A Mind for Numbers: How to Excel at Math and Science (Even If You Flunked Algebra)
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there will always be those who criticize or attempt to undermine any effort or achievement you make.
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Remind yourself that this situation is only temporary, and no circumstance is truly as overwhelming as it might seem at the time.
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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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Use your natural contrariness to defy the always-present prejudices from others about what you can do.
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Learning on your own is one of the deepest, most effective ways to approach learning: It improves your ability to think independently. It can help you answer the strange questions that teachers sometimes throw at you on tests.
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People are competitive as well as cooperative.
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Learn to deal dispassionately with these issues.
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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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Good learners vet their work to ensure that it makes sense.
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“The first principle is that you must not fool yourself—and you are the easiest person to fool.”
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Friends and teammates can serve as a sort of ever-questioning,
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questioning, larger-scale diffuse mode, outside your own brain, that can catch what you missed, or what you just can’t see.
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acquaintances such as class teammates tend to run in different circles—meaning that your access to the “outside your brain” interpersonal diffuse mode is exponentially larger.
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nonjudgmental, agreeable interactions are less productive than sessions where criticism is accepted
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gratuitously
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study groups can be powerfully effective for learning in math, science, engineering, and technology.
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The focused mode can allow you to make critical errors even though you feel confident you’ve done everything correctly.
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It is easiest of all to fool yourself.
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A qualitative understanding of an equation is more important than getting quantitatively correct numbers out of it.
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“Often, it takes way less time to check your work than to solve a problem.
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“Units of measurement are your friend.
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“You need to think about what the equation means, so that your math result and your intuition match.
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Testing is itself an extraordinarily powerful learning experience.
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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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The answer is to start with the hard problems—but quickly jump to the easy ones.
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when you start working problems, start first with what appears to be the hardest one. But steel yourself to pull away within the first minute or two if you get stuck or get a sense that you might not be on the right track.
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Both these activities can help allow the diffuse mode to begin its work.
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The only challenge with this approach is that you must have the self-discipline to pull yourself off a problem once you find yourself stuck for a minute or two.
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misplaced persistence can create unnecessary challenges with math and science.
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This may be why test takers sometimes find that the solution pops to mind right as they walk out the door.
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When they gave up, their attention switched, allowing the diffuse mode the tiny bit of traction it needed to go ...
This highlight has been truncated due to consecutive passage length restrictions.
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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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Another good tip for panicky test takers is to momentarily turn your attention to your breathing.
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“Paralysis by analysis.”
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“hard-start–jump-to-easy technique helps prevent this.
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The day before a test (or tests), have a quick look over the materials to brush up on them.
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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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Not getting enough sleep the night before a test can negate any other preparation you’ve done.
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Your mind can trick you into thinking that what you’ve done is correct, even if it isn’t. This means that, 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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persistence can sometimes be misplaced—that
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A central theme of this book is the paradoxical nature of learning. Focused attention is indispensable for problem solving—yet it can also block our ability to solve problems. Persistence is key—but it can also leave us unnecessarily pounding our heads. Memorization is a critical aspect of acquiring expertise—but it can also keep us focused on the trees instead of the forest. Metaphor allows us to acquire new concepts—but it can also keep us wedded to faulty conceptions.
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In the end, integrating the many paradoxes of learning adds value and meaning to everything we do.
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nothing beats grasping the chunked and simplified essence.
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(Handwriting builds stronger neural structures in memory than typing.)
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rereading is a waste of time.
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Not getting enough sleep.
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Prolonged fatigue allows toxins to build up in the brain that disrupt the neural connections you need to think quickly and well.
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“Get good at it, and then see if you still want to quit.”
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