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  • For as long as I remember, I've loved mathematics.

    譯者: Lilian Chiu 審譯者: Yanyan Hong

  • Actually, it's not 100 percent true.

    在我的記憶當中, 我一直都熱愛數學。

  • I've loved mathematics for all but a two-week period

    其實,這句話並非百分之百是對的。

  • in senior high school.

    我一直都熱愛數學, 除了一段兩星期的時間,

  • (Laughter)

    發生在高中時期。

  • I was top of my class,

    (笑聲)

  • and we were about to start the Extension Maths course.

    我在班上名列前茅,

  • I was really excited about this brand new topic coming up,

    我們即將要開始一門 叫做延伸數學的課,

  • complex numbers.

    我對於這個將要學到的 新主題感到十分興奮:

  • I like complex.

    複數。(註:直譯為複雜數字)

  • My teacher was priming us for the concepts

    我喜歡複雜。

  • with some questions about square roots.

    我的老師先給我們一些觀念,

  • Square of nine -- three;

    問到關於平方根的問題。

  • square of 256 -- sixteen.

    9 的平方根是 3;

  • Too easy.

    256 的平方根是 16;

  • Then she asked the trick question:

    太簡單了。

  • What about the square root of negative one?

    接著她問了一個腦筋急轉彎的問題:

  • Of course, we were all over it --

    那麼 -1 的平方根呢?

  • "Come on, Miss!

    當然,我們熱切地嘮叨著:

  • We all know you can't take the square root of a negative."

    「少來了,老師!

  • "That's true in the real world," she said.

    我們都知道負數不能開平方根。」

  • "But in the complex world,

    她說:「在真實世界是如此,

  • the square root of negative one is the imaginary number i."

    但在複數的世界裡,

  • (Laughter)

    -1 的平方根就是『虛數』 i。」 (註:照字面譯是「想像的數字」)

  • That day,

    (笑聲)

  • my entire mathematical world came crashing down on me.

    那一天,

  • (Laughter)

    我的整個數學世界垮在我身上。

  • "Imaginary numbers?

    (笑聲)

  • Seriously?

    「虛數?

  • But mathematics is a source of truth,

    當真嗎?

  • please don't go abstract on me.

    但數學是個真相的來源,

  • I would have studied art

    拜託別跟我來抽象的這一套。

  • if I wanted to play with imaginary numbers."

    如果我想要玩「想像的」數字,

  • (Laughter)

    早就去學藝術了。」

  • "This is Extension Maths, let's get back with our program!"

    (笑聲)

  • She didn't,

    「這是延伸數學, 咱們回來上我們的課吧!」

  • and over the next couple of weeks,

    她沒有,

  • I reluctantly performed meaningless calculations,

    在接下來的幾週,

  • (Laughter)

    我很不情願地做無意義的計算,

  • finding imaginary solutions to quadratic equations.

    (笑聲)

  • (Laughter)

    針對四次方程式,找出虛數解。

  • But then something amazing happened.

    (笑聲)

  • We began finding elegant solutions

    但接著,驚人的事發生了。

  • to real-world problems we previously had no answers to,

    對於以前無解的真實世界問題,

  • starting with the complex world of imaginary numbers.

    我們開始找到漂亮的答案,

  • So some mathematician 500 years ago

    答案就從複數世界的虛數開始。

  • decides to have some fun and make up these imaginary numbers,

    所以,五百年前的一些數學家

  • and because of that we can now derive these amazing identities

    想要找點樂子, 所以編造出了這些虛數,

  • with applications in the real world,

    正因如此,我們現在才能 導出這些驚人的恆等式,

  • in fields like electrical engineering.

    在真實世界中應用,

  • Wow!

    用到像是電子工程的領域上。

  • I gained a whole new level of appreciation for mathematics.

    哇!

  • And after my brief mistrust,

    我對數學的欣賞又再上了一層樓。

  • I was now in love with the subject more than ever.

