A Mind for Numbers: How to Excel at Math and Science (Even If You Flunked Algebra)
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There’s evidence that writing by hand helps get the ideas into mind more easily than if you type the answer.
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‘writing is the foundation of learning.’
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“Eat your frogs first thing in the morning.”
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Do the most important and most disliked jobs first, as soon as you wake up.
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Mixing other tasks up with your learning seems to make everything more enjoyable and keeps you from prolonged and unhealthy bouts of sitting.
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It’s important to transform distant deadlines into daily ones. Attack them bit by bit. Big tasks need to be translated into smaller ones that show up on your daily task list.
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But remember the Law of Serendipity: Lady Luck favors the one who tries.
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Pausing gives you time to access your library of chunks and allows your brain to make connections between a particular problem and the bigger picture.
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We develop a passion for what we are good at. The mistake is thinking that if we aren’t good at something, we do not have and can never develop a passion for it.
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Accomplishing a lot of difficult tasks is like eating a salami. You go slice by slice—bit by bit. Cheer every accomplishment, even the tiniest ones. You’re moving ahead!
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One of the best things you can do to not only remember but understand concepts in math and science is to create a metaphor or analogy for it—often, the more visual, the better.
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It’s often helpful to pretend you are the concept you are trying to understand.
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Focusing your attention brings something into your temporary working memory. But for that “something” to move from working memory to long-term memory, two things should happen: the idea should be memorable (there’s a gigantic flying mule braying f = ma on my couch!), and it must be repeated. Otherwise, your natural metabolic processes, like tiny vampires, simply suck away faint, newly forming patterns of connections.
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Writing appears to help you to more deeply encode (that is, convert into neural memory structures) what you are trying to learn.
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The more you can turn what you are trying to remember into something memorable, the easier it will be to recall. You will want to say the word and its meaning aloud, to start setting auditory hooks to the material.
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many educators have observed that there seems to be a muscle memory related to writing by hand.
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If you really want to boost your memory as well as your general ability to learn, it seems one of the best ways to do it is to exercise.
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Writing and saying what you are trying to learn seems to enhance retention.
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Exercise is powerfully important in helping your neurons to grow and make new connections.
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A superb working memory can hold its thoughts so tightly that new thoughts can’t easily peek through.
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“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.”
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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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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.”
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“Deficiencies of innate ability may be compensated for through persistent hard work and concentration. One might say that work substitutes for talent, or better yet that it creates talent.”6 —Santiago Ramón y Cajal
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but one thing is becoming clear—we can make significant changes in our brain by changing how we think.
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Quickness was taken as cleverness, memory for ability, and submissiveness for rightness.13 Cajal’s success despite his “flaws” shows us how even today, teachers can easily underestimate their students—and students can underestimate themselves.
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How can you avoid falling into the trap of thinking that quicker people are automatically more clever?
Diego Barragán Guerrero
Algo de lo cotidiano:
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There are hidden meanings in equations, just as there are in poetry.
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One of the most important things we can do when we are trying to learn math and science is to bring the abstract ideas to life in our minds.
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Surprisingly, simple explanations are possible for almost any concept, no matter how complex.
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You may think you really have to understand something in order to explain it. But observe what happens when you are talking to other people about what you are studying. You’ll be surprised to see how often understanding arises as a consequence of attempts to explain to others and yourself, rather than the explanation arising out of your previous understanding.
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You’ll be surprised to see how often understanding arises as a consequence of attempts to explain to others and yourself, rather than the explanation arising out of your previous understanding.
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Transfer is the ability to take what you learn in one context and apply it to something else.
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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.
Diego Barragán Guerrero
Toma tu maqueño!
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Persistence is often more important than intelligence.
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Good teachers and mentors are often very busy people, and you need to use their time wisely.
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If you do well in your studies, the people around you can feel threatened.
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Failures are better teachers than successes because they cause you to rethink your approach.
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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.
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Testing, it seems, has a wonderful way of concentrating the mind.
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Difficult problems also scream for the creative powers of the diffuse mode. But to access the diffuse mode, you need to not be focusing on what you want so badly to solve!
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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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Nothing is ever certain. Occasionally you can study hard and the test gods simply don’t cooperate. But if you prepare well by practicing and by building a strong mental library of problem-solving techniques, and approach test taking wisely, you will find that luck will increasingly be on your side.
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Learning is, of course, personally empirical. The ultimate evidence will come when you evaluate your performance and attitude once you earnestly deploy these strategies.