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 spent lots of time gaining this expertise — the better I got, the more I enjoyed what I was doing. And the more I enjoyed what I was doing, the more time I spent on it. My success reinforced my desire to practice, and that built more success.
As you first begin looking at a chapter or section of a book that teaches concepts of math or science, it helps to take a “picture walk” through the chapter, glancing not only at the graphics, diagrams, and photos, but also at the section headings, summary, and even questions at the end of the chapter, if the book has them. You’ll be surprised at how spending a minute or two glancing ahead before you read in depth will help you organize your thoughts. You’re creating little neural hooks to hang your thinking on, making it easier to grasp the concepts.
Focused problem solving in math and science is often more effortful than focused-mode thinking involving language and people. This may be because humans haven’t evolved over the millennia to manipulate mathematical ideas, which are frequently more abstractly encrypted than those of conventional language. Obviously, we can still think about math and science — it’s just that the abstractness and encryptedness adds a level — sometimes a number of levels — of complexity.
Einstellung effect is the development of a mechanized state of mind. Often called a problem solving set, Einstellung refers to a person’s predisposition to solve a given problem in a specific manner even though better or more appropriate methods of solving the problem exist.
One significant mistake students sometimes make in learning math and science is jumping into the water before they learn to swim. 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.
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. For most people, shifting from focused to diffuse mode happens naturally if you distract yourself and then allow a little time to pass. The key is to do something else until your brain is consciously free of any thought of the problem.
When faced with a difficult problem, instead of focusing intently on it, Edison, according to legend, took a nap. But he did so while sitting in a lounge chair, holding a ball bearing in his hand above a plate on the floor. As he relaxed, his thoughts moved toward free and open diffuse-mode thinking. When Edison fell asleep, the ball bearing fell from his hands. The clatter woke him so he could grasp the fragments of his diffuse-mode thinking to create new approaches.
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. Each interlude in which you are not directly focused on the problem allows your diffuse mode to look at it in a fresh way. When you turn your focused attention back to the problem, you consolidate new ideas and patterns that the diffuse mode has delivered.
As it turns out, 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.
Learning takes place in two ways. There is a bottom-up chunking process where practice and repetition can help you both build and strengthen each chunk, so you can easily gain access to it when needed. And there is a top-down “big picture” process that allows you to see where what you are learning fits in.
Intention to learn is helpful only if it leads to the use of good learning strategies. — Alan Baddeley
If you learn under mild stress, you can handle greater stress much more easily. For example, as researcher Sian Beilock describes in her book Choke, golfers who practice putting in front of others aren’t fazed later on when they have to perform before an audience in competitions. In the same way, if you get used to figuring things out under a mild time crunch, you are much less likely to choke later, when you are in a high-pressure test-taking situation.
The dread of doing a task uses up more time and energy than doing the task itself. — Rita Emmett
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.
Research has shown that testing isn’t just a means of measuring how much you know. 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.
When I am not working, I must relax — not work on something else! — B. F. Skinner
Focusing your attention brings something into your temporary working memory. But for that “something” to move from working memory to long-term memory, two things should happen: the idea should be memorable and it must be repeated.
Chess, that bastion of intellectuals, has some elite players with roughly average IQs. These seemingly middling intellects are able to do better than some more intelligent players because they practice more. That’s the key idea. Every chess player, whether average or elite, grows talent by practicing. It is the practice — particularly deliberate practice on the toughest aspects of the material — that can help lift average brains into the realm of those with more “natural” gifts.
There are only two ways to live your life. One is as though nothing is a miracle. The other is as if everything is. — Albert Einstein
There’s evidence that myelin sheaths, the fatty insulation that helps signals move more quickly along a neuron, often don’t finish developing until people are in their twenties. This may explain why teenagers often have trouble controlling their impulsive behavior — the wiring between intention and control areas isn’t completely formed.
Deficiencies of innate ability may be compensated for through persistent hard work and concentration. One might say that work substitutes for talent, or better yet that it creates talent. — Santiago Ramón y Cajal
You may think you really have to understand something in order to explain it. But observe what happens when you are talking to other people about what you are studying. You’ll be surprised to see how often understanding arises as a consequence of attempts to explain to others and yourself, rather than the explanation arising out of your previous understanding. This is why teachers often say that the first time they ever really understood the material was when they had to teach it.
The first principle is that you must not fool yourself — and you are the easiest person to fool.— Richard Feynman
One of the most-cited papers in sociology, “The Strength of Weak Ties,” by sociologist Mark Granovetter, describes how the number of acquaintances you have — not the number of good friends — predicts your access to the latest ideas as well as your success on the job market.
Those you study with should have, at least on occasion, an aggressively critical edge to them. Research on creativity in teams has shown that nonjudgmental, agreeable interactions are less productive than sessions where criticism is accepted and even solicited as part of the game.
If you compare how much you learn by spending one hour studying versus one hour taking a test on that same material, you will retain and learn far more as a result of the hour you spent taking a test. Testing, it seems, has a wonderful way of concentrating the mind.
Reshaping your brain is under your control. The key is patient persistence — working knowledgeably with your brain’s strengths and weaknesses.
There are two major memory systems:
Working memory — like a juggler who can keep only four items in the air.
Long-term memory — like a storage warehouse that can hold large amounts of material, but needs to be revisited occasionally to keep the memories accessible. Spaced repetition helps move items from working memory to long-term memory.
We procrastinate about things that make us feel uncomfortable. But what makes us feel good temporarily isn’t necessarily good for us in the long run. Procrastination can be like taking tiny amounts of poison. It may not seem harmful at the time. But the long-term effects can be very damaging.
Mental contrasting is a powerful motivating technique — think about the worst aspects of your present or past experiences and contrast these with the upbeat vision of your future.
In learning, persistence is often far more important than intelligence.
People are competitive as well as cooperative. There will always be those who criticize or attempt to undermine any effort or achievement you make. Learn to deal dispassionately with these issues
Ten rules of good studying
- Use recall
- Test yourself
- Chunk your problems
- Space your repetition
- Alternate different problem-solving techniques during your practice
- Take breaks
- Use explanatory questioning and simple analogies
- Focus
- Eat your frogs first
- Make a mental contrast
Ten rules of bad studying
- Passive rereading
- Letting highlights overwhelm you
- Merely glancing at a problem’s solution and thinking you know how to do it
- Waiting until the last minute to study
- Repeatedly solving problems of the same type that you already know how to solve
- Letting study sessions with friends turn into chat sessions
- Neglecting to read the textbook before you start working problems.
- Not checking with your instructors or classmates to clear up points of confusion
- Thinking you can learn deeply when you are being constantly distracted
- Not getting enough sleep
Source: https://medium.com/@sawantprasad/a-mind-for-numbers-by-barbara-oakley-notes-6daaaecb4fa9