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字幕列表 影片播放

  • The Khan Academy is most known

    Khan 學院因 The Khan Academy is most known

  • for its collection of videos,

    它豐富的影片資源而出名 for its collection of videos,

  • so before I go any further,

    在我開始演講前 so before I go any further,

  • let me show you a little bit of a montage.

    先讓我們看一段剪輯影片 let me show you a little bit of a montage.

  • (Video) Salman Khan: So the hypotenuse is now going to be five.

    於是這個直角三角形的斜邊就成了5 (Video) Salman Khan: So the hypotenuse is now going to be five.

  • This animal's fossils are only found in this area of South America --

    這種動物的化石只能在南美這個地區找到 This animal's fossils are only found in this area of South America --

  • a nice clean band here --

    一條很清楚的界限 a nice clean band here --

  • and this part of Africa.

    還有非洲的這個區域 and this part of Africa.

  • We can integrate over the surface,

    我們可以合併表面 We can integrate over the surface,

  • and the notation usually is a capital sigma.

    通常用 Σ 來標記 and the notation usually is a capital sigma.

  • National Assembly: They create the Committee of Public Safety,

    國民大會:他們創造了公共安全委員會 National Assembly: They create the Committee of Public Safety,

  • which sounds like a very nice committee.

    聽上去像是個不錯的委員會 which sounds like a very nice committee.

  • Notice, this is an aldehyde,

    注意,這是乙醛 Notice, this is an aldehyde,

  • and it's an alcohol.

    是一種酒精 and it's an alcohol.

  • Start differentiating into effector and memory cells.

    開始分化為效應與記憶細胞 Start differentiating into effector and memory cells.

  • A galaxy. Hey, there's another galaxy.

    一個銀河。哇,那裡又有一個銀河 A galaxy. Hey, there's another galaxy.

  • Oh look, there's another galaxy.

    看啊,那裡還有另外一個 Oh look, there's another galaxy.

  • And for dollars, is their 30 million,

    對美元來說,是三千萬 And for dollars, is their 30 million,

  • plus the 20 million dollars from the American manufacturer.

    加上從美國製造商來的兩千萬 plus the 20 million dollars from the American manufacturer.

  • If this does not blow your mind,

    如果這還不夠讓你瞠目結舌 If this does not blow your mind,

  • then you have no emotion.

    你就是麻木不仁 then you have no emotion.

  • (Laughter)

    (笑聲) (Laughter)

  • (Applause)

    (掌聲) (Applause)

  • SK: We now have on the order

    我們現在有 SK: We now have on the order

  • of 2,200 videos

    兩千兩百個影片 of 2,200 videos

  • covering everything from basic arithmetic

    從基本的算術 covering everything from basic arithmetic

  • all the way to vector calculus

    一直到向量微積分 all the way to vector calculus

  • and some of the stuff you saw there.

    還有一些你剛剛看到的科目 and some of the stuff you saw there.

  • We have a million students a month using the site,

    一個月有百萬個學生使用我們的網站 We have a million students a month using the site,

  • watching on the order of 100 to 200,000 videos a day.

    一天有一百到二十萬個影片被觀看 watching on the order of 100 to 200,000 videos a day.

  • But what we're going to talk about in this

    但我們今天所要談論的 But what we're going to talk about in this

  • is how we're going to the next level.

    是如何提升這項服務 is how we're going to the next level.

  • But before I do that,

    在我這樣做以前 But before I do that,

  • I want to talk a little bit about really just how I got started.

    我想先談談我究竟是如何開始的 I want to talk a little bit about really just how I got started.

  • And some of you all might know,

    你們其中的一些人或許知道 And some of you all might know,

  • about five years ago I was an analyst at a hedge fund,

    五年前我是個避險基金分析師 about five years ago I was an analyst at a hedge fund,

  • and I was in Boston,

    我當時人在波士頓 and I was in Boston,

  • and I was tutoring my cousins in New Orleans, remotely.

    給我在紐澳良的表弟上課 and I was tutoring my cousins in New Orleans, remotely.

  • And I started putting the first YouTube videos up

    當我把第一支影片放上 YouTube And I started putting the first YouTube videos up

  • really just as a kind of nice-to-have,

    不過是把它當成一種不錯的 really just as a kind of nice-to-have,

  • just a supplement for my cousins --

    輔助教材 just a supplement for my cousins --

  • something that might give them a refresher or something.

