For as long as I remember, I've loved mathematics. Actually, it's not 100 percent true. I've loved mathematics for all but a two-week period in senior high school.
在我的記憶當中, 我一直都熱愛數學。 其實,這句話並非百分之百是對的。 我一直都熱愛數學, 除了一段兩星期的時間, 發生在高中時期。
(Laughter)
(笑聲)
I was top of my class, and we were about to start the Extension Maths course. I was really excited about this brand new topic coming up, complex numbers. I like complex. My teacher was priming us for the concepts with some questions about square roots. Square of nine -- three; square of 256 -- sixteen. Too easy. Then she asked the trick question: What about the square root of negative one? Of course, we were all over it -- "Come on, Miss! We all know you can't take the square root of a negative." "That's true in the real world," she said. "But in the complex world, the square root of negative one is the imaginary number i."
我在班上名列前茅, 我們即將要開始一門 叫做延伸數學的課, 我對於這個將要學到的 新主題感到十分興奮: 複數。(註:直譯為複雜數字) 我喜歡複雜。 我的老師先給我們一些觀念, 問到關於平方根的問題。 9 的平方根是 3; 256 的平方根是 16; 太簡單了。 接著她問了一個腦筋急轉彎的問題: 那麼 -1 的平方根呢? 當然,我們熱切地嘮叨著: 「少來了,老師! 我們都知道負數不能開平方根。」 她說:「在真實世界是如此, 但在複數的世界裡, -1 的平方根就是『虛數』 i。」 (註:照字面譯是「想像的數字」)
(Laughter)
(笑聲)
That day, my entire mathematical world came crashing down on me.
那一天, 我的整個數學世界垮在我身上。
(Laughter)
(笑聲)
"Imaginary numbers? Seriously? But mathematics is a source of truth, please don't go abstract on me. I would have studied art if I wanted to play with imaginary numbers."
「虛數? 當真嗎? 但數學是個真相的來源, 拜託別跟我來抽象的這一套。 如果我想要玩「想像的」數字, 早就去學藝術了。」
(Laughter)
(笑聲)
"This is Extension Maths, let's get back with our program!" She didn't, and over the next couple of weeks, I reluctantly performed meaningless calculations,
「這是延伸數學, 咱們回來上我們的課吧!」 她沒有, 在接下來的幾週, 我很不情願地做無意義的計算,
(Laughter)
(笑聲)
finding imaginary solutions to quadratic equations.
針對四次方程式,找出虛數解。
(Laughter)
(笑聲)
But then something amazing happened. We began finding elegant solutions to real-world problems we previously had no answers to, starting with the complex world of imaginary numbers. So some mathematician 500 years ago decides to have some fun and make up these imaginary numbers, and because of that we can now derive these amazing identities with applications in the real world, in fields like electrical engineering. Wow! I gained a whole new level of appreciation for mathematics. And after my brief mistrust, I was now in love with the subject more than ever.
但接著,驚人的事發生了。 對於以前無解的真實世界問題, 我們開始找到漂亮的答案, 答案就從複數世界的虛數開始。 所以,五百年前的一些數學家 想要找點樂子, 所以編造出了這些虛數, 正因如此,我們現在才能 導出這些驚人的恆等式, 在真實世界中應用, 用到像是電子工程的領域上。 哇! 我對數學的欣賞又再上了一層樓。 在我那段短暫的不信任之後, 我現在對這個科目的熱愛 又更勝於過去。
Francis Su, the mathematician, sums it up beautifully when he says, "We study mathematics for play, for beauty, for truth, for justice and for love." But if you ask a student today, you'll probably hear a different story. You might hear "difficult" and "boring." And they might be right about difficult. But it's certainly not boring. In fact, I'd say being difficult to master is part of what makes it beautiful. Because nothing worth doing is easy.
