Mathematical Mindsets E-Book

Jo Boaler

• Herausgeber: John Wiley & Sons
• Kategorie: Bildung
• Serie: Mindset Mathematics
• Sprache: Englisch
• Veröffentlichungsjahr: 2015

Seitenzahl: 445

Beschreibung

Banish math anxiety and give students of all ages a clear roadmap to success Mathematical Mindsets provides practical strategies and activities to help teachers and parents show all children, even those who are convinced that they are bad at math, that they can enjoy and succeed in math. Jo Boaler--Stanford researcher, professor of math education, and expert on math learning--has studied why students don't like math and often fail in math classes. She's followed thousands of students through middle and high schools to study how they learn and to find the most effective ways to unleash the math potential in all students. There is a clear gap between what research has shown to work in teaching math and what happens in schools and at home. This book bridges that gap by turning research findings into practical activities and advice. Boaler translates Carol Dweck's concept of 'mindset' into math teaching and parenting strategies, showing how students can go from self-doubt to strong self-confidence, which is so important to math learning. Boaler reveals the steps that must be taken by schools and parents to improve math education for all. Mathematical Mindsets: * Explains how the brain processes mathematics learning * Reveals how to turn mistakes and struggles into valuable learning experiences * Provides examples of rich mathematical activities to replace rote learning * Explains ways to give students a positive math mindset * Gives examples of how assessment and grading policies need to change to support real understanding Scores of students hate and fear math, so they end up leaving school without an understanding of basic mathematical concepts. Their evasion and departure hinders math-related pathways and STEM career opportunities. Research has shown very clear methods to change this phenomena, but the information has been confined to research journals--until now. Mathematical Mindsets provides a proven, practical roadmap to mathematics success for any student at any age.

Leseprobe

Table of Contents

Title Page

Copyright

Foreword

Introduction: The Power of Mindset

Chapter 1: The Brain and Mathematics Learning

Chapter 2: The Power of Mistakes and Struggle

Mistakes in Life

Chapter 3: The Creativity and Beauty in Mathematics

Conclusion

Chapter 4: Creating Mathematical Mindsets: The Importance of Flexibility with Numbers

Number Sense

What about Math Facts?

How Important Is Math Practice?

What about Older Students?

Math Apps and Games

Conclusion

Chapter 5: Rich Mathematical Tasks

Case 1. Seeing the Openness of Numbers

Case 2. Growing Shapes: The Power of Visualization

Case 3. A Time to Tell?

Case 4. Seeing a Mathematical Connection for the First Time (Pascal's Triangle)

Case 5. The Wonders of Negative Space

Case 6. From Math Facts to Math Excitement

From Cases of Mathematics Excitement to the Design of Tasks

Conclusion

Chapter 6: Mathematics and the Path to Equity

The Elitist Construction of Math

The Myth of the Mathematically Gifted Child

When Math Inequalities in Course Placement Become Illegal

Equitable Strategies

Conclusion

Chapter 7: From Tracking to Growth Mindset Grouping

Opportunities to Learn

De-Tracking

Growth Mindset Grouping

Teaching Heterogeneous Groups Effectively: The Mathematics Tasks

Teaching Heterogeneous Groups Effectively: Complex Instruction

Conclusion

Chapter 8: Assessment for a Growth Mindset

Race to Nowhere

Assessment for Learning

Developing Student Self-Awareness and Responsibility

Advice on Grading

Conclusion

Chapter 9: Teaching Mathematics for a Growth Mindset

Encourage All Students

Believe in All of Your Students

Value Struggle and Failure

Give Growth Praise and Help

Opening Mathematics

Conclusion

References

Appendix A

Appendix B

About the Author

Index

End User License Agreement

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Guide

Cover

Table of Contents

Begin Reading

List of Illustrations

Chapter 1: The Brain and Mathematics Learning

Figure 1.1 A synapse fires

Figure 1.2 The Black Cab of London

Figure 1.3 Map of London

Figure 1.4 The hippocampus

Figure 1.5 Students with a growth mindset outperform those with a fixed mindset in mathematics

Figure 1.6 Mindset and mathematics

Chapter 2: The Power of Mistakes and Struggle

Figure 2.1 Brain activity in individuals with a fixed and a growth mindset

Figure 2.2 Feel comfortable being wrong

Figure 2.3 Try seemingly wild ideas

Figure 2.4 Are open to different experiences

Figure 2.5 Play with ideas without judging them

Figure 2.6 Are willing to go against traditional ideas

Figure 2.7 Keep going through difficulties

Figure 2.8 Students learn about brain growth

Figure 2.9 Student's poster of brain with messages

Figure 2.10 Solving the skateboard problem

Chapter 3: The Creativity and Beauty in Mathematics

Figure 3.1 Maryam Mirzakhani, winner of the Fields Medal, 2015

Figure 3.2 Some of the mathematics discussed in Jenya Sapir's mathematics PhD defense

Figure 3.3 The mathematics in snowflakes

Figure 3.4 Water molecules

Figure 3.5 Dolphins communicate

Figure 3.6 A spider web

Chapter 4: Creating Mathematical Mindsets: The Importance of Flexibility with Numbers

Figure 4.1 Mathematics methods and concepts

Figure 4.2 How Close to 100?

