About the Book:
Whether you are a student struggling to fulfill a math or science requirement, or you are embarking on a career change that requires a higher level of math competency, A Mind for Numbers offers the tools you need to get a better grasp of that intimidating but inescapable field. Engineering professor Barbara Oakley knows firsthand how it feels to struggle with math. She flunked her way through high school math and science courses, before enlisting in the army immediately after graduation. When she saw how her lack of mathematical and technical savvy severely limited her options—both to rise in the military and to explore other careers—she returned to school with a newfound determination to re-tool her brain to master the very subjects that had given her so much trouble throughout her entire life.

In A Mind for Numbers, Dr. Oakley lets us in on the secrets to effectively learning math and science—secrets that even dedicated and successful students wish they’d known earlier. Contrary to popular belief, math requires creative, as well as analytical, thinking. Most people think that there’s only one way to do a problem, when in actuality, there are often a number of different solutions—you just need the creativity to see them. For example, there are more than three hundred different known proofs of the Pythagorean Theorem. In short, studying a problem in a laser-focused way until you reach a solution is not an effective way to learn math. Rather, it involves taking the time to step away from a problem and allow the more relaxed and creative part of the brain to take over. A Mind for Numbers shows us that we all have what it takes to excel in math, and learning it is not as painful as some might think! 

About the Author:
Barbara Oakley is a professor of engineering at Oakland University in Rochester, Michigan. She has received many awards for her teaching, including the coveted National Science Foundation New Century Scholar Award.

Get the book here: https://goo.gl/rLUHLC

We have a very, very special guest with us today.

I remember reading Charlie Munger saying that he didn't know a smart man who didn't read all the time.

And he has characterized Warren Buffett as a learning machine.

The inspiration from there is how does 1 become a very effective learner?

And reading Barb's book, that is exactly what the book seems to be teaching us.

Not only loved reading her book, I could identify that the voice in that book is the voice of a teacher.

And that resonated a lot with me personally.

So I'm very glad Barb is here with us today.

So without further ado, Ladies and gentlemen, please join me in welcoming Barb Oakley.

And I'd like to begin by telling you a little story.

And this story is about, well, I think all of us love to watch other people, right, to some greater or lesser extent.

And so I have to tell you about this 1 guy who was 1 of the most interesting people I've ever watched.

And this was when I was working down in Antarctica at McMurdo Station.

And Neil was this thin, wispy little guy with kind of a high-pitched voice.

And he had a big head, so he looked like this sort of upside-down exclamation point.

And what Neil used to like to do is he liked to pick up the phone and answer it with a perfect imitation of the 6 foot 8 gorilla of a station manager, Art Brown.

And it was Art Brown on the other end of the line.

Or more unprintable words to that effect.

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 1 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 in growing up.

By the time I'd hit 10th grade, I'd lived in 10 different places.

Now, moving around a lot like this has some benefits, but it also has some drawbacks or potential drawbacks.

And 1 of the things for me was math is a very sequential topic.

And if you miss it anywhere along the line, somebody's a little bit further ahead and you're from a school where it was a little behind, all of a sudden you can actually fall off the bandwagon, and then you've fallen off.

I fell off the math bandwagon, just said, I can't do this.

I really want nothing to do with it at all.

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.

But 1 day, 1 of my students found out about my sordid past as a math flunky.

And he asked me, he said, how'd you do it?

And I thought, you know, how did I do it?

I mean, looking back on it, I was just this little kid.

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.

And so I really wanted to learn a language.

And so how could I study language in that kind of situation?

I could actually go and learn a language and get paid for it while I was doing it.

And there you see me looking incredibly nervous, about to throw a hand grenade.

And I ended up working out on Russian trawlers, Soviet trawlers up in the Bering Sea.

And 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.

But I loved having adventures and gaining new perspectives.

And so I also ended up at the South Pole Station in Antarctica.

So I always say, I had to go to the end of the earth to meet that man.

So the thing is, though, What was going on was I began to realize that I was always interested in these new perspectives, but they were always sort of perspectives that I was kind of comfortable with somehow.

And having adventures, that's sort of a comfortable thing.

But I wasn't actually kind of 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, you know, 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?

And so as I began to try to answer that student's question, how did you change your brain, I started working on a book to kind of 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 have been in schools realize that that's a pretty good website.

And I looked to see who are 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?

