"I remember as a kid in school being told by teachers to think harder and having no idea what to do. This book solves that once and for all. We now have a guide for people of all ages to learn how to think more effectively. I highly recommend this book."--Jack Canfield, cocreator of the New York Times best-selling Chicken Soup for the Soul® series andThe Success Principles
"Think...fail...question...understand...change...learn: in their powerful new book, Burger and Starbird show students, teachers, and everyone else how to harness the genius of learning.The 5 Elements argues that the door to knowledge is not opened by a magical test. Instead, the key is for each of us to boldly embrace a willingness to fail while organizing persistent approaches to thinking. Even more than helping one master content, this book can lead to a satisfying and rewarding life of the mind."--Dennis Van Roekel, president of the National Education Association
"The authors invoke Michael Jordan, Warren Buffett, and Winston Churchill to illustrate practical approaches--including failing--to understanding, creativity, and wisdom. Their observations apply to honing any skill from sports and school to leadership and citizenship. Knowing how to listen and learn has become a rare art--The 5 Elements is a timely tutorial."--Janet Brown, executive director of the Commission on Presidential Debates
"In this compact and remarkable book, two renowned professors share decades of teaching experience with anyone--from students to business people--seeking advice on how to improve skills and expand learning. It should be read, studied, and cherished--then reread."--Fay Vincent, former commissioner of Major League Baseball and former president of Columbia Pictures
"This book is just what American education needs. It guarantees invention and discovery."--Barbara Morgan, former NASA "Teacher in Space" astronaut
"The 5 Elements is an enormously insightful examination of what constitutes effective thinking. Everyone will find something of value in it."--Morton O. Schapiro, president of Northwestern University
"I highly recommend this book for instructors who care more about their students than test scores, for students who care more about learning than their GPA, for leaders of society and masters of the universe who care more about serving the public good than increasing their profit margin, and for artists who constantly remind us of the human condition.The 5 Elements of Effective Thinking provides comfort in a world that has lost its equilibrium."--Christopher J. Campisano, director of Princeton University's Program in Teacher Preparation
"Our brain is our greatest asset in life, so it is a 'no brainer' that we should invest some time learning how to use it effectively. In this concise and carefully crafted book, renowned professors Burger and Starbird demonstrate their talent for making difficult concepts accessible. An average reader can peruse this book in only a few hours, but for many people those will be the best hours ever spent on a book. Highly recommended."--Brett Walter, president of the Homeschool Buyers Co-op
"Edward Burger and Michael Starbird became renowned scholars and educators by demonstrating that mathematical expertise is within the reach of the general population and not confined to those with the 'right' aptitude. With the publication of this remarkably wise and useful book, they extend their pedagogical principles to the general realm of practical affairs and the entire range of academic endeavor. Regardless of the reader's background,The 5 Elements offers highly applicable and original lessons on how to think."--John W. Chandler, president emeritus of Hamilton College and W
The 5 Elements of Effective Thinking
By Edward B. Burger Michael StarbirdPRINCETON UNIVERSITY PRESS
Copyright © 2012 Edward B. Burger and Michael Starbird
All right reserved.
ISBN: 978-0-691-15666-8
Contents
Preface Thinking Makes the Difference...................................................viiIntroduction Elements of Effective Thinking, Learning, and Creating.....................1Earth 1. Grounding Your Thinking........................................................13Fire 2. Igniting Insights through Mistakes..............................................47Air 3. Creating Questions out of Thin Air...............................................73Water 4. Seeing the Flow of Ideas.......................................................95The Quintessential Element 5. Engaging Change...........................................119Summary A Way to Provoke Effective Thinking.............................................136Share Your Own Stories of Effective Thinking.............................................149Acknowledgments..........................................................................151About the Authors........................................................................155
Chapter One
Earth 1. Grounding Your Thinking Understand Deeply
He never did a thing so very bad. He don't know why he isn't quite as good As anyone.
–From "The Death of the Hired Man" by Robert Frost
Silas felt the nervous excitement that all students feel as their professor returns graded exams. When Silas saw the red "58%" on the top of his test paper, he was frustrated, annoyed, and bewildered. "I really knew the stuff on the test. I just made a bunch of stupid little mistakes. I really knew it. Really." And he really believed he knew it. Really. Sadly, such unpleasant surprises do not necessarily end after we receive our diplomas. Many people spend their entire careers confidently (and erroneously) thinking they know more and deserve more than their yearly evaluations, salaries, and success seem to reflect.
