at least based on my observations at Khan Academy,

這兩個概念是基於我對 可漢學院的觀察。

are kind of the core, or the key leverage points for learning.

有關於學習的核心， 或者說是學習的關鍵動機。

And it's the idea of mastery

一個是觀念的掌握，

and the idea of mindset.

另一個是思維方式。

I saw this in the early days working with my cousins.

幾年前，我陪我親戚 一起讀書的時候，就觀察到

A lot of them were having trouble with math at first,

他們之中很多人剛開始對 數學很頭疼，

because they had all of these gaps accumulated in their learning.

原因是他們在學習過程中， 不斷積累還沒掌握的知識漏洞。

And because of that, at some point they got to an algebra class

因此，當他們開始上代數課時，

and they might have been a little bit shaky on some of the pre-algebra,

在初級代數的課程中 可能就跟不太上，

and because of that, they thought they didn't have the math gene.

因此，他們會認為自己 沒有學習數學的天賦。

Or they'd get to a calculus class,

或者他們之後上微積分課時，

and they'd be a little bit shaky on the algebra.

才發現自己在代數環節上 的基礎也不太好。

I saw it in the early days

我知道這件事 是在前些年的時候，

when I was uploading some of those videos on YouTube,

當我在YouTube上， 上傳這些視頻的時候，

and I realized that people who were not my cousins were watching.

我才搞懂，原來看我影片的 不只有我的親戚。

(Laughter)

（笑聲）

And at first, those comments were just simple thank-yous.

一開始，有些留言 只是些簡單的謝謝。

I thought that was a pretty big deal.

我認為這樣真的很棒。

I don't know how much time you all spend on YouTube.

我不知道你們都花 多少時間在YouTube上。

Most of the comments are not "Thank you."

因為後來大多數的留言 並不是「謝謝」。

(Laughter)

（笑聲）

They're a little edgier than that.

他們越來越激動了。

But then the comments got a little more intense,

但之後的留言變得越來越有深度，

student after student saying that they had grown up not liking math.

越來越多的學生反映， 他們之前是在不喜歡數學的環境下長大。

It was getting difficult as they got into more advanced math topics.

進入高等數學後就更加痛苦了。

By the time they got to algebra,

當他們開始上代數的時候，

they had so many gaps in their knowledge they couldn't engage with it.

他們的知識中已累積太多漏洞 以至於他們無法投入在課堂之中。

They thought they didn't have the math gene.

他們會自以為沒有數學頭腦。

But when they were a bit older,

但當他們長大後，

they took a little agency and decided to engage.

他們有了一點動力 並決定要好好念書了，

They found resources like Khan Academy

他們找到了像可汗學院 這樣的資源，

and they were able to fill in those gaps and master those concepts,

能夠幫他們填補過去的 學習漏洞並掌握概念，

and that reinforced their mindset that it wasn't fixed;

從此改變了他們的思維方式， 糾正了他們的定式思維；

that they actually were capable of learning mathematics.

他們才知道其實他們自己 也有能力可以學好數學的。

And in a lot of ways, this is how you would master a lot of things in life.

在很多方面，這也是 你要如何掌握你人生事物的方法。

It's the way you would learn a martial art.

這就像你學習武術一樣。

In a martial art, you would practice the white belt skills

在武術當中，如果有必要，

as long as necessary,

你必須一直練習白帶的技巧。

and only when you've mastered it

只有當你們掌握了它，

you would move on to become a yellow belt.

你才能進階到黃帶。

It's the way you learn a musical instrument:

這也是你們學習樂器的方式：

you practice the basic piece over and over again,

一遍遍練習最基礎的曲目，

and only when you've mastered it,

只有當你們掌握了它，

you go on to the more advanced one.

你才會去挑戰更難的曲目。

But what we point out --

但我要說的是：

this is not the way a traditional academic model is structured,

這並非傳統學習模式的架構，

the type of academic model that most of us grew up in.

也不是我們成長過程中 所使用的學習方式。

In a traditional academic model,

在傳統學習模式當中，

we group students together, usually by age,

我們一般會將 同年齡的學生聚集在一起，

and around middle school,

在中學時期，

by age and perceived ability,

透過年齡和外顯的學習能力 把學生分組，

and we shepherd them all together at the same pace.

然後我們以齊頭式的教育 引領他們。

And what typically happens,

常常發生的是，

let's say we're in a middle school pre-algebra class,

假設我們身處某中學的 初級代數課堂中，

and the current unit is on exponents,

現在上的課程是指數，

the teacher will give a lecture on exponents,

老師就此內容來上課，

then we'll go home, do some homework.

