A Mind For Numbers

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A Mind For Numbers Page 8

by Barbara Oakley, PhD


  PAUSE AND RECALL

  Next time you are with a family member, friend, or classmate, relate the essence of what you have been learning, either from this book or in regard to a class you are taking. Retelling whatever you are learning about not only helps fuel and share your own enthusiasm, but also clarifies and cements the ideas in your mind, so you’ll remember them better in the weeks and months to come. Even if what you are studying is very advanced, simplifying so you can explain to others who do not share your educational background can be surprisingly helpful in building your understanding.

  OVERCOMING TRAUMATIC BRAIN INJURY AND LEARNING TO LEARN WITH LIMITED TIME—PAUL KRUCHKO’S STORY

  Paul Kruchko with his wife and daughter, who have helped provide the motivation for him to reshape his life.

  “I grew up poor, with a lot of domestic turmoil. I barely graduated from high school. Afterward, I enlisted in the army, where I was deployed as an infantryman to Iraq. My vehicle was hit eight out of the twelve times our platoon was ambushed with roadside bombs.

  “During my tour, through lucky chance, I met my wonderful wife. Meeting her convinced me to leave the service and start a family. The problem was I didn’t know what to do. Worse yet, after returning home I started to have problems with concentration, lack of cognition, and irritability that I had never experienced before. Sometimes I could barely finish a sentence. It was only later that I read about soldiers returning home from Iraq and Afghanistan having issues with undiagnosed traumatic brain injury (TBI).

  “I enrolled in a computer and electronics engineering technology program. My TBI was severe enough that at first I even struggled to comprehend fractions.

  “But it was a blessing in disguise: The learning was doing something to my brain. It was as if the mental concentration—difficult though it was—was retooling my mind and helping my brain heal. To me, this process seemed analogous to how I would apply physical effort in the gym, and blood would be forced into my muscles to build strength. In time my mind healed—I graduated with high honors and got a job as a civilian electronics technician.

  “I decided to go back to school again for an engineering degree. Mathematics—especially calculus—is far more important when studying engineering than it is when training as a hands-on technician. At this point, my lack of foundation of mathematics from the earliest years of grade school started to catch up with me.

  “By this time I was married, a new father, and working full-time. Now the challenge I faced was no longer just basic cognition, but time management. I had only a few hours each day to learn advanced concepts at a far deeper level than I ever had to before. It was only after a few hard knocks (I earned a D in my differential equations class—ouch!) that I started to approach learning in a more strategic way.

  “Each semester, I get a copy of the syllabi from my professors and begin reading the textbooks at least two to three weeks before the courses begin. I try to stay at least a chapter ahead of the class, although by the middle of the semester this is often impossible. Practice in problem solving—building chunks—is key. Over my learning career, I gradually developed the following rules, which have allowed me to satisfactorily complete my courses. My objective is a good career that will support my family—these techniques are helping me get there.”

  Paul’s Techniques for Limited Study Time

  1. Read (but don’t yet solve) assigned homework and practice exams/quizzes. With this initial step I prime my mental pump for learning new concepts—new chunks.

  2. Review lecture notes (attend every lecture as much as possible). One hour of lecture is worth two hours reading the book. I learn far more efficiently if I am faithful in attending lectures and taking detailed notes—not just staring at my watch and waiting for it to be over. I review my notes the following day while the subjects are still fresh in my mind. I’ve also found that thirty minutes with a professor asking questions is easily worth three hours reading the book.

  3. Rework example problems presented in lecture notes. It never helped me to practice problems given by either the instructor or the textbook that didn’t have solutions to provide feedback. With the example problems I already had a step-by-step solution available if necessary. Reworking helps solidify chunks. I use different-colored pens when I study: blue, green, red—not just black. I found that it helps me focus on reading my notes better; things pop out more, instead of blending together into a confusing collage of inexplicable mathematical chaos on the page.

  4. Work assigned homework and practice exam/quiz questions. This builds “muscle memory” chunks for the mind in solving certain types of problems.

  { 5 }

  preventing procrastination:

  Enlisting Your Habits (“Zombies”) as Helpers

  For centuries, arsenic was a popular choice for killers. A sprinkle on your morning toast would cause your painful death within a day. So you can imagine the shock at the forty-eighth meeting of the German Association of Arts and Sciences in 1875, when two men sat in front of the audience and blithely downed more than double a deadly dose of arsenic. The next day the men were back at the conference, smiling and healthy. Analysis of the men’s urine showed it was no trick. The men had indeed ingested the poison.1

  How is it possible to take something so bad for you and stay alive—and even look healthy?

  The answer has an uncanny relationship to procrastination. Understanding something of the cognitive psychology of procrastination, just like understanding the chemistry of poison, can help us develop healthy preventatives.

