I'm here today to talk about the two ideas that, at least based on my observations at Khan Academy,
今天，我要分享两个观点，至少基于我对可汗学院的观察得出的，
are kind of the core, or the key leverage points for learning.
有关于学习的核心，或者说是根基。
And it's the idea of mastery and the idea of mindset.
一个是掌握的技巧，另一个是思维方式。
I saw this in the early days working with my cousins.
早些年当我辅导小表亲们的时候就发现，
A lot of them were having trouble with math at first, because they had all of these gaps accumulated in their learning.
他们之中很多人刚开始对数学很头疼，因为他们在学习中不断积累着知识漏洞。
And because of that, at some point they got to an algebra class
所以当他们开始上代数课时，
and they might have been a little bit shaky on some of the pre-algebra,
由于在代数的预备课程中可能就不太跟得上，
and because of that, they thought they didn't have the math gene.
就导致了他们认为自己没有数学天赋。
Or they'd get to a calculus class, and they'd be a little bit shaky on the algebra.
或者他们之后上微积分课时，才发现自己的代数基础也不太好。
I saw it in the early days when I was uploading some of those videos on YouTube,
我发现这个问题是在前些年，当我在YouTube上上传这些视频的时候，
and I realized that people who were not my cousins were watching.
我意识到很多素不相识的人也在看这些视频。
And at first, those comments were just simple thank-yous. I thought that was a pretty big deal.
一开始，有些留言只是些简单的谢谢。 我认为这很值得重视。
I don't know how much time you all spend on YouTube. Most of the comments are not "Thank you."
我不知道你们都花多少时间在YouTube上。通常大多数评论都不是“谢谢”。
They're a little edgier than that.
通常措辞都更尖锐一些。
But then the comments got a little more intense, student after student saying that they had grown up not liking math.
但之后的留言内容越来越丰富多样，越来越多的学生反映，他们长大后变得更加不喜欢数学。
It was getting difficult as they got into more advanced math topics.
进入高等数学阶段后就更加困难。
By the time they got to algebra, they had so many gaps in their knowledge they couldn't engage with it.
当他们开始上代数的时候，知识中存在的大量漏洞导致他们完全更不上进度。
They thought they didn't have the math gene.
他们会自以为没有数学头脑。
But when they were a bit older, they took a little agency and decided to engage.
但当他们长大一点的时候，他们有了一点儿动力并决定下功夫去学。
They found resources like Khan Academy and they were able to fill in those gaps and master those concepts,
他们找到了像可汗学院这样的资源，帮助他们填充知识漏洞和掌握概念，
and that reinforced their mindset that it wasn't fixed; that they actually were capable of learning mathematics.
改善了他们的思维方式；他们才知道自己其实有能力学好数学。
And in a lot of ways, this is how you would master a lot of things in life.
在很多方面，这也是掌握新技能的一种途径。
It's the way you would learn a martial art.
好比学习武术。
In a martial art, you would practice the white belt skills as long as necessary,
在武术当中，你往往必须一直练习白带的技巧，
and only when you've mastered it you would move on to become a yellow belt.
只有当你掌握了它们，你才能进阶到黄带。
It's the way you learn a musical instrument: you practice the basic piece over and over again,
这也是你们学习乐器的方式：一遍遍练习最基本的曲目，
and only when you've mastered it, you go on to the more advanced one.
只有掌握了它们，才能去挑战更难的那些。
But what we point out -- this is not the way a traditional academic model is structured,
但我们要清楚：这并非传统学习模式的构成方法，
the type of academic model that most of us grew up in.
并不是我们成长过程中所经历的那种。
In a traditional academic model, we group students together, usually by age, and around middle school,
在一个传统学习模式当中，我们一般会按年龄将学生分组，在中学时期，
by age and perceived ability, and we shepherd them all together at the same pace.
则是通过年龄和外显的学习能力分组，然后我们以相同的节奏引领他们。
And what typically happens, let's say we're in a middle school pre-algebra class,
最常见的情况是，假设我们身处某中学的代数预备课堂，
and the current unit is on exponents, the teacher will give a lecture on exponents, then we'll go home, do some homework.
现在的专题是指数函数，老师就此内容来上课，然后我们回家做一些相关习题。
The next morning, we'll review the homework, then another lecture, homework, lecture, homework.
第二天早上，我们会检查这些作业。之后又是上课，做作业，上课，做作业。
That will continue for about two or three weeks, and then we get a test.