And I also reached out to top cognitive psychologists and neuroscientists, and My own background also informed this.

I've taught for several decades as an engineering professor, done active research in active learning.

And so all of these things kind of combine together.

And 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 kind of 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.

They all knew how to do it, but they didn't realize these other top professors were using the same approaches.

So what I'm going to tell you now is I'm going to give you some insight.

This, these are the key ideas related to learning that all of these people have discovered.

So first off, 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 2 fundamentally different modes.

And the second is what I'll call the diffuse mode.

And this is actually, it relates to the default mode network and other related, there's some 24 or 25 so far, neural resting states that have been detected.

And so all of these states all together, I'll just call the diffuse mode.

I mean, our best way to really understand these 2 different modes is to use a metaphor.

And the metaphor we're going to use is that of a pinball machine.

And a pinball machine, you all know how it works.

You just take the pinball and you pull back on the plunger, and a ball goes blinking 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.

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.

There's the pinball machine on the brain.

And you can see how you can pull back on the plunger there.

And you've got all these little pinballs and they're very, 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, Got these close together bumpers, and you often have patterns that are already there.

For example, if you've already learned how to multiply, and you're trying to do a multiplication problem, you would sit in focus 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?

Well, that's where this other way the brain works in diffuse mode thinking can actually be a benefit.

Now take a look, here's the diffuse, the representative of the diffuse mode, and it's just an analogy, but it's a very good 1 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.

Now you can't think in a tight-grained 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 focus mode.

In fact, sometimes when you're trying to solve a really difficult problem, The worst thing you can 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.

So 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 so 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.

If you look at this guy right here, he was Salvador Dali.

He was 1 of the most brilliant of the surrealist painters of the 20th century.

He's shown here with his pet ocelot, Babu.

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 relax so much, 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 focus mode where he could refine and really use them.

So you might think, well, that's just great for artists.

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 then finally, when he'd fall asleep, the ball bearings would fall from his hand.

And 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 focus mode, where he could refine and 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.

And you need to use some of these same creative approaches that these other brilliant thinkers have used.

And what you want to do, be aware of, is that you can be in focus 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.

Diffuse thinking is often not conscious, but it is also learning.

And so that's why that relaxation process can also be very important.

Now, 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?

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.

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.

And in some sense, you can almost think of it like this is a weightlifter.

And a weightlifter is, he doesn't really cram the night before a big meet and build muscles like that.

In the same way, it takes time to develop the neural scaffold that is involved in learning and in new thinking processes.

You may be thinking, I'm a procrastinator.

And So let's talk a little bit about procrastination.

And sometimes you can be a really effective human being, but still procrastinate about some things.

And so in that sense, there are things to learn to help improve your productivity and your effectiveness in what you do.

So 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.

I mean, it's the same pain as when you hammer your thumb with a hammer.

Well, you have 2 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 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 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.

And it is simply to use the Pomodoro technique.

And this is a technique that was developed by Francesco Cedillo in the 1980s.

And he called it the Pomodoro technique because he had a tomato-shaped timer.

And what he would do is he recommends you set a timer for 25 minutes.

Different time lengths are useful for different people.

But you set it in general for 25 minutes.

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.

And that's what you're doing in this technique.

You want to just Keep your mind on your work.

And 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.

And then 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 focus mode.

But then You want to train yourself to relax and enjoy and do something different.

Surf the web, go out for a walk, whatever floats your boat, you go off and do that.

And this actually is important because we know that some aspects of learning take place during this relaxed process.

So your tendency is to think, I'm not working when I'm not focusing.

So it kind of gives you a little bit of a feeling of relief and accomplishment that it is OK to relax.

First, don't sit down and do a Pomodoro and say, you know I'm going to finish off my work.

And 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.

Now, another aspect that's really important related to learning is we've often been told, hey, sleep's really important before a big test or something like that.

Actually, sleep is important in a lot of different ways.

And I'm going to talk to you, just mention a little bit of 1 of the primary important reasons that sleep's important for learning.

We 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.

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.

So when you go to sleep, though, here's what happens.

Now watch very carefully to what happens to those cells.

I'll do that again, because I just have so much fun doing this.

And because they shrink, what that does is that allows fluids to wash by the cells and wash these metabolites out.

So 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.

Now, Another very important aspect of learning or of sleep relates to neural synoptic 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 synoptic connections.

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Barbara Oakley | Learning How to Learn | Talks at Google