Mindset Mathematics: Visualizing and Investigating Big Ideas, Grade 4

ISBN-13: 9781119358800 / Angielski / Miękka / 2017 / 288 str.

Cathy Williams

Opis

Each grade level's materials will be structured as a single volume for teachers. Each volume will include a collection of mathematical tasks focused on the big mathematical ideas in the grade level that create space for students to engage in (1) visual mathematics, (2) play, and (3) investigation. For each big idea the text will unpack for teachers the big ideas and how to look for student thinking around these ideas to make instructional decisions. It will address the questions: What is the big idea and why is it important? How do students learn this big idea? What should I look for in student thinking and strategies? Further, each activity or task will be accompanied by ideas for how to launch and how to facilitate discussion after the activity. Activities in the three areas - visual math, play, and investigation - will be provided as reproducibles.

Spis treści

Introduction

Low Floor, High Ceiling Tasks

Youcubed Summer Camp

Memorization versus 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: Seeing Patterns inside Numbers

Visualize: Visualizing Numbers

Play: What Could It Be?

Investigate: How Flexible Is a Number?

Big Idea 2: Building and Designing with Shapes and Angles

Visualize: Tile It!

Play: Those Crazy Rep–Tiles

Investigate: Polyiamonds

Big Idea 3: Making and Naming Number Patterns

Visualize: Finding Fibonacci

Play: Pattern Carnival

Investigate: All Hail!

Big Idea 4: Units Are a Relationship

Visualize: It s All in the Axes

Play: Measure Up

Investigate: 10,000 Steps

Big Idea 5: Modeling with Unit Fractions

Visualize: Perplexing Measures

Play: Tangram Designs

Investigate: Pixeled Fractions

Big Idea 6: Fraction Equivalence

Visualize: Painting Pieces

Play: Color–Coding Fractions

Investigate: Tiling Rectangles

Big Idea 7: Illustrating Multiplication and Division

Visualize: Visual Proof

Play: Cover the Field

Investigate: Table Patterns

Big Idea 8: Using Operations Flexibly

Visualize: How Crowded Is the Crowd?

Play: Target 20

Investigate: Supply Parade

Big Idea 9: What Is a Decimal?

Visualize: Finding the Better Deal

Play: Decimals on a Line

Investigate: Can You Make It?

About the Authors

Acknowledgments

Index

O autorze

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 doctoral candidate at Stanford University, a professional developer, and a former classroom teacher. She works with teachers and school leaders across the U.S. to develop 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.

Blurb

Engage Your Students in Visual, Creative Explorations of the Big Ideas in Mathematics

The Mindset Mathematics series offers a unique, research–based visual approach to exploring the big ideas in mathematics, which is essential to future mathematics success. This hands–on resource is for any teacher who wants to engage their fourth grade students in reasoning and persisting through problems and provides activities that will engage students′ interest and show them the many ways that mathematics is important in their lives.

During their work with tens of thousands of teachers, authors Jo Boaler, Jen Munson, and Cathy Williams heard the same message: Teachers want to incorporate more brain science into their mathematics instruction, but they need guidance in the techniques that work best to promote learning of mathematics concepts. In this much–needed volume, the authors clearly show what the big ideas are at this grade level, why they are important to know, and how students can best learn those big ideas.

Filled with engaging questions, open–ended tasks, and four–color visuals, Mindset Mathematics is designed to be flexible so that it can be used with any current curriculum. All of the activities and tasks include instructions for launching in the classroom, suggestions for facilitating dynamic discussions, and guidance for what to look for in student thinking as it develops.