فصل 12

دوره: ذهنی برای اعداد / درس 13

فصل 12

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{ 12 }

learning to appreciate your talent

Work toward an Intuitive Understanding

We can learn a lot about how to do math and science from sports. In baseball, for example, you don’t learn how to hit in one day. Instead, your body perfects your swing from plenty of repetition over a period of years. Smooth repetition creates muscle memory, so that your body knows what to do from a single thought—one chunk—instead of having to recall all the complex steps involved in hitting a ball.

In the same way, once you understand why you do something in math and science, you don’t have to keep reexplaining the how to yourself every time you do it. It’s not necessary to go around with 100 beans in your pocket and to lay out 10 rows of 10 beans again and again so that you get that 10 × 10 = 100. At some point, you just know it from memory. For example, you memorize the idea that you simply add exponents—those little superscript numbers—when multiplying numbers that have the same base (104 × 105 = 109). If you use the procedure a lot, by doing many different types of problems, you will find that you understand both the why and the how behind the procedure far better than you do after getting a conventional explanation from a teacher or book. The greater understanding results from the fact that your mind constructed the patterns of meaning, rather than simply accepting what someone else has told you. Remember—people learn by trying to make sense out of information they perceive. They rarely learn anything complex simply by having someone else tell it to them. (As math teachers say, “Math is not a spectator sport.”) Chess masters, emergency room physicians, fighter pilots, and many other experts often have to make complex decisions rapidly. They shut down their conscious system and instead rely on their well-trained intuition, drawing on their deeply ingrained repertoire of chunks.2 At some point, self-consciously “understanding” why you do what you do just slows you down and interrupts flow, resulting in worse decisions.

Teachers and professors can inadvertently get too caught up in following rules. In an intriguing study that illustrates this, six people were filmed doing CPR, only one of whom was a professional paramedic.3 Professional paramedics were then asked to guess who was the real paramedic. Ninety percent of these “real deal” expert paramedics chose correctly, remarking along the lines of “he seemed to know what he was doing.”4 CPR instructors, on the other hand, could pick the real paramedic out of the lineup only 30 percent of the time. These overly picky theoreticians criticized the real experts in the films for issues such as not taking the time to stop and measure where to put their hands. Precise rule following had come to mean more to the instructors than practicality.

Once you understand why you do something in math and science, you shouldn’t keep reexplaining the how. Such overthinking can lead to choking.

No Need for Genius Envy

Just as Olympic athletes don’t build their athletic prowess simply by spending a few hours jogging on the weekends or lifting a few weights in their spare time, chess grand masters don’t construct their neural structures through last-minute cramming. Instead, their knowledge base is gradually built over time and with plenty of practice that builds their understanding of big-picture context. Practice like this places the memory traces prominently in the warehouse of long-term memory, where the neural pattern can be quickly and easily accessed when needed.5 Let’s return to chess master Magnus Carlsen—that fast-thinking genius of speed chess as well as regular chess. Carlsen has an extraordinary grasp of the patterns of thousands of previously played chess games—he can look at the arrangement of an endgame on a chess board and instantly tell you which of more than ten thousand games of past centuries it was drawn from. In other words, Carlsen has created a vast chunked library of potential solution patterns. He can quickly riffle through the chunks to see what others have done when faced with situations similar to what he is facing.6 Carlsen isn’t unusual in what he is doing, although he does it better than all but a very few past and present chess players. It is typical for grand masters to spend at least a decade practicing and studying to learn thousands of memory chunk patterns.7 These readily available patterns allow them to recognize the key elements in any game setup much more quickly than amateurs; they develop a professional eye so they can rapidly intuit the best course of action in any situation.8 But wait. Aren’t chess masters and people who can multiply six-digit numbers in their heads simply exceptionally gifted? Not necessarily. I’m going to tell it to you straight—sure, intelligence matters. Being smarter often equates to having a larger working memory. Your hot rod of a memory may be able to hold nine things instead of four, and you latch onto those things like a bulldog, which makes it easier to learn math and science.

But guess what? It also makes it more difficult for you to be creative.

How is that?

It’s our old friend and enemy—Einstellung. The idea you already are holding in mind blocks you from fresh thoughts. A superb working memory can hold its thoughts so tightly that new thoughts can’t easily peek through. Such tightly controlled attention could use an occasional whiff of ADHD-like fresh air—the ability, in other words, to have your attention shift even if you don’t want it to shift. Your ability to solve complex problems may make you overthink simple problems, going for the convoluted answer and overlooking the simple, more obvious solution. Research has shown that smart people can have more of a tendency to lose themselves in the weeds of complexity. People with less apparent intellectual horsepower, on the other hand, can cut more easily to simpler solutions.9 IT’S NOT WHAT YOU KNOW; IT’S HOW YOU THINK

“Experience has shown me an almost inverse correlation between high GRE scores and ultimate career success. Indeed, many of the students with the lowest scores became highly successful, whereas a surprising number of the ‘geniuses’ fell by the wayside for some reason or other.” —Bill Zettler, Ph.D., Professor of Biology, longtime academic advisor, and winner of the Teacher of the Year Award, University of Florida, Gainesville, Florida If you are one of those people who can’t hold a lot in mind at once—you lose focus and start daydreaming in lectures, and have to get to someplace quiet to focus so you can use your working memory to its maximum—well, welcome to the clan of the creative. Having a somewhat smaller working memory means you can more easily generalize your learning into new, more creative combinations. Because your working memory, which grows from the focusing abilities of the prefrontal cortex, doesn’t lock everything up so tightly, you can more easily get input from other parts of your brain. These other areas, which include the sensory cortex, not only are more in tune with what’s going on in the environment, but also are the source of dreams, not to mention creative ideas.11 You may have to work harder sometimes (or even much of the time) to understand what’s going on, but once you’ve got something chunked, you can take that chunk and turn it outside in and inside round—putting it through creative paces even you didn’t think you were capable of!

