This is a recent comic strip from the Los Angeles Times.
The punch line?
"On the other hand, I don't have to get up at four every single morning to milk my Labrador."
This is a recent cover of New York Magazine.
Best hospitals where doctors say they would go for cancer treatment, births, strokes, heart disease, hip replacements, 4 a.m. emergencies.
And this is a song medley I put together -- (Music) Did you ever notice that four in the morning has become some sort of meme or shorthand?
It means something like you are awake at the worst possible hour.
(Laughter) A time for inconveniences, mishaps, yearnings.
A time for plotting to whack the chief of police, like in this classic scene from "The Godfather."
Coppola's script describes these guys as, "exhausted in shirt sleeves.
It is four in the morning."
(Laughter) A time for even grimmer stuff than that, like autopsies and embalmings in Isabel Allende's "The House of the Spirits."
After the breathtaking green-haired Rosa is murdered, the doctors preserve her with unguents and morticians' paste.
They worked until four o'clock in the morning.
A time for even grimmer stuff than that, like in last April's New Yorker magazine.
This short fiction piece by Martin Amis starts out, "On September 11, 2001, he opened his eyes at 4 a.m. in Portland, Maine, and Mohamed Atta's last day began."
For a time that I find to be the most placid and uneventful hour of the day, four in the morning sure gets an awful lot of bad press -- (Laughter) across a lot of different media from a lot of big names.
And it made me suspicious.
I figured, surely some of the most creative artistic minds in the world, really, aren't all defaulting back to this one easy trope like they invented it, right?
Could it be there is something more going on here?
Something deliberate, something secret, and who got the four in the morning bad rap ball rolling anyway?
I say this guy -- Alberto Giacometti, shown here with some of his sculptures on the Swiss 100 franc note.
He did it with this famous piece from the New York Museum of Modern Art.
Its title -- "The Palace at Four in the Morning -- (Laughter) 1932.
Not just the earliest cryptic reference to four in the morning I can find.
I believe that this so-called first surrealist sculpture may provide an incredible key to virtually every artistic depiction of four in the morning to follow it.
I call this The Giacometti Code, a TED exclusive.
No, feel free to follow along on your Blackberries or your iPhones if you've got them.
It works a little something like -- this is a recent Google search for four in the morning.
Results vary, of course.
This is pretty typical.
The top 10 results yield you four hits for Faron Young's song, "It's Four in the Morning," three hits for Judi Dench's film, "Four in the Morning," one hit for Wislawa Szymborska's poem, "Four in the Morning."
But what, you may ask, do a Polish poet, a British Dame, a country music hall of famer all have in common besides this totally excellent Google ranking?
Well, let's start with Faron Young -- who was born incidentally in 1932.
(Laughter) In 1996, he shot himself in the head on December ninth -- which incidentally is Judi Dench's birthday.
(Laughter) But he didn't die on Dench's birthday.
He languished until the following afternoon when he finally succumbed to a supposedly self-inflicted gunshot wound at the age of 64 -- which incidentally is how old Alberto Giacometti was when he died.
Where was Wislawa Szymborska during all this?
She has the world's most absolutely watertight alibi.
On that very day, December 10, 1996 while Mr. Four in the Morning, Faron Young, was giving up the ghost in Nashville, Tennessee, Ms. Four in the Morning -- or one of them anyway -- Wislawa Szymborska was in Stockholm, Sweden, accepting the Nobel Prize for Literature.
100 years to the day after the death of Alfred Nobel himself.
Coincidence?
No, it's creepy.
(Laughter) Coincidence to me has a much simpler metric.
That's like me telling you, "Hey, you know the Nobel Prize was established in 1901, which coincidentally is the same year Alberto Giacometti was born?"
No, not everything fits so tidily into the paradigm, but that does not mean there's not something going on at the highest possible levels.
In fact there are people in this room who may not want me to show you this clip we're about to see.
