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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:
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.
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 PhD 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.
Introduction
Low Floor, High Ceiling Tasks
Youcubed Summer Camp
Memorization vs. Conceptual Engagement
Mathematical Thinking, Reasoning and Convincing
Big Ideas
Structure of the Book
Activities for Building Norms
Encouraging Good Group Work
Paper Folding: Learning to Reason, Convince, and Be Skeptical
Big Idea 1: Solving Problems with Data
Visualize: Tongues, Tails, and In Between
Play: Inspector Graph-It
Investigate: Data Tells Us About Ourselves
Big Idea 2: Thinking Around Shapes
Visualize: Get Your Arms Around It
Play: Shapes on a Plane
Investigate: Shape and Not a Shape
Big Idea 3: Thinking in Equal Groups
Visualize: Sharing Crackers
Play: Dozens of Dice
Investigate: Playing with Pairs
Big Idea 4: Tiling to Understand Area
Visualize: Cover Up
Play: A Whole New Alphabet
Investigate: Sharing an Area
Big Idea 5: Seeing Multiplication as Area
Visualize: Rods Around
Play: Squares and Near-Squares
Investigate: Connecting Area and Perimeter
Big Idea 6: Understanding Half
Visualize: I Spy ½
Play: Spotting ½
Investigate: The Many Shapes of ½
Big Idea 7: Seeing Fractions, Parts, Wholes, and Forms
Visualize: Seeing Parts and Wholes
Play: Cover, Cut, and Sort
Investigate: Taking a Fractional Walk
Big Idea 8: Being Flexible with Numbers
Visualize: How Many Do You See?
Play: How Close to 100?
Investigate: Tile and Table Patterns
Appendix
Centimeter Dot Paper
Isometric Dot Paper
Grid Paper
Dot Paper
Grid Paper
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