數學家法蘭西斯蘇用以下的說法, 做了很漂亮的總結: 「我們研究數學的目的是樂趣、美麗、 真相、 正義,和愛。」 但如果你去問現在的學生, 聽到的回應可能大不相同。 你可能會聽到「困難」及「無聊」。 說「困難」可能沒錯。 但它絕對不無聊。 事實上,我認為它之所以美麗, 部分原因是因為它很難精通。 因為,值得做的事都不容易。
So we need students to stick around long enough through the difficult parts to appreciate the beauty when it all ties together. Much like I did for that brief couple of weeks in high school. Unfortunately, our school systems -- we move students through mathematics in a lockstep process. So those who fall a little behind find it near impossible to ever catch up and appreciate that beauty.
所以我們需要學生能夠 撐久一點,撐過困難的部分, 才能在一切結合起來時 欣賞它的美麗。 就像我在高中時那短短幾週的情況。 不幸的是,我們的學校體系—— 我們讓學生用密集 連鎖步伐的過程來學數學。 所以,稍微落後一點的人, 就會覺得要趕上並欣賞 數學之美是幾乎不可能的。
But why is this a problem? Why should we care? Well today, more than ever, our world needs every citizen to be skilled in mathematics. With the advent of artificial intelligence and automation, many of the jobs we see today will either not exist or be transformed to require less routine work and more analysis and application of expertise. But we're not producing the extra mathematics students to fill these new roles.
這為什麼是個問題? 我們為什麼要在乎? 比起過去,現今, 我們的世界更需要 每位公民都具有數學技能。 隨著人工智慧和自動化的出現, 現今的許多工作 在將來不會繼續存在, 或是會被轉變成 比較不需要例行性的工作, 需要更多分析與專門知識的應用。 但我們並未產出額外的數學學生 來補這些新角色。
This graph shows the number of students taking Standard Mathematics and Advanced Mathematics over a period of 20 years in Australia. It's clear that while we have demand for mathematics skills rapidly increasing, supply is in steady decline. To put things in perspective, half of the students completing high school today in Australia are not prepared to understand any argument about rates of change in data. In this digital age where fake news can influence election results, this is very concerning.
這張圖上的是學生數目, 有修基礎數學的學生, 及有修進階數學的學生, 時間是過去二十年,地點是澳洲。 很顯然,雖然我們對於 數學技能的需求正在快速增加, 供應卻在穩定地下降。 正確地說, 在澳洲,有一半的高中畢業生 都沒有準備好了解任何關於 資料改變率的論點。 在這個數位時代, 連假新聞都能夠影響選舉結果, 這點很讓人憂心。
Let me give you a concrete example. Let's take a closer look at that graph. Can everyone see what I've done there to stress my point? If you can't, let me show you now, with the vertical axis starting at zero, where it should be. There, you see it now, right? It's the exact same data but I've manipulated the representation to influence you. And that's cool, that's my job up here.
讓我舉個具體的例子。 咱們更仔細看一下那張圖。 有沒有人看得出來, 我做了什麼來強調我的重點? 如果沒有,我現在做給各位看。 如果縱軸的起始點是零, 原本看起來應該像這樣。 你們現在看見了,對嗎? 資料都沒有變, 但我調整了呈現方式,來影響你們。 那很酷,那是我在台上的工作。
(Laughter)
(笑聲)
But in all seriousness, unless we do something to drastically improve student engagement with mathematics, we'll not only have a huge skills shortage crisis but a fickle population, easily manipulated by whoever can get the most air time. So what's the solution?
但,說正經的, 除非我們採取行動 來大大改善學生對於數學的投入, 不然,我們不僅會有 技能短缺的大危機, 還會有會動搖的人民, 很容易被取得最多 播送時間的人給操弄。 所以,怎麼解決?
There are a lot of things we have to do. We need curriculum reform. We need our best and brightest encouraged to become teachers. We need to put an end to high-stakes tests and instead follow a mastery-based learning approach. But all these things take time. And I'm impatient.