(Laughter) Video: Homer Simpson: We have a tennis court, a swimming pool, a screening room -- You mean if I want pork chops, even in the middle of the night, your guy will fry them up?
Herbert Powell: Sure, that's what he's paid for.
Now do you need towels, laundry, maids?
HS: Wait, wait, wait, wait, wait, wait -- let me see if I got this straight.
It is Christmas Day, 4 a.m.
There's a rumble in my stomach.
Marge Simpson: Homer, please.
Rives: Wait, wait, wait, wait, wait, wait, wait.
Let me see if I got this straight, Matt.
(Laughter) When Homer Simpson needs to imagine the most remote possible moment of not just the clock, but the whole freaking calendar, he comes up with 0400 on the birthday of the Baby Jesus.
And no, I don't know how it works into the whole puzzling scheme of things, but obviously I know a coded message when I see one.
(Laughter) I said, I know a coded message when I see one.
And folks, you can buy a copy of Bill Clinton's "My Life" from the bookstore bmcmillan@example.com.
Parse it cover to cover for whatever hidden references you want.
Or you can go to the Random House website where there is this excerpt.
And how far down into it you figure we'll have to scroll to get to the golden ticket?
Would you believe about a dozen paragraphs?
This is page 474 on your paperbacks if you're following along: "Though it was getting better, I still wasn't satisfied with the inaugural address.
My speechwriters must have been tearing their hair out because as we worked between one and four in the morning on Inauguration Day, I was still changing it."
Sure you were, because you've prepared your entire life for this historic quadrennial event that just sort of sneaks up on you.
And then -- (Laughter) three paragraphs later we get this little beauty: "We went back to Blair House to look at the speech for the last time.
It had gotten a lot better since 4 a.m."
Well, how could it have?
By his own writing, this man was either asleep, at a prayer meeting with Al and Tipper or learning how to launch a nuclear missile out of a suitcase.
What happens to American presidents at 0400 on inauguration day?
What happened to William Jefferson Clinton?
We might not ever know.
And I noticed, he's not exactly around here today to face any tough questions.
(Laughter) It could get awkward, right?
I mean after all, this whole business happened on his watch.
But if he were here -- (Laughter) he might remind us, as he does in the wrap-up to his fine autobiography, that on this day Bill Clinton began a journey -- a journey that saw him go on to become the first Democrat president elected to two consecutive terms in decades.
In generations.
The first since this man, Franklin Delano Roosevelt, who began his own unprecedented journey way back at his own first election, way back in a simpler time, way back in 1932 -- (Laughter) the year Alberto Giacometti (Laughter) made "The Palace at Four in the Morning."
The year, let's remember, that this voice, now departed, first came a-cryin' into this big old crazy world of ours.
(Music) (Applause)
If someone called you scum, you'd probably be offended, but scientifically, they might not be far off.
Have you ever thought about where your food comes from?
You might say it comes from plants, animals, or even fungi, but you'd probably rather not think about the rotting organisms and poop that feed those plants, animals, and fungi.
So really, you and most of the matter in your body are just two or three degrees of separation from things like pond scum.
All species in an ecosystem, from the creatures in a coral reef to the fish in a lake to the lions on the savannah, are directly or indirectly nourished by dead stuff.
Most of the organic matter in our bodies, if we trace it back far enough, comes from CO2 and water through photosynthesis.
Plants use the energy from sunlight to transform carbon dioxide and water from the environment into glucose and oxygen.
That glucose is then transformed into more complex organic molecules to form leaves, stems, roots, fruit, and so on.
The energy stored in these organic molecules supports the food chains with which we're familiar.
You've probably seen illustrations like this or this.
These green food chains start with living plants at their base.
But in real-life terrestrial ecosystems, less than 10% of plant matter is eaten while it's still alive.
What about the other 90?
Well, just look at the ground on an autumn day.
Living plants shed dead body parts: fallen leaves, broken branches, and even underground roots.
Many plants are lucky enough to go their whole lives without being eaten, eventually dying and leaving remains.
