Generally, you can hold about four items in your working memory, as shown in the four-item memory on the left. When you master a technique or concept in math or science, it occupies less space in your working memory. This frees your mental thinking space so that it can more easily grapple with other ideas, as shown on the right.
Your working memory is important in learning math and science because it’s like your own private mental blackboard where you can jot down a few ideas that you are considering or trying to understand.
How do you keep things in working memory? Often it’s through rehearsal; for example, 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.21 (Techie types sometimes equate short-term memory to random-access memory [RAM], and long-term memory to hard drive space.)
Long-term memory is important for learning math and science because it is where you store the fundamental concepts and techniques that you need to use in problem solving. It takes time to move information from working memory to long-term memory. To help with this process, use a technique called spaced repetition. As you may have guessed, this technique involves repeating what you are trying to retain, like a new vocabulary word or a new problem-solving technique, but spacing this repetition out over a number of days.
Putting a day between bouts of repetition—extending your practice over a number of days—does make a difference. 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.22 This is similar to building the brick wall we saw earlier. If you don’t leave time for the mortar to dry (time for the synaptic connections to form and strengthen), you won’t have a very good structure.
NOW YOU TRY!
Let Your Mind Work in the Background
The next time you are tackling a tough problem, work on it for a few minutes. When you get stuck, move on to another problem. Your diffuse mode can continue working on the tougher problem in the background. When you later return to the tougher problem, you will often be pleasantly surprised by the progress you’ve made.
ADVICE ON SLEEPING
“Many people will tell you that they can’t nap. The one thing I learned from a single yoga class I took many years ago was to slow down my breathing. I just keep breathing slowly in and out and don’t think I must fall asleep. Instead, I think things like, Sleepytime! and just focus on my breathing. I also make sure it’s dark in the room, or I cover my eyes with one of those airplane sleep masks. Also, I set my phone alarm for twenty-one minutes because turning a short power nap into a longer sleep can leave you groggy. This amount of time gives me what’s basically a cognitive reboot.”
—Amy Alkon, syndicated columnist and catnap queen
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.23 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. (Too little sleep is affiliated with conditions ranging from Alzheimer’s to depression—prolonged sleeplessness is lethal.)
Studies have shown that sleep is a vital part of memory and learning.24 Part of what this special sleep-time tidying does is erase trivial aspects of memories and simultaneously strengthen areas of importance. During sleep, your brain also rehearses some of the tougher parts of whatever you are trying to learn—going over and over neural patterns to deepen and strengthen them.25
Finally, sleep has been shown to make a remarkable difference in people’s ability to figure out difficult problems and to find meaning and understanding in what they are learning. 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.) It seems that if you go over the material right before taking a nap or going to sleep for the evening, you have an increased chance of dreaming about it. If you go even further and set it in mind that you want to dream about the material, it seems to improve your chances of dreaming about it still further.27 Dreaming about what you are studying can substantially enhance your ability to understand—it somehow consolidates your memories into easier-to-grasp chunks.28
If you’re tired, it’s often best to just go to sleep and get up a little earlier the next day, so your reading is done with a better-rested brain. 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. A sleep-deprived brain simply can’t make the usual connections you make during normal thinking processes. Going without sleep the night before an examination can mean that even if you are perfectly prepared, your mind is simply unable to function properly, so you do poorly on the test.
A METHOD FOR MANY DISCIPLINES
Focused and diffuse approaches are valuable for all sorts of fields and disciplines, not just math and science. As Paul Schwalbe, a senior majoring in English, notes:
“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.”
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 lear
ning and prune away trivialities.
PAUSE AND RECALL
Get up and take a little break—get a glass of water or snack, or pretend you’re an electron and orbit a nearby table. As you move, check your recall of the main ideas of this chapter.
ENHANCE YOUR LEARNING
1. Name some activities you would find helpful for switching from focused to diffuse mode.
2. Sometimes you can feel certain you have explored new approaches to analyzing a problem, when you actually haven’t. What can you do to become more actively aware of your thinking processes to help keep yourself open to other possibilities? Should you always keep yourself open to new possibilities?
3. Why is it important to use self-control to make yourself stop doing something? Can you think of times outside studying and academics when this skill might also be important?
4. When you are learning new concepts, you want to review the material within a day so that the initial changes you made in your brain don’t fade away. But your mind often becomes preoccupied with other matters—it’s easy to let several days or more pass before you get around to looking at the material. What kind of action plan could you develop to ensure that you review important new material in a timely fashion?
NEUROPSYCHOLOGIST ROBERT BILDER’S ADVICE ON CREATIVITY
Robert Bilder just doing it in Makapu’u, Hawaii
Psychiatry professor Robert Bilder is the director of UCLA’s Tennenbaum Center for the Biology of Creativity and leads the “Mind Well” initiative to enhance the creative achievement and psychological well-being of students, staff, and faculty at UCLA.
Research on the biology of creativity suggests several ingredients that we all can bake into our personal recipes for success. Number one is the Nike factor: Just do it!
Creativity is a numbers game: The best predictor of how many creative works we produce in our lifetime is . . . the number of works we produce. I sometimes find it excruciating to pull the trigger and expose my work to other people, but every time I do, it turns out for the best.
Dealing with fear: A motivational poster I received after giving a talk at Facebook headquarters reads: “What would you do if you weren’t afraid?” I try to look at this daily, and I aim to do something fearless every day. What are you afraid of? Don’t let it stop you!