我們需要做的事情很多。 我們需要課程改革。 我們需要鼓勵最好 和最聰明的人去當老師。 我們得停止用考試結果為補助依據, 改成使用以精通為基礎的學習方法。 但這些都要花時間。 我不是有耐心的人。
See, I've been thinking about this for eight years now. Ever since I left my job as a derivative trader to build a web application to help students learn mathematics. Today, our app is used by schools across the globe. And we're seeing big improvements for students who use the program regularly. But here's the thing -- we're only seeing it for students who use the program regularly. And most of them don't. So after years of developing and refining the application, our biggest challenge was not so much product related, our biggest challenge was motivating students to want to work on their gaps in understanding. You can imagine in today's attention economy, we're competing against Facebook, Snapchat and PlayStation to try and get these students' time.
我過去八年都在想這件事。 自從我辭掉衍生產品交易員的工作, 去建立網路應用程式來協助 學生學習數學,就開始想了。 現今,全球都有學校 在用我們的應用程式。 我們看到經常使用 這個程式的學生進步很大。 但,重點是 只有常用這個程式的學生才有進步。 而大部分學生並不常用。 所以,在花了數年時間發展 和改善這個應用程式之後, 我們最大的挑戰竟然 和產品沒有很大的關係, 我們最大的挑戰是要鼓勵學生, 讓他們「想要」去改善 他們在了解上的不足。 你們可以想像,在現今的 注意力經濟當中, 我們的競爭對手是臉書、 Snapchat、PlayStation 遊戲, 跟它們搶學生的時間。
So we went back to the drawing board and started to think about how we could make it worthwhile for students to spend some of their "attention budget" on their education. We tinkered with gamification elements like points, badges and avatars, and we'd see a temporary spike in engagement but things would go back to normal as soon as the novelty wore off.
所以,我們回到計畫階段, 開始思考,我們要如何讓學生覺得 值得花一些他們的「注意力預算」 在他們的教育上。 我們補上遊戲化的元素, 比如點數、徽章、頭像, 在參與度上有出現暫時性的提升, 但新鮮度不再時,馬上又回到原狀。
Then one day, my cofounder, Alvin, came across a study of students in Chicago led by the behavioral economist, Steven Levitt, where they paid students who improved on their test scores. He started telling me about some of the things they tested for and the interesting findings they had. For instance, they found that incentivizing students for inputs, like effort, worked a lot better than incentivizing for outputs, like test scores. They found that for younger students, you could win them over with a trophy but for older students, you really needed cash.
有一天,我的共同創辦人艾文 看到一篇關於芝加哥學生的研究, 主導研究的是行為經濟學家 史帝芬萊維特(Steven Levitt), 在研究中,他們付錢給學生, 要他們改善考試分數。 他開始告訴我研究做的一些測試, 以及有趣的發現。 比如,他們發現獎勵學生的投入, 比如努力, 效果大大優於獎勵他們的結果, 如考試成績。 他們發現,對年輕學生, 用獎品可以贏得他們的心, 但對較年長的學生, 他們要的是現金。
(Laughter)
(笑聲)
And the amount of cash mattered -- 10 dollars was good, 20 dollars -- even better. But perhaps most importantly, they found that the rewards had to be instant rather than promised at a later date. They went as far as to give the students 20 dollars and say, "Touch it, feel it, smell it --"
且現金的金額也很重要,$10 很好, $20 更好。 但也許,最重要的是, 他們發現,獎賞要「即時」, 不能向他們保證晚一點再給。 他們做到這種程度—— 給學生 $20,然後說: 「觸摸它,感受到,聞聞它。」
(Sniffing)
(鼻吸)
"It's all yours. But if you fail, I'm going to take it back." And that worked really well. I immediately got excited about the possibilities of implementing this in our program. But once the excitement settled down, there were a few concerns that crept in our minds. Firstly, was this ethical?
「這全是你的。 但若你失敗了,我會把它收回來。」 那樣做得效果非常好。 我馬上就很興奮, 心想有可能把這個點子 導入我們的程式中。 但等興奮感平靜下來之後, 我們慢慢想到了一些考量。 首先, 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, would the results be sustained if the students were no longer paid?
