for its collection of videos.

就是大量的影片

So before I go any farther, let me

在深入介紹之前 容我先

show you a little bit of a montage.

讓大家看一些片段

[VIDEO PLAYBACK]

[影片播放]

So the hypotenuse is now going to be five.

現在斜邊是5

This animal's fossils are only found

動物化石在

in this area of South America, nice, clean band

南美洲這個漂亮乾淨的帶狀區

here, and in this part of Africa.

以及一部分的非洲被發現

We could integrate over the surface,

我們能計算面積

and the notation usually is a capital sigma.

而通常用大寫的sigma符號

National Assembly, they create the committee

國家議會成立了公共安全委員會

of public safety, which sounds like a very nice committee.

聽起來是個相當不錯的委員會

Notice this is an aldehyde, and it's an alcohol.

注意 這是醛 這是醇

Start differentiating into effector and memory cells.

開始分化成效應與記憶細胞

A galaxy, hey, there's another galaxy.

這裡一個銀河系 那裡一個銀河系

Oh look, there's another galaxy.

看 那裡又一個銀河系

And for dollars is their 30 million plus the $20 million

用美金計價就是他們的3千萬加上

from the American manufacturer.

從美國生產廠商取得的2千萬

If this does not blow your mind, then you have no emotion.

如果這沒有讓你受到衝擊 你是個無情的人

[END VIDEO PLAYBACK]

[影片播放完畢]

SALMAN KHAN: We now have on the order of 2,200 videos

薩爾曼可汗：我們現在有2200支循序漸進的影片

covering everything from basic arithmetic all

包含所有事物 從基礎算術

the way to vector calculus and some of the stuff

到向量微積分 以及一些

that you saw up there.

剛剛在上面看到的

We have a million students a month using the site,

每個月有上百萬學生使用這個網站

watching on the order of 100,000 to 200,000 videos a day.

一天有100,000到200,000支影片被觀看

But what we're going to talk about in this

不過我們要講的是

is how we're going to the next level.

我們的下一個階段要怎麼做

But before I do that, I want to talk a little bit about how

在那之前 先講一下

I got started.

我開始網站的故事

And some of you all might know, about five years ago,

有些人可能知道 五年前

I was an analyst at a hedge fund.

我是個避險基金分析師

And I was in Boston.

那時候我住在波士頓

And I was tutoring my cousins in New Orleans remotely.

我幫紐奧良的表弟們遠端上課

And I started putting the first YouTube videos up, really just

我放上第一支YouTube影片

as a nice to have, just kind of a supplement, for my cousins,

只是想幫表弟做個輔助教材

something that might give them a refresher, or something.

讓他們能振作精神之類的

And as soon as I put those first YouTube videos up,

就在放上影片之後

something interesting happened.

有趣的事發生了

Actually, a bunch of interesting things happened.

事實上發生了很多有趣的事

The first was the feedback from my cousins.

第一個是我表弟們的回應

They told me that they preferred me on YouTube than in person.

他們說比起我教他們 他們比較愛看影片裡的我

[LAUGHTER]

[笑聲]

And once you get over the backhanded nature of that,

在克服這些挖苦之後

there was actually something very profound there.

有件事其實相當意義深遠

They were saying that they preferred the automated version

他們比較喜歡自動版本的表哥

of their cousin to their cousin.

比起真實的表哥

At first it's very unintuitive, but when you actually

一開始可能不太經過大腦 但當你真正

think about it from their point of view,

從他們的觀點來思考這件事

it makes a ton of sense.

就會覺得非常有道理

You have this situation where now they can pause and repeat

他們現在有個可以隨時暫停、重複播放

their cousin without feeling like they're wasting my time.

的表哥 不用擔心會浪費到我的時間

If they have to review something that they should have learned

如果他們要複習一些以前因該學過的東西，

a couple of weeks ago, or maybe a couple of years ago,

像是幾週或是幾年前學過的東西

they don't have to be embarrassed and ask

他們不需要不好意思來問我

their cousin.

這個表哥

They can just watch those videos.

