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

by Barbara Oakley

Recall Material While Outside Your Usual Place of Study: The Value of Walking

Doing something physically active is especially helpful when you have trouble grasping a key idea.

In addition, recalling material when you are outside your usual place of study helps you strengthen your grasp of the material by viewing it from a different perspective.

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

Continuing the study or practice after it is well understood is called overlearning. Overlearning can have its place—it can help produce an automaticity that is important when you are executing a serve in tennis or playing a perfect piano concerto. But be wary of repetitive overlearning during a single session in math and science learning—research has shown it can be a waste of valuable learning time.36 (Revisiting the approach mixed with other approaches during a subsequent study session, however, is just fine.)

You want your brain to become used to the idea that just knowing how to use a particular problem-solving technique isn’t enough—you also need to know when to use it.

Another idea is to open the book to a randomly chosen page and work a problem while, as much as possible, hiding from view everything but the problem.

It’s best to write the initial solution, or diagram, or concept, out by hand. There’s evidence that writing by hand helps get the ideas into mind more easily than if you type the answer.

common illusion of competence is to continue practicing a technique you know, simply because it’s easy and it feels good to successfully solve problems. 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.

Chunks are best built with: Focused attention. Understanding of the basic idea. Practice to help you gain big-picture context.

Simple recall—trying to remember the key points without looking at the page—is one of the best ways to help the chunking process along.

the routine, habitual responses your brain falls into as a result of specific cues. These zombie responses are often focused on making the here and now better.

This is a typical procrastination pattern. You think about something you don’t particularly like, and the pain centers of your brain light up. So you shift and narrow your focus of attention to something more enjoyable.8 This causes you to feel better, at least temporarily.

Finding ways to reward good study habits in math and science is vital to escaping procrastination.

“I often find that when I cannot bring myself to start something, if I go for a quick run or do something active first, when I come back to it, it is much easier

The trick to overwriting a habit is to look for the pressure point—your reaction to a cue. The only place you need to apply willpower is to change your reaction to the cue.

Cues usually fall into one of the following categories: location, time, how you feel, reactions to other people, or something that just happened.

The Pomodoro technique—the twenty-five-minute timer—can be especially helpful in shifting your reaction to cues. Also,

it helps to have something in your stomach when starting particularly difficult tasks. This ensures that you have mental energy for that momentary dollop of willpower as you are getting started.4 It also avoids the potential distraction of I’ll just go grab something to eat. . . .

Remember, habits are powerful because they create neurological cravings. It helps to add a new reward if you want to overcome your previous cravings. Only once your brain starts expecting the reward will the important rewiring take place that will allow you to create new habits.

It’s particularly important to realize that giving yourself even a small “attaboy” or “attagirl” jump-starts the process of rewiring your brain. This rewiring, sometimes called learned industriousness, helps brighten tasks you once thought were boring and uninteresting.5 As you will find, simply getting into the flow of your work can become its own reward, giving you a sense of productiveness you might not have imagined was possible

The Belief: The most important part of changing your procrastination habit is the belief that you can do it.

Belief that your new system works is what can get you through.

powerful approach is mental contrasting.6 In this technique, you think about where you are now and contrast it with what you want to achieve.

sometimes all it takes is one bad day to spark an important realization. After that, keeping your focus to find the way out of your current situation is much easier.”

If you find yourself avoiding certain tasks because they make you uncomfortable, there is a great way to reframe things: Learn to focus on process, not product. Process means the flow of time and the habits and actions associated with that flow of time—as in, “I’m going to spend twenty minutes working.”

To prevent procrastination, you want to avoid concentrating on product. Instead, your attention should be on building processes—habits—that coincidentally allow you to do the unpleasant tasks that need to be done.

The product is what triggers the pain that causes you to procrastinate. Instead, you need to focus on the process, the small chunks of time you need over days or weeks, to solve the homework problems or prepare for tests. Who cares whether you finished the homework or grasped key concepts in any one session? The whole point instead is that you calmly put forth your best effort for a short period—the process.

“One helpful tip is to just get started. This advice sounds relatively simple, but once you get off to a good start it is much easier to accomplish something.

The key is, when the distraction arises, which it inevitably will, you want to train yourself to ignore it.

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.

no chance to take root and flourish. When you multitask while doing schoolwork, you get tired more quickly. Each tiny shift back and forth of attention siphons off energy. Although each attention switch itself seems tiny, the cumulative result is that you accomplish far less for your effort. You also don’t remember as well, you make more mistakes, and you are less able to transfer what little you do learn into other contexts.

Next time you feel the urge to check your messages, pause and examine the feeling. Acknowledge it. Then ignore it. Practice ignoring distractions.

If you feel muzzy or featherbrained as you’re trying to look away and recall a key idea, or you find yourself rereading the same paragraphs over and over again, 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.

You are not your grade; you are better than that. Grades are indicators of time management and a rate of success.

Bad grades do not mean you are a bad person.

Procrastination is the death ...

Focusing on taking small, manageable steps forward and time ...

Preparation is key to...

We all have a failure rate. You will fail. So control your failures. That is why we do homework—...

I’ve found that the best learners are the ones who cope best with failure and use it as a learning tool.”