Redos come with the territory: If you don’t like the way it turned out—do it again!
Criticism makes us better: By exposing our work to others, and by externalizing it so we can inspect it ourselves, we gain unique perspective and insight and develop new and improved plans for the next version.
Be willing to be disagreeable. There is a negative correlation between the level of creativity and “agreeableness,” so those who are the most disagreeable tend to be most creative. Looking back at the few times when I found something novel, it was because I challenged the existing answers. So I believe the creative way is advanced whenever we strip a problem back to its roots and question our own assumptions (along with assumptions suggested by others); then repeat!
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chunking and avoiding illusions of competence:
The Keys to Becoming an “Equation Whisperer”
Solomon Shereshevsky first came to his boss’s attention because he was lazy. Or so his boss thought.
Solomon was a journalist. At that time, in the mid-1920s in the Soviet Union, being a journalist meant reporting what you were told, no more, no less. Daily assignments were given out—detailing whom to see, at what address, and to obtain what information. The editor in charge began to notice that everyone took notes. Everyone, that is, except Solomon Shereshevsky. Curious, the editor asked Solomon what was going on.
Solomon was surprised—why should he take notes, he asked, when he could remember whatever he heard? With that, Solomon repeated part of the morning’s lecture, word for word. What Solomon found surprising was that he thought everyone had a memory like his. Perfect. Indelible.1
Wouldn’t you love to have the gift of such a memory?
Actually, you probably wouldn’t. Because hand-in-hand with his extraordinary memory, Solomon had a problem. In this chapter, we’ll be talking about precisely what that problem is—involving how focus links to both understanding and memory.
What Happens When You Focus Your Attention?
We learned in the last chapter about that irritating situation when you become stuck in one way of looking at a problem and can’t step back to see easier, better ways—Einstellung. Focused attention, in other words, can often help solve problems, but it can also create problems by blocking our ability to see new solutions.
When you turn your attention to something, your attentional octopus stretches its neural tentacles to connect different parts of the brain. Are you focusing on a shape? If so, one tentacle of consciousness reaches from the thalamus back toward the occipital lobe, even as another tentacle reaches toward the wrinkled surface of the cortex. The result? A whispered sense of roundness.
Are you focusing instead on color? The attentional tentacle in the occipital lobe shifts slightly and a sense of green arises.
More tentacle connections. You conclude that you are looking at a particular type of apple—a Granny Smith. Yum!
Focusing your attention to connect parts of the brain is an important part of the focused mode of learning. Interestingly, when you are stressed, your attentional octopus begins to lose the ability to make some of those connections. This is why your brain doesn’t seem to work right when you’re angry, stressed, or afraid.2
Let’s say you want to learn how to speak Spanish. If you’re a child hanging around a Spanish-speaking household, learning Spanish is as natural as breathing. Your mother says “mama,” and you parrot “mama” back to her. Your neurons fire and wire together in a shimmering mental loop, cementing the relationship in your mind between the sound mama and your mother’s smiling face. That scintillating neural loop is one memory trace—connected, of course, to many other related memory traces.
The octopus of your focused attention (left) reaches out through the four slots of your working memory to deliberately connect the neural bumpers of your tightly focused brain. The diffuse mode (right) has its bumpers spread farther apart. This mode consists of a wild and crazy hodgepodge of potential connections.
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. The goal is to embed the basic words and patterns so you can speak as freely and creatively in your new language as you do in English.3
Focused practice and repetition—the creation of memory traces—are also at the heart of an impeccably played golf stroke, a master chef’s practiced flip of an omelet, or a basketball free throw. In dance, it’s a long way from a toddler’s clumsy pirouette to the choreographed grace of a professional dancer. But that path to expertise is built bit by bit. Small memorized free spins, heel turns, and kicks become incorporated into larger, more creative interpretations.
The left image symbolizes the compact connections when one chunk of knowledge is formed—neurons that fire together wire together. The image on the right shows the same pattern in your mind’s symbolic pinball machine. Such a memory trace is easy to recall when you need it.
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.
Chunks are pieces of information that are boun
d together through meaning. You can take the letters p, o, and p and bind them into one conceptual, easy-to-remember chunk, the word pop. It’s like converting a cumbersome computer file into a .zip file. Underneath that simple pop chunk is a symphony of neurons that have learned to trill in tune with one another. The complex neural activity that ties together our simplifying, abstract chunks of thought—whether those thoughts pertain to acronyms, ideas, or concepts—are the basis of much of science, literature, and art.
Let’s take an example. In the early 1900s, German researcher Alfred Wegener put together his theory of continental drift. As Wegener analyzed maps and thought about the information he’d gleaned from his studies and exploration, he realized that the different land masses fit together like puzzle pieces. The similarity of rocks and fossils between the land masses reinforced the fit. Once Wegener put the clues together, it was clear that all the continents had once, very long ago, been joined together in a single landmass. Over time, the mass had broken up and the pieces had drifted apart to form the continents separated by oceans we see today.
Continental drift! Wow—what a great discovery!
But if Solomon Shereshevsky had read this same story about the discovery of continental drift, he wouldn’t have gotten the point. Even though he would have been able to repeat every individual word in the story, the concept of continental drift would have been very difficult for him to grasp, since he was unable to link his individual memory traces together to create conceptual chunks.
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