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E-grāmata: Mindset Mathematics: Visualizing and Investigating Big Ideas, Grade 7

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  • Formāts: PDF+DRM
  • Sērija : Mindset Mathematics
  • Izdošanas datums: 05-Jul-2019
  • Izdevniecība: Jossey-Bass Inc.,U.S.
  • Valoda: eng
  • ISBN-13: 9781119357971
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  • Formāts: PDF+DRM
  • Sērija : Mindset Mathematics
  • Izdošanas datums: 05-Jul-2019
  • Izdevniecība: Jossey-Bass Inc.,U.S.
  • Valoda: eng
  • ISBN-13: 9781119357971
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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 seventh-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.

Introduction 1(26)
Low-Floor, High-Ceiling Tasks
2(1)
Youcubed Summer Camp
3(1)
Memorization versus Conceptual Engagement
4(1)
Mathematical Thinking, Reasoning, and Convincing
5(4)
Big Ideas
9(1)
Structure of the Book
9(8)
Note on Materials
17(1)
Manipulatives and Materials Used in This Book
18(3)
Activities for Building Norms
21(1)
Encouraging Good Group Work
21(1)
Paper Folding: Learning to Reason, Convince, and Be a Skeptic
22(5)
Big Idea 1 Connecting 2D and 3D Worlds
27(20)
Visualize: Seeing Slices
29(5)
Play: Playing with Clay
34(6)
Investigate: The Area of Slices
40(7)
Big Idea 2 Constructing Figures to Scale
47(22)
Visualize: What Is Scale?
50(5)
Play: A Fishy Image
55(6)
Investigate: Magnifying Solids
61(8)
Big Idea 3 Seeing Proportional Relationships
69(24)
Visualize: Growing Dough
72(8)
Play: Is It Proportional?
80(6)
Investigate: Sizing Up Proportions
86(7)
Big Idea 4 Understanding Percents in the World
93(26)
Visualize: Painting Percents
95(8)
Play: Building Benchmarks
103(6)
Investigate: What's It Going to Cost?
109(10)
Big Idea 5 Building Intuition about Probability
119(26)
Visualize: Is It Fair?
121(10)
Play: Fair Sums?
131(5)
Investigate: What's in the Bag?
136(9)
Big Idea 6 Modeling Probabilities
145(26)
Visualize: What's the Chance of That?
147(8)
Play: Probability Carnival
155(8)
Investigate: Go, Go Galton Board!
163(8)
Big Idea 7 Sampling to Understand Populations
171(26)
Visualize: Sampling Dots and Beads
173(7)
Play: Catch and Release
180(6)
Investigate: Wildlife Populations
186(11)
Big Idea 8 Operating with Opposites
197(28)
Visualize: Line Dancing
199(8)
Play: Integer Tic-Tac-Toe
207(9)
Investigate: Coordinating Multiplication
216(9)
Big Idea 9 Using Algebra as a Problem-Solving Tool
225(26)
Visualize: Case by Case
228(9)
Play: (Non) Linear Pattern Puzzles
237(8)
Investigate: Linear Letters
245(6)
Big Idea 10 Exploring Circles
251(22)
Visualize: Building Hunches about Circumference
253(7)
Play: Dissecting Circle Area
260(7)
Investigate: Unraveling Circles
267(6)
Appendix
273(6)
Centimeter Grid Paper
274(1)
1" Grid Paper
275(1)
Snap Cube Grid Paper
276(1)
Isometric Dot Paper
277(1)
Dot Paper
278(1)
About the Authors 279(2)
Acknowledgments 281(2)
Index 283
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.