这大概会持续两到三周，就该测验了。
On that test, maybe I get a 75 percent, maybe you get a 90 percent, maybe you get a 95 percent.
在考试中，我也许只会75%的题目，你也许会90%，他可能会95%。
And even though the test identified gaps in our knowledge, I didn't know 25 percent of the material.
即使考试能帮助我们查缺补漏，还是会有25%的内容我没有掌握。
Even the A student, what was the five percent they didn't know?
就算那些得A的学生，依旧有5%的内容没搞懂。
Even though we've identified the gaps, the whole class will then move on to the next subject,
即使我们认识到那些漏洞，课堂还是会继续进入下一个专题，
probably a more advanced subject that's going to build on those gaps.
可能是更加复杂的内容，但却会建立在我们的知识漏洞之上。
It might be logarithms or negative exponents.
可能会是对数函数或者是负指数函数。
And that process continues, and you immediately start to realize how strange this is.
随着课程不断推进，你会突然间发现这种感觉不太对劲。
I didn't know 25 percent of the more foundational thing, and now I'm being pushed to the more advanced thing.
我明明还有25%的基础知识不懂，现在却被逼去学更加深奥的东西。
And this will continue for months, years, all the way until at some point,
这会持续数月或数年，直到某一个时间点，
I might be in an algebra class or trigonometry class and I hit a wall.
我可能会在代数或是三角函数课堂上完全不知所云了。
And it's not because algebra is fundamentally difficult or because the student isn't bright.
这并非因为代数学本身很难学，或者是因为学生不够聪明。
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.
而是因为当我看见指数的等式时，其中有30%是我不懂的知识。
And then I start to disengage.
然后我就不想做了。
To appreciate how absurd that is, imagine if we did other things in our life that way. Say, home-building.
为了让大家体会这是多么夸张，可以想象一下，当我们在人生中以这种方式干其它的事情时，比如，造房子。
So we bring in the contractor and say, "We were told we have two weeks to build a foundation. Do what you can."
我们找承包商来，然后和他说：“我们被告知只有两周时间去打地基。所以能建多少就建多少吧。”
So they do what they can. Maybe it rains. Maybe some of the supplies don't show up.
然后他们就尽力去做了。中间也许下雨了。也许有些物资没到位。
And two weeks later, the inspector comes, looks around, says,
两周之后，房屋检查员来了，看了一下说：
"OK, the concrete is still wet right over there, that part's not quite up to code ... I'll give it an 80 percent."
“看起来这儿的水泥还没干，那块儿也还不大行……我就给个80分吧。”
You say, "Great! That's a C. Let's build the first floor."
然后你们说：“太好了，至少还是个C。我们开始建第一层吧！”
Same thing. We have two weeks, do what you can, inspector shows up, it's a 75 percent.
同样的事情接连发生。我们又努力了两周，然后房屋检查员来了，给了个75分。
Great, that's a D-plus. Second floor, third floor, and all of a sudden,
太好了，居然还有D+！继续建二楼，三楼，
while you're building the third floor, the whole structure collapses.
直到建第三层的时候，整栋建筑突然倒塌了。
And if your reaction is the reaction you typically have in education, or that a lot of folks have,
如果你的回应与上学时的回应一样，或者是很多人会有的那种反应，
you might say, maybe we had a bad contractor, or maybe we needed better inspection or more frequent inspection.
你也许会说，估计是承包商不够格，也可能是检查力度和次数不够多。
But what was really broken was the process.
但真正的问题其实是过程的本身。
We were artificially constraining how long we had to something, pretty much ensuring a variable outcome,
我们用人为的方式去限制完成某事的时间，几乎可以确定一定会有出入，
and we took the trouble of inspecting and identifying those gaps, but then we built right on top of it.
然后我们检查也发现了问题，但却又将错就错。
So the idea of mastery learning is to do the exact opposite.
然而掌握式教育的观念就是反其道而行之。
Instead of artificially constraining, fixing when and how long you work on something,
将人为的限制、僵化、何时学习和学多久、
pretty much ensuring that variable outcome, the A, B, C, D, F -- do it the other way around.
把结果按Ａ、B、C、D、F分级的行为，转换成另一种方式。
What's variable is when and how long a student actually has to work on something,
学生之间的差异应该是何时以及多久可以掌握好一门知识，
and what's fixed is that they actually master the material.
