Recent Comments
Urvi Shah on Burp www.feinakhabiby.com on Building on the Bayou justin medved on Math Games Day Candice Foulk on There is nothing to fear but f… fremtulla on There is nothing to fear but f…
Category Archives: TED talk
I have the answer to a question that we’ve all asked. The question is, Why is it that the letter X represents the unknown? Now I know we learned that in math class, but now it’s everywhere in the culture — The X prize, the X-Files, Project X, TEDx. Where’d that come from?
About six years ago I decided that I would learn Arabic, which turns out to be a supremely logical language. To write a word or a phrase or a sentence in Arabic is like crafting an equation, because every part is extremely precise and carries a lot of information. That’s one of the reasons so much of what we’ve come to think of as Western science and mathematics and engineering was really worked out in the first few centuries of the Common Era by the Persians and the Arabs and the Turks.
This includes the little system in Arabic called al-jebra. And al-jebr roughly translates to “the system for reconciling disparate parts.” Al-jebr finally came into English as algebra. One example among many.
The Arabic texts containing this mathematical wisdom finally made their way to Europe — which is to say Spain — in the 11th and 12th centuries. And when they arrived there was tremendous interest in translating this wisdom into a European language.
But there were problems. One problem is there are some sounds in Arabic that just don’t make it through a European voice box without lots of practice. Trust me on that one. Also, those very sounds tend not to be represented by the characters that are available in European languages.
Here’s one of the culprits. This is the letter SHeen, and it makes the sound we think of as SH — “sh.” It’s also the very first letter of the word shalan, which means “something” just like the the English word “something” — some undefined, unknown thing.
Now in Arabic, we can make this definite by adding the definite article “al.” So this is al-shalan — the unknown thing. And this is a word that appears throughout early mathematics, such as this 10th century derivation of proofs.
The problem for the Medieval Spanish scholars who were tasked with translating this material is that the letter SHeen and the word shalan can’t be rendered into Spanish because Spanish doesn’t have that SH, that “sh” sound. So by convention, they created a rule in which they borrowed the CK sound, “ck” sound, from the classical Greek in the form of the letter Kai.
Later when this material was translated into a common European language, which is to say Latin, they simply replaced the Greek Kai with the Latin X. And once that happened, once this material was in Latin, it formed the basis for mathematics textbooks for almost 600 years.
But now we have the answer to our question. Why is it that X is the unknown? X is the unknown because you can’t say “sh” in Spanish. (Laughter) And I thought that was worth sharing.
(Applause)
Thanks to Mr. Eaton for sharing this!
I have been teaching for a long time, and in doing so have acquired a body of knowledge about kids and learning that I really wish more people would understand about the potential of students. In 1931, my grandmother — bottom left for you guys over here — graduated from the eighth grade. She went to school to get the information because that’s where the information lived. It was in the books; it was inside the teacher’s head; and she needed to go there to get the information, because that’s how you learned. Fast-forward a generation: this is the one-room schoolhouse, Oak Grove, where my father went to a one-room schoolhouse. And he again had to travel to the school to get the information from the teacher, stored it in the only portable memory he has, which is inside his own head, and take it with him, because that is how information was being transported from teacher to student and then used in the world. When I was a kid, we had a set of encyclopedias at my house. It was purchased the year I was born, and it was extraordinary, because I did not have to wait to go to the library to get to the information. The information was inside my house and it was awesome. This was different than either generation had experienced before, and it changed the way I interacted with information even at just a small level. But the information was closer to me. I could get access to it.
In the time that passes between when I was a kid in high school and when I started teaching, we really see the advent of the Internet. Right about the time that the Internet gets going as an educational tool, I take off from Wisconsin and move to Kansas, small town Kansas, where I had an opportunity to teach in a lovely, small-town, rural Kansas school district, where I was teaching my favorite subject, American government. My first year — super gung-ho — going to teach American government, loved the political system. Kids in the 12th grade: not exactly all that enthusiastic about the American government system. Year two: learned a few things — had to change my tactic. And I put in front of them an authentic experience that allowed them to learn for themselves. I didn’t tell them what to do or how to do it. I posed a problem in front of them, which was to put on an election forum for their own community.