之後，我們回家， 做了一些相關的習題。

The next morning, we'll review the homework,

第二天早上， 我們會批改這些作業。

then another lecture, homework, lecture, homework.

之後又是上課、做作業、 上課、做作業。

That will continue for about two or three weeks,

這大概會持續兩到三周，

and then we get a test.

然後考試。

On that test, maybe I get a 75 percent,

在考試中， 我也許只會75%的題目，

maybe you get a 90 percent,

你也許會90%，

maybe you get a 95 percent.

或是95%。

And even though the test identified gaps in our knowledge,

即使考試能幫助 判斷我們知識的漏洞，

I didn't know 25 percent of the material.

我還是存在25%不知道的內容。

Even the A student, what was the five percent they didn't know?

即使得A的學生， 仍有5%不懂的內容。

Even though we've identified the gaps,

即使我們找到了那些漏洞，

the whole class will then move on to the next subject,

課堂還是會繼續， 進入下一個主題，

probably a more advanced subject that's going to build on those gaps.

可能是更加覆雜的內容， 但卻建立在我們知識漏洞之上。

It might be logarithms or negative exponents.

可能會是對數函數， 或者是負指數函數。

And that process continues, and you immediately start to realize

老師一直講課， 然後你會突然間發現，

how strange this is.

這一切怎麽那麽的陌生。

I didn't know 25 percent of the more foundational thing,

我明明還有25% 的基礎知識不懂，

and now I'm being pushed to the more advanced thing.

現在卻被迫繼續學 更加深奧的東西。

And this will continue for months, years, all the way until at some point,

這會持續數月或數年， 直到某一刻，

I might be in an algebra class or trigonometry class

我可能會在代數或 是三角函數課堂上

and I hit a wall.

遇到麻煩。

And it's not because algebra is fundamentally difficult

這並非因為代數學本身很困難，

or because the student isn't bright.

或者是學生不夠聰明。

It's because I'm seeing an equation and they're dealing with exponents

那是因為當我看見 指數的等式時，

and that 30 percent that I didn't know is showing up.

其中有30%是我不懂的知識。

And then I start to disengage.

然後我就不想做了。

To appreciate how absurd that is,

為了感受那是多麽的荒謬，

imagine if we did other things in our life that way.

各位想象一下，如果我們以同樣方式 來處理人生中其它事情的時後，

Say, home-building.

比如說，蓋房子。

(Laughter)

（笑聲）

So we bring in the contractor and say,

我們找承包商來，然後和他說：

"We were told we have two weeks to build a foundation.

「我們被告知只有兩周時間去打地基。

Do what you can."

所以你能蓋多少就蓋多少吧！」

(Laughter)

（笑聲）

So they do what they can.

所以他們就盡力去做了。

Maybe it rains.

施工過程中也許會下雨。

Maybe some of the supplies don't show up.

也許有些物資沒到場的情況。

And two weeks later, the inspector comes, looks around,

然後兩周之後， 房屋檢查員來了，他看了一下，

says, "OK, the concrete is still wet right over there,

說：「好吧，這邊的水泥還沒乾，

that part's not quite up to code ...

那邊的也不大符合標準……

I'll give it an 80 percent."

我就給你80分吧。」

(Laughter)

（笑聲）

You say, "Great! That's a C. Let's build the first floor."

然後你會說：「太好了，還有C等。 我們開始建第一層吧！”

(Laughter)

（笑聲）

Same thing.

同樣的事情一再發生。

We have two weeks, do what you can, inspector shows up, it's a 75 percent.

我們又努力了兩周 然後房屋檢查員來了，給了個75分。

Great, that's a D-plus.

太好了，居然還有D+！

Second floor, third floor,

繼續建二樓，三樓，

and all of a sudden, while you're building the third floor,

直到建三樓的時候，

the whole structure collapses.

整棟建築突然就倒塌了。

And if your reaction is the reaction you typically have in education,

如果你的回應與 受教育時的回應一樣，

or that a lot of folks have,

或者是很多人會有的那種反應，

you might say, maybe we had a bad contractor,

你也許會說，我們只是倒楣 遇到了爛承包商，

or maybe we needed better inspection or more frequent inspection.

或是我們檢查的力度和次數不夠多。

But what was really broken was the process.

但真正的問題，其實是過程的本身。

We were artificially constraining how long we had to something,

我們用人為的方式 去限制完成某事的時間，

pretty much ensuring a variable outcome,

幾乎可以確定，結果一定會有落差，

and we took the trouble of inspecting and identifying those gaps,

然後我們檢查也發現了問題，

but then we built right on top of it.

