A Mind for Numbers: How to Excel at Math and Science (Even If You Flunked Algebra)
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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.
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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.
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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.
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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.
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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.”
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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.
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Cajal felt the key to his success was his perseverance (the “virtue of the less brilliant”2) coupled with his flexible ability to change his mind and admit errors.
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Anyone, Cajal noted, even people with average intelligence, can sculpt their own brain, so
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we can make significant changes in our brain by changing how we think.
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Good chunks form neural patterns that resonate, not only within the subject we’re working in, but with other subjects and areas of our lives. The abstraction helps you transfer ideas from one area to another.
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Metaphors and physical analogies also form chunks that can allow ideas even from very different areas to influence one another.17 This is why people who love math, science, and technology often also find surprising help from their activities or knowledge of sports, music, language, art, or literature. My own knowledge of how to learn a language helped me in learning how to learn math and science.
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“What, after all, is mathematics but the poetry of the mind, and what is poetry but the mathematics of the heart?”
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There are hidden meanings in equations, just as there are in poetry.
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When you cultivate simple explanations by breaking down complicated material to its key elements, the result is that you have a deeper understanding of the material.
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You may think you’re learning in between checking your phone messages, but in reality, your brain is not focusing long enough to form the solid neural chunks that are central to transferring ideas from one area to another.
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Persistence is often more important than intelligence.
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students learn best when they themselves are actively engaged in the subject instead of simply listening to someone else speak.
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Taking responsibility for your own learning is one of the most important things you can do.
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They were ultimately surprised to discover that the qualities they saw as disadvantages helped propel them into being the thoughtful, attentive, creative instructors and professors they became.
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all you really needed to do was look at the material through different lenses as you were studying throughout the semester.
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Take pride in who you are, especially in the qualities that make you “different,” and use them as a secret talisman for success.
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In learning, persistence is often far more important than intelligence.
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when you whiz through a homework or test problem and don’t go back to check your work, you are acting a little like a person who is refusing to use parts of your brain.
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“The first principle is that you must not fool yourself—and you are the easiest person to fool.”8 —Physicist Richard Feynman, advising how to avoid pseudo-science that masquerades as science
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One of the most-cited papers in sociology, “The Strength of Weak Ties,” by sociologist Mark Granovetter, describes how the number of acquaintances you have—not the number of good friends—predicts your access to the latest ideas as well as your success on the job market.
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equations are NOT merely expressions you plug numbers into to get other numbers. Equations tell a story about how the physical world works.
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If you compare how much you learn by spending one hour studying versus one hour taking a test on that same material, you will retain and learn far more as a result of the hour you spent taking a test. Testing, it seems, has a wonderful way of concentrating the mind.
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If you shift your thinking from “this test has made me afraid” to “this test has got me excited to do my best!” it can make a significant improvement in your performance.
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whenever possible, you should blink, shift your attention, and then double-check your answers using a big-picture perspective, asking yourself, “Does this really make sense?”
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your desire to figure things out right now is what prevents you from being able to figure things out.
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Reshaping your brain is under your control. The key is patient persistence—working knowledgeably with your brain’s strengths and weaknesses.
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Rote memorization, often at the last minute, has given many lower-level learners the illusory sense that they understand math and science. As they climb to higher levels, their weak understanding eventually crumbles.
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Whereas everyone thought that safecracking wizardry was involved, it was a simple understanding of how the device arrived from the manufacturer that was fundamental.
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By understanding your brain’s default settings—the natural way it learns and thinks—and taking advantage of this knowledge, you, too, can become an expert.
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Remember—Lady Luck favors the one who tries. A little insight into learning how to learn best doesn’t hurt, either.
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Highlight very little, and never highlight anything you haven’t put in your mind first by recalling.
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Test yourself. On everything. All the time. Flash cards are your friend.
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Chunking is understanding and practicing with a problem solution so that it can all come to mind in a flash.
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Spread out your learning in any subject a little every day, just like an athlete.
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Mix it up and work on different types of problems. This teaches you both how and when to use a technique.
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go over your errors, make sure you understand why you made them, and then rework your solutions.
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(Handwriting builds stronger neural structures in memory than typing.)
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This is why a little study every day is much better than a lot of studying all at once.
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Focus intently for those twenty-five minutes and try to work as diligently as you can. After the timer goes off, give yourself a small, fun reward. A few of these sessions in a day can really move your studies forward.
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You need to be able to solve a problem step-by-step,
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well. If you don’t get a good sleep before a test, NOTHING ELSE YOU HAVE DONE WILL MATTER.
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