Understanding is not a yes-or-no proposition; it's not an on-or-off switch. Silas spent hours studying for his test. But he spent that time memorizing facts rather than building a deep understanding. He would have earned a higher grade had he invested the same amount of time mastering the fundamentals, identifying essential themes, attaching each idea to that core structure, and, finally, imagining what surrounds or extends the material he was studying. Instead, Silas's strategy was like that of a well-intentioned elementary school student who meticulously memorizes the mechanics of adding two-digit numbers but has no idea why the process works, and, as a result, finds adding three-digit numbers as alien as visiting another planet. Silas's understanding was, at best, thin and fragile. Even tiny variations threw him, because he viewed his job as pinning down a certain number of isolated facts rather than understanding the meaning and connections of the ideas.
When you learn anything, go for depth and make it rock solid. If you learn a piece of music for the piano, then, instead of just memorizing finger movements, learn to hear each note and understand the structure of the piece. Ask yourself, "Can I play the notes of the right hand while just humming the notes of the left hand?" If you study the Civil War, rather than memorizing some highlights—Lincoln was president; Lee was a general; slavery played a role—you can try to understand the background, competing forces, and evolving social values that ignited the bloody conflict. When you make political decisions, instead of focusing on a candidate's good looks and fifteen-second sound bites, you can objectively learn about the issues and develop your own reasoned opinions.
You can understand anything better than you currently do. Setting a higher standard for yourself for what you mean by understanding can revolutionize how you perceive the world. The following steps illustrate why a deep understanding is essential to a solid foundation for future thinking and learning.
Understand simple things deeply
The most fundamental ideas in any subject can be understood with ever-increasing depth. Professional tennis players watch the ball; mathematicians understand a nuanced notion of number; successful students continue to improve their mastery of the concepts from previous chapters and courses as they move toward the more advanced material on the horizon; successful people regularly focus on the core purpose of their profession or life. True experts continually deepen their mastery of the basics.
Trumpeting understanding through a note-worthy lesson. Tony Plog is an internationally acclaimed trumpet virtuoso, composer, and teacher. A few years ago we had the opportunity to observe him conducting a master class for accomplished soloists. During the class, each student played a portion of his or her selected virtuosic piece. They played wonderfully. Tony listened politely and always started his comments, "Very good, very good. That is a challenging piece, isn't it?" As expected, he proceeded to give the students advice about how the piece could be played more beautifully, offering suggestions about physical technique and musicality. No surprise. But then he shifted gears.
He asked the students to play a very easy warm-up exercise that any beginning trumpet player might be given. They played the handful of simple notes, which sounded childish compared to the dramatically fast, high notes from the earlier, more sophisticated pieces. After they played the simple phrase, Tony, for the first time during the lesson, picked up the trumpet. He played that same phrase, but when he played it, it was not childish. It was exquisite. Each note was a rich, delightful sound. He gave the small phrase a delicate shape, revealing a flowing sense of dynamics that enabled us to hear meaning in those simple notes. The students' attempts did not come close—the contrast was astounding. The fundamental difference between the true master and the talented students clearly occurred at a far more basic level than in the intricacies of complex pieces. Tony explained that mastering an efficient, nuanced performance of simple pieces allows one to play spectacularly difficult pieces with greater control and artistry.
The lesson was simple. The master teacher suggested that the advanced students focus more of their time on practicing simple pieces intensely—learning to perform them with technical efficiency and beautiful elegance. Deep work on simple, basic ideas helps to build true virtuosity—not just in music but in everything.
What is deep understanding? How can you realize when you don't know something deeply? When the advanced trumpet students played the simple phrase, they played every note and it sounded good to them. Before hearing the contrast between their renditions and the true virtuoso's performance, the students might not have realized that it was possible to play that phrase far, far better.
In everything you do, refine your skills and knowledge about fundamental concepts and simple cases. Once is never enough. As you revisit fundamentals, you will find new insights. It may appear that returning to basics is a step backward and requires additional time and effort; however, by building on firm foundations you will soon see your true abilities soar higher and faster.
* A WAY TO PROVOKE EFFECTIVE THINKING ...
