A Mind for Numbers: How to Excel at Math and Science (Even If You Flunked Algebra)

by Barbara Oakley

The Law of Serendipity: Lady Luck favors the one who tries

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.

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,

The harder you push your brain to come up with something creative, the less creative your ideas will be.

To learn about and be creative in math and science, we need to strengthen and use both the focused and diffuse modes.

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.

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.