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

by Barbara Oakley

You’ll be surprised at how spending a minute or two glancing ahead before you read in depth will help you organize your thoughts.

Mistakes are inevitable. To work past them, start early on your assignments and, unless you are really enjoying what you are doing, keep your working sessions short.

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

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. A good rule of thumb, when you are first learning new concepts, is not to let things go untouched for longer than a day.

Ask someone else for a different perspective on how to solve the problem or a different analogy to understand the concept; however, it’s best that you first wrestle with the problem yourself before you talk to anyone else, because it can embed the basic concepts deeply enough that you become receptive to the explanation.

During sleep, your cells shrink, causing a striking increase in the space between your cells.

Dreaming about what you are studying can substantially enhance your ability to understand—it somehow consolidates your memories into easier-to-grasp chunks.

neurons that fire together wire together.

Some instructors do not like to give students extra worked-out problems or old tests, as they think it makes matters too easy. But there is bountiful evidence that having these kinds of resources available helps students learn much more deeply.

Attempting to recall the material you are trying to learn—retrieval practice—is far more effective than simply rereading the material.10 Psychologist Jeffrey Karpicke and his colleagues have shown that many students experience illusions of competence when they are studying. Most students, Karpicke found, “repeatedly read their notes or textbook (despite the limited benefits of this strategy), but relatively few engage in self-testing or retrieval practice while studying.”

Using recall—mental retrieval of the key ideas—rather than passive rereading will make your study time more focused and effective.

Now you understand why it is key that you are the one doing the problem solving, not whoever wrote the solution manual. If you work a problem by just looking at the solution, and then tell yourself, “Oh yeah, I see why they did that,” then the solution is not really yours—you’ve done almost nothing to knit the concepts into your underlying neurocircuitry. Merely 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.

Incidentally, strengthening an initial learning pattern within a day after you first begin forming it is important.

In the same amount of time, by simply practicing and recalling the material, students learned far more and at a much deeper level than they did using any other approach,

Retelling whatever you are learning about not only helps fuel and share your own enthusiasm, but also clarifies and cements the ideas in your mind, so you’ll remember them better in the weeks and months to come.

For centuries, arsenic was a popular choice for killers.

But there’s something important to note. It was the anticipation that was painful. When the mathphobes actually did math, the pain disappeared.

One of the single most important pieces of advice I can give you on dealing with procrastination is to ignore distractions!

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.

Try to write this daily task list the evening before. Why the day before? Research has shown this helps your subconscious to grapple with the tasks on the list so you figure out how to accomplish them.9 Writing the list before you go to sleep enlists your zombies to help you accomplish the items on the list the next day.

If you really want to boost your memory as well as your general ability to learn, it seems one of the best ways to do it is to exercise. Several recent experiments in both animals and humans have found that regular exercise can make a substantive improvement in your memory and learning abilities. Exercise, it seems, helps create new neurons in areas that relate to memory. It also creates new signaling pathways.12 It seems that different types of exercise—running or walking, for example, versus strength training—may have subtly different molecular effects. But both aerobic and resistance exercise exert similarly powerful results on learning and memory.

You may think you really have to understand something in order to explain it. But observe what happens when you are talking to other people about what you are studying. You’ll be surprised to see how often understanding arises as a consequence of attempts to explain to others and yourself, rather than the explanation arising out of your previous understanding. This is why teachers often say that the first time they ever really understood the material was when they had to teach it.

You will also sometimes have a chance to interact with truly special mentors or teachers. When this lucky opportunity arises, seize it. Train yourself to get past the gulp stage and force yourself to reach out and ask questions—real and to-the-point questions, not questions meant to show off what you know. The more you do this, the easier it will become, and the more helpful it will be in ways you never anticipated—a simple sentence growing from their vast experience can change the course of your future. And also be sure to show appreciation for the people guiding you—it is essential to let them know that the help is meaningful.

“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

Research on creativity in teams has shown that nonjudgmental, agreeable interactions are less productive than sessions where criticism is accepted and even solicited as part of the game.12 If you or one of your study buddies thinks something is wrong in your understanding, it’s important to be able to plainly say so, and to hash out why it’s wrong without worrying about hurt feelings. Of course, you don’t want to go about gratuitously bashing other people, but too much concern for creating a “safe environment” for criticism actually kills the ability to think constructively and creatively, because you’re focusing on the other people rather than the material at hand. Like Feynman, you want to remember that criticism, whether you are giving or receiving it, isn’t really about you. It’s about what you are trying to understand. In a related vein, people often don’t realize that competition can be a good thing—competition is an intense form of collaboration that can help bring out people’s best.

It is easiest of all to fool yourself.

This approach works for some people, mostly because anything works for some people.