他們只要看影片就可以

If they're bored, they can go ahead.

如果他們覺得無趣 可以加速影片

They can watch it at their own time, at their own pace.

他們可以用自己的步調與時間看影片

And probably the least appreciated aspect of this

學習中最不需要的東西

is the notion that the very first time, the very first time

就是當你第一次

that you're trying to get your brain around a new concept,

在學新知識的時候

the very last thing you need is another human being saying

最不需要別人跑來問

do you understand this.

你懂了嗎

And that's what was happening with the interaction

這就是我之前與表弟們互動發生的事情

with my cousins before.

這就是我之前與表弟們互動發生的事情

And now they could just do it in the intimacy of their own room.

現在他們可以私下在自己的房間學

The other thing that happened is I put them on YouTube

另一件事就是我把影片放上YouTube

just for the....I saw no reason to make it private.

因為我覺得不需要設為隱私

So I let other people watch it.

所以我讓其他人也能觀看

And then people started stumbling on it.

接著開始有人點進來看影片

And I started getting some comments, and some letters,

然後我就開始收到一些評論、信件

and all sorts of feedback from random people around the world.

和來自全世界不固定人士的各種的回饋

And these are just a few.

這裡擷取了一些

This is actually from one of the original calculus videos.

這是微積分影片其中一支

And someone wrote on YouTube, it was a YouTube comment,

實際收到YouTube留言，這是一則YouTube的評論

"First time I smiled doing a derivative."

"我第一次在推導方程式的時候笑出來了"

Let's pause here.

暫停一下

This person did a derivative, and then they smiled.

這個人在推導方程式的時候笑出來了

And then in response to that same comment,

接著針對這則評論

this is on the thread.

有一些回覆

You could go on YouTube and look at these comments.

你可以上YouTube看這些評論

Someone else wrote, "Same thing here.

有人寫"我也是

I actually got a natural high and a good mood

一整天心情超好

for the entire day, since I remember

就在我發現

seeing all of this 'matrix text' in class.

課堂上的'矩陣'我都看過之後

And here I'm all like, I know Kung Fu."

突然覺得 我武功高強啊"

[LAUGHTER]

[笑聲]

And we got a lot of feedback along those lines.

我們這串回應裡還收到很多回覆

This clearly was helping people.

這真的對大家有幫助

But then, as the viewership kept growing, and kept growing,

之後 就在觀看人數越來越多 越來越多

I started getting letters from people.

我開始收到一些信

And it was starting to become clear

才開始明確的知道這些影片

that it was actually more than just a nice to have.

不是不錯而已 而是真的很棒

This is just an excerpt from one of those letters.

這是那些信中其中一封摘錄

"My 12-year-old son has autism, and has

"我12歲的兒子有自閉症

had a terrible time with math.

他的數學學習過程很艱辛

We have tried everything, viewed everything, bought everything.

我們試過各種方式 看了很多東西 買了各種東西

We stumbled on your video on decimals, and it got through.

我們看了你關於小數點的影片 然後他就懂了

Then we went on to the dreaded fractions.

接著我們進入可怕的分數

Again, he got it.

又一次 他懂了

We could not believe it.

無法置信

He is so excited."

他很興奮"

And so you can imagine, here I was,

你可以想像 我

an analyst at a hedge fund.

是一個避險基金分析師

It was very strange for me to do something of social value.

能做出有社會價值的東西是很奇怪的

[LAUGHTER AND APPLAUSE]

[笑聲與掌聲]

But I was excited.

但是我很興奮

So I kept going.

於是我繼續做下去

And then a few other things started to dawn on me.

接著有其他的事情開始降臨在我身上

That not only would it help my cousins right now,

這不只可以幫助我的表弟們

or these people who were sending letters.

或是那些寫信給我的人

But maybe that this content will never go old.

也許這些內容永遠不會退流行

That it could help their kids or their grandkids.

可以幫助他們的孩子、孫子

If Isaac Newton had done YouTube videos on calculus,

如果艾薩克牛頓在YouTube放上微積分影片

I wouldn't have to, assuming he was good.