但卻又立刻填鴨上去。

So the idea of mastery learning is to do the exact opposite.

掌握式教育的觀念 就是去做完全相反的事。

Instead of artificially constraining, fixing

將人為的限制、僵化、

when and how long you work on something,

何時學習和學多久、

pretty much ensuring that variable outcome,

確認Ａ、B、C、D、F成績

the A, B, C, D, F --

這些結果的行為，

do it the other way around.

轉換成另一種方式。

What's variable is when and how long

學生之間不同的 只有「何時」以及「多久」

a student actually has to work on something,

可以掌握好一門知識，

and what's fixed is that they actually master the material.

要堅持一致的是 學生真的掌握了該門知識。

And it's important to realize

我們必須了解到它的重要性，

that not only will this make the student learn their exponents better,

這樣不僅可以讓學生 更好地掌握指數函數，

but it'll reinforce the right mindset muscles.

同時也可以培養一種 正確的思維方式。

It makes them realize that if you got 20 percent wrong on something,

這可以讓他們體認到 如果他們答錯了20％，

it doesn't mean that you have a C branded in your DNA somehow.

不代表他們骨子裏就是個 C 咖，

It means that you should just keep working on it.

而是說明你還需要 在這個內容上繼續努力、

You should have grit; you should have perseverance;

你得堅持不懈、

you should take agency over your learning.

你得拿出熱情克服學習的障礙。

Now, a lot of skeptics might say, well, hey, this is all great,

現在很多懷疑的人會說， 這些聽起來都很棒，

philosophically, this whole idea of mastery-based learning

理論上來說， 這套以掌握為目的教學方式

and its connection to mindset,

與心智的連結，

students taking agency over their learning.

可以讓學生拿出熱情 來克服學習障礙。

It makes a lot of sense, but it seems impractical.

聽起來很有道理， 但不太實際。

To actually do it, every student would be on their own track.

為了要真正的辦到這一點， 每個學生都必須有自己的學習進度，

It would have to be personalized,

必須有客製化的教學方式。

you'd have to have private tutors and worksheets for every student.

每個學生都要有私人教師 和私人定制的練習題。

And these aren't new ideas --

但這並不是什麽新觀念——

there were experiments in Winnetka, Illinois, 100 years ago,

在100年前的伊利諾伊州， 溫內特卡市就有這樣的實驗：

where they did mastery-based learning and saw great results,

他們從事了這種以掌握為目的的教學， 也取得了不錯的結果，

but they said it wouldn't scale because it was logistically difficult.

但是他們表示很難普及化， 畢竟這在邏輯上就難以實現。

The teacher had to give different worksheets to every student,

老師要給每個學生不同的試題，

give on-demand assessments.

根據需求做出不同的評估方式。

But now today, it's no longer impractical.

但如今，這已經不再是 不實際的問題了。

We have the tools to do it.

我們有了工具的幫助。

Students see an explanation at their own time and pace?

學生可以按照自己的時間 和步調看錄影的講解，

There's on-demand video for that.

有很多適當的影片 可以符合學生的要求。

They need practice? They need feedback?

他們需要練習嗎？需要反饋嗎？

There's adaptive exercises readily available for students.

那些掌握度的評估測驗， 學生都可以自行測驗。

And when that happens, all sorts of neat things happen.

當這些條件都能成立的時候， 各種好事就會接踵而至。

One, the students can actually master the concepts,

首先，學生能夠真正掌握概念，

but they're also building their growth mindset,

其次，他們能培養積極的態度，

they're building grit, perseverance,

建立勇氣和不屈不撓的精神，

they're taking agency over their learning.

他們會拿出熱情來學習。

And all sorts of beautiful things can start to happen

這些美好的事情，

in the actual classroom.

已經可以進入實際的課堂當中了。

Instead of it being focused on the lecture,

取代老師專心講解課堂內容的是

students can interact with each other.

學生們可以互動學習。

They can get deeper mastery over the material.

他們能夠更加深入地 去掌握知識。

They can go into simulations, Socratic dialogue.

他們能夠模仿蘇格拉底的對話，

To appreciate what we're talking about

去感悟我們所說的事情，

and the tragedy of lost potential here,

去體會悲劇中的失落感，

I'd like to give a little bit of a thought experiment.

我想給各位一個 小型的思維實驗。

If we were to go 400 years into the past to Western Europe,

如果我們回到400年前的西歐，

which even then, was one of the more literate parts of the planet,

當時那邊是地球上 最文明的地方，

you would see that about 15 percent of the population knew how to read.