最後, 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. I'm a bit of a mathematical purist. So I'd be one of the first people to say that we should study mathematics for the sake of mathematics. Remember -- for play, for beauty, for truth, for justice and for love! Not for money!
先來看看道德的部分。 我有點算是數學純粹主義者。 我會是最先說我們應該要為了數學 而學數學的人之一。 記得嗎?目的是為了樂趣、 美麗、真相、正義,和愛! 不是為了錢!
(Laughter)
(笑聲)
As I struggled with this, I came to see that, while it's a way I look at mathematics now, it's only because I studied it long enough to appreciate it. It's very difficult to tell a student struggling with mathematics today to work hard for a payoff in the distant future. And it's not so much bribery that's at work here, because I could bribe students by telling them about my big bonuses in my derivative trading days as a reward for doing well at maths. But it doesn't pay off for a very long time. So it's practically naught. Behavioral economists call this hyperbolic discounting. And Levitt goes as far as to say that all motivating power vanishes when rewards are handed out with a delay. So, from a purely economic point of view: if we don't use immediate incentives, we are underinvesting in student outcomes. I took heart from that, and came to see that as a society, we're actually quite used to financial incentives. Whether it be by the government, by employers or at home.
我為此掙扎時,漸漸理解到, 雖然那是我現在看數學的一種方式, 也只是因為我研究數學夠久, 讓我能欣賞它。 很難告訴一個現在正在 因為數學而掙扎的學生, 只要努力,在遙遠的未來會有回報。 這裡其實還算不上有什麼行賄, 因為我可以賄賂學生, 告訴他們我還在當 衍生產品交易員的日子, 因為數學做得好而得到高額獎金。 但在很長一段時間內沒有回報。 所以,它其實是零。 行為經濟學家稱 這個現象為「雙曲貼現」。 萊維特竟然還說, 當獎賞的分發時間被延遲時, 所有的驅動力量都會消失。 所以,純粹從經濟的觀點來看: 如果我們不使用立即的獎勵, 我們對於學生成果的投資就是不足的。 那增加了我的信心,我漸漸了解, 我們這個社會其實 很習慣財務的獎勵。 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 an allowance or pocket money for doing chores in the house. So it wasn't really all that controversial. As I thought about that, it started to answer that second question of how we were going to fund this. Naturally, parents are the most invested in their children's education. So, let's charge them a weekly subscription fee to use our program, but -- if the students complete their weekly maths goal, we'll refund the subscription amount directly into the child's bank account. We chose three exercises completed over a one week period for a 10 dollar reward. That way we're incentivizing effort rather than performance over a short enough period and with a substantial enough payout for the students to care.
比如,許多父母會付錢給孩子, 給他們零用錢或私房錢 要他們做家事。 所以,這種做法並沒有那麼爭議。 當我想到這點時, 它也開始解答了第二個問題, 我們的資金從哪裡來。 自然地,在孩子的教育中 投資最多的人就是父母。 所以,咱們來向他們 收取每週的訂購費, 付費使用我們的程式, 但是, 如果學生完成了 他們的每週數學目標, 我們就把訂購費的金額直接 退還到孩子的銀行帳戶中。 我們選了三項練習 要在一週內完成, 獎賞為 $10。 這麼一來,我們在獎勵的 就是努力而非表現, 經過很短的時間就能得到獎勵, 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. If she had any doubt left that I've gone completely mad, that pretty much confirmed it for her. She said to me, "Mo ... you realize that if everybody does their homework, which you want, you're not going to make any revenue, which you don't want. Great 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。 如果她有一點點懷疑我完全瘋了, 那幾乎讓她確認了。 她對我說:「小穆…… 你要知道,如果人人都如你所願 好好地做他們的家庭作業, 你就不會有任何利潤,這非你所願。 好棒的商業模型。」
(Laughter)
(笑聲)
I say it's more like an antibusiness model, it's free if you use it, but you pay if you don't. Now, I knew from experience that not everybody in the country was going to jump on and do their maths homework every week. And if they did, sure we'd go bust pretty quickly, but hey, we would have solved the country's maths skills crisis.