    讓他們耳目一新之類的 something that might give them a refresher or something.

  • And as soon as I put those first YouTube videos up,

    當我把第一個 YouTube 影片放上去以後 And as soon as I put those first YouTube videos up,

  • something interesting happened --

    有趣的事發生了 something interesting happened --

  • actually a bunch of interesting things happened.

    事實上是許多有趣的事發生了 actually a bunch of interesting things happened.

  • The first was the feedback from my cousins.

    第一是我表弟的反應 The first was the feedback from my cousins.

  • They told me

    他們說 They told me

  • that they preferred me on YouTube than in person.

    他們喜歡 YouTube 上的我更勝真人 that they preferred me on YouTube than in person.

  • (Laughter)

    (笑聲) (Laughter)

  • And once you get over the backhanded nature of that,

    而且一旦你忘記話中那諷刺的部份 And once you get over the backhanded nature of that,

  • there was actually something very profound there.

    你便能聽見一件非常重要的訊息 there was actually something very profound there.

  • They were saying

    他們是說 They were saying

  • that they preferred the automated version of their cousin

    他們喜歡自動化版本的表哥 that they preferred the automated version of their cousin

  • to their cousin.

    勝於真正的表哥 to their cousin.

  • At first, it's very unintuitive,

    剛開始會覺得很反常 At first, it's very unintuitive,

  • but when you actually think about it from their point of view, it makes a ton of sense.

    但當你用他們的角度來想,事實上很合理 but when you actually think about it from their point of view, it makes a ton of sense.

  • You have this situation

    狀況是 You have this situation

  • where now they can pause and repeat their cousin,

    他們可以把表哥暫停或重複 where now they can pause and repeat their cousin,

  • without feeling like they're wasting my time.

    而不用感覺浪費了我的時間 without feeling like they're wasting my time.

  • If they have to review something

    如果他們要復習 If they have to review something

  • that they should have learned a couple of weeks ago,

    兩個禮拜前學的東西 that they should have learned a couple of weeks ago,

  • or maybe a couple of years ago,

    甚至是幾年前學的東西 or maybe a couple of years ago,

  • they don't have to be embarrassed and ask their cousin.

    他們不用不好意思地來問我 they don't have to be embarrassed and ask their cousin.

  • They can just watch those videos. If they're bored, they can go ahead.

    只要看這些影片就好。無聊了可以隨時關掉 They can just watch those videos. If they're bored, they can go ahead.

  • They can watch it at their own time, at their own pace.

    可以在自己想要的時間,用自己想要的速度看 They can watch it at their own time, at their own pace.

  • And probably the least appreciated aspect of this

    而最少人想到的是 And probably the least appreciated aspect of this

  • is the notion that the very first time,

    在你第一次 is the notion that the very first time,

  • the very first time

    第一次 the very first time

  • that you're trying to get your brain around a new concept,

    在你的大腦嘗試理解一個新概念時 that you're trying to get your brain around a new concept,

  • the very last thing you need

    你最不需要的事情就是 the very last thing you need

  • is another human being saying, "Do you understand this?"

    另外一個人在你旁邊說“到底懂了沒有?” is another human being saying, "Do you understand this?"

  • And that's what was happening with the interaction with my cousins before,

    但這就是我和我表弟互動時發生的 And that's what was happening with the interaction with my cousins before,

  • and now they can just do it

    現在他們可以 and now they can just do it

  • in the intimacy of their own room.

    在自己的房間看 in the intimacy of their own room.

  • The other thing that happened is --

    另外一件事就是 The other thing that happened is --

  • I put them on YouTube just --

    但我把影片放到 YouTube 上時 I put them on YouTube just --

  • I saw no reason to make it private,

    我覺得沒必要隱藏 I saw no reason to make it private,

  • so I let other people watch it,

    大家都可以看 so I let other people watch it,

  • and then people started stumbling on it,

    有人發現這些影片 and then people started stumbling on it,

  • and I started getting some comments and some letters

    我開始收到留言和一些信件 and I started getting some comments and some letters

  • and all sorts of feedback

    還有來自世界各地 and all sorts of feedback

  • from random people from around the world.

    很多不同的回應 from random people from around the world.

  • And these are just a few.

