Barbara Oakley [ Google Talk ] I’d like to begin by telling you a little story. This story is about– well, I think all of us love to watch other people, right? To some greater or lesser extent. I love people watching. I have to tell you about this one guy who was one of the most interesting people I’ve ever watched. This was when I was working down in Antarctica at McMurdo Station. The guy’s name was Neil.
Neil was this thin, wispy little guy with kind of a high-pitched voice. He had a big head, so he looked like this sort of upside-down exclamation point.
What Neil used to like to do is pick up the phone and answer it with a perfect imitation of the 6’8″ gorilla of a station manager, Art Brown.
One day, phone rings. Neil picks it up, as usual. (IN DEEP VOICE) “Hello. This is Art Brown speaking.” And it was Art Brown on the other end of the line.
So Art says, “who the heck is this?” Or more unprintable words to that effect.
And Neil says, “why, Art, this is you. I’m so glad you’ve finally gotten in touch with yourself.”
And so that’s actually what we’re going to do here today, is to help you to get more in touch with yourself and what you’re doing when you’re doing one of the most important things you can do as a human being, and that is to learn new things.
Now, to start, I have to tell you a little bit about my background and growing up. I grew up moving all over the place. By the time I’d hit 10th grade, I’d lived in 10 different places.
Moving around a lot like this has some benefits, but it also has some drawbacks, or potential drawbacks. And one of the things for me was math is a very sequential topic. And if you miss it anywhere along the line, right? Somebody’s a little bit further ahead, and you’re from the school where it was a little behind. All of a sudden, you can actually fall off the bandwagon, and then you’ve fallen off.
It’s hard to get back on.
And that’s what happened to me early on. I fell off the math bandwagon. Just said, I can’t do this. I hate it. I really want nothing to do with it at all.
Science is the same way.
And so I basically flunked my way through elementary, middle, and high school math and science. And it’s really funny, thinking back on it now, because I’m a professor of engineering. And I publish well in some of the top journals, so I do very well as an engineer. But one day, one of my students found out about my sordid past as a math flunky, and he asked me, he said, how’d you do it?
How’d you change your brain?
And I thought, you know, how did I do it? I mean, looking back on it, I was just this little kid, and I loved animals, and I liked fluffy, furry things, and I liked to knit, and I loved language and studying language.
And at that time, there weren’t college loans that were relatively straightforward to get.
So I really wanted to learn a language. And I couldn’t afford to go to school, and so how could I study language in that kind of situation? And there was one way I could do it. I could actually go and learn a language and get paid for it while I was doing it. And that was to join the Army.
So that’s what I did. I joined the Army.
There you see me, looking incredibly nervous, about to throw a hand grenade.
I did learn a language. I learned Russian. And I ended up working out on Russian trawlers, Soviet trawlers, up in the Bering Sea. That’s me standing on a bunch of fish there. I can still swear quite well in Russian, although the rest of the Russian’s a little rusty.
I loved having adventures and gaining new perspectives.
I also ended up at the South Pole station in Antarctica. And that’s where I met my husband. I always say, I had to go to the end of the Earth to meet that man, and I did.
So the thing is, though, what was going on was I began to realize that you know, I was always interested in these new perspectives, but they were always perspectives that I was kind of comfortable with somehow. You know, and having adventures, that’s sort of a comfortable thing .
But I wasn’t actually stretching myself to really have a totally new perspective.
I thought back on the engineers that I’d worked with, West Point engineers, who were in the military. And I realized that their problem-solving skills were, in many ways, exceptional. They could think in a way that I couldn’t think. And I thought, what if I could read these kinds of equations like they could read equations? What if I could, in some sense, learn the language that they were able to speak.
Could I actually change my brain to learn in that way? To learn what these people knew?