    在我那段短暫的不信任之後,

  • Francis Su, the mathematician, sums it up beautifully when he says,

    我現在對這個科目的熱愛 又更勝於過去。

  • "We study mathematics for play, for beauty,

    數學家法蘭西斯蘇用以下的說法, 做了很漂亮的總結:

  • for truth,

    「我們研究數學的目的是樂趣、美麗、

  • for justice and for love."

    真相、

  • But if you ask a student today,

    正義,和愛。」

  • you'll probably hear a different story.

    但如果你去問現在的學生,

  • You might hear "difficult" and "boring."

    聽到的回應可能大不相同。

  • And they might be right about difficult.

    你可能會聽到「困難」及「無聊」。

  • But it's certainly not boring.

    說「困難」可能沒錯。

  • In fact, I'd say being difficult to master

    但它絕對不無聊。

  • is part of what makes it beautiful.

    事實上,我認為它之所以美麗,

  • Because nothing worth doing is easy.

    部分原因是因為它很難精通。

  • So we need students to stick around long enough through the difficult parts

    因為,值得做的事都不容易。

  • to appreciate the beauty when it all ties together.

    所以我們需要學生能夠 撐久一點,撐過困難的部分,

  • Much like I did for that brief couple of weeks in high school.

    才能在一切結合起來時 欣賞它的美麗。

  • Unfortunately, our school systems --

    就像我在高中時那短短幾週的情況。

  • we move students through mathematics in a lockstep process.

    不幸的是,我們的學校體系——

  • So those who fall a little behind

    我們讓學生用密集 連鎖步伐的過程來學數學。

  • find it near impossible to ever catch up and appreciate that beauty.

    所以,稍微落後一點的人,

  • But why is this a problem?

    就會覺得要趕上並欣賞 數學之美是幾乎不可能的。

  • Why should we care?

    這為什麼是個問題?

  • Well today, more than ever,

    我們為什麼要在乎?

  • our world needs every citizen to be skilled in mathematics.

    比起過去,現今,

  • With the advent of artificial intelligence and automation,

    我們的世界更需要 每位公民都具有數學技能。

  • many of the jobs we see today will either not exist

    隨著人工智慧和自動化的出現,

  • or be transformed to require less routine work

    現今的許多工作 在將來不會繼續存在,

  • and more analysis and application of expertise.

    或是會被轉變成 比較不需要例行性的工作,

  • But we're not producing the extra mathematics students

    需要更多分析與專門知識的應用。

  • to fill these new roles.

    但我們並未產出額外的數學學生

  • This graph shows the number of students

    來補這些新角色。

  • taking Standard Mathematics

    這張圖上的是學生數目,

  • and Advanced Mathematics

    有修基礎數學的學生,

  • over a period of 20 years in Australia.

    及有修進階數學的學生,

  • It's clear that while we have demand for mathematics skills rapidly increasing,

    時間是過去二十年,地點是澳洲。

  • supply is in steady decline.

    很顯然,雖然我們對於 數學技能的需求正在快速增加,

  • To put things in perspective,

    供應卻在穩定地下降。

  • half of the students completing high school today in Australia

    正確地說,

  • are not prepared to understand any argument

    在澳洲,有一半的高中畢業生

  • about rates of change in data.

    都沒有準備好了解任何關於

  • In this digital age

    資料改變率的論點。

  • where fake news can influence election results,

    在這個數位時代,

  • this is very concerning.

    連假新聞都能夠影響選舉結果,

  • Let me give you a concrete example.

    這點很讓人憂心。

  • Let's take a closer look at that graph.

    讓我舉個具體的例子。

  • Can everyone see what I've done there to stress my point?

    咱們更仔細看一下那張圖。

  • If you can't, let me show you now,

    有沒有人看得出來, 我做了什麼來強調我的重點?

  • with the vertical axis starting at zero, where it should be.

