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.
Otkad znam za sebe, volim matematiku. U stvari, to nije baš 100 posto tačno. Voleo sam matematiku sve vreme osim neke dve nedelje u četvrtom srednje.
(Laughter)
(Smeh)
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."
Bio sam najbolji u razredu kada je trebalo da počnemo da učimo naprednu matematiku. Bio sam veoma uzbuđen zbog ove potpuno nove oblasti - kompleksnih brojeva. Ja volim složene stvari. Profesorka nas je pripremala za ovaj koncept postavljajući pitanja o kvadratnim korenovima. Koren iz 9 - tri; koren iz 256 - šesnaest. Prelako. Onda je postavila trik pitanje: koliko bi iznosio koren iz -1? Naravno, svi smo uzviknuli: „Dajte, profesorice! Svi znamo da ne možete izvući koren iz negativnog broja.” „To je tačno u stvarnom svetu”, kazala je. „Ali, u kompleksnom svetu, kvadratni koren broja -1 je imaginarni broj i.”
(Laughter)
(Smeh)
That day, my entire mathematical world came crashing down on me.
Tog dana, moj ceo matematički svet se sručio na mene.
(Laughter)
(Smeh)
"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."
„Imaginarni brojevi? Zaista? Ali matematika je izvor istine; nemojte mi pričati o apstraktnosti, molim vas. Studirao bih umetnost da sam želeo da se igram imaginarnim brojevima.”
(Laughter)
(Smeh)
"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,
„Ovo je produbljena matematika, vratimo se na prethodnu.” Nije se vratila, te sam sledećih par nedelja preko volje vršio besmislene proračune,
(Laughter)
(Smeh)
finding imaginary solutions to quadratic equations.
tražeći imaginarna rešenja kvadratnih jednačina.
(Laughter)
(Smeh)
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.
Ali, onda se nešto neverovatno desilo. Počeli smo da nalazimo elegantna rešenja problema iz stvarnog života za koja pre toga nismo imali rešenja, a koja su počinjala kompleksnim svetom imaginarnih brojeva. Neki matematičar se pre 500 godina odlučio da se zabavi, te je izmislio ove imaginarne brojeve i zbog toga možemo da izvodimo ove neverovatne transformacije koje imaju primenu u stvarnom svetu, kao, na primer, u polju elektroinžinjerstva. Strava! Počeo sam da se divim matematici na potpuno drugačijem nivou. Nakon svog kratkog nepoverenja, bio sam zaljubljen u ovaj predmet više nego ikada do tad.
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.
Frensis Su, matematičar, je to najlepše sumirao kada je rekao: „Učimo matematiku iz zabave, zbog lepote, radi istine, zbog pravde i iz ljubavi.” Ali, ako biste pitali današnje učenike, verovatno biste čuli drugačiji odgovor. Čuli biste možda reči „teško” i „dosadno”. Možda i jesu u pravu da je teško. Ali definitivno nije dosadno. Rekao bih da je baš činjenica da je teško savladiva ono što je čini prelepom. Jer ništa što zaista vredi nije lako raditi.
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.
Nama treba da okupiramo učenike dovoljno dugo da prođu teške delove kako bi cenili lepotu kada se sve poveže. Otprilike kao što sam i ja radio tih par nedelja u srednjoj školi. Nažalost, u našem školskom sistemu svi učenici zajedno uče matematiku. Stoga, oni koji malo zaostanu pronalaze da je skoro nemoguće da ikada ponovo sve pohvataju i cene tu lepotu.
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.
Zbog čega je ovo problem? Zašto bismo brinuli o tome? Danas više nego ikada pre, našem svetu je potrebno da svaki građanin bude vešt u matematici. Sa dolaskom veštačke inteligencije i automatizacije, veliki broj poslova koji postoje danas će ili nestati ili biti transformisani tako da zahtevaju manje rutinskog posla, a više analiziranja i primena veština. Ali, mi ne proizvodimo dodatne učenike matematike koji će ispuniti ove uloge.
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.
Ovaj grafikon prikazuje broj učenika koji pohađaju običnu matematiku i naprednu matematiku u periodu od preko 20 godina u Australiji. Jasno je da, dok potražnja za matematičkim veštinama ubrzano raste, ponuda je u stalnom opadanju. Kako bismo to sagledali, polovina učenika koji završavaju srednju školu danas u Australiji nisu spremni da razumeju nijedan argument vezan za stopu promena u podacima. U ovom digitalnom dobu, gde lažne veste mogu uticati na rezultate izbora, ovo je veoma zabrinjavajuće.
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.
Daću vam konkretan primer. Hajde da bolje proučimo ovaj grafikon. Da li svi vidite šta sam uradio kako bih naglasio svoju poentu? Ako ne vidite, dozvolite da vam to sada pokažem, na vertikalnoj osi sa početkom na nuli, gde i treba da bude. Eto, vidite sad? To je identičan podatak, ali sam izmanipulisao prikaz kako bih uticao na vas. I to je sjajno. To je moj posao ovde.
