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.
在我的印象中,我一直深爱数学。 其实这个说法也不是绝对准确。 确切地说,我一直深爱数学, 除了高中时期的两个礼拜。
(Laughter)
(笑声)
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."
我当时在班里名列前茅, 我们正要开始学习扩展数学课程。 我对这个全新的领域兴奋不已, 复数。 我喜欢复杂的东西。 老师给我们铺垫了一些概念, 提出了一些关于平方根的问题。 9开二次方是多少——3; 256开二次方是多少——16。 这太容易了。 之后老师问了我们一个难题: -1开平方是多少呢? 当然,我们都认为这不可能 —— “拜托,老师! 我们都知道不能对负数开方。” 老师说:“在实数域中确实是这样, 但是在复数的范畴里, -1的平方根是虚数 i。”
(Laughter)
(笑声)
That day, my entire mathematical world came crashing down on me.
那一天, 我的整个数学观都坍塌了。
(Laughter)
(笑声)
"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."
“虚数? 真的吗? 数学是真理的来源, 请别把它搞抽象了。 如果要和 虚构的数字打交道, 我情愿去学艺术。”
(Laughter)
(笑声)
"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,
“这是扩展数学 , 让我们回到数学的正题上来!” 但老师没有这么做, 在接下来的几周, 我不情愿地进行着没意义的计算,
(Laughter)
(笑声)
finding imaginary solutions to quadratic equations.
给二次方程式求虚数解。
(Laughter)
(笑声)
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.
但之后发生了令人惊讶的事情。 我们开始找到之前 在现实世界中无解问题的答案, 而这都要从复杂的虚数开始。 500年前的一群数学家 想找点乐子 , 于是构想出了这些虚数, 我们也因此将这些神奇的记号 运用到了现实世界中, 例如电力工程领域。 哇! 我对数学的欣赏 上升到了一个全新的阶段。 在经历了短暂的不信任之后, 现在的我比以往更爱这个学科了。
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.
数学家弗朗西斯·苏 有一句优美的总结: “我们学习数学 是为了乐趣,为了美好, 为了真理, 为了公正,也为了热爱。” 但现在,如果你问一个学生, 你可能会得到不同的答案。 你可能会听到“困难”和“无聊”。 说数学困难可能有些道理, 但数学肯定不是无聊的。 我其实觉得,数学的一大魅力 就在于它难以掌握。 因为有价值的事情 做起来都不会容易。
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.
我们需要学生们 长期坚持,面对数学之难, 将难的内容联系起来时 才能感受到数学的美。 这和我在高中 那几周的经历差不多。 遗憾的是,我们的教育体制—— 只是单纯地对所有学生采用 统一的教学进度。 那些落后一点的学生 会认为赶上别人、学会欣赏数学 几乎是不可能的事情。
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.
为什么这是个问题呢? 为什么我们应当关心这个问题? 当今世界对人们数学能力的需求 比以往任何时候都要迫切。 随着人工智能和自动化时代的到来, 我们现在的许多工作 未来都将不复存在, 或者被迫进行改革 , 以减少常规工作, 并加强专业化的分析和应用。 但我们没有足够的数学专业学生 来填补这些新增职位。
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.
这幅图显示了20年间, 在澳大利亚 学习普通数学 和高等数学的学生数量。 结果一目了然,虽然我们对 数学人才的需求快速增加, 具备这些能力的人数却在稳定下降。 也就是说, 如今在澳大利亚,一半高中毕业生 都不能够完全理解 有关数据变化率的 任何论点。 现在可是数字时代, 假新闻都能够影响选举结果, 这非常令人担忧。
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.
给大家一个具体的例子。 我们再看看这幅图。 大家能看出来 我为了突出重点做了什么吗? 如果你看不出来,我来告诉你, 纵轴的起始点本应该是0。 现在能看出来了吧? 本来是一模一样的数据, 但是我在展现方式上 做了手脚来影响你们。 这很酷,也正是我站在这儿目的。
(Laughter)
(笑声)
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?
但认真地讲, 除非我们做些什么 来大幅增加学生们 在数学课程上的投入, 否则我们将不仅面临 巨大的技能短缺, 而且人们的思想也将摇摆不定, 轻而易举地被电视里 出镜最多的人操控。 那么,有什么解决办法吗?
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.
这项工作任重道远。 我们需要课程改革。 我们需要最棒、 最聪明的人成为老师。 我们需要取消 “一考定终身”的制度, 改用以能力为基础的教学方法。 但所有这些都不能一蹴而就。 而我又没什么耐心。
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.
八年前,我辞掉了 金融衍生品交易员的工作。 从那时起我就一直致力于此, 开发网络应用,帮助学生学习数学。 如今,我们的应用 被全球各地学校广泛使用。 经常使用它的学生 在成绩上也有了显著提高。 但有一个问题—— 这种提高只体现在 经常使用应用的学生身上。 而这类学生只占少数。 因此,我们虽然 花费数年开发和改进应用, 但面临的最大挑战 却并非来自产品, 而是如何激励学生, 让他们愿意克服理解数学的障碍。 如今是注意力经济时代, 我们是在和Facebook, Snapchat,Playstation竞争, 努力争取学生们的时间。
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.
于是我们退后一步, 开始思考如何能让学生认为 分一些有限的精力在教育上 是值得的。 我们在应用中 添加了一些游戏元素, 例如积分、勋章、炫酷的形象等, 我们发现参与度短暂上升, 但当新鲜感褪去后, 一切又迅速回到正常水平。
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.
