A Mind For Numbers Read online

  “Being good at science and mathematics isn’t just something you are; it’s something you become. This users’ guide to the brain unmasks the mystery around achieving success in mathematics and science. I have seen far too many students opt out when they hit a rough patch. But now that learners have a handy guide for ‘knowing better,’ they will also be able to ‘do better.’”

  —SHIRLEY MALCOM, HEAD OF EDUCATION AND HUMAN RESOURCES PROGRAMS, AMERICAN ASSOCIATION FOR THE ADVANCEMENT OF SCIENCE

  “A Mind for Numbers is an excellent book about how to approach mathematics, science, or any realm where problem solving plays a prominent role.”

  —J. MICHAEL SHAUGHNESSY, PAST PRESIDENT OF THE NATIONAL COUNCIL OF TEACHERS OF MATHEMATICS

  “I have not been this excited about a book in a long time. Giving students deep knowledge on how to learn will lead to higher retention and student success in every field. It is a gift that will last them a lifetime.”

  —ROBERT R. GAMACHE, PH.D., ASSOCIATE VICE PRESIDENT, ACADEMIC AFFAIRS, STUDENT AFFAIRS, AND INTERNATIONAL RELATIONS, UNIVERSITY OF MASSACHUSETTS, LOWELL

  “A Mind for Numbers helps put students in the driver’s seat—empowering them to learn more deeply and easily. This outstanding book is also a useful resource for instructional leaders. Given the urgent need for America to improve its science and math education so it can stay competitive, A Mind for Numbers is a welcome find.”

  —GEOFFREY CANADA, PRESIDENT, HARLEM CHILDREN’S ZONE

  “An ingeniously accessible introduction to the science of human cognition—along with practical advice on how to think better.”

  —JAMES TARANTO, THE WALL STREET JOURNAL

  “It’s easy to say ‘work smarter, not harder,’ but Barbara Oakley actually shows you how to do just that, in a fast-paced and accessible book that collects tips based on experience and sound science. In fact, I’m going to incorporate some of these tips into my own teaching.”

  —GLENN HARLAN REYNOLDS, BEAUCHAMP BROGAN DISTINGUISHED PROFESSOR OF LAW, THE UNIVERSITY OF TENNESSEE

  “A Mind for Numbers is a splendid resource for how to approach mathematics learning and, in fact, learning in any area. Barbara Oakley’s authoritative guide is based on the latest research in the cognitive sciences, and provides a clear, concise, and entertaining road map for how to get the most out of learning. This is a must-read for anyone who has struggled with mathematics and anyone interested in enhancing their learning experience.”

  —DAVID C. GEARY, CURATORS’ PROFESSOR OF PSYCHOLOGICAL SCIENCES AND INTERDISCIPLINARY NEUROSCIENCE, UNIVERSITY OF MISSOURI

  “For students afraid of math and science and for those who love the subjects, this engaging book provides guidance in establishing study habits that take advantage of how the brain works.”

  —DEBORAH SCHIFTER, PRINCIPAL RESEARCH SCIENTIST, SCIENCE AND MATHEMATICS PROGRAMS, EDUCATION DEVELOPMENT CENTER, INC.

  JEREMY P. TARCHER/PENGUIN

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  Copyright © 2014 by Barbara Oakley

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  Library of Congress Cataloging-in-Publication Data

  Oakley, Barbara A.

  A mind for numbers : how to excel at math and science (even if you flunked algebra) / Barbara Oakley, Ph.D.

  p. cm.

  Includes bibliographical references and index.

  ISBN 978-1-101-62161-5

  1. Math anxiety. 2. Mathematics—Study and teaching—Psychological aspects. 3. Educational psychology. I. Title.

  QA11.2.O33 2014 2014003665

  501'.9—dc23

  Version_3

  A Mind for Numbers is dedicated to Dr. Richard Felder, whose brilliance and passion have launched extraordinary improvements worldwide in the teaching of science, mathematics, engineering, and technology. My own successes, like those of tens of thousands of other educators, grow out of his fertile educational approaches. Il miglior maestro.

  The Law of Serendipity: Lady Luck favors the one who tries

  contents

  PRAISE FOR A MIND FOR NUMBERS

  TITLE PAGE

  COPYRIGHT

  DEDICATION

  EPIGRAPH

  FOREWORD by Terrence J. Sejnowski, Francis Crick Professor, Salk Institute for Biological Studies

  PREFACE by Jeffrey D. Karpicke, James V. Bradley Associate Professor of Psychological Sciences, Purdue University

  NOTE TO THE READER

  1 Open the Door

  2 Easy Does It:

  Why Trying Too Hard Can Sometimes Be Part of the Problem

  3 Learning Is Creating:

  Lessons from Thomas Edison’s Frying Pan

  4 Chunking and Avoiding Illusions of Competence:

  The Keys to Becoming an “Equation Whisperer”

