--- ## Highlights Focused versus Diffuse Thinking (Location 306) back and forth between these two modes in your day-to-day activities. You’re in either one mode or the other—not consciously in both at the same time. The diffuse mode does seem to be able to work quietly in the background on something you are not actively focusing on.3 Sometimes you may also flicker for a rapid moment to diffuse-mode thinking. Focused-mode (Location 311) 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.4 Turn your attention to something and bam—the focused mode is on, like the tight, penetrating beam of a flashlight. (Location 314) 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. This relaxation can allow different areas of the brain to hook up and return valuable insights. Unlike the focused mode, the diffuse mode seems less affiliated with any one area of the brain—you can think of it as being “diffused” throughout the brain. (Location 321) the focused mode is used to concentrate on something that’s already tightly connected in your mind, often because you are familiar and comfortable with the underlying concepts. (Location 340) When you focus on something, the consciously attentive prefrontal cortex automatically sends out signals along neural pathways. These signals link different areas of your brain related to what you’re thinking about. This process is a little like an octopus that sends its tentacles to different areas of its surroundings to fiddle with whatever it’s working on. (Location 346) In our pinball analogy, it’s as if the abstractness and encryptedness of math can make the pinball bumpers a bit spongier—it takes extra practice for the bumpers to harden and the pinball to bounce properly. (Location 376) Einstellung effect (pronounced EYE-nshtellung). In this phenomenon, an idea you already have in mind, or your simple initial thought, prevents a better idea or solution from being found. (Location 379) one significant mistake students sometimes make in learning math and science is jumping into the water before they learn to swim.11 In other words, they blindly start working on homework without reading the textbook, attending lectures, viewing online lessons, or speaking with someone knowledgeable. (Location 390) 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, (Location 408) The harder you push your brain to come up with something creative, the less creative your ideas will be. (Location 416)