  In this and the next chapter, I’m going to teach you the lazy person’s approach to tackling procrastination. This means you’ll be learning about your inner zombies—the routine, habitual responses your brain falls into as a result of specific cues. These zombie responses are often focused on making the here and now better. As you’ll see, you can trick some of these zombies into helping you to fend off procrastination when you need to (not all procrastination is bad).2 Then we’ll interleave a chapter where you’ll deepen your chunking skills, before we return with a final chapter of wrap-up coverage on procrastination that provides tips, tricks, and handy technological tools.

  First things first. Unlike procrastination, which is easy to fall into, willpower is hard to come by because it uses a lot of neural resources. This means that the last thing you want to do in tackling procrastination is to go around spraying willpower on it like it’s cheap air freshener. You shouldn’t waste willpower on procrastination except when absolutely necessary! Best of all, as you will see, you don’t need to.

  Poison. Zombies. Could it get any better?

  Ah yes—there’s experimentation! Bwah hah hah—what could be more fun?

  DISTRACTION AND PROCRASTINATION

  “Procrastination is one of our generation’s biggest problems. We have so many distractions. I am always thinking, ‘Before I start my homework, let me just check my Facebook, Twitter, Tumblr, and e-mail.’ Before I even realize it, I have wasted at least an hour. Even after I finally start my homework, I have those distracting websites open in the background.

  “I need to find a way just to focus on my studying and homework. I think it depends a lot on my environment and the time. I should not be waiting until the last minute to do everything.”

  —A calculus student

  Procrastination and Discomfort

  Imagine how your calf muscles would scream if you prepared for a big race by waiting till midnight the night before your first marathon to do your first practice run. In just the same way, you can’t compete in math and science if you just cram at the last minute.

  For most people, learning math and science depends on two things: brief study sessions where the neural “bricks” are laid, and time in between for the mental mortar to dry. This means that procrastination, a terribly common problem for many students,3 is particularly
important for math and science students to master.

  We procrastinate about things that make us feel uncomfortable.4 Medical imaging studies have shown that mathphobes, for example, appear to avoid math because even just thinking about it seems to hurt. The pain centers of their brains light up when they contemplate working on math.5

  But there’s something important to note. It was the anticipation that was painful. When the mathphobes actually did math, the pain disappeared. Procrastination expert Rita Emmett explains: “The dread of doing a task uses up more time and energy than doing the task itself.”6

  Avoiding something painful seems sensible. But sadly, the long-term effects of habitual avoidance can be nasty. You put off studying math, and it becomes even more painful to think about studying it. You delay practicing for the SAT or ACT, and on the critical exam day, you choke because you haven’t laid the firm neural foundations you need to feel comfortable with the material. Your opportunity for scholarships evaporates.

  Perhaps you’d love a career in math and science, but you give up and settle on a different path. You tell others you couldn’t hack the math, when the reality was that you had simply let procrastination get the best of you.

  Procrastination is a single, monumentally important “keystone” bad habit.7 A habit, in other words, that influences many important areas of your life. Change it, and a myriad of other positive changes will gradually begin to unfold.

  And there’s something more—something crucially important. It’s easy to feel distaste for something you’re not good at. But the better you get at something, the more you’ll find you enjoy it.

  How the Brain Procrastinates

  Beep beep beep . . . It’s ten A.M. on Saturday, and your alarm clock pulls you from luscious sleep. An hour later you’re finally up, coffee in hand, poised over your books and your laptop. You’ve been meaning to put in a solid day of studying so you can wrap up that math homework that’s due on Monday. You also plan to get a start on the history essay, and to look at that confusing chemistry section.

  You look at your math textbook. There’s a subtle, barely detectable ouch. Your brain’s pain centers light up as you anticipate looking at the confusing graphs and tangle of strange verbiage. You really don’t want to be doing math homework now. The thought of spending the next several hours studying math, as you’d planned, makes the idea of opening the book even less pleasant.

  You shift your focus from your textbook to your laptop. Hmm, that’s more like it. No painful feelings there, just a little dollop of pleasure as you flip open the screen and check your messages. Look at that funny picture Jesse sent . . .

  Two hours later, you haven’t even started your math homework.

  This is a typical procrastination pattern. You think about something you don’t particularly like, and the pain centers of your brain light up. So you shift and narrow your focus of attention to something more enjoyable.8 This causes you to feel better, at least temporarily.

  Procrastination is like addiction. It offers temporary excitement and relief from boring reality. It’s easy to delude yourself that the most profitable use of any given moment is surfing the web for information instead of reading the textbook or doing the assigned problems. You start to tell yourself stories. For example, that organic chemistry requires spatial reasoning—your weakness—so of course you’re doing poorly at it. You devise irrational excuses that sound superficially reasonable: If I study too far ahead of a test, I’ll forget the material. (You conveniently forget the tests in other courses you’ll be taking during exam time, making it impossible to learn all the material at once.) Only when the semester is ending and you start your desperate cramming for the final exam do you realize that the real reason you are doing so badly in organic chemistry is that you have been continually procrastinating.

