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

by Barbara Oakley

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.

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.

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.

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.

Learning is creating.

But you can’t learn mathematics or science without also including a healthy dose of practice and repetition to help you build the chunks that will underpin your expertise.27

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,

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. People

Practice helps build strong neural patterns—that is, conceptual chunks of understanding. Practice gives you the mental fluidity and agility you need for tests. 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.

Chunking

We procrastinate about things that make us feel uncomfortable. But what makes us feel good temporarily isn’t necessarily good for us in the long run. 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.

Procrastinating

The Cue: This is the trigger that launches you into “zombie mode.” The cue may be something as simple as seeing the first item on your to-do list (time to start next week’s homework!) or seeing a text message from a friend (time to dawdle!). A cue by itself is neither helpful nor harmful. It’s the routine—what we do in reaction to that cue—that matters. 2. The Routine: This is your zombie mode—the routine, habitual response your brain is used to falling into when it receives the cue. Zombie responses can be harmless, useful, or, in the worst case, so destructive that they defy common sense. 3. The Reward: Habits develop and continue because they reward us—give us a dollop of pleasure. Procrastination is an easy habit to develop because the reward—moving your mind’s focus to something more pleasant—happens so quickly. But good habits can also be rewarded. Finding ways to reward good study habits in math and science is vital to escaping procrastination.

Procrastinating Cycle

mental contrasting.6 In this technique, you think about where you are now and contrast it with what you want to achieve. If you’re trying to get into medical school, for example, imagine yourself as a doctor, helping others even as you’re preparing for a great vacation that you can actually afford. Once you’ve got that upbeat image in mind, contrast it with images of your current life. Imagine your clunker of a car, your macaroni and cheese dinners, and your mountain of student debts. Yet there’s hope!

Mental contrasting

A little bit of work on something that feels painful can ultimately be very beneficial. Habits such as procrastination have four parts: The cue The routine The reward The belief Change a habit by responding differently to a cue, or even avoiding that cue altogether. Reward and belief make the change long-lasting. Focus on the process (the way you spend your time) instead of the product (what you want to accomplish). Use the twenty-five-minute Pomodoro to stay productive for brief periods. Then reward yourself after each successful period of focused attention. Be sure to schedule free time to nurture your diffuse mode. 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. Multitasking means that you are not able to make full, rich connections in your thinking, because the part of your brain that helps make connections is constantly being pulled away before neural connections can be firmed up.

Beating procrastination

Chunking means integrating a concept into one smoothly connected neural thought pattern. Chunking helps increase the amount of working memory you have available. Building a chunked library of concepts and solutions helps build intuition in problem solving. When you are building a chunked library, it’s important to keep deliberate focus on some of the toughest concepts and aspects of problem solving. Occasionally you can study hard and fate deals a bad hand. But remember the Law of Serendipity: If you prepare well by practicing and building a good mental library, you will find that luck will be increasingly on your side. In other words, you guarantee failure if you don’t try, but those who consistently give it a good effort will experience many more successes.

Chunking not choking