As I began to try to answer that student’s question, how did you change your brain? I started working on a book to describe what some of these key ideas were. And while I was working on this book, I did things like I went to ratemyprofessors.com. Probably a few of you who’ve been in schools realize that that’s a pretty good website. And I looked to see who were the top professors worldwide, teaching subjects like engineering, math, chemistry, physics, economics, a lot of really difficult subjects. And a lot of very relevant subjects, as well, like psychology, even English.
How did they teach so people could learn, and how did they learn themselves?
I also reached out to top cognitive psychologists and neuroscientists.
My background also informed this. I’ve taught for several decades as an engineering professor, done active research in active learning. All of these things kind of combined together. What I found, that I thought was very interesting, was when I reached out to all these professors, a lot of the ones in the STEM disciplines in particular– Science, Technology, Engineering, and Math– used these approaches that might involve things like metaphor or analogy.
But they were very embarrassed to say that, because other professors would be like, oh, you’re dumbing things down.
But it was actually something that all of these top professors used to more easily communicate the ideas. It was like this shared handshake. They all knew how to do it, but they didn’t realize these other top professors were using the same approaches. What I’m going to tell you now is I’m going to give you some insight.
These, are the key ideas related to learning that all of these people have discovered.
First, we know that the brain is really complicated. So what we’re going to do is simplify it. And you can simplify the brain’s operation into two fundamentally different modes. First one is what I’ll call focused mode, and the second is what I’ll call the diffuse mode. This relates to the default mode network and other related– there’s some 24 or 25 so far — neural resting states that have been detected. All of these states altogether, I’ll just call the diffuse mode.
Our best way to really understand these two different modes is to use a metaphor.
The metaphor we’re going to use is that of a pinball machine. A pinball machine, you all know how it works. You just take the pinball and you pull back on the plunger, and a ball was boinking around on the rubber bumpers, and that’s how you get points. And what we’re going to do is we’re going to take that pinball machine, and we’re going to superimpose it on the brain. And you see the brain right here. Here’s the little ears, and there’s the nose right there. And what we’re going to do, we’re going to take that pinball machine and we’re going to put it right on the brain. And there you go.
There’s the pinball machine on the brain.
You can see how you can pull back on the plunger there, and you’ve got all these little pinballs in there, or the rubber bumpers, and they’re all very close together. So what happens is in focused mode-type thinking, like what I’m showing right here, you’ve got these close together bumpers, and you often have patterns that are already here.
For example, if you’ve already learned how to multiply, and you’re trying to do a multiplication problem, you would sit in focused mode, and you’ve got these patterns that are already there. And you think a thought, and it takes off, and it moves roughly around the rubber bumpers along the pathways it’s already been in before, that you’ve developed as a consequence of previous learning.
But what if the pattern you’re trying to think is something new?
What if you already know about multiplication, but you’ve never encountered division before? So you’re trying to understand this idea.
Or the concept of limits in calculus.
How do you go at a completely new idea that you’ve never encountered before?
That’s where this other way the brain works, in diffuse mode thinking, can actually be a benefit.
Take a look. Here’s the representative of the diffuse mode. It’s just an analogy, but it’s a very good one that helps us understand. Look at how far apart those rubber bumpers are.
When you think a thought in diffuse mode, the thoughts can range much more widely. You can’t think in a tight-grain fashion to actually solve the particulars of a problem, but you can at least get to a new sort of way of thinking about things that you couldn’t have gotten if you were just in the focused mode.
In fact, sometimes, when you’re trying to solve a really difficult problem, the worst thing you could do is just keep sitting there and focusing and focusing on it. Because you can be up on that part of the brain, so to speak, and yet you need to be in a completely different place.
The best thing to do when you’re really stuck and frustrated on a problem is not to keep focusing on it.
You actually need to get in a very different mode of thinking. And that’s what’s represented here. What this means practically for you is, you’re sitting there, you’re working– hey, get out. Go for a run. Go down and have a– go take a shower if you need to. Or do something that really gets your mind totally off it. Because when you’re in this mode, as long as your attention is focused on that problem, you’re still in this mode, and you can’t get to this way of solving things.
So how can this play out for people?