(Laughter)
(Smeh)
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?
Ali, sada ozbiljno, ukoliko ne uradimo nešto kako bismo drastično poboljšali zanimanje učenika za matematiku, ne samo da ćemo imati veliku krizu manjka veština, već i nestalnu populaciju kojom lako manipuliše onaj ko dobije najviše prostora u medijima. Dakle, šta je rešenje?
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.
Postoji mnogo stvari koje treba da uradimo. Treba nam reforma nastavnog plana. Treba da ohrabrimo naše najbolje i najpametnije da postanu učitelji. Treba da ukinemo testove od kojih mnogo stvari zavisi i umesto njih uvedemo orijentacione testove znanja. Ali sve ove stvari zahtevaju vreme. A ja sam nestrpljiv.
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.
Razmišljam o ovome već osam godina. Otkako sam napustio posao trgovca zalihama kako bih izgradio aplikaciju kojom bih pomogao učenicima oko matematike. Danas se ona koristi u školama širom sveta i vidimo veliki napredak kod učenika koji koriste program redovno. Međutim, evo u čemu je stvar - primećujemo ga samo kod učenika koji program koriste redovno. A to nije slučaj sa većinom njih. Nakon godina razvoja i prerade aplikacije, naš najveći izazov nije bio toliko vezan za proizvod. Naš najveći izazov bio je motivisanje učenika da žele da popune rupe u svom znanju i razumevanju. Možete zamisliti koliko je teško sa današnjom ekonomijom pažnje, kada se takmičimo protiv Fejsbuka, Snepčeta i Plejstejšna, izboriti se za vreme učenika.
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.
Stoga smo se vratili na početak i počeli da razmišljamo o tome kako da ga učinimo vrednijim za učenike da bismo ih naveli da potroše malo od postojeće pažnje na svoje obrazovanje. Razmatrali smo da uvedemo elemente igre kao što su bodovi, značke i avatari, nakon čega bismo videli kratkotrajni skok u uključenju, ali čim bi ta novina izbledela, stvari bi se vratile u normalu.
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.
Onda je jednog dana moj suosnivač, Alvin, naišao na grupu studenata u Čikagu koju je vodio bihejvioralni ekonomista, Stiven Levit, u kojoj su plaćali studentima koji su poboljšali svoje ocene. Počeo je da mi priča o nekim stvarima koje su testirali, kao i novim interesantnim otkrićima. Na primer, otkrili su da je motivisanje studenata zbog njihovog ulaganja, kao što je trud, funkcionisalo mnogo bolje od motivisanja, kada je reč o učinku, kao što su ocene sa testova. Otkrili su da su mlađe studente mogli da stimulišu trofejima, ali za starije studente trebao vam je novac.
(Laughter)
(Smeh)
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 --"
Čak je i količina novca značila - 10 dolara je bilo dobro, 20 dolara - još bolje. Ali, možda je ono najbitnije da su otkrili da nagrade moraju da budu momentalne umesto da se daju naknadno. Otišli su toliko daleko da su dali studentima 20 dolara i rekli: „Dodirnite ih, osetite ih, pomirišite ih -”
(Sniffing)
(Njušenje)
"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?
„Sve je vaše. Ali, ukoliko padnete, uzimam ih nazad.” I to je uspevalo prilično dobro. Momentalno sam se uzbudio pri pomisli na mogućnost uključivanja ovog načina u naš program. Ali, kada se uzbuđenje stišalo, par briga nam se prišunjalo. Prvo, da li je ovo etično?
(Laughter)
(Smeh)
Secondly, how would we fund this thing?
Drugo, kako ćemo ovo finansirati?
(Laughter)
(Smeh)
And finally, would the results be sustained if the students were no longer paid?
I, naposletku, da li bi se rezultati održali ukoliko bismo prestali plaćati učenicima?
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!
Hajde prvo da se pozabavimo etičkim delom. Ja sam pomalo matematički čistunac. Stoga bih bio jedan od prvih koji bi rekli kako treba da učimo matematiku zbog nje same. Sećate se - iz zabave, zbog lepote, istine, pravičnosti i iz ljubavi! Ne zbog novca!
(Laughter)
(Smeh)
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.