All of these uneaten, undigested, and dead plant parts, that 90% of terrestrial plant matter?
That becomes detritus, the base of what we call the brown food chain, which looks more like this.
What happens to plants also happens to all other organisms up the food chain: some are eaten alive, but most are eaten only when they're dead and rotting.
And all along this food chain, living things shed organic matter and expel digestive waste before dying and leaving their remains to decay.
All that death sounds grim, right?
But it's not.
All detritus is ultimately consumed by microbes and other scavengers, so it actually forms the base of the brown food chain that supports many other organisms, including us.
Scientists are learning that this detritus is an unexpectedly huge energy source, fueling most natural ecosystems.
But the interactions within an ecosystem are even more complex than that.
What a food chain really represents is a single pathway of energy flow.
And within any ecosystem, many of these flows are linked together to form a rich network of interactions, or food web, with dead matter supporting that network at every step.
The resulting food web is so connected that almost every species is no more than two degrees from detritus, even us humans.
You probably don't eat rotting things, poop, or pond scum directly, but your food sources probably do.
Many animals we eat either feed directly on detritus themselves, like pork, poultry, mushrooms, shellfish, or catfish and other bottom feeders, or they are fed animal by-products.
So, if you're thinking nature is full of waste, you're right.
But one organism's garbage is another's gold, and all that rotting dead stuff ultimately provides the energy that nourishes us and most of life on Earth, as it passes through the food web.
Now that's some food for thought.
Thank you.
And I feel like this whole evening has been very amazing to me.
I feel it's sort of like the Vimalakirti Sutra, an ancient work from ancient India in which the Buddha appears at the beginning and a whole bunch of people come to see him from the biggest city in the area, Vaishali, and they bring some sort of jeweled parasols to make an offering to him.
All the young people, actually, from the city.
The old fogeys don't come because they're mad at Buddha, because when he came to their city he accepted -- he always accepts the first invitation that comes to him, from whoever it is, and the local geisha, a movie-star sort of person, raced the elders of the city in a chariot and invited him first.
So he was hanging out with the movie star, and of course they were grumbling: "He's supposed to be religious and all this.
What's he doing over there at Amrapali's house with all his 500 monks," and so on.
They were all grumbling, and so they boycotted him.
They wouldn't go listen to him.
But the young people all came.
And they brought this kind of a jeweled parasol, and they put it on the ground.
And as soon as they had laid all these, all their big stack of these jeweled parasols that they used to carry in ancient India, he performed a kind of special effect which made it into a giant planetarium, the wonder of the universe.
Everyone looked in that, and they saw in there the total interconnectedness of all life in all universes.
And of course, in the Buddhist cosmos there are millions and billions of planets with human life on it, and enlightened beings can see the life on all the other planets.
So they don't -- when they look out and they see those lights that you showed in the sky -- they don't just see sort of pieces of matter burning or rocks or flames or gases exploding.
They actually see landscapes and human beings and gods and dragons and serpent beings and goddesses and things like that.
He made that special effect at the beginning to get everyone to think about interconnection and interconnectedness and how everything in life was totally interconnected.
And then Leilei -- I know his other name -- told us about interconnection, and how we're all totally interconnected here, and how we've all known each other.
And of course in the Buddhist universe, we've already done this already billions of times in many, many lifetimes in the past.
And I didn't give the talk always.
You did, and we had to watch you, and so forth.
And we're all still trying to, I guess we're all trying to become TEDsters, if that's a modern form of enlightenment.
I guess so.
Because in a way, if a TEDster relates to all the interconnectedness of all the computers and everything, it's the forging of a mass awareness, of where everybody can really know everything that's going on everywhere in the planet.
And therefore it will become intolerable -- what compassion is, is where it will become intolerable for us, totally intolerable that we sit here in comfort and in pleasure and enjoying the life of the mind or whatever it is, and there are people who are absolutely riddled with disease and they cannot have a bite of food and they have no place, or they're being brutalized by some terrible person and so forth.