Here’s another point to put into your mental chunker: Chess, that bastion of intellectuals, has some elite players with roughly average IQs. These seemingly middling intellects are able to do better than some more intelligent players because they practice more.12 That’s the key idea. Every chess player, whether average or elite, grows talent by practicing. It is the practice—particularly deliberate practice on the toughest aspects of the material—that can help lift average brains into the realm of those with more “natural” gifts. Just as you can practice lifting weights and get bigger muscles over time, you can also practice certain mental patterns that deepen and enlarge in your mind. Interestingly, it seems that practice may help you expand your working memory. Researchers on recall have found that doing exercises to repeat longer and longer strings of digits backward seems to improve working memory.13 Gifted people have their own set of difficulties. Sometimes highly gifted kids are bullied, so they learn to hide or suppress their giftedness. This can be difficult to recover from.14 Smarter people also sometimes struggle because they can so easily imagine every complexity, good and bad. Extremely smart people are more likely than people of normal intelligence to procrastinate because it always worked when they were growing up, which means they are less likely to learn certain critical life skills early on.

Whether you are naturally gifted or you have to struggle to get a solid grasp the fundamentals, you should realize that you are not alone if you think you are an impostor—that it’s a fluke when you happen to do well on a test, and that on the next test, for sure they (and your family and friends) are finally going to figure out how incompetent you really are. This feeling is so extraordinarily common that it even has a name—the “impostor phenomenon.”15 If you suffer from these kinds of feelings of inadequacy, just be aware that many others secretly share them.

Everyone has different gifts. As the old saying goes, “When one door closes, another opens.” Keep your chin up and your eye on the open door.

REACHING TOWARD THE INFINITE

Some feel that diffuse, intuitive ways of thinking are more in tune with our spirituality. The creativity that diffuse thinking promotes sometimes seems beyond human understanding.

As Albert Einstein noted, “There are only two ways to live your life. One is as though nothing is a miracle. The other is as if everything is.”

DON’T UNDERESTIMATE YOURSELF

“I coach Science Olympiad at our school. We have won the state championship eight out of the last nine years. We fell one point short of winning the state this year, and we often finish in the top ten in the nation. We have found that many seemingly top students (who are getting an A+ in all their classes) do not perform as well under the pressure of a Science Olympiad event as those who can mentally manipulate the knowledge they have. Interestingly, this second tier (if you will) of students at times seem to think of themselves as less intelligent than these top students. I would much rather take ostensibly lower-performing students who can think creatively on their feet, as the Olympiad requires, than top students who get flustered if the questions being posed don’t exactly fit the memorized chunks in their brains.” —Mark Porter, biology teacher, Mira Loma High School, Sacramento, California

SUMMING IT UP

At some point, after you’ve got chunked material well in hand (and in brain), you start to let go of conscious awareness of every little detail and do things automatically.

It may seem intimidating to work alongside other students who grasp material more quickly than you do. But “average” students can sometimes have advantages when it comes to initiative, ability to get things done, and creativity.

Part of the key to creativity is to be able to switch from full focused concentration to the relaxed, daydreamy diffuse mode.

Focusing too intently can inhibit the solution you are seeking—like trying to hammer a screw because you think it’s a nail. When you are stuck, sometimes it’s best to get away from a problem for a while and move on to something else, or to simply sleep on it.

PAUSE AND RECALL

Close the book and look away. What were the main ideas of this chapter? Pause also to try to recall the essential ideas of the book as a whole so far.

ENHANCE YOUR LEARNING

  1. Think of an area where persistence has paid off for you in your life. Is there a new area where you would like to start developing your persistence? What backup plan can you develop for low times when you might feel like faltering?

  2. People often try to stop their daydreaming, because it interrupts activities they truly intend to focus on, like listening to an important lecture. What works better for you—forcing yourself to maintain focus, or simply bringing your attention back to the matter at hand when you notice your attention wandering?

FROM SLOW LEARNER TO SUPERSTAR: NICK APPLEYARD’S STORY

Nick Appleyard leads the Americas business unit as a vice president in a high-tech company that develops and supports advanced physics simulation tools used in aerospace, automotive, energy, biomedical, and many other sectors of the economy. He received his degree in mechanical engineering degree from the University of Sheffield in England.

“Growing up, I was branded a slow learner and a problem child because of it. These labels impacted me deeply. I felt like my teachers treated me as if they’d given up any hope that I could succeed. To make matters worse, my parents also became frustrated with me and my educational progress. I felt the disappointment most severely from my father, a senior physician at a major teaching hospital. (I learned later in life that he had had similar difficulties early in his childhood.) It was a vicious circle that impacted my confidence in every aspect of life.

“What was the problem? Math and everything associated with it—fractions, times tables, long division, algebra, you name it. It was all boring and completely pointless.

“One day, something began to change, although I didn’t realize it at the time. My father brought home a computer. I had heard about kids in their teens writing home computer games that everyone wanted to play, and becoming millionaires overnight. I wanted to be one of those kids.

“I read, practiced, and wrote harder and harder programs, all of which involved some kind of math. Eventually, a popular UK computer magazine accepted one of my programs for publication—a real thrill for me.

“Now I see every day how mathematics is applied for designing the next generation of automobiles, for helping to put rockets into space, and for analyzing how the human body works.

“Mathematics is no longer pointless. It is instead a source of wonder—and of a great career!”

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