If you look at this guy right here– he was Salvador Dali, one of the most brilliant of the Surrealist painters of the 20th century. He’s shown here with his pet ocelot, Babou. And what Dali used to do is this. He’d sit in a chair when he had kind of an intractable problem with his paintings to solve. He’d sit, and he’d relax, and he’d relax away. And just as he’d relaxed so much, you know, kind of letting his mind run free, he’d have a key in his hand. And just as he’d relax so much that he’d fall asleep, the key would fall from his hand, the clatter would wake him up, and off he’d go with this new idea from the diffuse mode, taking it back to the focused mode, where he could refine and really use them.
So you might think, well, you know, that’s just great for artists. But what if you’re an engineer?
If you look at this guy right here, this was Thomas Edison. And what Edison used to do, at least according to legend, was he’d sit in a chair with ball bearings in his hand. And he’d relax and relax, and then finally when he’d fall asleep, the ball bearings would fall from his hand. Whatever he’d, in his very relaxed way, been thinking about, he’d be able to take some of those ideas from that mode and bring them back with him to the focused mode, where he could refine it, analyze, and come up with some of those brilliant inventions.
So the lesson for us, out of all of this, is this.
I’m giving some exemplary innovators in various fields. But whenever you’re solving a problem, even if it’s a problem that thousands or even millions of other people have solved before, for you, it’s the very first time that you’ve solved that problem .
You need to use some of these same creative approaches that these other brilliant thinkers have used.
What you want to do, be aware of, is that you can be in focused mode or you can be in diffuse mode, but you can’t really– as far as we know, unless you’re an exceptionally well-trained monk– be in both modes at the same time.
So focused or diffuse. You want to develop both modes .
Diffuse thinking is often not conscious, but it is also learning. And so that’s why that relaxation process can also be very important.
I just wanted to give you a quick image here. This shows some of the brilliant connectivity of the default mode network . See all these connections here between various aspects of the brain? This is a web for one mode of working, but focused mode has a very different web. So if you’re only focusing, you’re not making access or getting access to a lot of the different connections that are available for you.
That’s why going back and forth between modes can be so very important .
It takes time to do this. That’s why you can’t sit down and just solve a difficult problem immediately. You often have to go back and forth between the modes.
In some sense, you can almost think of it like this is a weight-lifter. And a weight-lifter, he doesn’t cram the night before a big meet and build muscles like that. It takes time to develop those muscles. In the same way, it takes time to develop the neural scaffold that is involved in learning and in new thinking processes.
I know what you’re really thinking. You may be thinking, I’m a procrastinator. I wait. Sometimes I don’t have time to do stuff, right?
So let’s talk a little bit about procrastination.
Sometimes you can be a really effective human being but still procrastinate about some things. In that sense, there are things to learn to help improve your productivity and your effectiveness in what you do.
Procrastination arises in a very interesting way.
Studies have shown that if you look at something you don’t like, the pain centers of your brain actually activate. So if you look at a book for a subject you don’t like, you can actually feel a twinge, and we can see it in the brain , if you’re being imaged.
What do you do when you feel pain? I mean, it’s the same pain as when you hammer your thumb with a hammer .
Well, you have two different ways of handling it.
The first way is you can work through it, like 20 minutes or so, and the pain will gradually disappear .
But if you’re like most people, what you’ll do is you’ll just kind of turn your attention away to something more pleasant, and guess what? You’ll feel better immediately, right? And so in some sense, procrastination can actually be a little bit like an addiction . You do it once, you do it twice– it’s not that big a deal. You do it a lot of times, though, and it actually can be very, very detrimental for your life .
I’m an engineer. I believe in totally practical, useful things.
So what I’m going to do is cut right to the chase and say here’s the most effective way to help you deal with procrastination .
It is simply to use the Pomodoro Technique.
And this is a technique that was developed by Francesco Cirillo in the 1980s. He called it the Pomodoro Technique because he had a tomato-shaped timer, and pomodoro is Italian for tomato. He recommends you set a timer for 25 minutes.