It just becomes intolerable.
With all of us knowing everything, we're kind of forced by technology to become Buddhas or something, to become enlightened.
And of course, we all will be deeply disappointed when we do.
Because we think that because we are kind of tired of what we do, a little bit tired, we do suffer.
We do enjoy our misery in a certain way.
We distract ourselves from our misery by running around somewhere, but basically we all have this common misery that we are sort of stuck inside our skins and everyone else is out there.
And occasionally we get together with another person stuck in their skin and the two of us enjoy each other, and each one tries to get out of their own, and ultimately it fails of course, and then we're back into this thing.
Because our egocentric perception -- from the Buddha's point of view, misperception -- is that all we are is what is inside our skin.
And it's inside and outside, self and other, and other is all very different.
And everyone here is unfortunately carrying that habitual perception, a little bit, right?
You know, someone sitting next to you in a seat -- that's OK because you're in a theater, but if you were sitting on a park bench and someone came up and sat that close to you, you'd freak out.
What do they want from me?
Like, who's that?
And so you wouldn't sit that close to another person because of your notion that it's you versus the universe -- that's all Buddha discovered.
Because that cosmic basic idea that it is us all alone, each of us, and everyone else is different, then that puts us in an impossible situation, doesn't it?
Who is it who's going to get enough attention from the world?
Who's going to get enough out of the world?
Who's not going to be overrun by an infinite number of other beings -- if you're different from all the other beings?
So where compassion comes is where you surprisingly discover you lose yourself in some way: through art, through meditation, through understanding, through knowledge actually, knowing that you have no such boundary, knowing your interconnectedness with other beings.
You can experience yourself as the other beings when you see through the delusion of being separated from them.
When you do that, you're forced to feel what they feel.
Luckily, they say -- I still am not sure -- but luckily, they say that when you reach that point because some people have said in the Buddhist literature, they say, "Oh who would really want to be compassionate?
How awful!
I'm so miserable on my own.
My head is aching.
My bones are aching.
I go from birth to death.
I'm never satisfied.
I never have enough, even if I'm a billionaire, I don't have enough.
I need a hundred billion."
So I'm like that.
Imagine if I had to feel even a hundred other people's suffering.
It would be terrible.
But apparently, this is a strange paradox of life.
When you're no longer locked in yourself, and as the wisdom or the intelligence or the scientific knowledge of the nature of the world, that enables you to let your mind spread out, and empathize, and enhance the basic human ability of empathizing, and realizing that you are the other being, somehow by that opening, you can see the deeper nature of life.
And you can, you get away from this terrible iron circle of I, me, me, mine, like the Beatles used to sing.
You know, we really learned everything in the '60s.
Too bad nobody ever woke up to it, and they've been trying to suppress it since then.
I, me, me, mine.
It's like a perfect song, that song.
A perfect teaching.
But when we're relieved from that, we somehow then become interested in all the other beings.
And we feel ourselves differently.
It's totally strange.
It's totally strange.
The Dalai Lama always likes to say -- he says that when you give birth in your mind to the idea of compassion, it's because you realize that you yourself and your pains and pleasures are finally too small a theater for your intelligence.
It's really too boring whether you feel like this or like that, or what, you know -- and the more you focus on how you feel, by the way, the worse it gets.
Like, even when you're having a good time, when is the good time over?
The good time is over when you think, how good is it?
And then it's never good enough.
I love that Leilei said that the way of helping those who are suffering badly on the physical plane or on other planes is having a good time, doing it by having a good time.
I think the Dalai Lama should have heard that.
I wish he'd been there to hear that.
He once told me -- he looked kind of sad; he worries very much about the haves and have-nots.
He looked a little sad, because he said, well, a hundred years ago, they went and took everything away from the haves.
You know, the big communist revolutions, Russia and China and so forth.
They took it all away by violence, saying they were going to give it to everyone, and then they were even worse.
They didn't bmcmillan@example.com.
