A Mind for Numbers: How to Excel at Math and Science (Even If You Flunked Algebra)
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The biggest lie ever is that practice makes perfect. Not true—practice makes you better.
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Learning is the long game with life’s biggest rewards.
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We should ALWAYS be perpetual learners. Always in ALL WAYS.
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Learning fundamental concepts of math and science can be a lot easier than learning subjects that require a lot of rote memorization.
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once you start working on a math or science problem, you’ll notice that each step you complete signals the next step to you.
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Work a key problem all the way through on paper. (You should have the solution to this problem available, either because you’ve already worked it or because it’s a solved problem from your book.
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Do another repetition of the problem, paying attention to the key processes.
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Take a break. You can study other aspects of the subject if you need to, but then go do something different.
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Sleep. Before you go to sleep, work the problem again.3 If you get stuck, listen to the problem. Let your subconscious tell you what to do next.
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Do another repetition. As soon as you can the next day, work the problem again.
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Add a new problem. Pick another key problem and begin working on it in the same way that you did the first problem.
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Do “active” repetitions. Mentally review key problem steps in your mind while doing something active, such as walking to the library or exercising.
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Remember, Lady Luck favors the one who tries. So don’t feel overwhelmed with everything you need to learn about a new subject. Instead, focus on nailing down a few key ideas. You’ll be surprised at how much that simple framework can help.
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the more effort you put into recalling material, the deeper it embeds itself into your memory.7 Recall, not simple rereading, is the best form of deliberate practice in study.
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retrieval practice is one of the most powerful forms of learning.
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just staring at material that’s already on the page in front of you can fool you into thinking you know it when you actually don’t.
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Remember—it takes time to assimilate new knowledge. You will go through some periods when you seem to take an exasperating step backward in your understanding.
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The handwritten solution is important because writing by hand increases the odds that what is written will be retained in memory.
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Testing in itself is a powerful learning experience. It changes and adds to what you know, also making dramatic improvements in your ability to retain the material.
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remember the Law of Serendipity: If you prepare well by practicing and building a good mental library, you will find that luck will be increasingly on your side.
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“One of my mother’s Golden Rules was that ‘writing is the foundation of learning.’ From grade school through doctoral studies, I have found immense power in systematically understanding and writing each step of what I really wanted to learn.
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Research has confirmed that a special place devoted just to working is particularly helpful.
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A last important trick is to reframe your focus. One student, for example, is able to get himself up at four thirty each weekday morning, not by thinking about how tired he is when he wakes but about how good breakfast will be.
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It’s normal to sit down with a few negative feelings about beginning your work. It’s how you handle those feelings that matters.
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Also, different people function better in certain environments—some need a busy coffee shop, while others need a quiet library. You need to figure out what’s best for you.
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Writing the list before you go to sleep enlists your zombies to help you accomplish the items on the list the next day.
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Planning your quitting time is as important as planning your working time.
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Time after time, those who are committed to maintaining healthy leisure time along with their hard work outperform those who doggedly pursue an endless treadmill.
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It’s important to transform distant deadlines into daily ones.
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A little procrastination here and there is unavoidable. But to be effective in learning math and science, you must master your habits.
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remember the Law of Serendipity: Lady Luck favors the one who tries.
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“My military experience helped me develop good study habits. Not as in stare intently for hours, but as in only got a few minutes here, gotta figure out what I can! Some issue or other was always arising, which meant that I had to do my work in short bursts.
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learning math and science for an upcoming examination is very different from finishing a written report by a given due date.
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For many people, math- and science-related scaffolds develop slowly, alternating focused-mode and diffuse-mode thinking as the material is absorbed.
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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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Over the past decades, students who have blindly followed their passion, without rational analysis of whether their choice of career truly was wise, have been more unhappy with their job choices than those who coupled passion with rationality.8
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The student does little to no studying. It’s sad to say that misplaced self-confidence in one’s abilities can sometimes reach almost delusional levels. I’m convinced this is part of why employers like to hire people who are successful in math and science. Good grades in those disciplines are often based on objective data about a student’s ability to grapple with difficult material.
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taps into these naturally supersized visuospatial memorization abilities.
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The memory palace technique involves calling to mind a familiar place—like the layout of your house—and using it as a sort of visual notepad where you can deposit concept-images that you want to remember.
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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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Repetition is important; even when you make something memorable, repetition helps get that memorable item firmly lodged in long-term memory.
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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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Material that you do not review is more easily discounted or forgotten.
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This is why it’s wise to be careful about what you decide to skip when reviewing for tests. Your memory for related but nonreviewed material can become impaired.
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Many disciplines use memorable sentences to help students memorize concepts; the first letter of each word in the sentence is also the first letter of each word in a list that needs to be memorized.
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regular exercise can make a substantive improvement in your memory and learning abilities. Exercise, it seems, helps create new neurons in areas that relate to memory.
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learning to process ideas visually in math and science is a powerful way to become a master of the material.
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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.
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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.”)
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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.