
Investigate: Shapes on a Plane 65
Big Idea 3: Thinking in Equal Groups 75
Visualize: Sharing Crackers 78
Play: Dozens of Dice 85
Investigate: Playing with Pairs 91
Big Idea 4: Tiling to Understand Area 99
Visualize: Cover Up 101
Play: A Whole New Alphabet 111
Investigate: Sharing an Area 119
Big Idea 5: Seeing Multiplication as Area 125
Visualize: Rods Around 127
Play: Squares and Near-Squares 132
Investigate: Connecting Area and Perimeter 142
Big Idea 6: Understanding 1 2 149
Visualize: I Spy 1 2 151
Play: Spotting 1 2 160
Investigate: The Many Shapes of 1 2 171
Big Idea 7: Seeing Fractions: The Parts and the Wholes 183
Visualize: Seeing Parts and Wholes 185
Play: Cover, Cut, and Sort 191
Investigate: Taking a Fractional Walk 202
Big Idea 8: Being Flexible with Numbers 209
Visualize: How Many Do You See? 211
Play: How Close to 100? 217
Investigate: Tile and Table Patterns 222
Appendix 231
¼´´ Grid Paper 232
Grid Paper 233
1´´ Grid Paper 234
¼´´ Dot Paper 235
Centimeter Dot Paper 236
Isometric Dot Paper 237
Hundred Grids 238
About the Authors 239
Acknowledgments 241
Index 243
Om författaren
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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