Mindset Mathematics: Visualizing and Investigating Big Ideas, Grade 8

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 eighth-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.

List of contents

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
 
Paper Folding: Learning to Reason, Convince, and Be a Skeptic 22
 
Big Idea 1: Moving Shapes 27
 
Visualize: What Does It Mean to Be the Same? 29
 
Play: Pixel Puzzles 35
 
Investigate: Slide It, Flip It, Turn It 45
 
Big Idea 2: Zooming In and Out 53
 
Visualize: What is Similarity? 55
 
Play: Find the Fakes 60
 
Investigate: Growing on a Grid 65
 
Big Idea 3: Analyzing Proportional Relationships 71
 
Visualize: Dropping the Altitude 73
 
Play: Seeing Triangles under the Line 79
 
Investigate: Stairway to Eleven 85
 
Big Idea 4: Comparing Patterns of Growth 91
 
Visualize: Squared Squares 93
 
Play: Skip-Counting Arrays 100
 
Investigate: Stacking Pennies 107
 
Big Idea 5: The Ins and Outs of Functions 117
 
Visualize: Growing Functions 120
 
Play: Getting Warmer! 134
 
Investigate: The Functions of Near Squares 140
 
Big Idea 6: Finding Patterns in the Clouds 149
 
Visualize: What's Going On in This Graph? 151
 
Play: What's the Story Here? 158
 
Investigate: Creating Data Visualizations 166
 
Big Idea 7: Completing the Real Number System 177
 
Visualize: Square Sides 179
 
Play: Between 4 × 4 and 5 × 5 187
 
Investigate: The Hypotenuse Hypothesis 193
 
Big Idea 8: Discovering Pythagoras 201
 
Visualize: Unpacking Pythagoras 204
 
Play: Pythagorean Triples 209
 
Investigate: Approximating Square Roots 214
 
Big Idea 9: Exploring the Geometry of Ice Cream 221
 
Visualize: Building Intuition about Volume 223
 
Play: Comparing Cylinders 227
 
Investigate: Scooping Up Volume 233
 
Appendix 239
 
Centimeter Grid Paper 240
 
Grid Paper 241
 
Isometric Dot Paper 242
 
Dot Paper 243
 
About the Authors 245
 
Acknowledgments 247
 
Index 249

About the author

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 PhD in teacher education and mathematics education from Stanford University. Her research focuses on responsive, equitable mathematics instruction and coaching. 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.

Summary

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 eighth-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.

Product details

• Authors: J Boaler, Jo Boaler, Jo Munson Boaler, Boaler Jo, Je Munson, Jen Munson, Cathy Williams, Williams Cathy
• Publisher: Wiley, John and Sons Ltd
• Languages: English
• Product format: Paperback / Softback
• Released: 31.01.2020
• EAN: 9781119358749
• ISBN: 978-1-119-35874-9
• No. of pages: 272
• Series: Mindset Mathematics
• Subjects: Education and learning > Schoolbooks, general education schools; Guides > Self-help, everyday life > Family; Humanities, art, music > Education > School education, didactics, methodology; Mathematikunterricht, Mathematik, Education, Bildungswesen, Mathematics, Lehrpläne / Mathematik