Figure 4.3 Math cards

Figure 4.4 Mathematics strategies and achievement

Figure 4.5 A mindset intervention

Figure 4.6 Wuzzit Trouble figures

Figure 4.7 Wuzzit Trouble puzzle

Figure 4.8 The Mathbreakers game

Figure 4.9 The Number Rack app

Figure 4.10 Two Motion Math games: Hungry Fish and Pizza

Chapter 5: Rich Mathematical Tasks

Figure 5.1 Visual solutions to 18 × 5

Figure 5.2 Students' work

Figure 5.3 The Raindrop Method—cubes come from the sky like raindrops

Figure 5.4 The Bowling Alley Method—cubes are added like pins in a bowling alley

Figure 5.5 The Volcano Method—the middle column of cubes grows high and the rest follow like lava erupting from a volcano

Figure 5.6 The Parting of the Red Sea Method—the columns part and the middle column arrives

Figure 5.7 The Similar Triangles Method—the layers can be seen as triangles

Figure 5.8 The Slicing Method—the layers can be viewed diagonally

Figure 5.9 “Stairway to Heaven, Access Denied”—from Wayne's World

Figure 5.10 The Square Method—the shapes can be rearranged as a square each time

Figure 5.11 The Square Method 2

Figure 5.12 A 36-sided fence yields the largest enclosure area

Figure 5.13 The triangle formed from a 1-meter fence section

Figure 5.14 What is the volume of a lemon?

Figure 5.15 Calculating a lemon's volume by sections

Figure 5.16 Pascal's triangle in Cuisenaire rods

Figure 5.17 Parabola Dilemma

Figure 5.18 Third-grade student completes “How close to 100?”

Figure 5.19 Students share solutions to 1 ÷ 2/3

Figure 5.20 Rectangles with an area of 24

Figure 5.21 Color coding angles

Figure 5.22 Alonzo's extension problem

Figure 5.23 Teachers work on paper folding task

Chapter 6: Mathematics and the Path to Equity

Figure 6.1 Balancing different aspects of mathematics

Figure 6.2 Students work together in a group

Chapter 7: From Tracking to Growth Mindset Grouping

Figure 7.1 Open-ended tasks from Youcubed

Figure 7.2 SMILE cards

Figure 7.3 Pre-assessment test scores

Figure 7.4 Year 1 Assessment test scores

Figure 7.5 Year 2 Assessment test scores

Figure 7.6 Complex instruction

Figure 7.7 CPM task

Figure 7.8 Students work on finding the perimeter of a shape built from algebra lab gear

Figure 7.9 Students work to produce an equation representing the length of shoelaces needed for different shoes

Figure 7.10 Random assignment of groups and roles

Figure 7.11 A teacher generates posters of students' preferred group work behaviors

Chapter 8: Assessment for a Growth Mindset

Figure 8.1 Race to Nowhere poster

Figure 8.2 Delia, Beyond Measure

Figure 8.3 Assessment for Learning

Figure 8.4 Self-reflection faces

Figure 8.5 Traffic lights

Figure 8.6 Jigsaw groups

Figure 8.7 Math doodle

Chapter 9: Teaching Mathematics for a Growth Mindset

Figure 9.1 Inspiring all math learners

Figure 9.2 Algebra examples

Figure 9.3 Stairs

Figure 9.4 Pattern strip

Figure 9.5 Dog biscuits solution

Figure 9.6 Color coding brownies

Figure 9.7 Division quilts

Figure 9.8 A painted cube

Figure 9.9 Extended cube problem

Figure 9.10 Nine slices

Figure 9.11 Nine slices divided into quadrants

Figure 9.12 Tethered goat model

Figure 9.13 Bracelets for sale

Figure 9.14 Tap Tap Blocks

Figure 9.15 A Tap Tap Blocks shape from six different angles

List of Tables

Chapter 3: The Creativity and Beauty in Mathematics

Table 3.1 Fortune 500 “most valued” skills in 1970

Table 3.2 Fortune 500 “most valued” skills in 1999

JO BOALER

FOREWORD BY CAROL DWECK

MATHEMATICAL MINDSETS

Unleashing Students' POTENTIAL Through Creative Math, Inspiring Messages and INNOVATIVE TEACHING

Copyright © 2016 by Jo Boaler. All rights reserved.