So what could possibly change this terrible gap that has opened up in the world today?
And so then he bmcmillan@example.com.
So I said, "Well, you know, you're all in this yourself.
You teach: it's generosity," was all I could think of.
What is virtue?
But of course, what you said, I think the key to saving the world, the key to compassion is that it is more fun.
It should be done by fun.
Generosity is more fun.
That's the key.
Everybody has the wrong idea.
They think Buddha was so boring, and they're so surprised when they meet Dalai Lama and he's fairly jolly.
Even though his people are being genocided -- and believe me, he feels every blow on every old nun's head, in every Chinese prison.
He feels it.
He feels the way they are harvesting yaks nowadays.
I won't even say what they do.
But he feels it.
And yet he's very jolly.
He's extremely jolly.
Because when you open up like that, then you can't just -- what good does it do to add being miserable with others' misery?
You have to find some vision where you see how hopeful it is, how it can be changed.
Look at that beautiful thing Chiho showed us.
She scared us with the lava man.
She scared us with the lava man is coming, then the tsunami is coming, but then finally there were flowers and trees, and it was very beautiful.
It's really lovely.
So, compassion means to feel the feelings of others, and the human being actually is compassion.
The human being is almost out of time.
The human being is compassion because what is our brain for?
Now, Jim's brain is memorizing the almanac.
But he could memorize all the needs of all the beings that he is, he will, he did.
He could memorize all kinds of fantastic things to help many beings.
And he would have tremendous fun doing that.
So the first person who gets happy, when you stop focusing on the self-centered situation of, how happy am I, where you're always dissatisfied -- as Mick Jagger told us.
You never get any satisfaction that way.
So then you decide, "Well, I'm sick of myself.
I'm going to think of how other people can be happy.
I'm going to get up in the morning and think, what can I do for even one other person, even a dog, my dog, my cat, my pet, my butterfly?"
And the first person who gets happy when you do that, you don't do anything for anybody else, but you get happier, you yourself, because your whole perception broadens and you suddenly see the whole world and all of the people in it.
And you realize that this -- being with these people -- is the flower garden that Chiho showed us.
It is Nirvana.
And my time is up.
And I know the TED commandments.
Thank you.
Can I ask you to please recall a time when you really loved something -- a movie, an album, a song or a book -- and you recommended it wholeheartedly to someone you also really liked, and you anticipated that reaction, you waited for it, and it came back, and the person hated it?
So, by way of introduction, that is the exact same state in which I spent every working day of the last six years.
(Laughter) I teach high school math.
I sell a product to a market that doesn't want it, but is forced by law to buy it.
I mean, it's just a losing proposition.
So there's a useful stereotype about students that I see, a useful stereotype about you all.
I could give you guys an algebra-two final exam, and I would expect no higher than a 25 percent pass rate.
And both of these facts say less about you or my students than they do about what we call math education in the U.S. today.
To start with, I'd like to break math down into two categories.
One is computation; this is the stuff you've forgotten.
For example, factoring quadratics with leading coefficients greater than one.
This stuff is also really easy to relearn, provided you have a really strong grounding in reasoning.
Math reasoning -- we'll call it the application of math processes to the world around us -- this is hard to teach.
This is what we would love students to retain, even if they don't go into mathematical fields.
This is also something that, the way we teach it in the U.S.
all but ensures they won't retain it.
So, I'd like to talk about why that is, why that's such a calamity for society, what we can do about it and, to close with, why this is an amazing time to be a math teacher.
So first, five symptoms that you're doing math reasoning wrong in your classroom.
One is a lack of initiative; your students don't self-start.
You finish your lecture block and immediately you have five hands going up asking you to re-explain the entire thing at their desks.
Students lack perseverance.
They lack retention; you find yourself re-explaining concepts three months later, wholesale.
There's an aversion to word problems, which describes 99 percent of my students.
And then the other one percent is eagerly looking for the formula to apply in that situation.
This is really destructive.