They produced fliers. They called offices. They checked schedules. They were meeting with secretaries. They produced an election forum booklet for the entire town to learn more about their candidates. They invited everyone into the school for an evening of conversation about government and politics and whether or not the streets were done well, and really had this robust experiential learning. The older teachers — more experienced — looked at me and went, “Oh, there she is. That’s so cute. She’s trying to get that done.” (Laughter) “She doesn’t know what she’s in for.” But I knew that the kids would show up, and I believed it, and I told them every week what I expected out of them. And that night, all 90 kids — dressed appropriately, doing their job, owning it. I had to just sit and watch. It was theirs. It was experiential. It was authentic. It meant something to them. And they will step up.
From Kansas, I moved on to lovely Arizona, where I taught in Flagstaff for a number of years, this time with middle school students. Luckily, I didn’t have to teach them American government. Could teach them the more exciting topic of geography. Again, “thrilled” to learn. But what was interesting about this position I found myself in in Arizona, was I had this really extraordinarily eclectic group of kids to work with in a truly public school, and we got to have these moments where we would get these opportunities. And one opportunity was we got to go and meet Paul Rusesabagina, which is the gentleman that the movie “Hotel Rwanda” is based after. And he was going to speak at the high school next door to us. We could walk there. We didn’t even have to pay for the buses. There was no expense cost. Perfect field trip.
The problem then becomes how do you take seventh- and eighth-graders to a talk about genocide and deal with the subject in a way that is responsible and respectful, and they know what to do with it. And so we chose to look at Paul Rusesabagina as an example of a gentleman who singularly used his life to do something positive. I then challenged the kids to identify someone in their own life, or in their own story, or in their own world, that they could identify that had done a similar thing. I asked them to produce a little movie about it. It’s the first time we’d done this. Nobody really knew how to make these little movies on the computer, but they were into it. And I asked them to put their own voice over it. It was the most awesome moment of revelation that when you ask kids to use their own voice and ask them to speak for themselves, what they’re willing to share. The last question of the assignment is: how do you plan to use your life to positively impact other people? The things that kids will say when you ask them and take the time to listen is extraordinary.
Fast-forward to Pennsylvania, where I find myself today. I teach at the Science Leadership Academy, which is a partnership school between the Franklin Institute and the school district of Philadelphia. We are a nine through 12 public school, but we do school quite differently. I moved there primarily to be part of a learning environment that validated the way that I knew that kids learned, and that really wanted to investigate what was possible when you are willing to let go of some of the paradigms of the past, of information scarcity when my grandmother was in school and when my father was in school and even when I was in school, and to a moment when we have information surplus. So what do you do when the information is all around you? Why do you have kids come to school if they no longer have to come there to get the information?
In Philadelphia we have a one-to-one laptop program, so the kids are bringing in laptops with them everyday, taking them home, getting access to information. And here’s the thing that you need to get comfortable with when you’ve given the tool to acquire information to students, is that you have to be comfortable with this idea of allowing kids to fail as part of the learning process. We deal right now in the educational landscape with an infatuation with the culture of one right answer that can be properly bubbled on the average multiple choice test, and I am here to share with you: it is not learning. That is the absolute wrong thing to ask, to tell kids to never be wrong. To ask them to always have the right answer doesn’t allow them to learn. So we did this project, and this is one of the artifacts of the project. I almost never show them off because of the issue of the idea of failure.
My students produced these info-graphics as a result of a unit that we decided to do at the end of the year responding to the oil spill. I asked them to take the examples that we were seeing of the info-graphics that existed in a lot of mass media, and take a look at what were the interesting components of it, and produce one for themselves of a different man-made disaster from American history. And they had certain criteria to do it. They were a little uncomfortable with it, because we’d never done this before, and they didn’t know exactly how to do it. They can talk — they’re very smooth, and they can write very, very well, but asking them to communicate ideas in a different way was a little uncomfortable for them. But I gave them the room to just do the thing. Go create. Go figure it out. Let’s see what we can do. And the student that persistently turns out the best visual product did not disappoint. This was done in like two or three days. And this is the work of the student that consistently did it.