Actually, you can have different times. Different time lengths are useful for different people.
But you set it, in general, for 25 minutes, and then you turn off everything else . So no alarms, no instant messages– anything that can disturb your concentration, you turn that off. And then you work with as careful a focused attention as you can for those 25 minutes.
Now sometimes, I’ll be working away, and I’ll think, am I really focusing as hard as I can? And then I think, well, obviously not, because I just got distracted, and I’m wondering whether I’m focusing instead of actually working. But I let that thought just drift by, and then I get back to my work, right? And that’s what you’re doing in this technique. You want to just keep your mind on your work.
What happens is because you’re only focusing on the task and the time, and not the pain of “I must complete this task,” it somehow makes it so much easier to do.
I mean, anybody, virtually anybody, can sit for 25 minutes and work.
When you’re done, you reward yourself. And that reward is actually very important . Because what you’re doing is you’re focusing during the focused mode, but then you want to train yourself to relax, and enjoy, and do something different. Just surf the web, go out for a– whatever floats your boat, you go off and do that.
This is important .
Because we know that some aspects of learning take place during this relaxed process .
Our tendency is to think, I’m not working when I’m not focusing. But you actually are.
So it gives you a little bit of a feeling of relief and accomplishment that is OK to relax.
Acouple of little pointers. First, don’t sit down and do a Pomodoro and say, you know, I’m going to finish off my work. Don’t focus on the task.
Only focus on the time .
That’s the trick to this technique. Because it gets you past that pain in the brain and allows you to just relax comfortably and get into the flow of the task .
The other thing is: don’t say, “OK, I’m going to do 20 Pomodoros today”, and think that you’re going to beat yourself into more productivity that way. You want to just gradually start getting used to this technique , and you’ll see that it works very, very well.
Another aspect that’s really important, related to learning, is we’ve also been told, “hey, sleep’s really important before a big test” or something like that.
Sleep is important in a lot of different ways. I’m going to talk to you, just mention a little bit of one of the primary important reasons that sleep’s important for learning .
We’ve found that if you look at the cells– these little circles here represent cells, neurons, in the brain. And what happens when you go to sleep is this. Well, when you’re awake– first, when you’re awake, these metabolites will come out, and they’ll go in between the junctions.
They kind of sit out there, and they’re essentially toxins in your brain .
So when you’re awake, these toxins are gradually accumulating in your brain. And they affect your judgment . That’s why, when you stay awake a longer and longer time, it’s more and more difficult to think clearly.
When you go to sleep, though, here’s what happens.
Watch very carefully to what happens to those cells.
You go to sleep, they shrink. I’ll do that again, because I just have so much fun doing this. See? They shrink when you go to sleep. And because they shrink, what that does is that allows fluids to wash by the cells and wash these metabolites out .
A very important part of sleep is just the housekeeping, the cleaning that takes place, that allows your brain to function so much more effectively.
Another very important aspect of sleep relates to neural synaptic growth . In this wonderful paper by Guang Yang — she’s out of Langone– is if you look at the top picture, you can see here what’s going on. This is the same neuron at the top and the bottom.
The top neuron is before learning and before sleep. The bottom neuron is after learning and after sleep.
All of these little triangles are new synaptic connections.
When you learn something and you go to sleep, that’s when the new synaptic connections are forming. This is what’s going on when you’re learning.
That’s why it’s very important, when you’re learning something new– again, you don’t want to cram at the last minute .
You want to have many short learning periods, sleep, learning, sleep , and that’s helping you build that neural scaffold that helps you learn so much better.
There’s another aspect of learning, and people often think this is so completely disconnected from real learning that they even are taking away recess from kids. Because they’re like, “oh, that doesn’t help them learn”. Only when they’re sitting in front of us, learning from us, that’s when they really learn.
But that’s not true at all.
We’re now finding how incredibly important exercise is to the learning process .