  5 Preventing Procrastination:

  Enlisting Your Habits (“Zombies”) as Helpers

  6 Zombies Everywhere:

  Digging Deeper to Understand the Habit of Procrastination

  7 Chunking versus Choking:

  How to Increase Your Expertise and Reduce Anxiety

  8 Tools, Tips, and Tricks

  9 Procrastination Zombie Wrap-Up

  10 Enhancing Your Memory

  11 More Memory Tips

  12 Learning to Appreciate Your Talent

  13 Sculpting Your Brain

  14 Developing the Mind’s Eye through Equation Poems

  15 Renaissance Learning

  16 Avoiding Overconfidence:

  The Power of Teamwork

  17 Test Taking

  18 Unlock Your Potential

  AFTERWORD BY DAVID B. DANIEL, PH.D., PROFESSOR, PSYCHOLOGY DEPARTMENT, JAMES MADISON UNIVERSITY

  ACKNOWLEDGMENTS

  ENDNOTES

  REFERENCES

  CREDITS

  INDEX

  foreword

  Your brain has amazing abilities, but it did not come with an instruction manual. You’ll find that manual in A Mind for Numbers. Whether you’re a novice or an expert, you will find great new ways to improve your skills and techniques for learning, especially related to math and science.

  Henri Poincaré was a nineteenth-century mathematician who once described how he cracked a difficult mathematical problem that he had been intensively working on for weeks without success. He took a vacation. As he was getting on a bus in the south of France, the answer to the problem suddenly came to him, unbidden, from a part of his brain that had continued to work on the problem while he was enjoying his vacation. He knew he had the right solution even though he did not write down the details until he later returned to Paris.

  What worked for Poincaré can work for
you too, as Barbara Oakley explains in this insightful book. Surprisingly, your brain can also work on a problem even while you are sleeping and are not aware of anything. But it does this only if you concentrate on trying to solve the problem before falling asleep. In the morning, as often as not, a fresh insight will pop to mind that can help you solve the problem. The intense effort before a vacation or falling asleep is important for priming your brain; otherwise it will work on some other problem. There is nothing special about math or science in this regard—your brain will work just as hard at solving social problems as on math and science problems, if that is what has been on your mind recently.

  You will find many more insights and techniques about how to learn effectively in this fascinating and timely book, which looks at learning as an adventure rather than hard labor. You will see how you can fool yourself about whether you actually know the material; you will find ways to hold your focus and space out your practice; and you will learn to condense key ideas so you can hold them more easily in your mind. Master the simple, practical approaches outlined here and you will be able to learn more effectively and with less frustration. This wonderful guide will enrich both your learning and your life.

  —Terrence J. Sejnowski, Francis Crick Professor, Salk Institute for Biological Studies

  preface

  This book can make a profound difference in how you look at and understand learning. You will learn the simplest, most effective, and most efficient techniques researchers know about how to learn. And you’ll have fun while you’re doing it.

  What’s surprising is that a lot of learners use ineffective and inefficient strategies. In my laboratory, for example, we have surveyed college students about their learning. They most commonly use the strategy of repeated reading—simply reading through books or notes over and over. We and other researchers have found that this passive and shallow strategy often produces minimal or no learning. We call this “labor in vain”—students are putting in labor but not getting anywhere.

  We don’t engage in passive rereading because we are dumb or lazy. We do it because we fall prey to a cognitive illusion. When we read material over and over, the material becomes familiar and fluent, meaning it is easy for our minds to process. We then think that this easy processing is a sign that we have learned something well, even though we have not.

  This book will introduce you to this and other illusions of learning and give you tools to overcome them. And it will introduce great new tools, such as retrieval practice, that can have a powerful effect in boosting the “bang for your buck” from your time spent in learning. It’s a deeply practical yet inspiring book that helps you see clearly why some approaches are so much more effective than others.

  We’re on the edge of an explosion in knowledge about how to learn most effectively. In this new world of insight, you’ll find A Mind for Numbers to be an indispensable guide.

  —Jeffrey D. Karpicke, James V. Bradley Associate Professor of Psychological Sciences, Purdue University

  note to the reader

  People who work professionally with math and science often spend years discovering effective learning techniques. Once they’ve figured these methods out, great! They have unwittingly passed the initiation rites needed to join the mysterious society of math and science practitioners.

  I’ve written this book to lay out these simple techniques so that you can immediately begin using them. What takes years for practitioners to discover is now at your fingertips.

  Using these approaches, no matter what your skill levels in math and science, you can change your thinking and change your life. If you’re already an expert, this peek under the mental hood will give you ideas for turbocharging successful learning, including counterintuitive test-taking tips and insights that will help you make the best use of your time on homework and problem sets. If you’re struggling, you’ll see a structured treasure trove of practical techniques that walk you through what you need to do to get on track. If you’ve ever wanted to become better at anything, this book will help serve as your guide.

