Thought I was getting a book about math, but ended up being a surprisingly good book about learning in general. Main points are about diffused thinking vs focused thinking.
Your brain can work on a problem while you are sleeping only if you concentrate on trying to solve the problem before falling asleep.
Toggle your thinking - getting a glimpse of what you are learning before returning later to more fully understand what’s going on.
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.
Focused mode is used to concentrate on something that’s already tightly connected in your mind, because you are familiar and comfortable with the underlying concepts.
The diffuse approach involves a big-picture perspective. Useful when you are learning something new. If you are trying to understand or figure out something new, turn off your precision-focused thinking and turn on your “big picture” diffuse mode.
As long as we are consciously focusing on a problem, we are blocking the diffuse mode.
Do something else until your brain is consciously free of any thought of the problem.
Accepting the first idea that comes to mind can prevent you from finding a better solution.
A few hours is long enough for the diffuse mode to make significant progress but not so long that its insights fade away.
When you are first learning new concepts, don't let things go untouched for longer than a day.
Frustration is usually a good time-out signal.
Repeating something twenty times in one evening, it won’t stick nearly as well as it will if you practice it the same number of times over several days or weeks.
Einstellung: “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. The Einstellung effect is the negative effect of previous experience when solving new problems.”
The best language programs incorporate structured practice that includes plenty of repetition and rote, focused-mode learning of the language, along with more diffuse-like free speech with native speakers.
Once you chunk an idea or concept, you don’t need to remember all the little underlying details; you’ve got the main idea - the chunk - and that’s enough.
Rereading text seems to be effective if you let time pass between rereadings so that it becomes more of an exercise in spaced repetition.
Glancing at the solution to a problem and thinking you truly know it yourself is one of the most common illusions of competence in learning.
Key to the slow hunch is simply having mental access to aspects of an idea. That way, some aspects can tentatively and randomly combine with others until eventually, beautiful novelty can emerge.
A key difference between creative scientists and technically competent but nonimaginative ones is their breadth of interest.
Strengthening an initial learning pattern within a day after you first begin forming it is important.
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.
Practice by doing a mixture of different kinds of problems requiring different strategies.
Overlearning means a student continues to study or practice immediately after some criterion has been achieved. Once they understand ‘X,’ they should move on to something else and return to ‘X’ on another day.
Rather than devote a long session to the study or practice of the same skill, students should divide their effort across several shorter sessions.
Two men sat in front of the audience and blithely downed more than double a deadly dose of arsenic. In tiny doses, arsenic doesn’t seem harmful. You can even build up an immunity to its effects. This can allow you to take large doses and look healthy even as the poison is slowly increasing your risk of cancer and ravaging your organs. Procrastinators put off just that one little thing. They do it again and again, gradually growing used to it. They can even look healthy.
The dread of doing a task uses up more time and energy than doing the task itself.
Learned industriousness helps brighten tasks you once thought were boring.
Use the “Pomodoro”.
If you learn under mild stress, you can handle greater stress much more easily.
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.
Work a key problem all the way through. Do another repetition of the problem. Before you go to sleep, work the problem again. As soon as you can the next day, work the problem again. You should see that you are able to solve the problem more quickly now. Your understanding should be deeper. You may even wonder why you ever had any trouble with it.
We trick ourselves into doing what we ought to be doing. The highest-performing people I know are those who have installed the best tricks in their lives. The smart part of us sets up things for us to do that the not-so-smart part responds to almost automatically,
Those who are committed to maintaining healthy leisure time along with their hard work outperform those who doggedly pursue an endless treadmill.
Transform distant deadlines into daily ones.
Calculus Made Easy, by Silvanus Thompson, has helped generations of students master the subject.
“Do you know the crazy shape of the crankshaft in a car?”
“Yeah, what of it?”
“Good. Now tell me: How did you describe it when you were talking to yourself?”
It was then that Feynman realized that thoughts can be visual as well as verbal.