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What do I mean by abstractness? You can point to a real live cow chewing its cud in a pasture and equate it with the letters c-o-w on the page. But you can’t point to a real live plus sign that the symbol “+” is modeled after—the idea underlying the plus sign is more abstract. By encryptedness, I mean that one symbol can stand for a number of different operations or ideas, just as the multiplication sign symbolizes repeated addition.
This is why dealing with procrastination, while important in studying any discipline, is particularly important in math and science. We’ll be talking more about this later.
its really important to pay attention
Einstellung effect
This kind of wrong approach is especially easy to do in science because sometimes your initial intuition about what’s happening is misleading. You have to unlearn your erroneous older ideas even while you’re learning
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.
please review
And just having a little knowledge of the relevant math can help prevent you from defaulting on your mortgage—a situation that can have a major negative impact on your life.
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,
Similar things happened when I was writing a school paper, trying to come up with an idea for a school project, or trying to solve a difficult math problem. I now follow the rule of thumb that is basically: 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.
Videoo editing
“Befuddlement is a healthy part of the learning process. When students approach a problem and don’t know how to do it, they’ll often decide they’re no good at the subject.
Old me
are leaving yourself only enough time to do superficial focused-mode learning. You are also increasing your stress level because you know you have to complete what feels like an unpleasant task.
Start a habit to stop this
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.
Why is procrastination sometimes a special challenge for those who are studying math and science?
on understanding the problem itself.
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). 2. 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
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Lessons from Thomas Edison’s Frying
The key is to do something else until your brain is consciously free of any thought of the problem.
the bed, the bath, or the bus.2 One
The 3 B's
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.
“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.
When you are working start early
But the longer you spend in focused mode, the more mental resources you use. It’s like a concentrated, extended set of mental weight lifting. That’s why brief interludes that involve movement or talking with friends, where you don’t have to concentrate intently, can be so refreshing.
you have a limit on yoor mental will power
Taking time off between weight sessions helps build strong muscles in the long run. Consistency over time is key!
lighter load of math and science courses can, for many, be the equivalent of a heavy load of other types of courses. Especially in the early stages of college, avoid the temptation to keep up with your peers.
Incidentally, Carlsen probably also knew his bouncing from his chair would distract Kasparov. Even slight distractions at that level of play can be disconcerting—a reminder for you that deep focused attention is an important resource that you don’t want to get pulled out of. (Unless,
tried taking a break today with a calculus problem that was tricky and was starting to infuriate me. In the car on the way to the Renaissance festival, it came to me and I had to write it on a napkin before I forgot! (Always have napkins in your car. You never know.)”
good rule of thumb, when you are first learning new concepts, is not to let things go untouched for longer than a day.
And don’t wait until the week before midterms or final exams for this assistance. Go early and often. The teacher can often rephrase or explain in a different way that allows you to grasp the topic.
Putting a day between bouts of repetition—extending your practice over a number of days—does make a difference. Research has shown that if you try to glue things into your memory by repeating something twenty times in one evening, for example, it won’t stick nearly as well as it will if you practice it the same number of times over several days or weeks.
Dealing with fear: A motivational poster I received after giving a talk at Facebook headquarters reads: “What would you do if you weren’t afraid?” I try to look at this daily, and I aim to do something fearless every day. What are you afraid of? Don’t let it stop you!
Defense Language Institute,
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