Master the basics
Consider a skill you want to improve or a subject area that you wish to understand better. Spend five minutes writing down specific components of the skill or subject area that are basic to that theme. Your list will be a free-flowing stream of consciousness. Now pick one of the items on your list, and spend thirty minutes actively improving your mastery of it. See how working deeply on the basics makes it possible for you to hone your skill or deepen your knowledge at the higher levels you are trying to attain. Apply this exercise to other things you think you know or would like to know.
* Illustration: A student's response in trying to understand basic economics
Step 1: A brainstorming list of components: Maximize profits; free markets; supply and demand; equilibrium of supply and demand. (Note that the student's list is neither organized nor complete, which is great.) Step 2: Improve understanding of "equilibrium of supply and demand": First, I need to understand what the graphs of the supply and demand curves mean. The horizontal axis is the quantity and the vertical axis is the price; so I see why the demand graph curves down to the right and the supply graph curves up to the right. I think that equilibrium is the point of intersection of those two graphs. But if the quantity level is to the left of that intersection, then the price for demand is higher than the price for supply. I don't know what that means. (Note that this student successfully identified a lack of understanding of a basic idea, namely, what the supply and demand graphs represent. He now knows what he should work on first. A firm understanding of that basic idea will allow him to progress further and faster in the future.)
... UNDERSTAND DEEPLY
The whole of science is merely a refinement of everyday thinking. –Albert Einstein
A commonsense approach leads to the core. Many of the most complicated, subtle, and profound ideas arise from looking unmercifully clearly at simple, everyday experiences. Calculus is one of the most influential concepts in history. It has fundamentally changed the way we experience life today—a wide range of technological innovations, from space exploration to plasma TVs, computers, and cell phones, would not exist without calculus. And calculus is based on thinking deeply about simple, everyday motion—like an apple falling from a tree.
In 1665, England suffered an epidemic of bubonic plague. Cambridge University was closed to stem the dreaded disease's spread, so Isaac Newton and the other students were sent home. Newton spent the next two years on his aunt's farm, during which time he formulated the fundamental ideas of calculus and the laws of physics. The famous story about Newton sitting under an apple tree when an apple fell on his head, giving him the idea of universal gravitation and calculus, may be almost literally true. Thinking about the speed of a falling apple can generate the idea of the derivative—the profound extension of the basic notion that speed equals distance divided by time. Thinking about how far the apple would fall if you knew its speed at each instant leads to the idea of the ITL∫ITL—the abstraction that distance equals speed multiplied by time.
The grandest, most cosmic ideas, such as how the planets move, arise from thinking deeply about an apple beaning Newton. Newton described the universe—the behavior of the sun, planets, and distant stars—using the same laws that describe everyday occurrences like apples falling from trees. The simple and familiar hold the secrets of the complex and unknown. The depth with which you master the basics influences how well you understand everything you learn after that.
Today, when math teachers are asked what makes calculus so difficult to teach, most reply, "My students don't know the basic mathematics that they saw in the eighth or ninth grade." One secret to mastering calculus is to truly master basic algebra. In any class, when preparing for your next exam, make sure you can earn a 100% on all the previous exams—if you can't, then you're not ready for the test looming in your future. Instructors should also embrace this fundamental reality and help their students have a firmer grasp of the basics that preceded the material currently being explored.
To learn any subject well and to create ideas beyond those that have existed before, return to the basics repeatedly. When you look back after learning a complicated subject, the basics seem far simpler; however, those simple basics are a moving target. As you learn more, the fundamentals become at once simpler but also subtler, deeper, more nuanced, and more meaningful. The trumpet virtuoso found limitless beauty in a simple exercise and, in turn, found deep insights into the more interesting difficult pieces.
* A WAY TO PROVOKE EFFECTIVE THINKING ...
Ask: What do you know?
Do you or don't you truly know the basics? Consider a subject you think you know or a subject you are trying to master. Open up a blank document on your computer. Without referring to any outside sources, write a detailed outline of the fundamentals of the subject. Can you write a coherent, accurate, and comprehensive description of the foundations of the subject, or does your knowledge have gaps? Do you struggle to think of core examples? Do you fail to see the overall big picture that puts the pieces together? Now compare your effort to external sources (texts, Internet, experts, your boss). When you discover weaknesses in your own understanding of the basics, take action. Methodically learn the fundamentals. Thoroughly understand any gap you fill in as well as its surrounding territory. Make these new insights part of your base knowledge and connect them with the parts that you already understood. Repeat this exercise regularly as you learn more advanced aspects of the subject (and save your earlier attempts so that you can look back and see how far you've traveled). Every return to the basics will deepen your understanding of the entire subject.