If you look here, this study is of a mouse, and they were training this mouse to differentiate between two different symbols. And if you look in the background, what’s happening is all of these blue blobs are old neurons .
We used to think you are born with all the neurons that you have, and that’s what you got for the rest of your life. Well, of course, now we know that’s not true. But it was wisdom, received wisdom, for many decades. What they found was– see these red lines here? Those are actually the new neurons that are being born every day in all of us, as well as in this mouse, in the hippocampus . And that is how– those are absolutely essential to our ability to learn and remember new information.
There’s two ways to allow these new neurons to grow and survive.
One is you get exposed to new environments . That’s why travel can be so good. That’s where your learning can be effective. And these kinds of things can help those new neurons survive.
But the other way of helping these neurons survive that’s just as powerful as learning is simply to exercise .
Exercise is profoundly important.
I’m not talking, hey, I’ve got to be an Olympic weight-lifter, or be a marathon runner. Even simple walking can be very, very effective .
I’m sure you’ve all had the experience. You’re all muzzy-brained, and then you go out for a walk, and it clears up your way of thinking. But even a few days of an exercise program is doing much more than that. It’s actually enhancing the ability of your neurons to grow and survive .
Now, if you look, there’s a name right here, Terrence Sejnowski.
He was on one of the original papers doing this original research. He’s the Francis Crick Professor at the Salk Institute , and he’s also my colleague in doing the Massive Open Online Course that’s based on the book.
Terry is a remarkable guy.
It was really a lot of fun making the Massive Open Online Course with him. We went and we did some filming together and I asked him, “Terry, you’re talking all this stuff about the importance of exercise. Do you exercise? What do you do? And he’s like, do I exercise?
What he does is he goes and every day, or every few days, he goes down– he’s like a mountain goat. The guy’s 65, and he climbs down. You know, I’m scrambling after him. And he goes running on the beach, just like you see here. And this is how he gets his exercise. I love how he finishes here. Watch this. Look at that.
He is a legend in neuroscience .
I’m convinced that part of it is because he uses some of these ideas that he’s found in his research to help him really keep his edge intellectually .
Let’s just talk a little bit about something called working memory.
Working memory is how you keep a brief thought in mind . It used to be we thought that you had seven slots in working memory, and that’s why you could hold a phone number of seven numbers. But now we’re kind of realizing it’s more like maybe there’s four slots in working memory.
So maybe for me, it’s like two slots in working memory.
But anyway, you have four slots, and it in your prefrontal– you can kind of think of it as your working memory, you’re holding things in your prefrontal cortex . So I’ve got it kind of symbolized right there as your four slots of working memory.
When you are remembering something, are thinking about something with working memory, you can think of it symbolically, at least, as something like an octopus, the Octopus of Attention , that reaches through those slots of working memory and makes connections between different ideas.
That’s why you can’t hold too many ideas at once in your brain before you get all confused.
But what happens if you’re multitasking? What happens if you’ve got a little bit of an eye out here on some, you know– am I getting an instant message?
In some sense, that’s like taking one of those tentacles away of your working memory.
And you don’t have a lot of tentacles.
So it really is making whatever intellectual heft you have, you’re kind of losing some of it. You’re getting a little stupider when you’re multitasking. That’s why careful focused attention is so incredibly important, especially when you’re working on something that’s rather difficult.
I like to contrast this with the diffuse mode.
The diffuse mode, it’s a lot of connections, but they’re much more random in how they take place .
How do you take something from working memory into long-term memory, which is more distributed around in your brain? The best way is through practice. Practice makes , in some sense, permanent . The more you practice, the broader that little neural pathway becomes, and the more deeply embedded it becomes.
If you’re learning something and you practice, those patterns get deeper and deeper. That’s how you can learn something and draw it from long-term memory into working memory. If you don’t practice, what’s going to happen is you’ve got those neurons, and it’s almost like you’ve got these little metabolic vampires that just come and they suck those patterns away before they can get deepened.