  This book is for high school students who love art and English classes but loathe math. It is meant as well as for college students who already excel in math, science, engineering, and business, but who suspect there are mental tools to be added to their learning toolkits. It’s for parents whose children are either falling off the math track or trying to rocket toward math and science stardom. It’s for the frazzled nine-to-five worker who hasn’t been able to pass an important certification test, and for the night-shift convenience store clerk who has dreamed of becoming a nurse—or even a doctor. It’s for the growing army of homeschoolers. It’s for teachers and professors—not only in math, science, engineering, and technology, but also in fields such as education, psychology, and business. It’s for the retiree who finally has the time to embrace new knowledge in computing, for example, or the intricacies of great cooking. And it’s for readers of all ages who love to learn a little about everything.

  In short, this book is for you. Enjoy!

  —Barbara Oakley, Ph.D., P.E., Fellow, American Institute for Medical & Biological Engineering and Vice President, Institute for Electrical and Electronics Engineers—Engineering in Medicine and Biology Society

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  open the door

  What are the odds you’d open your refrigerator door and find a zombie in there, knitting socks? The odds are about the same that a touchy-feely, language-oriented person like me would end up as a professor of engineering.

  Growing up, I hated math and science. I flunked my way through high school math and science courses, and only started studying trigonometry—remedial trigonometry—when I was twenty-six years old.

  As a youngster, even the simple concept of reading a clock face didn’t seem to make sense to me. Why should the little hand point toward the hour? Shouldn’t it be the big hand, since the hour was more important than the minute? Did the clock read ten ten? Or one fifty? I was perpetually confused. Worse than my problems with clocks was the television. In those days before the remote control, I didn’t even know which button turned the television on. I watched a show only in the company of my brother or sister. They not only could turn the TV on, but could also tune the channel to the program we wanted to watch. Nice.

  All I could conclude, looking at my technical ineptitude and flunking grades in math and science, was that I wasn’t very smart. At least, not that way. I didn’t realize it then, but my self-portrait as being technically, scientifically, and mathematically incapable was shaping my life. At the root of it all was my problem with mathematics. I had come to think of numbers and equations as akin to one of life’s deadly diseases—to be avoided at all costs. I didn’t realize then that there were simple mental tricks that could have brought math into focus for me, tricks that are helpful not only for people who are bad at math, but also for those who are already good at it. I didn’t understand that my type of thinking is typical of people who believe they can’t do math and science. Now, I realize that my problem was rooted in two distinctly different modes for viewing the world. Back then, I only knew how to tap one mode for learning—and the result was that I was deaf to the music of math.

  Mathematics, as it’s generally taught in American school systems, can be a saintly mother of a subject. It climbs logically and majestically from addition through subtraction, multiplication, and division. Then it sweeps up toward the heavens of mathematical beauty. But math can also be a wicked stepmother. She is utterly unforgiving if you happen to miss any step of the logical sequence—and missing a step is easy to do. All you need is a disruptive family life, a burned-out teacher, or an unlucky extended bout with illness—even a week or two at a critical time can throw you off your game.

  Or, as was the case with me, simply no interest or seeming talent whatsoever.

  In seventh grade, disaster struck my family. My father lost his job after
a serious back injury. We ended up in a hardscrabble school district where a crotchety math teacher made us sit for hours in the sweltering heat doing rote addition and multiplication. It didn’t help that Mr. Crotchety refused to provide any explanations. He seemed to enjoy seeing us flounder.

  Me at age ten with Earl the lamb. I loved critters, reading, and dreaming. Math and science weren’t on my play list.

  By this time, I not only didn’t see any use for math—I actively loathed it. And as far as the sciences went—well, they didn’t. In my first chemistry experiment, my teacher chose to give my lab partner and me a different substance than the rest of the class. He ridiculed us when we fudged the data in an attempt to match everyone else’s results. When my well-meaning parents saw my failing grades and urged me to get help during the teacher’s office hours, I felt I knew better. Math and science were worthless, anyway. The Gods of Required Coursework were determined to shove math and science down my throat. My way of winning was to refuse to understand anything that was taught, and to belligerently flunk every test. There was no way to outmaneuver my strategy.

  I did have other interests, though. I liked history, social studies, culture, and especially language. Luckily, those subjects kept my grades afloat.

  Right out of high school, I enlisted in the army because they would actually pay me to learn another language. I did so well in studying Russian (a language I’d selected on a whim) that an ROTC scholarship came my way. I headed off to the University of Washington to get a bachelor’s degree in Slavic languages and literature, where I graduated with honors. Russian flowed like warm syrup—my accent was so good that I found myself on occasion mistakenly taken for a native speaker. I spent lots of time gaining this expertise—the better I got, the more I enjoyed what I was doing. And the more I enjoyed what I was doing, the more time I spent on it. My success reinforced my desire to practice, and that built more success.