你會發現人群中 大概有15％的人識字，

And I suspect that if you asked someone who did know how to read,

然後我猜，當你去詢問 一個識字的人，

say a member of the clergy,

比如一個神職人員，

"What percentage of the population do you think is even capable of reading?"

「你認為大概有多少人 有識字的能力呢？」

They might say, "Well, with a great education system,

他們也許會說： 「嗯，在這個強大的教育體系下，

maybe 20 or 30 percent."

大概有個20%或30%吧。」

But if you fast forward to today,

但如果你快進到當下，

we know that that prediction would have been wildly pessimistic,

我們都知道 那樣的預測實在太悲觀了，

that pretty close to 100 percent of the population is capable of reading.

現在幾乎是人人都識字。

But if I were to ask you a similar question:

但如果我問各位一個類似的問題：

"What percentage of the population do you think is capable

「你們認為目前人口中有多少

of truly mastering calculus,

是真正掌握微積分的，

or understanding organic chemistry,

或是真正懂有機化學的，

or being able to contribute to cancer research?"

或是有能力能夠 為癌症研究作出貢獻的？」

A lot of you might say, "Well, with a great education system,

你們中的很多就會回答： 「就目前的強大教育體系下

maybe 20, 30 percent."

大概有個20%或30%吧。」

But what if that estimate

但假如那些判斷

is just based on your own experience in a non-mastery framework,

僅僅是基於你們尚未 掌握觀念的個人經驗，

your own experience with yourself or observing your peers,

僅僅是基於你們的自身經歷 或僅是對周圍人的觀察而已呢？

where you're being pushed at this set pace through classes,

當時你就是被迫推進課堂進度，

accumulating all these gaps?

不斷積累漏洞情況的人啊？

Even when you got that 95 percent,

即使你掌握了95%的知識，

what was that five percent you missed?

那剩下的5%呢？

And it keeps accumulating -- you get to an advanced class,

漏洞持續積累， 直到進入進階課程，

all of a sudden you hit a wall and say,

突然碰壁，然後你就會說：

"I'm not meant to be a cancer researcher;

「我天生就不是個癌症研究人員、

not meant to be a physicist; not meant to be a mathematician."

不是物理學家、不是數學家。」

I suspect that that actually is the case,

我認為這就是現實情況。

but if you were allowed to be operating in a mastery framework,

但如果你能從掌握知識的視角去審視，

if you were allowed to really take agency over your learning,

如果你能從培養學習動力的角度來看，

and when you get something wrong,

當你做錯題目的時候，

embrace it -- view that failure as a moment of learning --

把這種失敗當作學習的一部分 並坦然接受，

that number, the percent that could really master calculus

那真正掌握微積分的人數比例

or understand organic chemistry,

或是真正掌握有機化學的人數比例

is actually a lot closer to 100 percent.

就會接近100%了。

And this isn't even just a "nice to have."

而這並不僅僅只是「有人就好」 的意義而已，

I think it's a social imperative.

我認為社會急需要這些人才。

We're exiting what you could call the industrial age

用你們的話來說， 我們正處於一個工業時代，

and we're going into this information revolution.

而我們正在進入 資訊革命的時代。

And it's clear that some things are happening.

很明確的是， 一些變化正在發生。

In the industrial age, society was a pyramid.

在工業時代， 社會是一個金字塔。

At the base of the pyramid, you needed human labor.

在金字塔底端，我們需要的是人力。

In the middle of the pyramid, you had an information processing,

在金字塔中間，資訊需要處理

a bureaucracy class,

所以有官僚特權階層，

and at the top of the pyramid, you had your owners of capital

而金字塔頂端， 就會是那些資本家、

and your entrepreneurs

那些企業家、

and your creative class.

還有那些創業家。

But we know what's happening already,

但當我們進入到資訊革命的年代，

as we go into this information revolution.

我們就知道將要發生什麽事了。

The bottom of that pyramid, automation, is going to take over.

在金字塔底端， 自動化將取代人力。

Even that middle tier, information processing,

甚至中間層資訊處理的這一段

that's what computers are good at.

電腦做的都比他們好。

So as a society, we have a question:

所以對一個社會而言， 我們有一個問題：

All this new productivity is happening because of this technology,

科技帶來了新的生產力，

but who participates in it?

是誰會參與其中呢？

Is it just going to be that very top of the pyramid, in which case,

是不是只有處於金字塔頂端的人？ 這種情況下，

what does everyone else do?

其他人還能做些甚麼？

How do they operate?

他們會如何操作？

Or do we do something that's more aspirational?

或者我們是否要從事 更加遠大的事業呢？

Do we actually attempt to invert the pyramid,