A Mind for Numbers: How to Excel at Math and Science (Even If You Flunked Algebra)
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Diffuse-mode thinking is also essential for learning math and science. It allows us to suddenly gain a new insight on a problem we’ve been struggling with and is associated with “big-picture” perspectives. Diffuse-mode thinking is what happens when you relax your attention and just let your mind wander.
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Diffuse-mode insights often flow from preliminary thinking that’s been done in the focused mode. (The diffuse mode must have clay to make bricks!)
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If you are trying to understand or figure out something new, your best bet is to turn off your precision-focused thinking and turn on your “big picture” diffuse mode, long enough to be able to latch on to a new, more fruitful approach.
Hussain Abbas
This explains why an interview is a poor setting for actual job performance. Interviewees are in a focused mode during the interview and that only allows them to perform well on tasks they have already done. On the other hand, they perform poorly for tasks that require creativity.
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The harder you push your brain to come up with something creative, the less creative your ideas will be. So far, I have not found a single situation where this does not apply. Ultimately, this means that relaxation is an important part of hard work—and good work, for that matter.”
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But as long as we are consciously focusing on a problem, we are blocking the diffuse mode.
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Figuring out a difficult problem or learning a new concept almost always requires one or more periods when you aren’t consciously working on the problem.
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There is a bottom-up chunking process where practice and repetition can help you both build and strengthen each chunk, so you can easily gain access to it when needed. And there is a top-down “big picture” process that allows you to see where what you are learning fits in.9 Both processes are vital in gaining mastery over the material.
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Attempting to recall the material you are trying to learn—retrieval practice—is far more effective than simply rereading the material.
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When you have the book (or Google!) open right in front of you, it provides the illusion that the material is also in your brain. But it’s not. Because it can be easier to look at the book instead of recalling, students persist in their illusion—studying in a far less productive way.
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Ultimately, both bottom-up chunking and top-down big-picture approaches are vital if you are to become an expert with the material. We love creativity and the idea of being able to learn by seeing the big picture. But you can’t learn mathematics or science without also including a healthy dose of practice and repetition to help you build the chunks that will underpin your expertise.
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“The dread of doing a task uses up more time and energy than doing the task itself.”
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We procrastinate about things that make us feel uncomfortable. But what makes us feel good temporarily isn’t necessarily good for us in the long run.
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habits are powerful because they create neurological cravings. It helps to add a new reward if you want to overcome your previous cravings. Only once your brain starts expecting the reward will the important rewiring take place that will allow you to create new habits.
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A master violinist, for example, doesn’t just play a musical piece from beginning to end, over and over again. Instead, she focuses on the hardest parts of the piece—the parts where the fingers fumble and the mind becomes confused.5 You should be like that in your own deliberate practice, focusing and becoming quicker at the hardest parts of the solution procedures you are trying to learn.
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Students think they are just checking how well they’re doing when they do a mini-test of their recall. But this active test of recall is one of the best learning methods—better than just sitting passively and rereading! By building your library of chunks, with plenty of active practicing at retrieving material over and over again, and testing your recall, you are using some of the best methods possible for learning deeply and well.
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Whenever I find my spirit bending low, I discover it is because I have stopped looking for people’s positive attributes. This means it is time for me to look within and make changes.
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Highlighting should be avoided because, at least in my experience, it provides only an illusion of competence. Retrieval practice is far more powerful. Try to get the main ideas of each page you are reading cemented in your mind before you turn the page.
Hussain Abbas
Ironically, I am highlighting this.
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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. The only way to walk a journey of a thousand miles is to take one step at a time.
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Chronic procrastinators, as it turns out, tend to see each act of procrastination as a unique, unusual act, a “just this one time” phenomenon that won’t be repeated again. Even though it isn’t true, it sounds great—so great that you will believe it again and again, because without your planner-journal, there’s nothing to counter your thoughts.
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Emotions that goad you by saying, “Just do it, it feels right,” can be misleading in other ways. In choosing your career, for example, “Follow your passion” may be like deciding to marry your favorite movie star.
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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.
Hussain Abbas
This is the point covered in the book “So good they can’t ignore you”
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“I now also do things at the same general time every week—my body likes structure and routine; that’s why it was so hard at the beginning to break out of my procrastination habits, but it is also why it has been so easy to keep up with new habits after a month of forcing myself into it.”
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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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Exercise, it seems, helps create new neurons in areas that relate to memory. It also creates new signaling pathways.12 It seems that different types of exercise—running or walking, for example, versus strength training—may have subtly different molecular effects. But both aerobic and resistance exercise exert similarly powerful results on learning and memory.
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Writing and saying what you are trying to learn seems to enhance retention.
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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.
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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.
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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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When you use neural circuits, however, it seems you help build the myelin sheath over them—not to mention making many other microscopic changes.7 Practice appears to strengthen and reinforce connections between different brain regions, creating highways between the brain’s control centers and the centers that store knowledge.
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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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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.10 Learning expert Scott Young has developed this idea in what he calls the Feynman technique, which asks people to find a simple metaphor or analogy to help them grasp the essence of an idea.
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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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One of the most problematic aspects of procrastination—constantly interrupting your focus to check your phone messages, e-mails, or other updates—is that it interferes with transfer. Students who interrupt their work constantly not only don’t learn as deeply, but also aren’t able to transfer what little they do learn as easily to other topics.
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Teacher-centered approaches, where the teacher is considered to be the one with the answers, may sometimes inadvertently foster a sense of helplessness about learning among students.6 Surprisingly, teacher evaluation systems may foster the same helplessness—these systems allow you to place the blame for failure on your teacher’s inability to motivate or instruct.
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In learning, persistence is often far more important than intelligence.
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Friends and teammates can serve as a sort of ever-questioning, larger-scale diffuse mode, outside your own brain, that can catch what you missed, or what you just can’t see. And of course, as mentioned earlier, explaining to friends helps build your own understanding.
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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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“Starting hard” loads the first, most difficult problem in mind, and then switches attention away from it. Both these activities can help allow the diffuse mode to begin its work.
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The hard-start–jump-to-easy technique may make more efficient use of your brain by allowing different parts of the brain to work simultaneously on different thoughts.
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misplaced persistence can create unnecessary challenges with math and science.
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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.