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El. knyga: Mindset Mathematics: Visualizing and Investigating Big Ideas, Grade 8

4.35/5 (32 ratings by Goodreads)
  • Formatas: PDF+DRM
  • Serija: Mindset Mathematics
  • Išleidimo metai: 23-Dec-2019
  • Leidėjas: Jossey-Bass Inc.,U.S.
  • Kalba: eng
  • ISBN-13: 9781119358855
  • Formatas: PDF+DRM
  • Serija: Mindset Mathematics
  • Išleidimo metai: 23-Dec-2019
  • Leidėjas: Jossey-Bass Inc.,U.S.
  • Kalba: eng
  • ISBN-13: 9781119358855

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Designed around the principle of active student engagement, with tasks that reflect the latest brain science on learning, this guide shows teachers how to engage students in mathematics by using growth mindset techniques that help them believe in their own potential. Original.

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.

Introduction 1(16)
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(4)
Manipulatives and Materials Used in This Book
18(3)
Activities for Building Norms
21(218)
Encouraging Good Group Work
21(1)
Paper Folding: Learning to Reason, Convince, and Be a Skeptic
22(5)
Big Idea 1 Moving Shapes
27(26)
Visualize: What Does It Mean to Be the Same?
29(6)
Play: Pixel Puzzles
35(10)
Investigate: Slide It, Flip It, Turn It
45(8)
Big Idea 2 Zooming In and Out
53(18)
Visualize: What Is Similarity?
55(5)
Play: Find the Fakes
60(5)
Investigate: Growing on a Grid
65(6)
Big Idea 3 Analyzing Proportional Relationships
71(20)
Visualize: Dropping the Altitude
73(6)
Play: Seeing Triangles under the Line
79(6)
Investigate: Stairway to Eleven
85(6)
Big Idea 4 Comparing Patterns of Growth
91(26)
Visualize: Squared Squares
93(7)
Play: Skip-Counting Arrays
100(7)
Investigate: Stacking Pennies
107(10)
Big Idea 5 The Ins and Outs of Functions
117(32)
Visualize: Growing Functions
120(14)
Play: Getting Warmer!
134(6)
Investigate: The Functions of Near Squares
140(9)
Big Idea 6 Finding Patterns in the Clouds
149(28)
Visualize: What's Going On in This Graph?
151(7)
Play: What's the Story Here?
158(8)
Investigate: Creating Data Visualizations
166(11)
Big Idea 7 Completing the Real Number System
177(24)
Visualize: Square Sides
179(8)
Play: Between 4 × 4 and 5 × 5
187(6)
Investigate: The Hypotenuse Hypothesis
193(8)
Big Idea 8 Discovering Pythagoras
201(20)
Visualize: Unpacking Pythagoras
204(5)
Play: Pythagorean Triples
209(5)
Investigate: Approximating Square Roots
214(7)
Big Idea 9 Exploring the Geometry of Ice Cream
221(18)
Visualize: Building Intuition about Volume
223(4)
Play: Comparing Cylinders
227(6)
Investigate: Scooping Up Volume
233(6)
Appendix
239(6)
Centimeter Grid Paper
240(1)
Grid Paper
241(1)
Isometric Dot Paper
242(1)
Dot Paper
243(2)
About the Authors 245(2)
Acknowledgments 247(2)
Index 249
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.