David Milch, creator of "Deadwood" and other amazing TV shows, has a really good description for this.
He swore off creating contemporary drama, shows set in the present day, because he saw that when people fill their mind with four hours a day of, for example, "Two and a Half Men," no disrespect, it shapes the neural pathways, he said, in such a way that they expect simple problems.
He called it, "an impatience with irresolution."
You're impatient with things that don't resolve quickly.
You expect sitcom-sized problems that wrap up in 22 minutes, three commercial breaks and a laugh track.
And I'll put it to all of you, what you already know, that no problem worth solving is that simple.
I am very concerned about this because I'm going to retire in a world that my students will run.
I'm doing bad things to my own future and well-being when I teach this way.
I'm here to tell you that the way our textbooks -- particularly mass-adopted textbooks -- teach math reasoning and patient problem solving, it's functionally equivalent to turning on "Two and a Half Men" and calling it a day.
(Laughter) In all seriousness.
Here's an example from a physics textbook.
It applies equally to math.
Notice, first of all here, that you have exactly three pieces of information there, each of which will figure into a formula somewhere, eventually, which the student will then compute.
I believe in real life.
And ask yourself, what problem have you solved, ever, that was worth solving where you knew all of the given information in advance; where you didn't have a surplus of information and you had to filter it out, or you didn't have sufficient information and had to go find some.
I'm sure we all agree that no problem worth solving is like that.
And the textbook, I think, knows how it's hamstringing students because, watch this, this is the practice problem set.
When it comes time to do the actual problem set, we have problems like this right here where we're just swapping out numbers and tweaking the context a little bit.
And if the student still doesn't recognize the stamp this was molded from, it helpfully explains to you what sample problem you can return to to find the formula.
You could literally, I mean this, pass this particular unit without knowing any physics, just knowing how to decode a textbook.
That's a shame.
So I can diagnose the problem a little more specifically in math.
Here's a really cool problem.
I like this.
It's about defining steepness and slope using a ski lift.
But what you have here is actually four separate layers, and I'm curious which of you can see the four separate layers and, particularly, how when they're compressed together and presented to the student all at once, how that creates this impatient problem solving.
I'll define them here: You have the visual.
You also have the mathematical structure, talking about grids, measurements, labels, points, axes, that sort of thing.
You have substeps, which all lead to what we really want to talk about: which section is the steepest.
So I hope you can see.
I really hope you can see how what we're doing here is taking a compelling question, a compelling answer, but we're paving a smooth, straight path from one to the other and congratulating our students for how well they can step over the small cracks in the way.
That's all we're doing here.
So I want to put to you that if we can separate these in a different way and build them up with students, we can have everything we're looking for in terms of patient problem solving.
So right here I start with the visual, and I immediately ask the question: Which section is the steepest?
And this starts conversation because the visual is created in such a way where you can defend two answers.
So you get people arguing against each other, friend versus friend, in pairs, journaling, whatever.
And then eventually we realize it's getting annoying to talk about the skier in the lower left-hand side of the screen or the skier just above the mid line.
And we realize how great would it be if we just had some A, B, C and D labels to talk about them more easily.
And then as we start to define what does steepness mean, we realize it would be nice to have some measurements to really narrow it down, specifically what that means.
And then and only then, we throw down that mathematical structure.
The math serves the conversation, the conversation doesn't serve the math.
And at that point, I'll put it to you that nine out of 10 classes are good to go on the whole slope, steepness thing.
But if you need to, your students can then develop those substeps together.
Do you guys see how this, right here, compared to that -- which one creates that patient problem solving, that math reasoning?
It's been obvious in my practice, to me.
And I'll yield the floor here for a second to Einstein, who, I believe, has paid his dues.
He talked about the formulation of a problem being so incredibly important, and yet in my practice, in the U.S. here, we just give problems to students; we don't involve them in the formulation of the problem.
So 90 percent of what I do with my five hours of prep time per week is to take fairly compelling elements of problems like this from my textbook and rebuild them in a way that supports math reasoning and patient problem solving.