    如果沒有,我現在做給各位看。

  • There, you see it now, right?

    如果縱軸的起始點是零, 原本看起來應該像這樣。

  • It's the exact same data

    你們現在看見了,對嗎?

  • but I've manipulated the representation to influence you.

    資料都沒有變,

  • And that's cool, that's my job up here.

    但我調整了呈現方式,來影響你們。

  • (Laughter)

    那很酷,那是我在台上的工作。

  • But in all seriousness,

    (笑聲)

  • unless we do something

    但,說正經的,

  • to drastically improve student engagement with mathematics,

    除非我們採取行動

  • we'll not only have a huge skills shortage crisis

    來大大改善學生對於數學的投入,

  • but a fickle population,

    不然,我們不僅會有 技能短缺的大危機,

  • easily manipulated by whoever can get the most air time.

    還會有會動搖的人民,

  • So what's the solution?

    很容易被取得最多 播送時間的人給操弄。

  • There are a lot of things we have to do.

    所以,怎麼解決?

  • We need curriculum reform.

    我們需要做的事情很多。

  • We need our best and brightest encouraged to become teachers.

    我們需要課程改革。

  • We need to put an end to high-stakes tests

    我們需要鼓勵最好 和最聰明的人去當老師。

  • and instead follow a mastery-based learning approach.

    我們得停止用考試結果為補助依據,

  • But all these things take time.

    改成使用以精通為基礎的學習方法。

  • And I'm impatient.

    但這些都要花時間。

  • See, I've been thinking about this for eight years now.

    我不是有耐心的人。

  • Ever since I left my job as a derivative trader

    我過去八年都在想這件事。

  • to build a web application to help students learn mathematics.

    自從我辭掉衍生產品交易員的工作,

  • Today, our app is used by schools across the globe.

    去建立網路應用程式來協助 學生學習數學,就開始想了。

  • And we're seeing big improvements

    現今,全球都有學校 在用我們的應用程式。

  • for students who use the program regularly.

    我們看到經常使用 這個程式的學生進步很大。

  • But here's the thing --

    但,重點是

  • we're only seeing it for students who use the program regularly.

    只有常用這個程式的學生才有進步。

  • And most of them don't.

    而大部分學生並不常用。

  • So after years of developing and refining the application,

    所以,在花了數年時間發展 和改善這個應用程式之後,

  • our biggest challenge was not so much product related,

    我們最大的挑戰竟然 和產品沒有很大的關係,

  • our biggest challenge was motivating students

    我們最大的挑戰是要鼓勵學生,

  • to want to work on their gaps in understanding.

    讓他們「想要」去改善 他們在了解上的不足。

  • You can imagine in today's attention economy,

    你們可以想像,在現今的 注意力經濟當中,

  • we're competing against Facebook, Snapchat and PlayStation

    我們的競爭對手是臉書、 Snapchat、PlayStation 遊戲,

  • to try and get these students' time.

    跟它們搶學生的時間。

  • So we went back to the drawing board

    所以,我們回到計畫階段,

  • and started to think about how we could make it worthwhile

    開始思考,我們要如何讓學生覺得

  • for students to spend some of their "attention budget"

    值得花一些他們的「注意力預算」

  • on their education.

    在他們的教育上。

  • We tinkered with gamification elements

    我們補上遊戲化的元素,

  • like points, badges and avatars,

    比如點數、徽章、頭像,

  • and we'd see a temporary spike in engagement

    在參與度上有出現暫時性的提升,

  • but things would go back to normal as soon as the novelty wore off.

    但新鮮度不再時,馬上又回到原狀。

  • Then one day, my cofounder, Alvin,

    有一天,我的共同創辦人艾文

  • came across a study of students in Chicago

    看到一篇關於芝加哥學生的研究,

  • led by the behavioral economist, Steven Levitt,

    主導研究的是行為經濟學家 史帝芬萊維特(Steven Levitt),

  • where they paid students who improved on their test scores.