  Researchers have found that procrastination can even become a source of pride as well as an excuse for doing poorly. “I crammed for the quiz last night after finishing the lab report and the marketing interview. Of course I could have done better. But with so many things on my plate, what do you expect?”9 Even when people work hard at their studies, they sometimes like to falsely claim they procrastinated because it makes them seem cool and smart: “I finally made myself cram last night for the midterm.”

  Like any habit, procrastination is something you can simply fall into. You get your procrastination cue and unthinkingly relax into your comfortable procrastination response. Over time, your habitual, zombielike response in obtaining those temporary dollops of pleasure can gradually lower your self-confidence, leaving you with even less of a desire to learn how to work effectively. Procrastinators report higher stress, worse health, and lower grades.10 As time goes on, the habit can become entrenched. At that point, fixing it can feel hopeless.11

  CHANGE IS POSSIBLE

  “I used to be a procrastinator but I’ve changed. I had an AP class in high school that really helped get me into gear. My teacher assigned four to six hours of American history homework a night. What I learned is to take it one task at a time. I’ve found that if I feel like I’ve accomplished something, it’s easier to keep moving forward and stay on track.”

  —Paula Meerschaert, freshman, creative writing

  Occasionally you can pull an all-nighter in your studies and still get a decent grade. You can even feel a sort of high when you’ve finished. Much as with gambling, this minor win can serve as a reward that prompts you to take a chance and procrastinate again. You may even start telling yourself that procrastination is an innate characteristic—a trait that is as much a part of you as your height or the color of your hair. After all, if procrastination were easily fixable, wouldn’t you have fixed it by now?

  The higher you go in math and science, however, the more important it is to take control of procrastination. Habits that worked in earlier years can turn around and bite you. What I’ll show you in these next few chapters is how you can become the master of your habits. You should be making your decisions, not your well-meaning, but unthinking, zombies—your habits. As you will see, the strategies for dealing with procrastination are simple. It’s just that they aren’t intuitively obvious.

  Let’s return to the story that began this chapter. The arsenic eaters started with tiny doses of arsenic. In tiny doses, arsenic doesn’t seem harmful. You can even build up an immunity to its effects. This can allow you to take large doses and look healthy even as the poison is slowly increasing your risk of cancer and ravaging your organs.

  In a similar way, procrastinators put off just that one little thing. They do it again and again, gradually growing used to it. They can even look healthy. But the long-term effects?

  Not so good.

  A LITTLE GOES A LONG WAY

  “When a student complains of failing and tells me he studied for ten whole hours the day before the exam, I answer, ‘That’s why you failed.’ When the student looks at me in disbelief, I say, ‘You should have been studying a little bit all along.’”

  —Richard Nadel, Senior Instructor of Mathematics, Florida International University, Miami, Florida

  SUMMING IT UP

  We procrastinate about things that make us feel uncomfortable. But what makes us feel good temporarily isn’t necessarily good for us in the long run.

  Procrastination can be like taking tiny amounts of poison. It may not seem harmful at the time. But the long-term effects can be very damaging.

  PAUSE AND RECALL

  In chapter 4, we learned that it can help to recall material when you are in a physically different location from where you originally learned it. This helps you become independent of location cues. Later, you will find yourself thinking more comfortably about the material no matter where you are—this is often important when you are being tested.

  Let’s try this idea now. What were the main ideas of this chapter? You can recall them w
here you are currently sitting, but then try recalling the ideas again in a different room, or better yet, when you are outside.

  ENHANCE YOUR LEARNING

  1. Have habits of procrastination had an impact on your life? If so, how?

  2. What types of stories have you heard other people tell about why they procrastinate? Can you see the holes in some of these stories? What holes are in your own stories about procrastination?

  3. List some specific actions you could take that would help you curb habits of procrastination without relying very much on willpower.

  ACTIVELY SEEK GOOD ADVICE! INSIGHTS FROM NORMAN FORTENBERRY, A NATIONAL LEADER IN ENGINEERING EDUCATION

  “When I was a first-year college student, I already knew I wanted to be an engineer, so I signed up for Calculus with Applications instead of the regular calculus being taken by most of my classmates. This was a mistake. Many of the students in this class had already taken calculus in high school and were expanding their knowledge base. So I was at a competitive disadvantage.

  “More critical, since far fewer students were in the version of calculus that I was taking, there were few potential study partners. Unlike in high school, there is no premium (indeed there is a penalty) for going it alone in college. Professors in engineering, a field where teamwork is an important professional trait, often assume that you’re working with others and design homework accordingly. I squeaked through with a B but always felt that I had an inadequate conceptual and intuitive understanding of the fundamentals of calculus and of the subsequent courses that depended on it. I did lots of studying on my own in a just-in-time fashion for the calculus portions of subsequent classes. But that cost me a lot of time that could have been devoted to other pursuits.

 

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