A Mind for Numbers Quotes

“I think most clearly when I’m driving. Sometimes I’ll just take a break and drive around—this helps a lot.”
― Barbara Oakley, A Mind for Numbers: How to Excel at Math and Science

“A synthesis—an abstraction, chunk, or gist idea—is a neural pattern. Good chunks form neural patterns that resonate, not only within the subject we’re working in, but with other subjects and areas of our lives. The abstraction helps you transfer ideas from one area to another.15 That’s why great art, poetry, music, and literature can be so compelling. When we grasp the chunk, it takes on a new life in our own minds—we form ideas that enhance and enlighten the neural patterns we already possess, allowing us to more readily see and develop other related patterns.”
― Barbara Oakley, A Mind for Numbers: How to Excel at Math and Science

“Incidentally, the little book Calculus Made Easy, by Silvanus Thompson, has helped generations of students master the subject.”
― Barbara Oakley, A Mind for Numbers: How to Excel at Math and Science

“As writing coach Daphne Gray-Grant recommends to her writing clients: “Eat your frogs first thing in the morning.” Do the most important and most disliked jobs first, as soon as you wake up. This is incredibly effective.”
― Barbara Oakley, A Mind for Numbers: How to Excel at Math and Science

“If you don’t make a point of repeating what you want to remember, your “metabolic vampires” can suck away the neural pattern related to that memory before it can strengthen and solidify.”
― Barbara Oakley, A Mind for Numbers: How to Excel at Math and Science

“Interleaving means practice by doing a mixture of different kinds of problems requiring different strategies.”
― Barbara Oakley, A Mind for Numbers: How to Excel at Math and Science

“The number one thing I stress when students come to see me is that there is a direct connection between your hand and your brain, and the act of rewriting and organizing your notes is essential to breaking large amounts of information down into smaller digestible chunks. I have many students who prefer to type their notes in a Word document or on slides, and when these students are struggling, the first thing I recommend is to quit typing and start writing. In every case, they perform better on the next section of material.”
― Barbara Oakley, A Mind for Numbers: How to Excel at Math and Science

“As you can see from the following “top-down, bottom-up” illustration, 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. Both processes are vital in gaining mastery over the material.”
― Barbara Oakley, A Mind for Numbers: How to Excel at Math and Science

“Try doing a few situps, pushups, or jumping jacks. A little physical exertion can have a surprisingly positive effect on your ability to understand and recall.”
― Barbara Oakley, A Mind for Numbers: How to Excel at Math and Science

“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.”
― Barbara Oakley, A Mind for Numbers: How to Excel at Math and Science

“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.5 Diffuse-mode insights often flow from preliminary thinking that’s been done in the focused mode. (The diffuse mode must have clay to make bricks!)”
― Barbara Oakley, A Mind for Numbers: How to Excel at Math and Science

“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.”
― Barbara Oakley, A Mind for Numbers: How to Excel at Math and Science

“There is much creativity underlying math and science problem solving. Many people think that there’s only one way to do a problem, but there are often a number of different solutions, if you have the creativity to see them. For example, there are more than three hundred different known proofs of the Pythagorean theorem.”
― Barbara Oakley, A Mind for Numbers: How to Excel at Math and Science

“There are chunks related to both concepts and procedures that reinforce one another. Solving a lot of math problems provides an opportunity to learn why the procedure works the way it does or why it works at all. Understanding the underlying concept makes it easier to detect errors when you make them.”
― Barbara Oakley, A Mind for Numbers: How to Excel at Math and Science

“The first principle is that you must not fool yourself—and you are the easiest person to fool.”8 —Physicist Richard Feynman, advising how to avoid pseudo-science that masquerades as science”
― Barbara Oakley, A Mind for Numbers: How to Excel at Math and Science

“blinking is a vital activity that provides another means of reevaluating a situation. 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.16”
― Barbara Oakley, A Mind for Numbers: How to Excel at Math and Science

“The key is to do something else until your brain is consciously free of any thought of the problem.”
― Barbara Oakley, A Mind for Numbers: How to Excel at Math and Science

“You may want your learning to progress more quickly—to somehow command your diffuse mode to assimilate new ideas faster. But compare it to exercise. Constantly lifting weights won’t make your muscles any bigger— your muscles need time to rest and grow before you use them again.”
― Barbara Oakley, A Mind for Numbers: How to Excel at Math and Science

“The harder you push your brain to come up with something creative, the less creative your ideas will be. So far, I have not found a single situation where this does not apply. Ultimately, this means that relaxation is an important part of hard work— and good work, for that matter.”
― Barbara Oakley, A Mind for Numbers: How to Excel at Math and Science

“Persistence is often more important than intelligence.1 Approaching material with a goal of learning it on your own gives you a unique path to mastery. Often,”
― Barbara Oakley, A Mind for Numbers: How to Excel at Math and Science

“It seems people can enhance the development of their neuronal circuits by practicing thoughts that use those neurons.9 We’re still in the infancy of understanding neural development, but one thing is becoming clear—we can make significant changes in our brain by changing how we think.”
― Barbara Oakley, A Mind for Numbers: How to Excel at Math and Science

“Let Your Mind Work in the Background The next time you are tackling a tough problem, work on it for a few minutes. When you get stuck, move on to another problem. Your diffuse mode can continue working on the tougher problem in the background. When you later return to the tougher problem, you will often be pleasantly surprised by the progress you’ve made.”
― Barbara Oakley, A Mind for Numbers: How to Excel at Math and Science

“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. Chess players who experience Einstellung truly believe they are scanning the board for a different solution. But careful study of where their eyes are moving shows that they are keeping their focus on the original solution. Not only their eyes, but their mind itself can’t move away enough to see a new approach to the problem.15 According to recent research, blinking is a vital activity that provides another means of reevaluating a situation. 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.16”
― Barbara Oakley, A Mind for Numbers: How to Excel at Math and Science

“But be wary of the idea that some people are “left-brain” or “right-brain” dominant—research indicates that is simply not true.17”
― Barbara Oakley, A Mind for Numbers: How to Excel at Math and Science

“The complex neural activity that ties together our simplifying, abstract chunks of thought—whether those thoughts pertain to acronyms, ideas, or concepts—are the basis of much of science, literature, and art.”
― Barbara Oakley, A Mind for Numbers: How to Excel at Math and Science

“You may be surprised to learn that simply being awake creates toxic products in your brain. During sleep, your cells shrink, causing a striking increase in the space between your cells. This is equivalent to turning on a faucet—it allows fluid to wash past and push the toxins out.23 This nightly housecleaning is part of what keeps your brain healthy. When you get too little sleep, the buildup of these toxic products is believed to explain why you can’t think very clearly. (Too”
― Barbara Oakley, A Mind for Numbers: How to Excel at Math and Science

“This approach [solving easiest problems first, during the test] works for some people, mostly because anything works for some people.”
― Barbara Oakley, A Mind for Numbers: How to Excel at Math and Science

“I have not failed. I’ve just found 10,000 ways that won’t work.”10”
― Barbara Oakley, A Mind for Numbers: How to Excel at Math and Science

“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.”
― Barbara Oakley, A Mind for Numbers: How to Excel at Math and Science

“There are hidden meanings in equations, just as there are in poetry. If you are a novice looking at an equation in physics, and you’re not taught how to see the life underlying the symbols, the lines will look dead to you. It is when you begin to learn and supply the hidden text that the meaning slips, slides, then finally leaps to life.”
― Barbara Oakley, A Mind for Numbers: How to Excel at Math and Science