Dok sam se mučio sa ovim, shvatio sam da je jedini razlog zbog kog ovako vidim matematiku to što sam je dovoljno dugo učio kako bih je cenio. Veoma je teško reći učeniku koji se danas muči sa matematikom da vredno radi jer će se trud isplatiti u dalekoj budućnosti. Ni podmićivanje nije toliko uspešno ovde, zato što bih ih mogao podmititi pričajući im o velikim bonusima koje sam dobijao dok sam radio sa finansijama kao nagradu za dobro znanje matematike. Ali se ne isplati veoma dugo. Stoga je praktično bezvredno. Bihejvioralni ekonomisti ovo nazivaju hiperboličkim diskontovanjem. Levit ide toliko daleko da kaže da sva motivaciona moć nestaje kada se nagrade dele sa zakašnjenjem. Stoga, sa čisto ekonomske tačke gledišta: ukoliko ne koristimo momentalne podsticaje, ne uspevamo da uložimo dovoljno u krajnji ishod. To me je ohrabrilo jer, kada posmatramo društvo, vidimo da smo prilično naviknuti na finansijske podsticaje. Bilo od strane vlade, poslodavca ili kod kuće.
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.
Na primer, mnogi roditelji bi dali svojoj deci džeparac u zamenu za kućne poslove. Stoga ovo nije baš toliko kontroverzno. Dok sam razmišljao o tome, počeo je da mi se javlja odgovor na pitanje kako ćemo to finansirati. Prirodno, roditelji su najviše uključeni u obrazovanje svoje dece. Stoga, zašto im ne bismo uveli nedeljnu pretplatu kako bi koristili naš program, ali - ukoliko učenici ispune svoj nedeljni cilj u matematici, mi ćemo refundirati taj iznos direktno na bankovni račun deteta. Izabrali smo cilj od tri zadatka nedeljno nakon kojih će dobiti nagradu od 10 dolara. Na taj način više podstičemo trud nego učinak u dovoljno kratkom periodu i sa dovoljnom isplatom kako bi učenicima stalo do toga.
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."
Sećam se kada sam prvi put ispričao svojoj ženi o ovom novom načinu poslovanja. Ukoliko je imalo sumnjala da sam skrenuo sa uma, ovo je bila dovoljna potvrda za nju. Kazala mi je: „Mo, shvataš da ukoliko svi budu radili domaći, što je upravo ono što ti želiš, nećeš imati nikakve zarade, što je ono što ne želiš. Sjajan primer poslovanja.”
(Laughter)
(Smeh)
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.
Rekao bih da je više suprotno od poslovnog modela. Ako ga koristiš, besplatan je, ali plaćaš ako ga ne koristiš. Iz iskustva sam znao da neće svi u državi da se upecaju i rade svoj domaći iz matematike. Kada bi to radili, doživeli bismo neuspeh prilično brzo ali, hej, rešili bismo matematičku krizu u državi.
(Laughter)
(Smeh)
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.
Kao kompanija uvek izračunamo profit i uticaj na društvo, pokušavajući da vratimo investitorima, kao i da unapredimo rezultate učenika. Znamo da je put ka našoj dugoročnoj profitabilnosti povezan sa poboljšanjem rezultata učenika. Stoga ta dva cilja ne bi trebalo suprotstavljati. Uvek pokušavamo da donesemo odluke vezane za proizvod koje pomažu učenicima da postignu svoj nedeljni cilj u matematici, čime ćemo efikasno osigurati da oni budu plaćeni, a ne mi.
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.
Verovatno se pitate kako ovaj nenormalni poslovni sistem funkcioniše. Biće vam drago da čujete da i dalje radimo. Proteklih pet meseci ovo sprovodimo na našim privatnim korisnicima u Australiji pre nego što počnemo da ga puštamo u škole. I evo ranih rezultata. Zeleno predstavlja učenike koji su ispunili svoj nedeljni cilj iz matematike, a crveno one koji nisu. Vidite da ima mnogo više onih koji su uradili domaći od onih koji nisu. U stvari, uz porast naše korisničke baze, otkrili smo da je procenat prilično stabilan, oko 75 posto. Dakle, u proseku, mi primimo našu nedeljnu naknadu za pretplatu jednom u svake četiri nedelje, a tokom ostale tri nedelje nagrađujemo učenike. Naravno da jedan deo novca ostavljamo i nama, ali znate šta? Ispostavlja se da su ovi učenici oko 70 procenata više angažovani od onih koji nisu korisnici programa. Odrađeno.
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.
Sa poslovne tačke gledišta, manja je verovatnoća da će se predomisliti, a veća da će nas preporučiti prijateljima. Stoga se nadamo da ćemo izbalansirati manju zaradu po korisniku sa većom i angažovanijom korisničkom bazom. Odrađeno i odrađeno.
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.
Sada, poslednje pitanje. Da li bi nastavili da ga koriste ukoliko im se više ne bi plaćalo? Matematika je mnogo više od predmeta koji učite u školi. Ona je ljudski trud. Ono što nam pomaže da razumemo svet oko nas. I što više znate, više želite da saznate. Stoga da, pokrenuli smo početno angažovanje sa novčanom nagradom. Ali, na duge staze, novac više neće biti važan. Jer na duge staze, matematička čuda će biti podsticaj, a njihovo razumevanje će biti nagrada.
Thank you.
Hvala.
(Applause)
(Aplauz)