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I'm here today to talk about the two ideas that, at least based on my observations at Khan Academy,
今天，我要分享兩個觀點，至少基于我對可汗學院的觀察得出的，
are kind of the core, or the key leverage points for learning.
有關于學習的核心，或者說是根基。
And it's the idea of mastery and the idea of mindset.
一個是掌握的技巧，另一個是思維方式。
I saw this in the early days working with my cousins.
早些年當我輔導小表親們的時候就發現，
A lot of them were having trouble with math at first, because they had all of these gaps accumulated in their learning.
他們之中很多人剛開始對數學很頭疼，因為他們在學習中不斷積累著知識漏洞。
And because of that, at some point they got to an algebra class
所以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,
由于在代數的預備課程中可能就不太跟得上，
and because of that, they thought they didn't have the math gene.
就導致了他們認為自己沒有數學天賦。
Or they'd get to a calculus class, and they'd be a little bit shaky on the algebra.
或者他們之后上微積分課時，才發現自己的代數基礎也不太好。
I saw it in the early days when I was uploading some of those videos on YouTube,
我發現這個問題是在前些年當我在YouTube上上傳這些視頻的時候，
and I realized that people who were not my cousins were watching.
我意識到很多素不相識的人也在看這些視頻。
And at first, those comments were just simple thank-yous. I thought that was a pretty big deal.
一開始，有些留言只是些簡單的謝謝。我認為這很值得重視。
I don't know how much time you all spend on YouTube. Most of the comments are not "Thank you."
我不知道你們都花多少時間在YouTube上。通常大多數評論都不是“謝謝”。
They're a little edgier than that. But then the comments got a little more intense,
通常措辭都更尖銳一些。但之后的留言內容越來越豐富多樣，
student after student saying that they had grown up not liking math.
越來越多的學生反映，他們長大后，變得更加不喜歡數學。
It was getting difficult as they got into more advanced math topics.
進入高等數學階段后就更加困難。
By the time they got to algebra, they had so many gaps in their knowledge they couldn't engage with it.
當他們開始上代數的時候，知識中存在的大量漏洞導致他們完全更不上進度。
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, they took a little agency and decided to engage.
但當他們長大一點的時候，他們有了一點兒動力并決定下功夫去學。
They found resources like Khan Academy and they were able to fill in those gaps and master those concepts,
他們找到了像可汗學院這樣的資源，幫助他們填充知識漏洞和掌握概念，
and that reinforced their mindset that it wasn't fixed; that they actually were capable of learning mathematics.
改善了他們的思維方式；他們才知道自己其實有能力學好數學。