如果他的影片不錯的話 我就不用放我的了

We don't know.

誰知道呢

[LAUGHTER]

[笑聲]

The other thing that happened, and even at this point, I said,

就在這時 另一件事發生了 我想說

OK, maybe it's a good supplement.

嗯 這是一個好的補充教材

It's good for motivated students.

對積極的學生有幫助

It's good for maybe homeschoolers.

也對在家學習的學生有幫助

But I didn't think it would be something that would somehow

但我沒想到這居然會

penetrate the classroom.

滲透進學校的課程

But then I started getting letters from teachers.

我開始收到老師們寄來的信

And the teachers would write saying,

老師們寫說

we've used your videos to flip the classroom.

我們用你的影片執行翻轉教室

You've given the lectures.

你有一份講義

So now what we do...and this could actually

所以接下來我們要做的 這可能會

happen in every classroom in America tomorrow... what I do

發生在未來的美國學校 我要做的

is I assign the lectures for homework.

就是將講義指派為回家作業

And what used to be homework, I now

而之前當作回家作業的 現在

have the students doing in the classroom.

則讓學生在課堂上做

[APPLAUSE]

[掌聲]

I want to pause here for a second

在這邊要稍微暫停一下

because there's a couple of interesting things.

因為有一些有趣的事

One, when those teachers are doing that,

第一，當那些老師們這樣做的時候

there's the obvious benefit.

有很明顯的好處

There's the benefit that now their students

好處是當學生們這麼做的的時候

can enjoy the videos in the way that my cousins did.

他們可以像我表弟們一樣自由看影片

They can pause, repeat at their own pace, at their own time.

他們可以根據自己的步調與時間暫停、重複觀看影片

But the more interesting thing-- and this

但更有趣的事是

is the unintuitive thing when you talk about technology

聽起來也許不直覺 但當你在課堂上使用科技

in the classroom-- by removing the "one size fits all"

移除掉給學生的"單一教材"

lecture from the classroom and letting students have

讓學生們可以

a self-paced lecture at home, and then when

在家使用自己的步調 接著

you go to the classroom, letting them do work,

上課的時候讓他們做作業

having the teacher walk around, having the peers actually

老師可以在旁邊觀察

be able to interact with each other,

讓師生可以互動

these teachers have used technology

這些老師就是運用科技

to humanize the classroom.

進行人性化教學

They took a fundamentally dehumanizing experience,

以前基本上是採用非人性化的教學

a bunch of 30 kids with their fingers on their lips,

讓30個孩子安靜聽

not allowed to interact with each other.

不讓他們彼此互動

A teacher, no matter how good, has

一個老師 不論再怎麼厲害

to give this kind of "one size fits all"

都要將"單一教材"

lecture to 30 students-- blank faces, slightly antagonistic.

教給30個學生 面無表情 些許的對立著

And now it's a human experience.

而現在則是人性化的體驗

Now they're actually interacting with each other.

他們現在可以彼此互動

So once the Khan Academy-- I quit my job.

所以當可汗學院 我辭掉工作

And we turned into a real organization,

投入組織的實際運作

or a not-for-profit.

或說是非營利組織

The question is, how do we take this to the next level?

問題是 我們要如何進入下一階段

How do we take what those teachers were

要如何將老師們之前

doing to their natural conclusion?

所做的帶到結論？

And so what I'm showing over here,

所以我接著要讓大家在這裡看到

these are actual exercises that I

這是我實際上寫給

started writing for my cousins.

表弟們的測驗題

The ones I started were much more primitive.

一開始的很陽春

This is a more competent version of it.

這是升級版本

But the paradigm here is we'll generate as many questions

這個範例是為了讓你了解內容

as you need until you get that concept,

所需要的所有問題

until you get 10 in a row.

直到你在這一列中得到10分

And the Khan Academy videos are there.

請看可汗學院影片

You get hints, the actual steps for that problem,

每個問題都有實際步驟與提示

if you don't know how to do it.

如果不懂的話可以看

But the paradigm, it seems like a very simple thing.