我们的联合创始人埃尔文 某天偶然看到芝加哥 一项关于学生的研究, 这项研究由行为经济学家 斯蒂芬·莱维特发起, 他们付钱给测验成绩提高的学生。 他告诉我了一些测试的内容, 以及一些有趣的研究发现。 例如,他们发现 对学生的努力程度等投入 进行奖励, 其效果要好于对分数等结果 进行奖励。 他们还发现, 可以给年龄小的学生奖杯, 但对于年龄大一些的学生, 则需要给他们金钱奖励。
(Laughter)
(笑声)
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 --"
钱的额度也很重要, 10美元还不错, 20美元就更好了。 但也许更重要的一点是, 他们发现这种奖励必须及时, 不能延迟发放。 研究人员甚至 拿出20美元对学生们说: “摸摸它,感受它,再闻闻它——
(Sniffing)
(闻一下)
"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?
这都是你的。 但如果你失败,我就得把它拿回来。” 这样做的效果非常好。 我立刻意识到将这项研究 应用到我们的项目上是可行的, 我对此十分兴奋。 但一旦冷静下来, 我的脑海里冒出了几个问题。 第一, 这符合伦理道德么?
(Laughter)
(笑声)
Secondly, how would we fund this thing?
第二,我们如何筹措资金?
(Laughter)
(笑声)
And finally, would the results be sustained if the students were no longer paid?
第三, 如果以后停止给学生金钱奖励, 这种效果还会持续么?
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!
我们先来看看伦理问题, 我算是一个数学方面的 纯粹主义者。 我就是那种认为应该为了数学 而学习数学的人。 要记住, 是为了乐趣、美好 真理、正义和热爱而学习数学。 不是为了钱!
(Laughter)
(笑声)
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.
在内心挣扎的同时,我意识到 我现在这样看待数学 是因为学习了足够长的时间, 能够欣赏它的魅力。 但对学数学很痛苦的学生来说, 你难以诱导他们, 努力学习终将有所回报。 这种诱导在这里行不通, 我满可以告诉学生们 做金融衍生品交易员有高额奖金, 这就是学好数学的回报。 但这种回报要等很久才能实现。 因此,这种鼓励几乎没什么作用。 行为经济学家称之为“双曲贴现” (相比后期大回报,更看重眼前的小酬劳)。 莱维特甚至说, 当延迟发放奖励时, 一切激励作用都会消失。 因此,从一个纯粹的 经济视角来看: 如果不给予及时的奖励, 就等于没有对学生的成绩 进行足够的奖励。 我认真思考了这个问题, 发现不论经济奖励的提供者 是政府、雇主还是家庭, 我们其实早就习惯了它的存在。
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.
打个比方 , 很多孩子会帮忙做家务, 家长会因此奖励给孩子零花钱。 因此,用钱激励学生 也并没有太大争议性。 想到这儿, 我开始思考第二个问题, 即我们如何提供资金支持? 父母自然是 孩子教育的最大投资方。 于是我们开始按周收取 软件使用费, 但是—— 如果学生达成了每周数学目标, 我们会把这笔费用 退回到他自己的银行账户。 我们设置了三个练习, 如果能在一周之内完成, 就可得到10美元奖励。 我们奖励学生们付出的努力, 而不是他们的成绩, 这段时间比较短, 奖励也足够大, 能够引起学生的重视。
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."
我还记得,当我最初 把这个新商业模式告诉妻子时, 如果之前她还不确定我是否疯了, 我的这种想法就能 让她确定我真的疯了。 她说:"穆... 你意识到没有,要是每个孩子 都如你所愿,完成作业, 你可就一分钱都赚不到啦。 这真是厉害的商业模式啊。“
(Laughter)
(笑声)
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.
我认为这更像是个反商业模式, 使用就免费,不使用则付费。 根据以往经验, 我知道在这个国家, 不是每个人都能斗志昂扬 每周做数学作业。 如果真是如此 , 我们很快就破产了, 但是这样一来,数学能力 不足的问题不就解决了吗?
(Laughter)
(笑声)
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.
作为一家公司 , 我们总会有一条双重底线, 既要给投资商回报, 也要提高学生成绩。 我们清楚,如果要长期盈利, 就要提高学生们的成绩。 我们的双重目标就不会相悖。 正因为如此, 我们一直都努力 让我们的产品决策 能够帮助学生达成每周数学目标, 确保他们能够拿到钱, 而不管我们是否盈利。
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.
你可能会问,这个疯狂的 商业模式如何运作? 令人高兴的是我们仍在运营。 在过去的五个月, 在我们将其推广到学校之前, 我们针对澳大利亚的 个人使用者进行了试验。 以下是初期结果。 绿色代表完成每周数学任务的学生, 红色代表没有完成的学生。 可以看出完成作业的人数 远高于未完成的人数。 事实上,随着我们的用户增多, 我们发现完成的人数比例 稳定在大约75% 。 平均来看, 我们每四周就会收到一次使用费, 而在其他三周发放奖励给学生。 当然,我们已经赚了一些钱, 但你可能想不到, 与没有奖金回报的学生相比, 获得奖金的学生 参与度高出了70%。 目标达成!
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.
从商业视角来看, 这些学生用户很稳定, 也更倾向于把应用推荐给朋友, 我们希望通过 给单个用户更低的奖赏来 换取更大、参与度更高的用户群。 这两项都已经完成。
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.
现在,还有最后一个问题。 如果不再付钱给学生, 他们还会继续使用这个应用么? 数学绝不仅仅是 在学校学习的一个科目。 它是人类的事业。 它帮助我们了解周围的世界。 当你了解的越多 , 你就会更加希望深入这个领域。 因此,问题的答案是肯定的, 学生们的兴趣已经 被奖励激发出来了。 而长远来看, 钱不再是问题, 因为从长远来看, 数学的奇妙就是最好的激励, 而理解了数学, 就是最好的回报。
Thank you.
谢谢。
(Applause)
(掌声)