And here's how it works.
I like this question.
It's about a water tank.
The question is: How long will it take you to fill it up?
First things first, we eliminate all the substeps.
Students have to develop those, they have to formulate those.
And then notice that all the information written on there is stuff you'll need.
None of it's a distractor, so we lose that.
Students need to decide, "All right, well, does the height matter?
Does the side of it matter?
Does the color of the valve matter?
What matters here?"
Such an underrepresented question in math curriculum.
So now we have a water tank.
How long will it take you to fill it up?
And that's it.
And because this is the 21st century and we would love to talk about the real world on its own terms, not in terms of line art or clip art that you so often see in textbooks, we go out and we take a picture of it.
So now we have the real deal.
How long will it take it to fill it up?
And then even better is we take a video, a video of someone filling it up.
And it's filling up slowly, agonizingly slowly.
It's tedious.
Students are looking at their watches, rolling their eyes, and they're all wondering at some point or another, "Man, how long is it going to take to fill up?"
(Laughter) That's how you know you've baited the hook, right?
And that question, off this right here, is really fun for me because, like the intro, I teach kids -- because of my inexperience -- I teach the kids that are the most remedial, all right?
And I've got kids who will not join a conversation about math because someone else has the formula; someone else knows how to work the formula better than me, so I won't talk about it.
But here, every student is on a level playing field of intuition.
Everyone's filled something up with water before, so I get kids answering the question, "How long will it take?"
I've got kids who are mathematically and conversationally intimidated joining the conversation.
We put names on the board, attach them to guesses, and kids have bought in here.
And then we follow the process I've described.
And the best part here, or one of the better parts is that we don't get our answer from the answer key in the back of the teacher's edition.
We, instead, just watch the end of the movie.
(Laughter) And that's terrifying, because the theoretical models that always work out in the answer key in the back of a teacher's edition, that's great, but it's scary to talk about sources of error when the theoretical does not match up with the practical.
But those conversations have been so valuable, among the most valuable.
So I'm here to report some really fun games with students who come pre-installed with these viruses day one of the class.
These are the kids who now, one semester in, I can put something on the board, totally new, totally foreign, and they'll have a conversation about it for three or four minutes more than they would have at the start of the year, which is just so fun.
We're no longer averse to word problems, because we've redefined what a word problem is.
We're no longer intimidated by math, because we're slowly redefining what math is.
This has been a lot of fun.
I encourage math teachers I talk to to use multimedia, because it brings the real world into your classroom in high resolution and full color; to encourage student intuition for that level playing field; to ask the shortest question you possibly can and let those more specific questions come out in conversation; to let students build the problem, because Einstein said so; and to finally, in total, just be less helpful, because the textbook is helping you in all the wrong ways: It's buying you out of your obligation, for patient problem solving and math reasoning, to be less helpful.
And why this is an amazing time to be a math teacher right now is because we have the tools to create this high-quality curriculum in our front pocket.
It's ubiquitous and fairly cheap, and the tools to distribute it freely under open licenses has also never been cheaper or more ubiquitous.
I put a video series on my blog not so long ago and it got 6,000 views in two weeks.
I get emails still from teachers in countries I've never visited saying, "Wow, yeah.
We had a good conversation about that.
Oh, and by the way, here's how I made your stuff better," which, wow.
I put this problem on my blog recently: In a grocery store, which line do you get into, the one that has one cart and 19 items or the line with four carts and three, five, two and one items.
And the linear modeling involved in that was some good stuff for my classroom, but it eventually got me on "Good Morning America" a few weeks later, which is just bizarre, right?
And from all of this, I can only conclude that people, not just students, are really hungry for this.
Math makes sense of the world.
Math is the vocabulary for your own intuition.
So I just really encourage you, whatever your stake is in education -- whether you're a student, parent, teacher, policy maker, whatever -- insist on better math curriculum.
We need more patient problem solvers.
Thank you.
(Applause)