Mind for Numbers

Question 1

Why is diffused mode thinking essential?

Answer 1

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.

Question 2

What is the key to moving on from a subject?

Answer 2

The key is to do something else until your brain is consciously free of any thought of the problem

Question 3

How do focused and diffused mode work together?

Answer 3

Even if the solution doesn’t appear, you will often be further along in your understanding. It can take a lot of hard focused-mode work beforehand, but the sudden, unexpected solution that emerges from the diffuse mode can make it feel almost like the “aha!” mode.

Question 4

Why are naps important?

Answer 4

Salvador Dalí, like Thomas Edison, also used a nap and the clatter of an object falling from his hand to tap into his diffuse-mode creative perspectives. (Dalí called this “sleeping without sleeping.”6)

Question 5

What happens to your brain when you relax?

Answer 5

Every time you relax and think of nothing in particular, your brain enters into a natural default mode that’s a form of diffuse thinking.

Question 6

What should you not do when working on an assignment or test problem?

Answer 6

Remember, accepting the first idea that comes to mind when you are working on an assignment or test problem can prevent you from finding a better solution.

Question 7

How does closing your eyes help to renew consciousness?

Answer 7

Closing our eyes seems to provide a micropause that momentarily deactivates our attention and allows us, for the briefest of moments, to refresh and renew our consciousness and perspective.

Question 8

How long should you give the diffuse mode?

Answer 8

Usually a few hours is long enough for the diffuse mode to make significant progress but not so long that its insights fade away before being passed on to the focused mode.

Question 9

What should you do when you are genuinely stuck?

Answer 9

when you’re genuinely stuck, nothing is more helpful than getting insight from classmates, peers, or the instructor. Ask someone else for a different perspective on how to solve the problem or a different analogy to understand the concept;

Question 10

What speeds up learning during the chunking stage?

Answer 10

Closing the book and testing yourself on how to solve the problems will also speed up your learning at this stage.

Question 11

How to know when not to use chunks?

Answer 11

practicing with both related and unrelated problems so you see not only when to use the chunk, but when not to use it.

Question 12

What is good practice after a lecture?

Answer 12

rewrite your notes during the evening after a lecture.

Question 13

How to learn a new concept?

Answer 13

Pick a mathematical or scientific concept from your notes or from a page in the book. Read it over, then look away and see what you can recall—working toward understanding what you are recalling at the same time. Then glance back, reread the concept, and try it again.

Question 14

What does the retrieval process do?

Answer 14

the retrieval process itself enhances deep learning and helps us begin forming chunks.

Question 15

What is interleaving?

Answer 15

Interleaving means practice by doing a mixture of different kinds of problems requiring different strategies.

Question 16

How to use interleaving when preparing for a test?

Answer 16

Interleaving your studies—making a point to review for a test, for example, by skipping around through problems in the different chapters and materials—can sometimes seem to make your learning more difficult. But in reality, it helps you learn more deeply.

Question 17

Name the steps to approach new material.

Answer 17

1. 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.
2. Review lecture notes (attend every lecture as much as possible). One hour of lecture is worth two hours reading the book. I learn far more efficiently if I am faithful in attending lectures and taking detailed notes—not just staring at my watch and waiting for it to be over. I review my notes the following day while the subjects are still fresh in my mind.
3. Rework example problems presented in lecture notes. It never helped me to practice problems given by either the instructor or the textbook that didn’t have solutions to provide feedback. With the example problems I already had a step- by- step solution available if necessary. Reworking helps solidify chunks. I use different- colored pens when I study: blue, green, red— not just black. I found that it helps me focus on reading my notes better; things pop out more, instead of blending together into a confusing collage of inexplicable mathematical chaos on the page.
4. Work assigned homework and practice exam/quiz questions. This builds “muscle memory” chunks for the mind in solving certain types of problems.

Question 18

What are the benefits of having a smaller working memory?

Answer 18

Having a somewhat smaller working memory means you can more easily generalize your learning into new, more creative combinations

Question 19

How to go from average to natural gifts?

Answer 19

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” gift

Question 20

How to improve working memory?

Answer 20

Researchers on recall have found that doing exercises to repeat longer and longer strings of digits backward seems to improve working memory.

Question 21

How did Einstein’s theory of relativity come about?

Answer 21

Einstein’s theories of relativity arose not from his mathematical skills (he often needed to collaborate with mathematicians to make progress) but from his ability to pretend. He imagined himself as a photon moving at the speed of light, then imagined how a second photon might perceive him. What would that second photon see and feel?

Question 22

How to relax before a test?

Answer 22

If you write about your thoughts and feelings about an upcoming test immediately before you take the test, it can lessen the negative impact of pressure on performance.