This are some quotes extracted from the book “A Mind For Number” by Barbara Oakley
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“They most commonly use the strategy of repeated reading—simply reading through books or notes over and over. We and other researchers have found that this passive and shallow strategy often produces minimal or no learning. We call this “labor in vain”—students are putting in labor but not getting anywhere”
“the focused mode and diffuse mode, respectively—these modes are highly important for learning.2 It seems you frequently switch back and forth between these two modes in your day-to-day activities”
“The diffuse mode does seem to be able to work quietly in the background on something you are not actively focusing on.”
“Focused-mode thinking is essential for studying math and science. It involves a direct approach to solving problems using rational, sequential, analytical approaches”
“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 what happens when you relax your attention and just let your mind wander. This relaxation can allow different areas of the brain to hook up and return valuable insights.”
“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”
“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”
“When you relax your mind, releasing your attention and focusing on nothing in particular, the solution can most easily come to you.”
“some children get this exercise instantly, while some highly intelligent professors finally just give up”
“Our brain uses two very different processes for thinking—the focused and diffuse modes. It seems you toggle back and forth between these modes, using one or the other. It is typical to be stumped by new concepts and problems when we first focus on them. To figure out new ideas and solve problems, it’s important not only to focus initially, but > also to subsequently turn our focus away from what we want to learn. The Einstellung effect refers to getting stuck in solving a problem or understanding a concept as a result of becoming fixated on a flawed approach. Switching modes from focused to diffuse can help free you from this effect. Keep in mind, then, that sometimes you will need to be flexible in your thinking. You may need to switch modes to solve a problem or understand a concept. Your initial ideas about problem solving can sometimes be very misleading.”
“The key is to do something else until your brain is consciously free of any thought of the problem.”
“three B’s usually seems to do the trick: the bed, the bath, or the bus”
“USE THESE DIFFUSE-MODE TOOLS AS REWARDS AFTER FIRM FOCUSED-MODE WORK14
General Diffuse-Mode Activators Go to the gym Play a sport like soccer or basketball Jog, walk, or swim Dance Go for a drive (or tag along for the ride) Draw or paint Take a bath or shower Listen to music, especially without words Play songs you know well on a musical instrument Meditate or pray Sleep (the ultimate diffuse mode!)”
“Play video games Surf the web Talk to friends Volunteer to help someone with a simple task Read a relaxing book Text friends Go to a movie or play Television (dropping a remote if you fall asleep doesn’t count)”
“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”
“1. The first step in chunking, then, is to simply focus your attention on the information you want to chunk”
“2. The second step in chunking is to understand the basic idea you are trying to chunk, ”
“3. The third step to chunking is gaining context so you see not just how, but also when to use this chunk. ”
“Using recall—mental retrieval of the key ideas—rather than passive rereading will make your study time more focused and effective”
“Most difficult problems are solved through intuition, because they make a leap away from what you are familiar with.”
“Metaphors can help you learn difficult ideas more quickly. Repetition is critical in allowing you to firm up what you want to remember before the ideas fade away. Meaningful groups and abbreviations can allow you to simplify and chunk what you are trying to learn so you can store it more easily in memory. Stories—even if they are just used as silly memory tricks—can allow you to more easily retain what you are trying to learn. Writing and saying what you are trying to learn seems to enhance retention. Exercise is powerfully important in helping your neurons to grow and make new connections.”
“when you start working problems, start first with what appears to be the hardest one. But steel yourself to pull away within the first minute or two if you get stuck or get a sense that you might not be on the right track.”
TEN RULES OF GOOD STUDYING
Use recall. After you read a page, look away and recall the main ideas. Highlight very little, and never highlight anything you haven’t put in your mind first by recalling. Try recalling main ideas when you are walking to class or in a different room from where you originally learned it. An ability to recall—to generate the ideas from inside yourself—is one of the key indicators of good learning.
Test yourself. On everything. All the time. Flash cards are your friend.
Chunk your problems. Chunking is understanding and practicing with a problem solution so that it can all come to mind in a flash. After you solve a problem, rehearse it. Make sure you can solve it cold—every step. Pretend it’s a song and learn to play it over and over again in your mind, so the information combines into one smooth chunk you can pull up whenever you want.
Space your repetition. Spread out your learning in any subject a little every day, just like an athlete. Your brain is like a muscle—it can handle only a limited amount of exercise on one subject at a time.
Alternate different problem-solving techniques during your practice. Never practice too long at any one session using only one problem-solving technique—after a while, you are just mimicking what you did on the previous problem. Mix it up and work on different types of problems. This teaches you both how and when to use a technique. (Books generally are not set up this way, so you’ll need to do this on your own.) After every assignment and test, go over your errors, make sure you understand why you made them, and then rework your solutions. To study most effectively, handwrite (don’t type) a problem on one side of a flash card and the solution on the other. (Handwriting builds stronger neural structures in memory than typing.) You might also photograph the card if you want to load it into a study app on your smartphone. Quiz yourself randomly on different types of problems. Another way to do this is to randomly flip through your book, pick out a problem, and see whether you can solve it cold.
Take breaks. It is common to be unable to solve problems or figure out concepts in math or science the first time you encounter them. This is why a little study every day is much better than a lot of studying all at once. When you get frustrated with a math or science problem, take a break so that another part of your mind can take over and work in the background.
Use explanatory questioning and simple analogies. Whenever you are struggling with a concept, think to yourself, How can I explain this so that a ten-year-old could understand it? Using an analogy really helps, like saying that the flow of electricity is like the flow of water. Don’t just think your explanation—say it out loud or put it in writing. The additional effort of speaking and writing allows you to more deeply encode (that is, convert into neural memory structures) what you are learning.
Focus. Turn off all interrupting beeps and alarms on your phone and computer, and then turn on a timer for twenty-five minutes. Focus intently for those twenty-five minutes and try to work as diligently as you can. After the timer goes off, give yourself a small, fun reward. A few of these sessions in a day can really move your studies forward. Try to set up times and places where studying—not glancing at your computer or phone—is just something you naturally do.
Eat your frogs first. Do the hardest thing earliest in the day, when you are fresh.
Make a mental contrast. Imagine where you’ve come from and contrast that with the dream of where your studies will take you. Post a picture or words in your workspace to remind you of your dream. Look at that when you find your motivation lagging. This work will pay off both for you and those you love!”