    在研究中,他們付錢給學生, 要他們改善考試分數。

  • He started telling me about some of the things they tested for

    他開始告訴我研究做的一些測試,

  • and the interesting findings they had.

    以及有趣的發現。

  • For instance, they found that incentivizing students for inputs,

    比如,他們發現獎勵學生的投入,

  • like effort,

    比如努力,

  • worked a lot better than incentivizing for outputs,

    效果大大優於獎勵他們的結果,

  • like test scores.

    如考試成績。

  • They found that for younger students, you could win them over with a trophy

    他們發現,對年輕學生, 用獎品可以贏得他們的心,

  • but for older students,

    但對較年長的學生,

  • you really needed cash.

    他們要的是現金。

  • (Laughter)

    (笑聲)

  • And the amount of cash mattered -- 10 dollars was good,

    且現金的金額也很重要,$10 很好,

  • 20 dollars -- even better.

    $20 更好。

  • But perhaps most importantly,

    但也許,最重要的是,

  • they found that the rewards had to be instant

    他們發現,獎賞要「即時」,

  • rather than promised at a later date.

    不能向他們保證晚一點再給。

  • They went as far as to give the students 20 dollars and say,

    他們做到這種程度—— 給學生 $20,然後說:

  • "Touch it, feel it, smell it --"

    「觸摸它,感受到,聞聞它。」

  • (Sniffing)

    (鼻吸)

  • "It's all yours.

    「這全是你的。

  • But if you fail, I'm going to take it back."

    但若你失敗了,我會把它收回來。」

  • And that worked really well.

    那樣做得效果非常好。

  • I immediately got excited

    我馬上就很興奮,

  • about the possibilities of implementing this in our program.

    心想有可能把這個點子 導入我們的程式中。

  • But once the excitement settled down,

    但等興奮感平靜下來之後,

  • there were a few concerns that crept in our minds.

    我們慢慢想到了一些考量。

  • Firstly,

    首先,

  • was this ethical?

    這樣合乎道德嗎?

  • (Laughter)

    (笑聲)

  • Secondly, how would we fund this thing?

    第二,我們哪來的資金?

  • (Laughter)

    (笑聲)

  • And finally,

    最後,

  • would the results be sustained if the students were no longer paid?

    如果不再付錢給學生, 結果會維持下去嗎?

  • Now, let's look at the ethical part first.

    先來看看道德的部分。

  • I'm a bit of a mathematical purist.

    我有點算是數學純粹主義者。

  • So I'd be one of the first people to say that we should study mathematics

    我會是最先說我們應該要為了數學

  • for the sake of mathematics.

    而學數學的人之一。

  • Remember -- for play, for beauty, for truth, for justice and for love!

    記得嗎?目的是為了樂趣、 美麗、真相、正義,和愛!

  • Not for money!

    不是為了錢!

  • (Laughter)

    (笑聲)

  • As I struggled with this, I came to see that,

    我為此掙扎時,漸漸理解到,

  • while it's a way I look at mathematics now,

    雖然那是我現在看數學的一種方式,

  • it's only because I studied it long enough to appreciate it.

    也只是因為我研究數學夠久, 讓我能欣賞它。

  • It's very difficult to tell a student struggling with mathematics today

    很難告訴一個現在正在 因為數學而掙扎的學生,

  • to work hard for a payoff in the distant future.

    只要努力,在遙遠的未來會有回報。

  • And it's not so much bribery that's at work here,

    這裡其實還算不上有什麼行賄,

  • because I could bribe students

    因為我可以賄賂學生,

  • by telling them about my big bonuses in my derivative trading days

    告訴他們我還在當 衍生產品交易員的日子,

  • as a reward for doing well at maths.

    因為數學做得好而得到高額獎金。

  • But it doesn't pay off for a very long time.

    但在很長一段時間內沒有回報。

  • So it's practically naught.

