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We don’t engage in passive rereading because we are dumb or lazy. We do it because we fall prey to a cognitive illusion. When we read material over and over, the material becomes familiar and fluent, meaning it is easy for our minds to process. We then think that this easy processing is a sign that we have learned something well, even though we have not.
I began to pick up little tricks about not only how to study but when to quit.
Diffuse-mode thinking is what happens when you relax your attention and just let your mind wander.
(The diffuse mode must have clay to make bricks!)
(Metaphors are powerful tools for learning in math and science.)
Related to these difficulties in math and science is another challenge. It’s called the Einstellung effect (pronounced EYE-nshtellung). In this phenomenon, an idea you already have in mind, or your simple initial thought, prevents a better idea or solution from being found.
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.
The harder you push your brain to come up with something creative, the less creative your ideas will be.
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.
But the learning process is all about working your way out of confusion. Articulating your question is 80 percent of the battle. By the time you’ve figured out what’s confusing, you’re likely to have answered the question yourself!”
when you procrastinate, you are leaving yourself only enough time to do superficial focused-mode learning.
If you cram for a test at the last minute or quickly breeze through your homework, you won’t have time for either learning mode to help you tackle the tougher concepts and problems or to help you synthesize the connections in what you are learning.
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 (but not in a row).
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.
I think most clearly when I’m driving. Sometimes I’ll just take a break and drive...
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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.4 After your break, when you return to the problem at hand, you will often be surprised at how easily the solution pops into place.
We learn a great deal from our failures in math and science.
“I have not failed. I’ve just found 10,000 ways that won’t work.”
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.
Every time you relax and think of nothing in particular, your brain enters into a natural default mode that’s a form of diffuse thinking.
But the longer you spend in focused mode, the more mental resources you use.
According to recent research, blinking is a vital activity that provides another means of reevaluating a situation
So blinking may momentarily disconnect us from our focused-mode perspective. But on the other hand, deliberately closing our eyes may help us focus more deeply—people
Rising frustration is usually a good time-out signal for you, signaling that you need to shift to diffuse mode.
The teacher can often rephrase or explain in a different way that allows you to grasp the topic.
You may be surprised to learn that simply being awake creates toxic products in your brain. During sleep, your cells shrink, causing a striking increase in the space between your cells. This is equivalent to turning on a faucet—it allows fluid to wash past and push the toxins out.
Use the focused mode to first start grappling with concepts and problems in math and science. After you’ve done your first hard focused work, allow the diffuse mode to take over. Relax and do something different! When frustration arises, it’s time to switch your attention to allow the diffuse mode to begin working in the background.
It’s best to work at math and science in small doses—a little every day. This gives both the focused and diffuse modes the time they need to do their thing so you can understand what you are learning. That’s how solid neural structures are built.
Spaced repetition helps move items from working memory to long-term memory.
Interestingly, when you are stressed, your attentional octopus begins to lose the ability to make some of those connections.
one of the first steps toward gaining expertise in math and science is to create conceptual chunks—mental leaps that unite separate bits of information through meaning.
Chunking the information you deal with helps your brain run more efficiently.
just understanding how a problem was solved does not necessarily create a chunk that you can easily call to mind later.
Context means going beyond the initial problem and seeing more broadly, repeating and practicing with both related and unrelated problems so you see not only when to use the chunk, but when not to use it.
Ultimately, practice helps you broaden the networks of neurons connected to your chunk, ensuring that it is not only firm, but also accessible from many different paths.
Using recall—mental retrieval of the key ideas—rather than passive rereading will make your study time more focused and effective.
Merely glancing at the solution to a problem and thinking you truly know it yourself is one of the most common illusions of competence in learning.
Pick a mathematical or scientific concept from your notes or from a page in the book. Read it over, then look away and see what you can recall—working toward understanding what you are recalling at the same time. Then glance back, reread the concept, and try it again. At the end of this exercise, you will probably be surprised to see how much this simple recall exercise helped improve your understanding of the concept.
Lady Luck favors the one who tries.
Most difficult problems are solved through intuition, because they make a leap away from what you are familiar with.
Solving problems in math and science is like playing a piece on the piano. The more you practice, the firmer, darker, and stronger your mental patterns become.
I also talk about the need to study every day, not necessarily for long periods of time but just enough to keep what you are learning at the tip of your tongue.
recalling material when you are outside your usual place of study helps you strengthen your grasp of the material by viewing it from a different perspective.
thirty minutes with a professor asking questions is easily worth three hours reading the book.