That’s why sometimes you can learn something from a professor– you even understand it. You’ve had that great stroke of insight. You walk away. You don’t look at it for a few days, and those little metabolic vampires just suck that pattern away. And you can’t really remember or understand what you had learned previously.
So the best way to get patterns well-embedded in your long-term memory is to practice through spaced repetition . So you might practice Monday, Tuesday, Wednesday, maybe again on Friday. And by spacing things out, you realize, now, that you’re getting those new synaptic connections growing every time you learn a little and then you sleep on it.
What you don’t want to do is this kind of thing, where you’re just kind of cramming like crazy. And then look, that metabolic vampire just kind of sucks at all away, and you’re left with very little. It’s hard to remember what you were learning.
A good way to think about this is just the analogy of a wall.
If you’re building a brick wall and you give yourself time between layers of mortar , it can set, and you can build a solid, sturdy wall. But if you don’t, it’s all kind of a jumble. And it doesn’t turn into a really good structure that you can actually use.
Let’s go back again, and we’re going to talk a little bit more, quickly, about attention, and the relationship with working memory . Now, if you look here, you can see you’ve got one slot in your working memory that’s filled. When you have one slot filled, you could put other things in your working memory. But here’s the trick. How do you get things into just one slot? It turns out that if you create a chunk, one chunk, of the material, it’s easy to pull into working memory .
So here’s what I mean by that.
If you look here, here’s a raw pattern of information, right? It’s a puzzle. It’s hard to figure out. It looks like a mad scramble. And look what’s going on in your working memory. It’s kind of going a little crazy, trying to figure things out.
Recent research at Stanford has shown children who are trying to learn math facts, their little prefrontal cortexes are going crazy as they try to assimilate and master the material. But once they’ve got those math facts down, this relaxes. What’s actually happening is this. They’ve got the essential idea, and what that essential idea is like is one smooth, single ribbon they can easily pull into working memory when they need to, in order to understand and make connections with other problems that they’re trying to solve.
If you just memorize and you’re not understanding what you’re memorizing, that’s like creating that little circle there. And you can see it. You’ve got it. It really is a chunk. But you can’t fit it very well with other chunks.
So there’s another important idea about chunking, and that’s this.
Once you’ve compressed an idea– one of the most brilliant mathematicians was mentioning one of the great aspects of math is simply that idea that you can compress it . You grapple, grapple, grapple, and all of a sudden, it clicks, and you’ve got it compressed.
Once you’ve got it compressed in a chunk, there’s actually– you can make that chunk bigger, right? Just like learning a little piece of song?
You can actually learn another piece and join them together, and you’ve got a bigger chunk. Or you can also learn similar chunks of other disciplines, and it’s very, very helpful. That’s an idea of transfer.
What you’re really doing when you’re learning and mastering a topic is you are, in some sense, creating a library of chunks.
And you can draw on that library and make connections between things. And that’s how great creativity arises , is making connections with those chunks. True experts often have enormous libraries of chunks that they’ve developed .
When you’re learning, there’s sort of a– you can think of it as there’s a top-down approach.
If you’re learning a new topic, you can almost think of it like there’s a chunk there, that’s that tire, and here’s a chunk that’s the man’s face, and another tire. So you’re learning all these chunks, and when you get them all learned, it forms the big picture of the material. Even if you’re missing a few pieces here and there, you’ve still got that big picture.
But if you don’t practice and repeat and really master your chunks , it’s like this. It’s like you’re trying to put together the big picture with chunks that are faint .
And it’s much harder to put together the big picture with that in mind.
So again, as I was saying, you’ve got one ribbon of thought. That’s a chunk. Here is another chunk in another field, but it’s of a similar shape. And that’s the idea of transfer.
If you’re a physicist, you may be able to learn economics more easily, because some of the chunks are really similar in their shape.
If you are a language learner and you’re learning math and science, there are meta-chunks available. For example, that idea of practice and repetition for language also applies in learning math and science.
