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April 5, 2020
Focused-mode thinking is essential for studying math and science. It involves a direct approach to solving problems using rational, sequential, analytical approaches. The focused mode is associated with the concentrating abilities of the brain’s prefrontal cortex, located right behind your forehead.
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.
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!)
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,
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.
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,
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.
People with strong self-control can have the most difficulty in getting themselves to turn off their focused mode so that the diffuse mode can begin its work.
Working memory is the part of memory that has to do with what you are immediately and consciously processing in your mind.
Generally, you can hold about four items in your working memory, as shown in the four-item memory on the left. When you master a technique or concept in math or science, it occupies less space in your working memory. This frees your mental thinking space so that it can more easily grapple with other ideas, as shown on the right.
spaced repetition. As you may have guessed, this technique involves repeating what you are trying to retain, like a new vocabulary word or a new problem-solving technique, but spacing this repetition out over a number of days.
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.
Creativity is a numbers game: The best predictor of how many creative works we produce in our lifetime is . . . the number of works we produce.
Solomon Shereshevsky’s extraordinary memory came with a surprising drawback. His individual memory traces were each so colorful and emotional—so rich with connections—that they interfered with his ability to put those traces together and create conceptual chunks.
Chunks are pieces of information that are bound together through meaning.
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.
when you are first trying to understand how to work a problem, you have a heavy cognitive load—so it helps to start out with a fully worked-through example.
The first step in chunking, then, is to simply focus your attention on the information you want to chunk.
The second step in chunking is to understand the basic idea you are trying to chunk,
The third step to chunking is gaining context so you see not just how, but also when to use this chunk.
Attempting to recall the material you are trying to learn—retrieval practice—is far more effective than simply rereading the material.
You must have information persisting in your memory if you are to master the material well enough to do well on tests and think creatively with it.
Steven Johnson, in his brilliant book Where Good Ideas Come From,
In the same amount of time, by simply practicing and recalling the material, students learned far more and at a much deeper level than they did using any other approach,
the retrieval process itself enhances deep learning and helps us begin forming chunks.
Doing something physically active is especially helpful when you have trouble grasping a key idea.
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.
Interleaving means practice by doing a mixture of different kinds of problems requiring different strategies.
Rather than devote a long session to the study or practice of the same skill or concept so that overlearning occurs, students should divide their effort across several shorter sessions.
There’s evidence that writing by hand helps get the ideas into mind more easily than if you type the answer.
Simple recall—trying to remember the key points without looking at the page—is one of the best ways to help the chunking process along.
Paul’s Techniques for Limited Study Time
Read (but don’t yet solve) assigned homework and practice exams/quizzes. With this initial step I prime my mental pump for learning new concepts—new chunks.
Review lecture notes
Rework example problems presented in lecture notes.
Work assigned homework and practice exam/quiz questions. This builds “muscle memory” chunks for the mind in solving certain types of problems.
We procrastinate about things that make us feel uncomfortable.
As procrastination expert Piers Steel, author of The Procrastination Equation, points out, “If you protect your routine, eventually it will protect you.”3
By focusing on process rather than product, you allow yourself to back away from judging yourself (Am I getting closer to finishing?) and allow yourself to relax into the flow of the work.
Multitasking is like constantly pulling up a plant. This kind of constant shifting of your attention means that new ideas and concepts have no chance to take root and flourish.
on average, students who allow themselves to multitask while studying or sitting in class have been found to receive consistently lower grades.
the generation effect. Generating (that is, recalling) the material helps you learn it much more effectively than simply rereading it.
You will go through some periods when you seem to take an exasperating step backward in your understanding. This a natural phenomenon that means your mind is wrestling deeply with the material. You’ll find that when you emerge from these periods of temporary frustration, your knowledge base will take a surprising step forward.
Choking—panicking to the point where you freeze—can happen when your working memory is filled to capacity, yet you still don’t have enough room for the additional critical pieces you need to solve a problem.
Chunking compresses your knowledge and makes room in your working memory for those pieces so you don’t go into mental overload so easily.
Testing in itself is a powerful learning experience. It changes and adds to what you know, also making dramatic improvements in your ability to retain the material.
Research has confirmed that a special place devoted just to working is particularly helpful.2