我說,它比較像是個反商業模型, 用它就是免費的,不用它就要付費。 根據經驗,我知道, 不可能全國每個人都會因此動起來, 並每週完成數學的家庭作業。 若大家都做到,我們很快就會破產, 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, looking to both make a return for investors as well as improve student outcomes. We know that our path to long-term profitability is through improving student outcomes. So our dual objectives should never be at odds. So we're always looking to make our product decisions around helping students reach their weekly maths goal, effectively ensuring that they get paid and not us.
我們開公司總是會有雙重底線, 期望能為投資者取得收益, 同時也要改善學生的結果。 我們知道若想要有長期收益性, 就要去改善學生的結果。 所以,我們的雙重方針 應該永遠不會不一致。 所以,我們總是在注意, 當要做產品決策時, 要考量能協助學生達成 他們的每週數學目標, 有效地確保他們會賺到錢, 而不是我們。
Now you must be wondering: How is this crazy business model going? You'll be glad to know we're still in business. We've been testing this now for the last five months on just our personal home users in Australia before we think about rolling it out to schools. And here are the early results. The green represents students who are completing their weekly maths goal and the red those who aren't. You can see a lot more completing their homework than not. In fact, as our user base has grown, we found the percentage to be pretty steady, at around 75 percent. So on average, we receive our weekly subscription fee once every four weeks, and the other three weeks, we're rewarding the students. Now of course we're leaving some money on the table here, but guess what? It turns out these students are 70 percent more engaged than students not on the reward program. Check.
你們現在一定在納悶: 這瘋狂的商業模型進展如何? 你們會很高興知道,我們還在營運。 過去五個月,我們一直在測試, 對象只有我們在澳洲的 居家個人使用者, 之後才會考慮把它推展到學校。 這些是早期的結果。 綠色代表的是完成 每週數學目標的學生, 紅色則是沒有完成。 你們能看到,完成的人 比沒完成的人多很多。 事實上,隨著我們的 使用者基礎變大, 我們發現,百分比 相當穩定,大約在 75%。 所以,平均來說, 我們每四週會收到 一次的每週訂購費, 剩下的三週則是在獎勵學生。 當然,我們有把一些錢留在桌上, 但,你們猜如何? 結果發現,這些學生 比沒有參與獎勵方案的學生, 投入程度還要高 70%。 打勾(確認)。
From a business perspective, they are less likely to churn and more likely to refer friends, so we're hoping to trade off a lower revenue per user for a bigger and more engaged user base. Check and check.
從商業的角度, 他們是比較不會流失的客戶, 比較有可能推薦朋友, 所以,我們希望能把 「每位使用者利潤」較低的使用者 換成比較大、比較投入的使用者基礎。 打勾再打勾。
Now for that final question. Would they keep coming back if they were no longer paid? Mathematics is so much more than just a subject you study at school. It's a human endeavor. It's what helps us to understand the world around us. And the more you know, the more you want to know. So yes, we've triggered initial engagement with a financial reward. But in the long run, the money won't matter anymore. Because in the long run, the wonder of mathematics will be the incentive and understanding it will be the reward.
至於最後一個問題。 如果不再付錢給他們, 他們會持續回來嗎? 數學絕對不只是 你在學校學的一個科目。 它是人類的努力。 它能協助我們 了解我們周遭的世界。 你知道的越多,會想要知道更多。 所以,是的,我們用財務獎勵來觸發 初始的投入。 但從長期來說, 錢就不再重要了。 因為,長期來說, 獎勵,將會是見證數學的驚奇, 報酬,則是讓你我真正了解它。
Thank you.
謝謝。
(Applause)
(掌聲)