要坚持一致的是学生真的掌握了这门知识。
And it's important to realize that not only will this make the student learn their exponents better,
我们必须意识到它的重要性，这样不仅可以让学生更好地掌握指数函数，
but it'll reinforce the right mindset muscles.
同时也可以培养一种正确的思维方式。
It makes them realize that if you got 20 percent wrong on something,
这可以让他们认识到，如果你答错了20%，
it doesn't mean that you have a C branded in your DNA somehow.
不代表你天生就只有C的水平，
It means that you should just keep working on it.
而是说明你还需要在这个内容上继续努力。

You should have grit; you should have perseverance; you should take agency over your learning.
你要坚持不懈、迎难而上，拿出热情克服学习中的障碍。
Now, a lot of skeptics might say, well, hey, this is all great, philosophically,
现在，很多怀疑者可能会说，这听起来不错，理论上来说，
this whole idea of mastery-based learning and its connection to mindset, students taking agency over their learning.
这套以掌握为目的教学方式以及与思维方式的连结，可以让学生积极克服学习中的障碍。
It makes a lot of sense, but it seems impractical. To actually do it, every student would be on their own track.
这听起来很有道理，但不太实际。要实现一点，每个学生都必须遵循自己的学习进度。
It would have to be personalized, you'd have to have private tutors and worksheets for every student.
必须有个性化的教学方式，一对一辅导和有针对性的练习题。
And these aren't new ideas -- there were experiments in Winnetka, Illinois, 100 years ago,
但这并不是什么新观念，在100年前的伊利诺伊州温内特卡市就有这样的实践：
where they did mastery-based learning and saw great results, but they said it wouldn't scale because it was logistically difficult.
他们尝试了这种以掌握为目的的教学，成果很显著，但是他们表示很难大面积推广，毕竟可行性太低了。
The teacher had to give different worksheets to every student, give on-demand assessments.
老师要给每个学生不同的试题，视情况打分。
But now today, it's no longer impractical.
但如今，这已经不再是空想了。
We have the tools to do it. Students see an explanation at their own time and pace? There's on-demand video for that.
我们有了辅助工具。学生可以通过看分类视频，按照自己的进度去寻找解答。
They need practice? They need feedback?
他们需要练习吗？需要反馈吗？
There's adaptive exercises readily available for students.
学生很容易就能进行适应性练习。
And when that happens, all sorts of neat things happen.
当万事俱备的时候，就会出现良性循环。
One, the students can actually master the concepts, but they're also building their growth mindset,
首先，学生能够真正掌握知识，此外还能培养他们积极的心理，
they're building grit, perseverance, they're taking agency over their learning.
建立勇气和不屈不挠的精神，他们会对学习产生热情。
And all sorts of beautiful things can start to happen in the actual classroom.
在实际的课堂中，一切也慢慢开始走上正轨。
Instead of it being focused on the lecture, students can interact with each other.
学生们之间可以进行更多学习上的互动，而不必拘泥于专心听讲。
They can get deeper mastery over the material. They can go into simulations, Socratic dialogue.
他们能够更加深入地去掌握知识。他们能够模拟苏格拉底式对话。
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.
为了强化这一点，让大家体会无法激发潜能的遗憾，我想带大家进行一个思维小实验。
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,
假设我们回到400年前的西欧，在当时就已经是地球上文明最发达的地区之一，
you would see that about 15 percent of the population knew how to read.
你会发现大概有15％的人口识字。
And I suspect that if you asked someone who did know how to read, say a member of the clergy,
估计当你去询问一个识字的人，比如一个神职人员，
"What percentage of the population do you think is even capable of reading?"
“你认为大概有多少人有识字的能力呢？”
They might say, "Well, with a great education system, maybe 20 or 30 percent."
他们也许会说：“嗯，基于这强大的教育体系，大概有个20%或30%吧。”
But if you fast forward to today, we know that that prediction would have been wildly pessimistic,
但如果你快进到当下，我们会发现那样的预测实在太悲观了，
that pretty close to 100 percent of the population is capable of reading.
现在几乎是人人都识字。
But if I were to ask you a similar question:
但是当我问你们一个类似的问题：
"What percentage of the population do you think is capable of truly mastering calculus, or understanding organic chemistry,
“你们认为总人口中有多少是真正掌握微积分的，或是真正懂有机化学的，
or being able to contribute to cancer research?"
或是有能力为癌症研究作出贡献的呢？”
A lot of you might say, "Well, with a great education system, maybe 20, 30 percent."