    所以,它其實是零。

  • Behavioral economists call this hyperbolic discounting.

    行為經濟學家稱 這個現象為「雙曲貼現」。

  • And Levitt goes as far as to say

    萊維特竟然還說,

  • that all motivating power vanishes

    當獎賞的分發時間被延遲時,

  • when rewards are handed out with a delay.

    所有的驅動力量都會消失。

  • So, from a purely economic point of view:

    所以,純粹從經濟的觀點來看:

  • if we don't use immediate incentives,

    如果我們不使用立即的獎勵,

  • we are underinvesting in student outcomes.

    我們對於學生成果的投資就是不足的。

  • I took heart from that, and came to see that as a society,

    那增加了我的信心,我漸漸了解,

  • we're actually quite used to financial incentives.

    我們這個社會其實 很習慣財務的獎勵。

  • Whether it be by the government, by employers or at home.

    不論是由政府提供、 僱主提供,或家裡提供的獎勵。

  • For instance, many parents would pay their children

    比如,許多父母會付錢給孩子,

  • an allowance or pocket money for doing chores in the house.

    給他們零用錢或私房錢 要他們做家事。

  • So it wasn't really all that controversial.

    所以,這種做法並沒有那麼爭議。

  • As I thought about that,

    當我想到這點時,

  • it started to answer that second question of how we were going to fund this.

    它也開始解答了第二個問題, 我們的資金從哪裡來。

  • Naturally, parents are the most invested in their children's education.

    自然地,在孩子的教育中 投資最多的人就是父母。

  • So, let's charge them a weekly subscription fee

    所以,咱們來向他們 收取每週的訂購費,

  • to use our program,

    付費使用我們的程式,

  • but --

    但是,

  • if the students complete their weekly maths goal,

    如果學生完成了 他們的每週數學目標,

  • we'll refund the subscription amount directly into the child's bank account.

    我們就把訂購費的金額直接 退還到孩子的銀行帳戶中。

  • We chose three exercises completed

    我們選了三項練習

  • over a one week period

    要在一週內完成,

  • for a 10 dollar reward.

    獎賞為 $10。

  • That way we're incentivizing effort rather than performance

    這麼一來,我們在獎勵的 就是努力而非表現,

  • over a short enough period

    經過很短的時間就能得到獎勵,

  • and with a substantial enough payout for the students to care.

    獎勵的金額也足夠讓學生在乎。

  • Now, I remember when I first told my wife about this new business model.

    我記得我初次告訴我太太 這個新的商業模型時的狀況。

  • If she had any doubt left that I've gone completely mad,

    如果她有一點點懷疑我完全瘋了,

  • that pretty much confirmed it for her.

    那幾乎讓她確認了。

  • She said to me, "Mo ...

    她對我說:「小穆……

  • you realize that if everybody does their homework, which you want,

    你要知道,如果人人都如你所願 好好地做他們的家庭作業,

  • you're not going to make any revenue, which you don't want.

    你就不會有任何利潤,這非你所願。

  • Great business model."

    好棒的商業模型。」

  • (Laughter)

    (笑聲)

  • I say it's more like an antibusiness model,

    我說,它比較像是個反商業模型,

  • it's free if you use it, but you pay if you don't.

    用它就是免費的,不用它就要付費。

  • Now, I knew from experience

    根據經驗,我知道,

  • that not everybody in the country was going to jump on

    不可能全國每個人都會因此動起來,

  • and do their maths homework every week.

    並每週完成數學的家庭作業。

  • And if they did, sure we'd go bust pretty quickly,

    若大家都做到,我們很快就會破產,

  • but hey, we would have solved the country's maths skills crisis.

    但,嘿,我們就能解決 這個國家的數學技能危機呢。

  • (Laughter)

    (笑聲)

  • As a company, we've always run a double bottom line,

    我們開公司總是會有雙重底線,