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

by Barbara Oakley

NOW YOU TRY! Prime Your Mental Pump As you first begin looking at a chapter or section of a book that teaches concepts of math or science, it helps to take a “picture walk” through the chapter, glancing not only at the graphics, diagrams, and photos, but also at the section headings, summary, and even questions at the end of the chapter, if the book has them. This seems counterintuitive—you haven’t actually read the chapter yet, but it helps prime your mental pump. So go ahead now and glance through this chapter and the questions at the end of the chapter. You’ll be surprised at how spending a minute or two glancing ahead before you read in depth will help you organize your thoughts. You’re creating little neural hooks to hang your thinking on, making it easier to grasp the concepts.

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.

sometimes your initial intuition about what’s happening is misleading.

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.

The diffuse mode is also often an important part of problem solving, especially when the problem is difficult. But as long as we are consciously focusing on a problem, we are blocking the diffuse mode.

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. You are also increasing your stress level because you know you have to complete what feels like an unpleasant task.

To figure out new ideas and solve problems, it’s important not only to focus initially, but also to subsequently turn our focus away from what we want to learn.

PAUSE AND RECALL Close the book and look away. What were the main ideas of this chapter? Don’t worry if you can’t recall very much when you first begin trying this. As you continue practicing this technique, you’ll begin noticing changes in how you read and how much you recall.

There is much creativity underlying math and science problem solving.

You may be surprised to discover that learning slowly can mean you learn more deeply than your fast-thinking classmates.

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.

Each interlude in which you are not directly focused on the problem allows your diffuse mode to look at it in a fresh way. When you turn your focused attention back to the problem, you consolidate new ideas and patterns that the diffuse mode has delivered.

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

SUMMING IT UP Use the focused mode to first start grappling with concepts and problems in math and science. After you’ve done your first hard focused work, allow the diffuse mode to take over. Relax and do something different! When frustration arises, it’s time to switch your attention to allow the diffuse mode to begin working in the background. It’s best to work at math and science in small doses—a little every day. This gives both the focused and diffuse modes the time they need to do their thing so you can understand what you are learning. That’s how solid neural structures are built. If procrastination is an issue, try setting a timer for twenty-five minutes and focusing intently on your task without allowing yourself to be drawn aside by text messages, web surfing, or other attractive distractions. There are two major memory systems: Working memory—like a juggler who can keep only four items in the air. Long-term memory—like a storage warehouse that can hold large amounts of material, but needs to be revisited occasionally to keep the memories accessible. Spaced repetition helps move items from working memory to long-term memory. Sleep is a critical part of the learning process. It helps you: Make the neural connections needed for normal thinking processes—which is why sleep the night before a test is so important. Figure out tough problems and find meaning in what you are learning. Strengthen and rehearse the important parts of what you are learning and prune away t...

one of the first steps toward gaining expertise in math and science is to create conceptual chunks—mental leaps that unite separate bits of information through meaning.

Pay attention to what’s going on around you when you’re with the guide, and soon you’ll find yourself able to get there on your own. You will even begin to figure out new ways of getting there that the guide didn’t show you.

Do not confuse the “aha!” of a breakthrough in understanding with solid expertise!

Attempting to recall the material you are trying to learn—retrieval practice—is far more effective than simply rereading the material.

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.

Once they understand ‘X,’ they should move on to something else and return to ‘X’ on another day.”40

You shouldn’t waste willpower on procrastination except when absolutely necessary!

Procrastination can be like taking tiny amounts of poison. It may not seem harmful at the time. But the long-term effects can be very damaging.

Habits have power because of your belief in them.

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.

If you learn under mild stress, you can handle greater stress much more easily.

Time after time, top performers in fields as different as surgery and computer programming deliberately seek coaches who place them under stress by challenging them and driving them to perform better.

Multitasking is like constantly pulling up a plant. This kind of constant shifting of your attention means that new ideas and concepts have no chance to take root and flourish.

Next time you feel the urge to check your messages, pause and examine the feeling. Acknowledge it. Then ignore it. Practice ignoring distractions. It is a far more powerful technique than trying to will yourself to not feel those distractions in the first place.

Mental contrasting is a powerful motivating technique—think about the worst aspects of your present or past experiences and contrast these with the upbeat vision of your future.

If you’ve failed in the past, you may not realize how important that it can be in fueling your success.

Generating (that is, recalling) the material helps you learn it much more effectively than simply rereading it.

The handwritten solution is important because writing by hand increases the odds that what is written will be retained in memory.

You will find yourself improving quickly as you become more realistic about what you can reasonably do in any given time.

One of the best things you can do to not only remember but understand concepts in math and science is to create a metaphor or analogy for it

One trait that successful professionals in science, math, and technology gradually learn is how to chunk—to abstract key ideas.

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.

If you compare how much you learn by spending one hour studying versus one hour taking a test on that same material, you will retain and learn far more as a result of the hour you spent taking a test. Testing, it seems, has a wonderful way of concentrating the mind.