    這些是其中一些 And these are just a few.

  • This is actually from one of the original calculus videos.

    這個回應是給最早的那些微積分影片的 This is actually from one of the original calculus videos.

  • And someone wrote just on YouTube --

    有人在 Youtube And someone wrote just on YouTube --

  • it was a YouTube comment:

    上留言到 it was a YouTube comment:

  • "First time I smiled doing a derivative."

    “這是我第一次算導數會微笑” "First time I smiled doing a derivative."

  • (Laughter)

    (笑聲) (Laughter)

  • And let's pause here.

    等等 And let's pause here.

  • This person did a derivative

    這個人在算導數 This person did a derivative

  • and then they smiled.

    然後他微笑了 and then they smiled.

  • And then in a response to that same comment -- this is on the thread.

    然後有人回應了這個微笑的人 And then in a response to that same comment -- this is on the thread.

  • You can go on YouTube and look at these comments --

    你可以上 YouTube 去看這些回應 You can go on YouTube and look at these comments --

  • someone else wrote: "Same thing here.

    另外一個人說“我也是” someone else wrote: "Same thing here.

  • I actually got a natural high and a good mood for the entire day.

    那天我整個人飄飄欲仙 I actually got a natural high and a good mood for the entire day.

  • Since I remember seeing

    以前我 Since I remember seeing

  • all of this matrix text in class,

    在課堂上看見這些天書 all of this matrix text in class,

  • and here I'm all like, 'I know kung fu.'"

    現在我好像學得了絕世功夫 and here I'm all like, 'I know kung fu.'"

  • (Laughter)

    (笑聲) (Laughter)

  • And we get a lot of feedback all along those lines.

    我們得到了很多這種回應 And we get a lot of feedback all along those lines.

  • This clearly was helping people.

    很明顯地,這幫助了很多人 This clearly was helping people.

  • But then, as the viewership kept growing and kept growing,

    觀影人數越來越多 But then, as the viewership kept growing and kept growing,

  • I started getting letters from people,

    我開始收到這些信件 I started getting letters from people,

  • and it was starting to become clear

    漸漸的你開始明白 and it was starting to become clear

  • that it was actually more than just a nice-to-have.

    這不只是輔助教材 that it was actually more than just a nice-to-have.

  • This is just an excerpt

    這裡有一封信 This is just an excerpt

  • from one of those letters.

    是這樣說的 from one of those letters.

  • "My 12 year-old son has autism

    “我12歲的自閉症兒子 "My 12 year-old son has autism

  • and has had a terrible time with math.

    對數學一籌莫展 and has had a terrible time with math.

  • We have tried everything,

    我們試過所有方法 We have tried everything,

  • viewed everything, bought everything.

    看過所有書籍,買了所有教材 viewed everything, bought everything.

  • We stumbled on your video on decimals and it got through.

    我們發現了你的十進位影片,他看懂了 We stumbled on your video on decimals and it got through.

  • Then we went on to the dreaded fractions. Again, he got it.

    於是我們播可怕的分數影片,他又懂了 Then we went on to the dreaded fractions. Again, he got it.

  • We could not believe it.

    我們不可置信 We could not believe it.

  • He is so excited."

    他超興奮的。” He is so excited."

  • And so you can imagine,

    你可以想像 And so you can imagine,

  • here I was an analyst at a hedge fund.

    身為一位避險基金分析師 here I was an analyst at a hedge fund.

  • It was very strange for me to do something of social value.

    做一些有益社會的事對我來說非常陌生 It was very strange for me to do something of social value.

  • (Laughter)

    (笑聲) (Laughter)

  • (Applause)

    (掌聲) (Applause)

  • But I was excited, so I kept going.

    但我很興奮,於是我繼續製作這些影片 But I was excited, so I kept going.

  • And then a few other things started to dawn on me.

    一些其它事情開始發生了 And then a few other things started to dawn on me.

  • That, not only would it help my cousins right now,

    這些影片不但能幫助我表弟 That, not only would it help my cousins right now,

  • or these people who are sending letters,

    和這些寫信給我的人 or these people who are sending letters,

  • but that this content will never go old,

    而且這些影片永遠不會變老 but that this content will never go old,

  • that it could help their kids

    它可以幫助他們的孩子 that it could help their kids

  • or their grandkids.

    或孫子 or their grandkids.