And when I sat the students down, I said, “Who’s got the best one?” And they immediately went, “There it is.” Didn’t read anything. “There it is.” And I said, “Well what makes it great?” And they’re like, “Oh, the design’s good, and he’s using good color. And there’s some … ” And they went through all that we processed out loud. And I said, “Go read it.” And they’re like, “Oh, that one wasn’t so awesome.” And then we went to another one — it didn’t have great visuals, but it had great information — and spent an hour talking about the learning process, because it wasn’t about whether or not it was perfect, or whether or not it was what I could create. It asked them to create for themselves, and it allowed them to fail, process, learn from. And when we do another round of this in my class this year, they will do better this time, because learning has to include an amount of failure, because failure is instructional in the process.
There are a million pictures that I could click through here, and had to choose carefully — this is one of my favorites — of students learning, of what learning can look like in a landscape where we let go of the idea that kids have to come to school to get the information, but instead, ask them what they can do with it. Ask them really interesting questions. They will not disappoint. Ask them to go to places, to see things for themselves, to actually experience the learning, to play, to inquire. This is one of my favorite photos, because this was taken on Tuesday, when I asked the students to go to the polls. This is Robbie, and this was his first day of voting, and he wanted to share that with everybody and do that. But this is learning too, because we asked them to go out into real spaces.
The main point is that, if we continue to look at education as if it’s about coming to school to get the information and not about experiential learning, empowering student voice and embracing failure, we’re missing the mark. And everything that everybody is talking about today isn’t possible if we keep having an educational system that does not value these qualities, because we won’t get there with a standardized test, and we won’t get there with a culture of one right answer. We know how to do this better, and it’s time to do better.
(Applause)
We’ve got a real problem with math education right now. Basically, no one’s very happy. Those learning it think it’s disconnected, uninteresting and hard. Those trying to employ them think they don’t know enough. Governments realize that it’s a big deal for our economies, but don’t know how to fix it. And teachers are also frustrated. Yet math is more important to the world than at any point in human history. So at one end we’ve got falling interest in education in math, and at the other end we’ve got a more mathematical world, a more quantitative world than we ever have had.
So what’s the problem, why has this chasm opened up, and what can we do to fix it? Well actually, I think the answer is staring us right in the face: Use computers. I believe that correctly using computers is the silver bullet for making math education work. So to explain that, let me first talk a bit about what math looks like in the real world and what it looks like in education. See, in the real world math isn’t necessarily done by mathematicians. It’s done by geologists, engineers, biologists, all sorts of different people — modeling and simulation. It’s actually very popular. But in education it looks very different — dumbed-down problems, lots of calculating, mostly by hand. Lots of things that seem simple and not difficult like in the real world, except if you’re learning it. And another thing about math: math sometimes looks like math — like in this example here — and sometimes it doesn’t — like “Am I drunk?” And then you get an answer that’s quantitative in the modern world. You wouldn’t have expected that a few years back. But now you can find out all about — unfortunately, my weight is a little higher than that, but — all about what happens.
So let’s zoom out a bit and ask, why are we teaching people math? What’s the point of teaching people math? And in particular, why are we teaching them math in general? Why is it such an important part of education as a sort of compulsory subject? Well, I think there are about three reasons: technical jobs so critical to the development of our economies, what I call “everyday living” — to function in the world today, you’ve got to be pretty quantitative, much more so than a few years ago: figure out your mortgages, being skeptical of government statistics, those kinds of things — and thirdly, what I would call something like logical mind training, logical thinking. Over the years we’ve put so much in society into being able to process and think logically. It’s part of human society. It’s very important to learn that math is a great way to do that.
So let’s ask another question. What is math? What do we mean when we say we’re doing math, or educating people to do math? Well, I think it’s about four steps, roughly speaking, starting with posing the right question. What is it that we want to ask? What is it we’re trying to find out here? And this is the thing most screwed up in the outside world, beyond virtually any other part of doing math. People ask the wrong question, and surprisingly enough, they get the wrong answer, for that reason, if not for others. So the next thing is take that problem and turn it from a real world problem into a math problem. That’s stage two. