I'm here today to talk about the two ideas that, at least based on my observations at Khan Academy, are kind of the core, or the key leverage points for learning. And it's the idea of mastery and the idea of mindset.
我今天來這裡是要談談兩個概念, 這兩個概念是基於我對 可漢學院的觀察。 有關於學習的核心, 或者說是學習的關鍵動機。 一個是掌握的觀念, 另一個是思維方式。
I saw this in the early days working with my cousins. A lot of them were having trouble with math at first, because they had all of these gaps accumulated in their learning. And because of that, at some point they got to an algebra class and they might have been a little bit shaky on some of the pre-algebra, and because of that, they thought they didn't have the math gene. Or they'd get to a calculus class, and they'd be a little bit shaky on the algebra. I saw it in the early days when I was uploading some of those videos on YouTube, and I realized that people who were not my cousins were watching.
幾年前,我陪我堂兄弟 一起讀書的時候,就觀察到 他們之中很多人對數學很頭疼, 原因是他們在學習過程中, 不斷積累還沒掌握的知識漏洞。 因此,當他們開始上代數課時, 在初級代數的課程中 可能就跟不太上, 因此,他們會認為自己 沒有學習數學的天賦。 或者他們之後上微積分課時, 才發現自己在代數的 基礎也不太好。 我知道這件事是在前些年的時候, 當我在 YouTube上, 上傳這些視頻的時候, 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. I thought that was a pretty big deal. I don't know how much time you all spend on YouTube. Most of the comments are not "Thank you."
一開始,有些留言 只是些簡單的謝謝。 我認為這樣真的很棒。 我不知道你們都花 多少時間在 YouTube 上。 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. But then the comments got a little more intense, student after student saying that they had grown up not liking math. It was getting difficult as they got into more advanced math topics. By the time they got to algebra, they had so many gaps in their knowledge they couldn't engage with it. They thought they didn't have the math gene. But when they were a bit older, they took a little agency and decided to engage. They found resources like Khan Academy and they were able to fill in those gaps and master those concepts, and that reinforced their mindset that it wasn't fixed; that they actually were capable of learning mathematics.
他們越來越激動了。 但之後的留言變得越來越有深度, 越來越多的學生反應, 他們長大後不喜歡數學。 進入高等數學後就更加痛苦了。 當他們開始上代數的時候, 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。 他們會自以為沒有數學頭腦。 但當他們長大後, 他們有了一點動力 並決定要好好念書了, 他們找到了像可漢學院這樣的資源, 能夠幫他們填補過去的 學習漏洞並掌握概念, 從此改變了他們的思維方式, 糾正了他們的定式思維; 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. It's the way you would learn a martial art. In a martial art, you would practice the white belt skills as long as necessary, and only when you've mastered it you would move on to become a yellow belt. It's the way you learn a musical instrument: you practice the basic piece over and over again, and only when you've mastered it, you go on to the more advanced one.
在很多方面,這也是 你要如何掌握你人生事物的方法。 這就像你學習武術一樣。 在武術當中,如果有必要, 你必須一直練習白帶的技巧。 只有當你們掌握了它, 你才能進階到黃帶。 這也是你們學習樂器的方式: 一遍遍練習最基礎的曲目, 只有當你們掌握了它, 你才會去挑戰更難的曲目。
But what we point out -- this is not the way a traditional academic model is structured, the type of academic model that most of us grew up in. In a traditional academic model, we group students together, usually by age, and around middle school, by age and perceived ability, and we shepherd them all together at the same pace. And what typically happens, let's say we're in a middle school pre-algebra class, and the current unit is on exponents, the teacher will give a lecture on exponents, then we'll go home, do some homework. The next morning, we'll review the homework, then another lecture, homework, lecture, homework. That will continue for about two or three weeks, and then we get a test. On that test, maybe I get a 75 percent, maybe you get a 90 percent, maybe you get a 95 percent. And even though the test identified gaps in our knowledge, I didn't know 25 percent of the material. Even the A student, what was the five percent they didn't know?
但我要說的是: 這並非傳統學習模式的架構, 也不是我們成長過程中 所使用的學習方式。 在傳統學習模式當中, 我們會將學生分組, 一般是以年齡來分, 在中學時期, 則以年齡和外顯的學習能力分組, 然後我們以齊頭式的教育引領他們。 常常發生的是, 假設我們身處某中學的 初級代數課堂中, 現在上的課程是指數, 老師就此內容來上課, 之後,我們回家, 做了一些相關的習題。 第二天早上, 我們會批改這些作業。 之後又是上課、做作業、 上課、做作業。 這大概會持續兩到三周, 然後考試。 在考試中,我也許只會 75 %, 你也許會 90%, 或是 95%。 即使考試能幫助 判斷我們知識的漏洞, 我還是存在 25% 不知道的內容。 即使得 A 的學生, 仍有 5% 不懂的內容。
Even though we've identified the gaps, the whole class will then move on to the next subject, probably a more advanced subject that's going to build on those gaps. It might be logarithms or negative exponents. And that process continues, and you immediately start to realize how strange this is. I didn't know 25 percent of the more foundational thing, and now I'm being pushed to the more advanced thing. And this will continue for months, years, all the way until at some point, I might be in an algebra class or trigonometry class and I hit a wall. And it's not because algebra is fundamentally difficult or because the student isn't bright. It's because I'm seeing an equation and they're dealing with exponents and that 30 percent that I didn't know is showing up. And then I start to disengage.
即使我們找到了那些漏洞, 課堂還是會繼續,進入下一個主題, 可能是更加複雜的內容, 但卻建立在我們知識漏洞之上。 可能會是對數函數, 或者是負指數函數。 老師一直講課, 然後你會突然間發現, 這一切怎麽那麽的陌生。 我明明還有 25% 的基礎知識不懂, 現在卻被迫繼續學更加深奧的東西。 這會持續數月或數年,直到某一刻, 我可能會在代數或是三角函數課堂上 遇到麻煩。 這並非因為代數本身很困難, 或者是學生不夠聰明。 那是因為當我看見指數的公式時, 其中有 30% 是我不懂的知識。 然後我就不想做了。
To appreciate how absurd that is, imagine if we did other things in our life that way. Say, home-building.
為了感受那是多麽的荒謬, 各位想像一下,如果我們以同樣方式 來處理人生中其它事情的時候, 比如說,蓋房子。
(Laughter)
(笑聲)
So we bring in the contractor and say, "We were told we have two weeks to build a foundation. Do what you can."
我們找承包商來,然後和他說: 「我們被告知只有兩周時間去打地基。 所以你能蓋多少就蓋多少吧!」
(Laughter)
(笑聲)
So they do what they can. Maybe it rains. Maybe some of the supplies don't show up. And two weeks later, the inspector comes, looks around, says, "OK, the concrete is still wet right over there, that part's not quite up to code ... I'll give it an 80 percent."
所以他們就盡力去做了。 施工過程中也許會下雨。 也許有些物資沒到場的情況。 然後兩周之後, 房屋檢查員來了,他看了一下, 說:「好吧,這邊的水泥還沒乾, 那邊的也不大符合標準…… 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. We have two weeks, do what you can, inspector shows up, it's a 75 percent. Great, that's a D-plus. Second floor, third floor, and all of a sudden, while you're building the third floor, the whole structure collapses. And if your reaction is the reaction you typically have in education, or that a lot of folks have, you might say, maybe we had a bad contractor, or maybe we needed better inspection or more frequent inspection. But what was really broken was the process. We were artificially constraining how long we had to something, pretty much ensuring a variable outcome, and we took the trouble of inspecting and identifying those gaps, but then we built right on top of it.
同樣的事情一再發生。 我們又努力了兩周, 然後檢查員來了,給了個 75 分。 太好了,居然還有 D+! 繼續建二樓,三樓, 直到建三樓的時候, 整棟建築突然就倒塌了。 如果你的回應與 受教育時的回應一樣, 或者是很多人會有的那種反應, 你也許會說,我們只是倒楣 遇到了爛承包商, 或是我們檢查的力度和次數不夠多。 但真正的問題,其實是過程的本身。 我們用人為的方式 去限制完成某事的時間, 幾乎可以確定,結果一定會有落差, 然後我們檢查也發現了問題, 但卻又立刻填鴨上去。
So the idea of mastery learning is to do the exact opposite. Instead of artificially constraining, fixing when and how long you work on something, pretty much ensuring that variable outcome, the A, B, C, D, F -- do it the other way around. What's variable is when and how long a student actually has to work on something, and what's fixed is that they actually master the material.
掌握式教育的觀念 就是去做完全相反的事。 將人為的限制、僵化、 何時學習和學多久、 確認 A、B、C、D、F 成績 這些結果的行為, 轉換成另一種方式。 學生之間不同的 只有「何時」以及「多久」 可以掌握好一門知識, 這個方法修正的是 學生真的掌握了該門知識。
And it's important to realize that not only will this make the student learn their exponents better, but it'll reinforce the right mindset muscles. It makes them realize that if you got 20 percent wrong on something, it doesn't mean that you have a C branded in your DNA somehow. It means that you should just keep working on it. You should have grit; you should have perseverance; you should take agency over your learning.
我們必須了解到它的重要性, 這樣不僅可以讓學生 更好地掌握指數函數, 同時也可以培養一種 正確的思維方式。 這可以讓他們體認到 如果他們答錯了 20%, 不代表他們骨子裡就是個 C 咖, 而是說明你還需要 在這個內容上繼續努力、 你得堅持不懈、 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, philosophically, this whole idea of mastery-based learning and its connection to mindset, students taking agency over their learning. It makes a lot of sense, but it seems impractical. To actually do it, every student would be on their own track. It would have to be personalized, you'd have to have private tutors and worksheets for every student. And these aren't new ideas -- there were experiments in Winnetka, Illinois, 100 years ago, where they did mastery-based learning and saw great results, but they said it wouldn't scale because it was logistically difficult. The teacher had to give different worksheets to every student, give on-demand assessments.
現在很多懷疑的人會說, 這些聽起來都很棒, 理論上來說, 這套以掌握為目的教學方式 與心智的連結, 可以讓學生拿出熱情 來克服學習障礙。 聽起來很有道理,但不太實際。 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, 必須有客製化的教學方式。 每個學生都要有私人教師 和私人定制的練習題。 但這並不是什麼新觀念—— 在 100 年前的伊利諾伊州, 溫內特卡市就有這樣的實驗: 他們以掌握式的教學 取得了不錯的結果, 但是他們表示很難普及化, 畢竟這在後勤上很難配合。 老師要給每個學生不同的試題, 根據需求做出不同的評估方式。
But now today, it's no longer impractical. We have the tools to do it. Students see an explanation at their own time and pace? There's on-demand video for that. They need practice? They need feedback? There's adaptive exercises readily available for students.
但如今,這已經不再是 不實際的問題了。 我們有了工具的幫助。 學生可以按照自己的時間 和步調看錄影的講解, 有很多適當的影片 可以符合學生的要求。 他們需要練習嗎?需要反饋嗎? 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. One, the students can actually master the concepts, but they're also building their growth mindset, they're building grit, perseverance, they're taking agency over their learning. And all sorts of beautiful things can start to happen in the actual classroom. Instead of it being focused on the lecture, students can interact with each other. They can get deeper mastery over the material. They can go into simulations, Socratic dialogue.
當這些條件都能成立的時候, 各種好事就會接踵而至。 首先,學生能夠真正掌握概念, 其次,他們能培養積極的態度, 建立勇氣和不屈不撓的精神, 他們會拿出熱情來學習。 這些美好的事情, 已經可以進入實際的課堂當中了。 取代老師講解課堂內容的是 學生們可以互動學習。 他們能夠更加深入地去掌握知識。 他們可以用模擬法, 可以用蘇格拉底問答法。
To appreciate what we're talking about and the tragedy of lost potential here, I'd like to give a little bit of a thought experiment. If we were to go 400 years into the past to Western Europe, which even then, was one of the more literate parts of the planet, you would see that about 15 percent of the population knew how to read. And I suspect that if you asked someone who did know how to read, say a member of the clergy, "What percentage of the population do you think is even capable of reading?" They might say, "Well, with a great education system, maybe 20 or 30 percent." But if you fast forward to today, we know that that prediction would have been wildly pessimistic, that pretty close to 100 percent of the population is capable of reading. But if I were to ask you a similar question: "What percentage of the population do you think is capable of truly mastering calculus, or understanding organic chemistry, or being able to contribute to cancer research?" A lot of you might say, "Well, with a great education system, maybe 20, 30 percent."