不過這個範例 很簡單

10 in a row, you move on.

得到10分 可以繼續下一題

But it's fundamentally different than what's

但基本上和現在的上課是不一樣的

happening in classrooms right now.

但基本上和現在的上課是不一樣的

In a traditional classroom, you have

傳統的上課 你會有一些

a couple of-- homework, lecture, homework, lecture,

作業、講義、作業、講義

and then you have a snapshot exam.

接著會有考試

And that exam, whether you get a 70%, an 80%, a 90% or a 95%,

不論你懂70%、80%、90%還是95%

the class moves on to the next topic.

課程都會繼續下去

And even that 95% student, what was the 5% they didn't know?

就算是懂95%的學生 剩下不懂的5%怎麼辦？

Maybe they didn't know what happens

也許他們不懂

when you raise something to the 0-th power.

什麼是0次方

And then you go build on that in the next concept.

你用這個當基礎繼續下個教學

That's analogous to-- imagine learning to ride a bicycle.

這就像是--想像你學騎腳踏車

And I give you a bicycle.

我給你一台腳踏車

Maybe I give you a lecture ahead of time.

也許我給你一個事前講課

And I give you that bicycle for two weeks.

再給你一台腳踏車兩週

And then I come back after two weeks.

兩週之後我再回來

And I say, well, let's see.

然後說 我們來看結果

You're having trouble taking left turns.

也許你左轉不太會

You can't quite stop.

也許你不會煞車

You're an 80% bicyclist.

你80%會騎了

So I put a big C stamp on your forehead.

然後我就在你額頭印個成績C

And then I say here's a unicycle.

接著就給你一台單輪車

But as ridiculous as that sounds,

聽起來就是這麼荒謬

that's exactly what's happening in our classrooms right now.

這是現在上課的實際狀況

And the idea is you fast forward.

然後你快速的上著課

And good students start failing algebra all of a sudden,

好學生開始突然就不懂代數

and start failing calculus all of a sudden,

突然就不懂微積分

despite being smart, despite having good teachers.

即使很聰明 即使有個好老師

And it's usually because they had these Swiss cheese

通常是因為在他們的基本知識上

gaps that kept building throughout their foundations.

一直累積一小片段一小片段的不了解

So our model is learn math the way you would learn anything.

我們的宗旨是讓你學數學像是你學所有東西一樣

Like the way you would learn a bicycle.

就像你學騎腳踏車一樣

Stay on that bicycle.

學騎一台腳踏車

Fall off that bicycle.

跌倒在同一台腳踏車

Do it as long as necessary until you have mastery.

一直騎一直騎直到你精通

The traditional model, it penalizes you

傳統的教學 就像在懲罰你的

for experimentation and failure.

實驗與失敗

But it does not expect mastery.

卻不期待你能精通

We encourage you to experiment.

我們鼓勵你多實驗

We encourage you to failure.

鼓勵你失敗

But we do expect mastery.

但我們期待你能精通

This is just another one of the modules.

這是另外一個教學模組

This is trigonometry.

這是個三角形

This is shifting and reflecting functions.

這是平移與鏡射

And they all fit together.

這些教材結合在一起

We have about 90 of these right now.

我們現在有90個這種教學

And you could go to the site right now.

都可以在網站上看到

It's all free.

全部免費

Not trying to sell anything.

不會兜售任何東西

But the general idea is that they all

但總體思路是這些全都

fit into this knowledge map.

結合在知識地圖

That top node right there, that's

上面那個點

literally single-digit addition.

是個位數加法

It's like 1 plus 1 is equal to 2.

就像1+1=2

And the paradigm is, once you get 10 in a row on that,

這裡的範例是 一旦你得到10分

then it keeps forwarding you to more and more advanced modules.

課程就會進入越來越進階的題目

So keep-- this is further down the knowledge map.

所以--知識地圖就會越來越往下

We're getting into more advanced arithmetic.

學到更進階的算術

Further down, you start getting into

一直往下 就會開始學到

pre-algebra and early algebra.

初級代數的相關知識

Further down, you start getting into algebra one, algebra two,