  • If Isaac Newton

    如果牛頓 If Isaac Newton

  • had done YouTube videos on calculus,

    上傳一個微積分的 YouTube 影片 had done YouTube videos on calculus,

  • I wouldn't have to.

    就用不著我了 I wouldn't have to.

  • (Laughter)

    (笑聲) (Laughter)

  • Assuming he was good. We don't know.

    當然,那得要他很會教,我們無從得知 Assuming he was good. We don't know.

  • (Laughter)

    (笑聲) (Laughter)

  • The other thing that happened --

    就算發生了這些事 The other thing that happened --

  • and even at this point, I said, "Okay, maybe it's a good supplement.

    就算到了那個時候,我仍想“好吧,或許它是不錯的輔助教材 and even at this point, I said, "Okay, maybe it's a good supplement.

  • It's good for motivated students.

    很能激勵學生 It's good for motivated students.

  • It's good for maybe home schoolers."

    給在家上課的學生也很有用” It's good for maybe home schoolers."

  • But I didn't think it would be something

    但我從來沒想到 But I didn't think it would be something

  • that would somehow penetrate the classroom.

    它竟然能打進課堂 that would somehow penetrate the classroom.

  • But then I started getting letters from teachers.

    但我開始收到老師的信 But then I started getting letters from teachers.

  • And the teachers would write, saying,

    這些老師寫著 And the teachers would write, saying,

  • "We've used your videos to flip the classroom.

    “我們在課堂上播你的影片 "We've used your videos to flip the classroom.

  • You've given the lectures, so now what we do ... " --

    你已經解釋過了,那我們呢⋯⋯” You've given the lectures, so now what we do ... " --

  • and this could happen in every classroom in America tomorrow --

    說真的,這件事可以明天就在美國每個學校發生 and this could happen in every classroom in America tomorrow --

  • " ... what I do is I assign the lectures for homework,

    “⋯⋯ 我們只要把看影片變成他們的功課 " ... what I do is I assign the lectures for homework,

  • and what used to be homework,

    然後把以前的回家作業 and what used to be homework,

  • I now have the students doing in the classroom."

    變成在課堂上的習作” I now have the students doing in the classroom."

  • And I want to pause here for --

    我想要在這裡打個岔 - And I want to pause here for --

  • (Applause)

    (掌聲) (Applause)

  • I want to pause here for a second,

    我想在這裡打個岔 I want to pause here for a second,

  • because there's a couple of interesting things.

    因為這裡有幾項有趣的事 because there's a couple of interesting things.

  • One, when those teachers are doing that,

    一,當這些老師開始這麼做的時候 One, when those teachers are doing that,

  • there's the obvious benefit --

    比較明顯的好處是 there's the obvious benefit --

  • the benefit that now their students

    現在這些學生 the benefit that now their students

  • can enjoy the videos in the way that my cousins did.

    都可以像我的表弟一樣 can enjoy the videos in the way that my cousins did.

  • They can pause, repeat at their own pace,

    用自己的節奏學習 They can pause, repeat at their own pace,

  • at their own time.

    隨時暫停或復習 at their own time.

  • But the more interesting thing is --

    但更有趣的事是 But the more interesting thing is --

  • and this is the unintuitive thing when you talk about technology in the classroom --

    當你把科技帶到課堂裡 and this is the unintuitive thing when you talk about technology in the classroom --

  • by removing the one-size-fits-all lecture from the classroom

    便實現了因材施教的理想 by removing the one-size-fits-all lecture from the classroom

  • and letting students have a self-paced lecture at home,

    學生們可以回家用自己的方式學習 and letting students have a self-paced lecture at home,

  • and then when you go to the classroom, letting them do work,

    當他們到了課堂,開始做作業 and then when you go to the classroom, letting them do work,

  • having the teacher walk around,

    老師可以作為輔助 having the teacher walk around,

  • having the peers actually be able to interact with each other,

    甚至讓學生互相教導學習 having the peers actually be able to interact with each other,

  • these teachers have used technology

    這些老師用科技 these teachers have used technology

  • to humanize the classroom.

    把教室變得更人性 to humanize the classroom.

  • They took a fundamentally dehumanizing experience --

    過去的課堂經驗是很去人性的 They took a fundamentally dehumanizing experience --

  • 30 kids with their fingers on their lips,

    30個孩子不許開口 30 kids with their fingers on their lips,

  • not allowed to interact with each other.

