Working Back and Forth between Modes to Master Material

Know that you are making progress with each mistake you catch when trying to solve a problem—finding errors should give you a sense of satisfaction. Edison himself is said to have noted “I have not failed. I’ve just found 10,000 ways that won’t work.”

unless you are really enjoying what you are doing, keep your working sessions short. Remember, when you take breaks, your diffuse mode is still working away in the background.

just using your diffuse mode doesn’t mean you can lollygag around and expect to get anywhere. As the days and weeks pass, it’s the distributed practice—the back and forth between focused-mode attention and diffuse-mode relaxation—that does the trick.

Entering focus mode consumes willpower, and we only have limited amount of such mental energy.
When your energy flags, you can break by jumping to other focused-type tasks, such as switching from studying math to studying French vocabulary.
But the longer you spend in focused mode, the more mental resources you use.

Constantly lifting weights won’t make your muscles any bigger—your muscles need time to rest and grow before you use them again. Taking time off between weight sessions helps build strong muscles in the long run. Consistency over time is key!

Go to the gym
Play a sport like soccer or basketball
Jog, walk, or swim
Go for a drive
Draw or paint
Take a bath or shower
Listen to music, especially without words
Play songs you know well on a musical instrument
Meditate or pray
Sleep (the ultimate diffuse mode!)

The following diffuse-mode activators are best used briefly, as rewards:

Don’t Worry about Keeping Up with the Intellectual Joneses

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

Avoid Einstellung (Getting Stuck)

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.
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.
deliberately closing our eyes may help us focus more deeply—people often look away or close or cover their eyes to avoid distractions as they concentrate on thinking of an answer.

When Carlsen stood and turned his glance—and his attention—toward other chess boards, he may have been helping his mind leap momentarily out of focused mode. Turning his eyes and attention elsewhere likely was critical in allowing his diffuse intuition to go to work on his game with Kasparov.

Learning well means allowing time to pass between focused learning sessions, so the neural patterns have time to solidify properly. It’s like allowing time for the mortar to dry when you are building a brick wall.
Trying to learn everything in a few cram sessions doesn’t allow time for neural structures to become consolidated in your long-term memory—the result is a jumbled pile of bricks.


Usually a few hours is long enough for the diffuse mode to make significant progress.
A good rule of thumb, when you are first learning new concepts, is not to let things go untouched for longer than a day.

Working in the focused mode is like providing the bricks, while working in the diffuse mode is like gradually joining the bricks together with mortar.

Rising frustration is usually a good time-out signal for you, signaling that you need to shift to diffuse mode.

What to Do When You’re Really Stumped

People with strong self-control can have the most difficulty in getting themselves to turn off their focused mode so that the diffuse mode can begin its work.

Learning is often paradoxical.
We need to focus intently to be able to solve problems—yet that focus can also block us from accessing the fresh approach we may need.
Persistence is key—but misplaced persistence causes needless frustration.

Introduction to Working and Long-Term Memory

Working memory is the part of memory that has to do with what you are immediately and consciously processing in your mind.
the working memory holds only about four chunks of information.

You can think of working memory as the mental equivalent of a juggler. The four items only stay in the air—or in working memory—because you keep adding a little energy.

you can repeat a phone number to yourself until you have a chance to write it down. You may find yourself shutting your eyes to keep any other items from intruding into the limited slots of your working memory as you concentrate.

In contrast, long-term memory might be thought of as a storage warehouse. Once items are in there, they generally stay put. The warehouse is large, with room for billions of items, and it can be easy for stored parcels to get buried so deeply that it’s difficult to retrieve them.
Research has shown that when your brain first puts an item of information in long-term memory, you need to revisit it a few times to increase the chances you’ll later be able to find it when you need it.

spaced repetition: spacing this repetition out over a number of days.
Research has shown that if you try to glue things into your memory by repeating something twenty times in one evening, for example, it won’t stick nearly as well as it will if you practice it the same number of times over several days or weeks.

The Importance of Sleep in Learning

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.
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.

It’s as if the complete deactivation of the conscious “you” in the prefrontal cortex helps other areas of the brain start talking more easily to one another, allowing them to put together the neural solution to your problem as you sleep.26 (Of course, you must plant the seed for your diffuse mode by first doing focused-mode work.)

Experienced learners will attest to the fact that reading for one hour with a well-rested brain is better than reading for three hours with a tired brain.

“If I have trouble working on a problem, I lie down in my bed with an open notebook and pen and just write out thoughts about the problem as I fall asleep, as well as sometimes right after waking up. Some of what I write makes no sense, but sometimes I gain a totally new way of looking at my problem.”




{ 4 } Chunking and avoiding illusions of competence: The Keys to Becoming an “Equation Whisperer”

What Happens When You Focus Your Attention?

The best language programs—such as those at the Defense Language Institute, where I learned Russian—incorporate structured practice that includes plenty of repetition and rote, focused-mode learning of the language, along with more diffuse-like free speech with native speakers.

What Is a Chunk? Solomon’s Chunking Problem

Solomon Shereshevsky’s extraordinary memory came with a surprising drawback. His individual memory traces were each so colorful and emotional—so rich with connections—that they interfered with his ability to put those traces together and create conceptual chunks. He couldn’t see the forest, in other words, because his imagery of each of the individual trees was so vivid.

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.
Chunking the information you deal with helps your brain run more efficiently.
Once you chunk an idea or concept, you don’t need to remember all the little underlying details; you’ve got the main idea—the chunk—and that’s enough.

Basic Steps to Forming a Chunk

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.

It’s more like using a guide to help you when traveling to a new place. 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.

The first step in chunking is to simply focus your attention on the information you want to chunk.

The second step in chunking is to understand the basic idea you are trying to chunk.
Understanding is like a superglue that helps hold the underlying memory traces together.

Closing the book and testing yourself on how to solve the problems will also speed up your learning.

The third step to chunking is gaining context so you see not just how, but also when to use this chunk.
you may have a tool in your strategy or problem-solving toolbox, but if you don’t know when to use that tool, it’s not going to do you a lot of good.

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.

Skimming through a chapter can allow you to gain a sense of the big picture.

Illusions of Competence and the Importance of Recall

Attempting to recall the material you are trying to learn—retrieval practice—is far more effective than simply rereading the material.
many students experience illusions of competence. Most students repeatedly read their notes or textbook but relatively few engage in self-testing or retrieval practice while studying.
When you have the book (or Google!) open right in front of you, it provides the illusion that the material is also in your brain.
Because it can be easier to look at the book instead of recalling, students persist in their illusion—studying in a far less productive way.
This, indeed, is why just wanting to learn the material, and spending a lot of time with it, doesn’t guarantee you’ll actually learn it.
“Intention to learn is helpful only if it leads to the use of good learning strategies.”

The only time rereading text seems to be effective is if you let time pass between rereadings so that it becomes more of an exercise in spaced repetition.


“Getting a concept in class versus being able to apply it to a genuine physical problem is the difference between a simple student and a full-blown scientist or engineer. The only way I know of to make that jump is to work with the concept until it becomes second nature, so you can begin to use it like a tool.”

That dangling strand of chunked material has, in some sense, increased the amount of information available to your working memory, as if the slot in working memory is a hyperlink that has been connected to a big webpage.

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.