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Library of Congress Cataloging-in-Publication Data

Boaler, Jo, 1964–

    Mathematical mindsets : unleashing students' potential through creative math, inspiring messages, and innovative teaching / Jo Boaler.

      1 online resource.

    “A Wiley brand.”

    Includes bibliographical references and index.

    Description based on print version record and CIP data provided by publisher; resource not viewed.

    ISBN 978-1-118-41827-7 (pdf) – ISBN 978-1-118-41553-5 (epub) – ISBN 978-0-470-89452-1 (pbk.)

1. Mathematics–Study and teaching (Middle school) 2. Mathematics–Study and teaching (Secondary) I. Title.

    QA135.6

    510.71′2–dc23

2015031316

Cover Design: Wiley

Cover Image: Illustration © agsandrew/Shutterstock; Schoolchildren © monkeybusinessimages/iStockphoto.com

FIRST EDITION

Foreword

One of my former Stanford students teaches fourth grade in the South Bronx, an area of New York City with many underserved, underachieving minority students. Her students invariably believe they are bad at math, and if you looked at their past performance, you might be tempted to think so too. And yet, after one year in her class, her fourth graders became the #1 fourth-grade class in the state of New York: 100% of them passed the state math test, with 90% of them earning the top score. And this is just one of many examples of how all students can learn math.

When people think that some kids just can't do math, that success in math is reserved for only certain kids, thought of as “smart,” or that it's just too late for kids who haven't had the right background, then they can easily accept that many students fail math and hate math. In fact, we have found that many teachers actually console their students by telling them not to worry about doing poorly in math because not everyone can excel in it. These adult enablers—parents and teachers alike—allow kids to give up on math before they've barely gotten started. No wonder more than a few students simply dismiss their own poor performance by declaring: “I'm not a math person.”

Where do parents, teachers, and students get the idea that math is just for some people? New research shows that this idea is deeply embedded in the field of mathematics. Researchers polled scholars (at American universities) in a range of disciplines. They asked them how much they thought that success in their field depended on fixed, innate ability that cannot be taught, as opposed to hard work, dedication, and learning. Of all the STEM fields (science, technology, engineering, and math), math scholars were the most extreme in emphasizing fixed, innate ability (Leslie, Cimpian, Meyer, & Freeland, 2015). Other researchers are finding that many math instructors begin their courses by referring to students who have the aptitude and those who do not. One college instructor, on the first day of an introductory college course, was heard to say, “If it's not easy for you, you don't belong here” (Murphy, Garcia, & Zirkel, in prep). If this message is passed down from generation to generation, no wonder students are afraid of math. And no wonder they conclude they're not math people when it doesn't come easily.

But when we begin to see evidence that most students (and maybe almost all students) are capable of excelling in and enjoying math, as the following chapters show, it is no longer acceptable that so many students fail math and hate math. So what can we do to make math learning happen for all students? How can we help teachers and children believe that math ability can be developed, and then show teachers how to teach math in a way that brings this belief to life? That's what this book is about.

In this unique and wonderful book, Jo Boaler distills her years of experience and her powerful wisdom to show teachers exactly how to present math work, structure math problems, guide students through them, and give feedback in a way that helps students toward a “growth mindset” and keeps them there. Boaler is one of those rare and remarkable educators who not only know the secret of great teaching but also know how to give that gift to others. Thousands of teachers have learned from her, and here's what they say:

“Throughout my schooling years …I was left feeling stupid and incapable of doing [math] …I cannot tell you the relief I now have that I can learn math myself, and I can teach students that they can too.”

“[You have] helped me think about the transition to common core and how to help my students develop a love and curiosity for math.”

“I was searching for a process of learning math that would change the attitude of students from dislike to enjoy …this was the change I needed.”

Imagine your students joyfully immersed in really hard math problems. Imagine them begging to have their mistakes discussed in front of the class. Imagine them saying, “I am a math person!” This utopian vision is happening in classrooms around the world, and as you follow the advice in this book, you may well see it happening in your classroom too.

Carol DweckProfessor of psychology and author ofMindset: The New Psychology of Success

Introduction: The Power of Mindset

I remember clearly the fall afternoon that I sat down with my dean in her office, waiting for what would turn out to be a very important meeting. I had only recently returned to Stanford University from England where I was the Marie Curie Professor for Mathematics Education. I was still getting used to the change from the grey cloudy skies that seemed to be my constant companion during the three years I was on the Sussex coast in England to the sunshine that shines down on Stanford's campus almost continuously. I walked into the dean's office that day with some anticipation, as I was going to meet Carol Dweck for the first time. I was a little nervous to meet the famous researcher whose books on mindset had revolutionized people's lives, across continents, and whose work had moved governments, schools, parents, and even leading sports teams to approach life and learning differently.