    不許和彼此交談 not allowed to interact with each other.

  • A teacher, no matter how good,

    無論一個老師多優秀 A teacher, no matter how good,

  • has to give this one-size-fits-all lecture

    都得用一樣的方法 has to give this one-size-fits-all lecture

  • to 30 students --

    教30個不同的孩子 to 30 students --

  • blank faces, slightly antagonistic --

    面無表情,還帶著些敵意 blank faces, slightly antagonistic --

  • and now it's a human experience.

    現在人性多了 and now it's a human experience.

  • Now they're actually interacting with each other.

    現在他們總算可以交流了 Now they're actually interacting with each other.

  • So once the Khan Academy --

    於是有了 Khan 學院 So once the Khan Academy --

  • I quit my job

    我辭掉工作 I quit my job

  • and we turned into a real organization --

    把學院變成一個真正的組織 and we turned into a real organization --

  • we're a not-for-profit --

    我們是個非營利組織 we're a not-for-profit --

  • the question is, how do we take this to the next level?

    問題是,下一步該怎麼走? the question is, how do we take this to the next level?

  • How do we take what those teachers are doing

    我們該如何幫助這些老師的做法 How do we take what those teachers are doing

  • to their natural conclusion?

    讓它變得更好? to their natural conclusion?

  • And so what I'm showing you over here,

    我現在所要展示的 And so what I'm showing you over here,

  • these are actual exercises

    都是當時我為了我表弟 these are actual exercises

  • that I started writing for my cousins.

    所做的題目 that I started writing for my cousins.

  • The ones I started were much more primitive.

    當時的畫面比較原始 The ones I started were much more primitive.

  • This is a more competent version of it.

    現在的比較好用 This is a more competent version of it.

  • But the paradigm here is, we'll generate as many questions as you need

    這個範例所展現的是,我們讓你做許多題目 But the paradigm here is, we'll generate as many questions as you need

  • until you get that concept,

    直到你理解了這個概念 until you get that concept,

  • until you get 10 in a row.

    直到你連續答對十題 until you get 10 in a row.

  • And the Khan Academy videos are there.

    如果你不知道怎麼做 And the Khan Academy videos are there.

  • You get hints, the actual steps for that problem,

    Khan 學院影片在這 You get hints, the actual steps for that problem,

  • if you don't know how to do it.

    有提示,還有解題的步驟 if you don't know how to do it.

  • But the paradigm here, it seems like a very simple thing:

    這個範例看上去很簡單: But the paradigm here, it seems like a very simple thing:

  • 10 in a row, you move on.

    十題,然後繼續 10 in a row, you move on.

  • But it's fundamentally different than what's happening in classrooms right now.

    它和現在的教室有所不同 But it's fundamentally different than what's happening in classrooms right now.

  • In a traditional classroom,

    在傳統的教室裡 In a traditional classroom,

  • you have a couple of homework,

    你有一些作業 you have a couple of homework,

  • homework, lecture, homework, lecture,

    作業、講課、作業、講課 homework, lecture, homework, lecture,

  • and then you have a snapshot exam.

    然後你有個短短的考試 and then you have a snapshot exam.

  • And that exam, whether you get a 70 percent, an 80 percent,

    無論你在考試裡拿了70分、80分 And that exam, whether you get a 70 percent, an 80 percent,

  • a 90 percent or a 95 percent,

    90或95分 a 90 percent or a 95 percent,

  • the class moves on to the next topic.

    課堂都會繼續 the class moves on to the next topic.

  • And even that 95 percent student,

    但就算你拿了95分 And even that 95 percent student,

  • what was the five percent they didn't know?

    他不知道的那5分怎麼辦 what was the five percent they didn't know?

  • Maybe they didn't know what happens when you raise something to the zero power.

    或許他們不知道你把數提到零功率的時候會怎樣 Maybe they didn't know what happens when you raise something to the zero power.

  • And then you go build on that in the next concept.

    但你已經開始講解下個概念了 And then you go build on that in the next concept.

  • That's analogous to

    那就像是 That's analogous to

  • imagine learning to ride a bicycle,

    想像你在學騎腳踏車 imagine learning to ride a bicycle,

  • and maybe I give you a lecture ahead of time,

    我事先和你講解 and maybe I give you a lecture ahead of time,

  • and I give you that bicycle for two weeks.

