A Mind for Numbers: How to Excel at Math and Science (Even If You Flunked Algebra)
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your brain can also work on a problem even while you are sleeping and are not aware of anything.
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I reflected on the progress of my career and realized that I’d followed my inner passions without also being open to developing new ones.
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I learned that internalizing certain concepts and techniques could be a powerful tool. I also learned not to take on too much at once, allowing myself plenty of time to practice even if it meant my classmates would sometimes graduate ahead of me because I wasn’t taking as many courses each semester as they were.
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You’ll be surprised at how spending a minute or two glancing ahead before you read in depth will help you organize your thoughts. You’re creating little neural hooks to hang your thinking on, making it easier to grasp the concepts.
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The diffuse mode does seem to be able to work quietly in the background on something you are not actively focusing on.
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Focused-mode thinking is essential for studying math and science. It involves a direct approach to solving problems using rational, sequential, analytical approaches.
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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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This relaxation can allow different areas of the brain to hook up and return valuable insights.
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You have to unlearn your erroneous older ideas even while you’re learning new ones.
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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,
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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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The left side of the brain is somewhat more associated with careful, focused attention. It also seems more specialized for handling sequential information and logical thinking—the first step leads to the second step, and so on.
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The right seems more tied to diffuse scanning of the environment and interacting with other people, and seems more associated with processing emotions.15 It also is linked with handling simultaneous, big-picture processing.
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Evidence suggests that to grapple with a difficult problem, we must first put hard, focused-mode effort into it.
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The diffuse mode is also often an important part of problem solving, especially when the problem is difficult. But as long as we are consciously focusing on a problem, we are blocking the diffuse mode.
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the learning process is all about working your way out of confusion.
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write a few key things that you would like to work on the next day.
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the issues are almost always that they are fixated on looking at the details of the problem for clues on how to solve it, and not on understanding the problem itself.
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I understand better when I read the book rather than listen to someone speak, so I always read the book. I skim first so I know basically what the chapter is trying to get at and then I read it in detail. I read the chapter more than once
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If after reading the book, I still don’t fully understand what’s going on, I Google or look at YouTube videos on the subject. This isn’t because the book or professor isn’t thorough, but rather because sometimes hearing a slightly different way of phrasing something can make your mind look at the problem from a different angle and spark understanding.
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Shifting between the Focused and Diffuse Modes
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shifting from focused to diffuse mode happens naturally if you distract yourself and then allow a little time to pass. You can go for a walk, take a nap, or go to the gym.
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The key is to do something else until your brain is consciously free of any thought of the problem.
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if you simply switch your focus to other things you need to do, and mix in a little relaxing break time.
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the bed, the bath, or the bus.
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a solitary walk was worth a week in the laboratory in helping him progress in his work.
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Once you are distracted from the problem at hand, the diffuse mode has access and can begin pinging about in its big-picture way to settle on a solution.
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It can take a lot of hard focused-mode work beforehand, but the sudden, unexpected solution that emerges from the diffuse mode can make it feel almost like the “aha!” mode.
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part of the magic behind Edison’s extraordinary creativity. When faced with a difficult problem, instead of focusing intently on it, Edison, according to legend, took a nap.
Julian Franco
take naps
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(This is a reminder that falling asleep is a good way to get the brain thinking loosely about a problem you want to solve, or anything you are working on creatively.)
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We all have the ability to make new neural connections and pull from memory something that was never put there in the first place—what
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We learn a great deal from our failures in math and science.
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Mistakes are inevitable. To work past them, start early on your assignments and, unless you are really enjoying what you are doing, keep your working sessions short. Remember, when you take breaks, your diffuse mode is still working away in the background. It’s the best deal around—you continue to learn while you are taking it easy.
Julian Franco
Esto es cierto
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One way to think of the diffuse mode is as a base station when you are mountain climbing. Base stations are essential resting spots in the long journey to difficult mountaintops. You use them to pause, reflect, check your gear, and make sure you’ve got the right route picked out.
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you would never confuse resting at a base station with the hard work of getting to the top of a mountain. In other words, just using your diffuse mode doesn’t mean you can lollygag around and expect to get anywhere. As the days and weeks pass, it’s the distributed practice—the back and forth between focused-mode attention and diffuse-mode relaxation—that does the trick.
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General Diffuse-Mode Activators
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Take a step back and look dispassionately at your strengths and weaknesses. If you need more time to learn math and science, that’s simply the reality.
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avoid the temptation to keep up with your peers.
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You may be surprised to discover that learning slowly can mean you learn more deeply than your fast-thinking classmates.
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accepting the first idea that comes to mind when you are working on an assignment or test problem can prevent you from finding a better solution.
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their mind itself can’t move away enough to see a new approach to the problem.
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Turning his eyes and attention elsewhere likely was critical in allowing his diffuse intuition to go to work on his game with Kasparov.
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His expertise in chess probably played a role, along with his own intuitive practice skills. This is a hint that you, too, may be able to develop ways to quickly toggle between the focused and diffuse modes as you develop your expertise in a subject.
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deep focused attention is an important resource that you don’t want to get pulled out of.
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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. Each interlude in which you are not directly focused on the problem allows your diffuse mode to look at it in a fresh way. When you turn your focused attention back to the problem, you consolidate new ideas and patterns that the diffuse mode has delivered.
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Learning well means allowing time to pass between focused learning sessions, so the neural patterns have time to solidify properly. It’s like allowing time for the mortar to dry when you are building a brick wall, as shown on the left. Trying to learn everything in a few cram sessions doesn’t allow time for neural structures to become consolidated in your long-term memory—the