* Illustration: Voting
How well do you know the candidates running for office—their records, their positions? Write a list of issues that are important to you. Then list what you believe to be the positions of the candidates on each issue—their stated opinions, their voting records, and their other actions associated with the issue. Most voters will have inaccurate or only meager knowledge, particularly for candidates they don't support. Then look up the actual records and see the differences. Fleshing out your knowledge will lead to more informed decisions—on Election Day and beyond.
... UNDERSTAND DEEPLY
When faced with a difficult challenge—don't do it! In a speech delivered to Congress on May 25, 1961, John F. Kennedy challenged the country with the words "I believe that this nation should commit itself to achieving the goal, before this decade is out, of landing a man on the Moon and returning him safely to the Earth." On May 26, the National Space Council didn't suit up an astronaut. Instead their first goal was to hit the moon—literally. And just over three years later, NASA successfully smashed Ranger 7 into the moon at an impact velocity of 5,861 miles per hour (after the unmanned spacecraft transmitted over four thousand photographs of the lunar surface). It took fifteen ever-evolving iterations before the July 16, 1969, gentle moon landing and subsequent moon walk by the crew of the Apollo 11 spacecraft.
Great scientists, creative thinkers, and problem solvers do not solve hard problems head-on. When they are faced with a daunting question, they immediately and prudently admit defeat. They realize that there is no sense in wasting energy vainly grappling with complexity when, instead, they can productively grapple with simpler cases that will teach them how to deal with the complexity to come.
If you can't solve a problem, then there is an easier problem you can't solve: find it.
–George Polya
When the going gets tough, creative problem solvers create an easier, simpler problem that they can solve. They resolve that easier issue thoroughly and then study that simple scenario with laser focus. Those insights often point the way to a resolution of the original difficult problem.
Apply this mind-set to your work: when faced with a difficult issue or challenge, do something else. Focus entirely on solving a subproblem that you know you can successfully resolve. Be completely confident that the extraordinarily thorough work that you invest on the subproblem will later be the guide that allows you to navigate through the complexities of the larger issue. But don't jump to that more complex step while you're at work on the subissue. First just try to hit the moon ... walking on its surface is for another day.
* A WAY TO PROVOKE EFFECTIVE THINKING ...
Sweat the small stuff
Consider some complex issue in your studies or life. Instead of tackling it in its entirety, find one small element of it and solve that part completely. Understand the subissue and its solution backwards and forwards. Understand all its connections and implications. Consider this small piece from many points of view and in great detail. Choose a subproblem small enough that you can give it this level of attention. Only later should you consider how your efforts could help solve the larger issue.
* Illustration: A student's response to this exercise applied to time management
Time management is too big an issue for me, so I'll just focus on getting my homework done. That's still too big a task, so let me just focus on starting my homework. I could commit ten minutes right after each lecture to review class notes and think about the homework assignment. Then five minutes before the next lecture I could review the notes from the previous lecture—great, but not always realistic. So to make it practical, when I return to my room for the night, I'll commit at least ten minutes to reviewing the class notes of the day and beginning the assigned homework. In fact, my problem is not just procrastination but focus. Ah ha! So for those ten minutes, I'll turn off my computer and cell phone and spend that short uninterrupted time knowing there will be no distractions. Without text messages and emails, those ten minutes will be qualitatively different from and better than thirty minutes of interrupted time. That weird serenity will bring me to a meditation-like, focused state of mind. And looking at the homework on the day it was assigned—when it's still fresh in my mind—is better than investing the same amount of time the day before the homework is due—when I'd have to spend time just remembering what was going on. Once I've made this little ten-minute practice a daily habit, I'll revisit the larger challenge of time management. (See how this exercise did its job—it brought out some important principles to consider when facing the daunting challenge of time management: the value of uninterrupted, focused time and the value of carving out small regular intervals of time when they will be most effective.)
(Continues...)
Excerpted from The 5 Elements of Effective Thinkingby Edward B. Burger Michael Starbird Copyright © 2012 by Edward B. Burger and Michael Starbird. Excerpted by permission of PRINCETON UNIVERSITY PRESS. All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
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