    然後把腳踏車給你兩個禮拜 and I give you that bicycle for two weeks.

  • And then I come back after two weeks,

    兩個禮拜後我回來說 And then I come back after two weeks,

  • and I say, "Well, let's see. You're having trouble taking left turns.

    “我看看,你左轉有問題 and I say, "Well, let's see. You're having trouble taking left turns.

  • You can't quite stop.

    不太停的下來 You can't quite stop.

  • You're an 80 percent bicyclist."

    你是個80分的旗手” You're an 80 percent bicyclist."

  • So I put a big C stamp on your forehead

    然後我在你額頭上打個C印 So I put a big C stamp on your forehead

  • and then I say, "Here's a unicycle."

    然後說“這是你的單輪車。” and then I say, "Here's a unicycle."

  • But as ridiculous as that sounds,

    就算它聽上去很可笑 But as ridiculous as that sounds,

  • that's exactly what's happening

    這就是每天 that's exactly what's happening

  • in our classrooms right now.

    發生在我們教室裡的事 in our classrooms right now.

  • And the idea is you fast forward

    把情況往前快轉 And the idea is you fast forward

  • and good students start failing algebra all of a sudden

    好學生突然當掉了代數 and good students start failing algebra all of a sudden

  • and start failing calculus all of a sudden,

    當掉微積分 and start failing calculus all of a sudden,

  • despite being smart, despite having good teachers,

    就算他們聰明,又有好老師 despite being smart, despite having good teachers,

  • and it's usually because they have these Swiss cheese gaps

    往往是來自那些打基礎時 and it's usually because they have these Swiss cheese gaps

  • that kept building throughout their foundation.

    造成的那些瑞士乳酪孔隙一樣的差距 that kept building throughout their foundation.

  • So our model

    我們的模式是 So our model

  • is learn math the way you'd learn anything,

    用你學其它事物的方式學習數學 is learn math the way you'd learn anything,

  • like the way you would learn a bicycle.

    就像你學騎腳踏車一樣 like the way you would learn a bicycle.

  • Stay on that bicycle. Fall off that bicycle.

    坐在腳踏車上,從腳踏車上跌下 Stay on that bicycle. Fall off that bicycle.

  • Do it as long as necessary until you have mastery.

    直到你真正學會為止 Do it as long as necessary until you have mastery.

  • The traditional model,

    傳統的模式 The traditional model,

  • it penalizes you for experimentation and failure,

    懲罰學生的嘗試和失敗 it penalizes you for experimentation and failure,

  • but it does not expect mastery.

    它不期待你完全理解 but it does not expect mastery.

  • We encourage you to experiment. We encourage you to failure.

    我們鼓勵你實驗,鼓勵你失敗 We encourage you to experiment. We encourage you to failure.

  • But we do expect mastery.

    但我們要你完全理解掌控 But we do expect mastery.

  • This is just another one of the modules.

    這是另外一個課題 This is just another one of the modules.

  • This is trigonometry.

    這是三角習題 This is trigonometry.

  • This is shifting and reflecting functions.

    這是移位和反射函數 This is shifting and reflecting functions.

  • And they all fit together.

    他們全都有關聯 And they all fit together.

  • We have about 90 of these right now.

    我們現在大概有90個這樣的課程 We have about 90 of these right now.

  • And you can go to the site right now. It's all free. Not trying to sell anything.

    你可以自己上網站看,全免費,沒有要賣甚麼 And you can go to the site right now. It's all free. Not trying to sell anything.

  • But the general idea is that they all fit into this knowledge map.

    重點是他們全都包含在這知識地圖裡 But the general idea is that they all fit into this knowledge map.

  • That top node right there, that's literally single digit addition.

    上面那個最高的結是個位數加法 That top node right there, that's literally single digit addition.

  • It's like one plus one is equal to two.

    像一加一等於二 It's like one plus one is equal to two.

  • And the paradigm is, once you get 10 in a row on that,

    它的用法是,一旦你連續答對十題 And the paradigm is, once you get 10 in a row on that,

  • it keeps forwarding you to more and more advanced modules.

    你就會進階到下一個課題 it keeps forwarding you to more and more advanced modules.