Let’s go to some other aspect that I think relates to learning. Some of you may may have wonderful memories here. But some of you may wish you had better memories. Well, let me give you a little awareness. What you think may be a negative attribute actually can be a very, very positive attribute. It turns out that when you have a poor working memory, what that really means is you can’t hold things in mind very well, right? So you’re looking at your colleague who can remember all this different stuff. They can hold it in their working memory, turn somersaults with it, and come up with new ideas really quickly.
And you’re lucky to remember what they were even talking about.
But here’s the thing. Research has shown that if you have a poor working memory, and your four slots are pretty weak, other stuff is always slipping in. That’s why you can’t hold ideas very well in your mind. But because the other stuff is slipping in, you’re actually more creative . And research has shown that if you have Attention Deficit Disorder, or your attention wanders– oh, shiny! Then what that means is you have much more potential for being creative.
Do you have to work harder than some other people in order to make up for that? Yeah, you do.
But that comes with the trade-off that you are highly creative. So you can be very, very valuable in your job, even though you may have to work harder sometimes to have that achievement. Now, you may say, well, that’s all well and good, but I’m actually a slow thinker.
I see these other people, and they’ve got like a super race car brain.
They can pick up these ideas so fast, and I move along more slowly. One of my heroes in the history of science is the Nobel Prize winner Santiago Ramon y Cajal, who’s known as the father of modern neuroscience. Ramon y Cajal was not a genius, and he said so himself. Part of what he did was he worked hard and was persistent. But he said, these with race car brains– which he was not– often race along and they jump to conclusions that he didn’t miss. He would see them, and he was more flexible in his thinking.
When he’d see a mistake, he would go, wait a minute.
Whereas the race car driver is so used to being right and being fast that they’re much less able to be persistent and to flexibly change in the light of contradictory data .
So if you have a slow brain, think of it like this.
There’s the person with the race car brain. Great. But you’re the hiker, and your experience is completely different . You walk along. You can see the little rabbit trails that they’ve missed. You can reach out and touch the pine needles. You can smell the pine forest.
All of this is missed by the race car driver.
So your way of thinking can be exceptionally valuable, as well. In fact, Maryam Mirzakhani, she won the Fields Medal, which is the top award in mathematics, the equivalent for mathematics of the Nobel Prize. And she was told as a young person, you think too slowly to be a mathematician.
Well, guess what? She’s one of the most creative mathematicians alive.
So if you think slowly, more power to you. You’re doing good.
I also want to bring up another aspect, and that is the aspect of the Impostor Syndrome. This is so important and so common. It’s a feeling like you’re the fake in the room, right? I’m working here? Maybe I’m working at Google and I’m really not as good as they say that I am, and I’m kind of an impostor here. And people feel this all over the world, no matter what they’re doing. You’re a professor? Oh, wait a minute. You know, they’re going to find out what the real truth is. I took a test, and I did well. But next time, I’m gonna fail it, because I know they’ll find out what the real truth is.
Really, really common feeling.
The best way to address the Impostor Syndrome is to just be aware how common it is.
So next time you have a thought like, I’m really not as good as they say I am, remember, that’s the Impostor Syndrome talking.
Probably one of the most important things that I could bring up– and so that’s why I’m doing it towards the end here– is this idea of illusions of competence in learning.
Let’s say that suddenly, for some reason, a bear came hurtling out of this screen and rampaging through the room. Would you feel a surge of adrenaline and nervous energy? I mean, suddenly your body would react physiologically to this feeling of intense fear as you realized the bear was actually in front of you. But the thing is, when you think about learning situations– we often say, students will come up and say, you know, I have test anxiety. That’s why I didn’t do well on this test.
But for a lot of students, sadly, sitting down and looking at a test is like there’s a bear there. They just realized, at that moment, that they really didn’t know the material, even though they thought they did.
Students, and people, can fool themselves that they’re learning something when they’re actually not learning something.