你们中的很多就会回答：“嗯，基于这强大的教育体系，大概有个20%或30%吧。”
But what if that estimate is just based on your own experience in a non-mastery framework,
但假如那些判断仅仅是基于你们“非掌握体系”的个人经验，
your own experience with yourself or observing your peers,
是基于你们的自身经历或仅是对周围人的观察而已呢？
where you're being pushed at this set pace through classes, accumulating all these gaps?
或是基于被迫跟从课堂进度，不断积累漏洞情况的呢？
Even when you got that 95 percent, what was that five percent you missed?
即使你掌握了95%的知识，那剩下的5%呢？
And it keeps accumulating -- you get to an advanced class, all of a sudden you hit a wall and say,
漏洞持续积累，直到进入高等课堂突然碰壁，然后你们说：
"I'm not meant to be a cancer researcher; not meant to be a physicist; not meant to be a mathematician."
“我生来就不是个癌症研究人员，我不是做物理学家的料，我当不了数学家。”
I suspect that that actually is the case, but if you were allowed to be operating in a mastery framework,
我认为这就是现实情况。但当我们能够从掌握知识的视角去审视，
if you were allowed to really take agency over your learning,
如果我们能够从培养学习动力的角度来看，
and when you get something wrong, embrace it -- view that failure as a moment of learning
当我们做错题目的时候，我们把这种失败当作学习的一部分坦然接受，
that number, the percent that could really master calculus or understand organic chemistry, is actually a lot closer to 100 percent.
那真正掌握微积分或者有机化学的人数比例就会接近100%了。
And this isn't even just a "nice to have." I think it's a social imperative.
而其意义并不仅仅在于锦上添花。我认为这是社会进化的必然过程。
We're exiting what you could call the industrial age and we're going into this information revolution.
用你们的话来说，我们正处于一个工业时代，而我们正在进入信息革命的时代。
And it's clear that some things are happening.
很明确的是，一些变化正在发生。
In the industrial age, society was a pyramid. At the base of the pyramid, you needed human labor.
在工业时代，社会是一个金字塔。在金字塔底端，我们需要的是人力。
In the middle of the pyramid, you had an information processing, a bureaucracy class,
在金字塔中间，我们需要处理信息，所以有官僚特权阶层，
and at the top of the pyramid, you had your owners of capital and your entrepreneurs and your creative class.
等到了顶端，就会是那些资本家，企业家还有创新人群。
But we know what's happening already, as we go into this information revolution.
但当我们进入信息革命的那一刻，我们就知道将要发生什么事了。
The bottom of that pyramid, automation, is going to take over.
在金字塔底端，自动化将取代人力。
Even that middle tier, information processing, that's what computers are good at.
甚至中间层信息处理的这一段，计算机做的都比他们好。
So as a society, we have a question:
所以对一个社会而言，我们有一个问题：
All this new productivity is happening because of this technology, but who participates in it?
科技带来的这些新生产力，是谁参与其中呢？
Is it just going to be that very top of the pyramid, in which case, what does everyone else do?
是不是只有处于金字塔顶端的人，而其他人都置身事外？
How do they operate? Or do we do something that's more aspirational?
他们会如何操作？或者我们是否要从事更加远大的事业呢？
Do we actually attempt to invert the pyramid, where you have a large creative class,
我们是否真的愿意尝试去倒转金字塔，让创新人群起主导作用呢，
where almost everyone can participate as an entrepreneur, an artist, as a researcher?
让每个人都可以成为企业家、艺术家或是研究人员呢？
And I don't think that this is utopian.
我并不认为这仅仅是空想。
I really think that this is all based on the idea that if we let people tap into their potential by mastering concepts,
我认为这一切都建立在一个理念之上，就是如果我们能够借由掌握概念，
by being able to exercise agency over their learning, that they can get there.
挖掘学生的学习热情，激发他们的学习潜力，他们就能够达成目标。
And when you think of it as just a citizen of the world, it's pretty exciting.
当你想到自己置身于这种理想环境，其实是很让人激动的一件事。
I mean, think about the type of equity we can we have, and the rate at which civilization could even progress.
想象一下我们所能拥有的那种平等，想象文明所能达到的那种境界。
And so, I'm pretty optimistic about it.
对此，我充满信心。
I think it's going to be a pretty exciting time to be alive. Thank you.
我认为这个时刻将令人无比激动人心。谢谢！