要讓大家了解 我們在這裡所說的事情, 體會我們有可能失去什麼, 我想給各位一個小型的思維實驗。 如果我們回到 400 年前的西歐, 當時那邊是地球上 識字人口眾多的地方, 你會發現人群中 大概有 15% 的人識字, 然後我猜,當你去詢問 一個識字的人, 比如一個神職人員, 「你認為大概有多少人 有識字的能力呢?」 他們也許會說:「嗯, 如果有個強大的教育體系, 大概有個 20% 或 30% 吧。」 但如果你快進到當下, 我們都知道那樣的預測 實在太悲觀了, 現在幾乎是人人都識字。 但如果我問各位一個類似的問題: 「你們認為目前人口中有多少 是真正掌握微積分的, 或是真正懂有機化學的, 或是有能力能夠 為癌症研究作出貢獻的?」 你們中的很多就會回答: 「就目前的強大教育體系下 大概有個 20% 或 30% 吧。」
But what if that estimate is just based on your own experience in a non-mastery framework, your own experience with yourself or observing your peers, where you're being pushed at this set pace through classes, accumulating all these gaps? Even when you got that 95 percent, what was that five percent you missed? And it keeps accumulating -- you get to an advanced class, all of a sudden you hit a wall and say, "I'm not meant to be a cancer researcher; not meant to be a physicist; not meant to be a mathematician." I suspect that that actually is the case, but if you were allowed to be operating in a mastery framework, if you were allowed to really take agency over your learning, and when you get something wrong, embrace it -- view that failure as a moment of learning -- that number, the percent that could really master calculus or understand organic chemistry, is actually a lot closer to 100 percent.
但假如那些判斷 僅僅是基於你們尚未 掌握觀念的個人經驗, 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? 當時你就是被迫推進課堂進度, 不斷積累漏洞情況的人啊? 即使你掌握了 95% 的知識, 那剩下的 5% 呢? 漏洞持續積累,直到進入進階課程, 突然碰壁,然後你就會說: 「我天生就不是個癌症研究人員、 不是物理學家、不是數學家。」 我認為這就是現實情況。 但如果你能從 掌握知識的視角去審視, 如果你能從培養 學習動力的角度來看, 當你做錯題目的時候, 把這種失敗當作 學習的一部分並坦然接受, 那真正掌握微積分的人數比例, 或是真正掌握有機化學的人數比例 就會接近 100% 了。
And this isn't even just a "nice to have." I think it's a social imperative. We're exiting what you could call the industrial age and we're going into this information revolution. And it's clear that some things are happening. In the industrial age, society was a pyramid. At the base of the pyramid, you needed human labor. In the middle of the pyramid, you had an information processing, a bureaucracy class, and at the top of the pyramid, you had your owners of capital and your entrepreneurs and your creative class. But we know what's happening already, as we go into this information revolution. The bottom of that pyramid, automation, is going to take over. Even that middle tier, information processing, that's what computers are good at.
而這並不僅僅只是 「有人就好」的意義而已, 我認為社會急需要這些人才。 我們正在離開所謂的工業時代, 而我們正在進入資訊革命的時代。 很明確的是,一些變化正在發生。 在工業時代,社會是一個金字塔。 在金字塔底端,我們需要的是人力。 在金字塔中間,資訊需要處理 所以有官僚特權階層, 而金字塔頂端,就會是那些資本家、 那些企業家、 還有那些創業家。 但當我們進入到資訊革命的年代, 我們知道發生什麼事了。 在金字塔底端,自動化將取代人力。 甚至中間層資訊處理的這一段 電腦做的都比他們好。
So as a society, we have a question: All this new productivity is happening because of this technology, but who participates in it? Is it just going to be that very top of the pyramid, in which case, what does everyone else do? How do they operate? Or do we do something that's more aspirational? Do we actually attempt to invert the pyramid, where you have a large creative class, where almost everyone can participate as an entrepreneur, an artist, as a researcher?
所以對一個社會而言, 我們有一個問題: 科技帶來了新的生產力, 是誰會參與其中呢? 是不是只有處於金字塔頂端的人? 這種情況下,其他人還能做些甚麼? 他們會如何操作? 或者我們是否要從事 更加遠大的事業呢? 我們是否真的願意 嘗試去翻轉金字塔? 讓我們有一大群創意人才、 讓每個人都是企業家、 藝術家,或是研究人員?
And I don't think that this is utopian. I really think that this is all based on the idea that if we let people tap into their potential by mastering concepts, by being able to exercise agency over their learning, that they can get there. And when you think of it as just a citizen of the world, it's pretty exciting. I mean, think about the type of equity we can we have, and the rate at which civilization could even progress. And so, I'm pretty optimistic about it. I think it's going to be a pretty exciting time to be alive.
我並不認為這是空想。 我認為這一切都建立在一個理念, 就是讓學生的潛力獲得十足的發揮, 藉由掌握概念 及激發學生的學習熱忱, 這樣,他們就能夠達到理想境界。 當你去想像,你就是 那樣理想世界中的一員, 那真的是令人興奮的一件事。 我的意思是,想像一下 我們能做到、能擁有的那種平等, 以及文明進步所能達到的那種境界。 因此,我很有信心。 我認為,當我們達到的那一刻, 將令人無比激動。
Thank you.
謝謝!
(Applause)
(掌聲)