So I’ll give you some of the best ways for truly learning something. First off, tests are the best . Test yourself on everything, all the time. The same hour spent testing as opposed to that hour spent studying, you will learn far more by taking a test. And use flashcards.
Flashcards are not just for language learners. Why let them have all the fun?
Flashcards are for ordinary– for learning in math and science, for example.
If you talk to great poets, what great poets will tell you is memorize the poem, because you’ll feel the passion and the power of the poem much more deeply.
Why should mathematicians not be able to share in this fun? How about engineers? When we have equations, if you memorize the equation, and really look at what does it mean while you’re doing that, it actually can bring out the richness of what you’re learning .
When you’re having homework. Homework– a lot of times, people make the mistake of thinking, hey, you know, I did my homework problem. And it’s like saying, I’m learning the piano and I played this piano piece one time, and so I’ve got it. Well, nobody does that when they’re learning a musical instrument. And in the same way, when you’re studying, you don’t want to just do a homework problem once.
You don’t have time to do all of them and kind of repeat them, but pick some of the key ones and see if you can do it again. Practice it, and do it in your mind.
Can you step through all the steps? If you can play it almost like a song in your mind, you’ve really got it. You’ve got it down as a chunk, and that can help build your knowledge of the material.
Probably the most valuable technique when you’re trying to really understand something difficult is simple recall.
When you’re reading material on a page, you read away, and your tendency is to– well, I’m going to underline it, right? Because when you’re hand is moving on the page, you think it’s moving it into your brain somehow . But it actually is not . So resist the urge . You can do a little bit of underlining. But it’s better to write it, because you’re helping to neurally encode these ideas.
Then when you read the page, simply look away and see what you can recall. That, as it turns out, is very powerful in building your understanding of the material in a way that other techniques, including mind mapping and re-reading– they’re not nearly as good as recall.
So another very important aspect is simply to study judiciously with other people , or talk about what you’re trying to understand with other people.
Now, this has to be done judiciously.
Obviously, all learning does not take place in a cooperative fashion. Sometimes you have to go off .
When you’re learning something sort of in focused mode, there’s a part-and-parcel of that focused mode, and that is a feeling that what you’ve just learned is correct, right? This sort of rightness feeling. And the only way you can really disabuse yourself, sometimes, is to go off and bounce your ideas off of other people. And they can almost serve like a greater kind of diffuse mode, to help disabuse you when you do make mistakes.
So judicious studying with friends and conversation with colleagues can be incredibly helpful.
Also, explain in a way that a 10-year-old can understand . So frequently we explain electricity, the flow of electricity, as water, the flow of water. It’s an analogy. It breaks down. All analogies break down. But Richard Feynman, the Nobel Prize-winning physicist, used to go around and challenge top mathematicians in the world to explain in a simple way, like in a way that their grandmothers could understand, what they were doing.
And you know what? They could.
So this means that no matter how difficult that problem is that you’re working on, if you find a way to explain it simply, you’ll be able to understand it much more deeply.
One thing to do is insert yourself into whatever the problem is. Like, here I am in a copper matrix, right? Barbara McClintock, the Nobel Prize-winning geneticist, used to kind of imagine herself down at a genetic level, so she could understand and see how the genes might actually be operating. So that’s a trick that’s often used by some of the greatest thinkers. Try to find a way to get yourself into almost like a play, whatever you’re trying to understand.
If you want some more information about what I’ve talked about here, there’s much more in the book, “A Mind For Numbers.” And there’s a lot more– and it’s all free– in the Massive Open Online Course for Coursera, through UC San Diego, Learning How to Learn.
And that is the key, except for one thing. I’d like to leave you with this last thought.
We’re often told, “follow your passion”. That is the key to everything. Just follow your passion, and your life will really be a better place for it. We’re told that. But some things– your passion develops about what you really good at . And some things take much longer to get good at . So don’t just follow your passions. Broaden your passions. And your lives will be greatly enriched.
FEATURED IMAGE CREDIT: Alex Berger