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,
由于在代数的预备課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. But then the comments got a little more intense,
通常措辞都更尖锐一些。但之后的留言内容越来越丰富多样，
student after student saying that they had grown up not liking math.
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。
