More on this book
Community
Kindle Notes & Highlights
The intense effort before a vacation or falling asleep is important for priming your brain; otherwise it will work on some other problem.
Growing up, I hated math and science. I flunked my way through high school math and science courses, and only started studying trigonometry—remedial trigonometry—when I was twenty-six years old.
Focused-mode thinking is essential for studying math and science. It involves a direct approach to solving problems using rational, sequential, analytical approaches.
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 insights often flow from preliminary thinking that’s been done in the focused mode.
(Metaphors are powerful tools for learning in math and science.)
the focused-mode thought is following along a route you’ve already practiced or experienced.
The focused approach relates to intense concentration on a specific problem or concept. But while in focused mode, sometimes you inadvertently find yourself focusing intently and trying to solve a problem using erroneous thoughts that are in a different place in the brain from the “solution” thoughts you need to actually solve the problem.
The diffuse approach on the right often involves a big-picture perspective. This thinking mode is useful when you are learning something new. As you can see, the diffuse mode doesn’t allow you to focus tightly and intently to solve a specific problem—but it can allow you to get closer to where that solution lies because you’re able to travel much farther before running into another bumper.
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.
You have to unlearn your erroneous older ideas even while you’re learning new ones.
This is precisely why one significant mistake students sometimes make in learning math and science is jumping into the water before they learn to swim.11 In other words, they blindly start working on homework without reading the textbook, attending lectures, viewing online lessons, or speaking with someone knowledgeable. This is a recipe for sinking. It’s like randomly allowing a thought to pop off in the focused-mode pinball machine without paying any real attention to where the solution truly lies.
The harder you push your brain to come up with something creative, the less creative your ideas will be.
Evidence suggests that to grapple with a difficult problem, we must first put hard, focused-mode effort into it. (We learned that in grade school!) Here’s the interesting part: 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.
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.
Know that you are making progress with each mistake you catch when trying to solve a problem—finding errors should give you a sense of satisfaction.
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
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.
One of the most important tricks that helped me retool my brain was learning to avoid the temptation to take too many math and science classes at once.
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
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.
A good rule of thumb, when you are first learning new concepts, is not to let things go untouched for longer than a day.
Make it a rule to listen to study partners, friends, or loved ones who can sense when you are becoming dangerously frustrated. Sometimes it’s easier to listen to someone else than to yourself.
Ask someone else for a different perspective on how to solve the problem or a different analogy to understand the concept; however, it’s best that you first wrestle with the problem yourself before you talk to anyone else, because it can embed the basic concepts deeply enough that you become receptive to the explanation.
Research has shown that when your brain first puts an item of information in long-term memory, you need to revisit it a few times to increase the chances you’ll later be able to find it when you need it.
The next time you are tackling a tough problem, work on it for a few minutes. When you get stuck, move on to another problem. Your diffuse mode can continue working on the tougher problem in the background. When you later return to the tougher problem, you will often be pleasantly surprised by the progress you’ve made.
It’s as if the complete deactivation of the conscious “you” in the prefrontal cortex helps other areas of the brain start talking more easily to one another, allowing them to put together the neural solution to your problem as you sleep.26 (Of course, you must plant the seed for your diffuse mode by first doing focused-mode work.) It seems that if you go over the material right before taking a nap or going to sleep for the evening, you have an increased chance of dreaming about it. If you go even further and set it in mind that you want to dream about the material, it seems to improve your
...more
If you’re tired, it’s often best to just go to sleep and get up a little earlier the next day, so your reading is done with a better-rested brain.
“If I have trouble working on a problem, I lie down in my bed with an open notebook and pen and just write out thoughts about the problem as I fall asleep, as well as sometimes right after waking up. Some of what I write makes no sense, but sometimes I gain a totally new way of looking at my problem.”
It’s best to work at math and science in small doses—a little every day.
“What would you do if you weren’t afraid?”
This is why your brain doesn’t seem to work right when you’re angry, stressed, or afraid.
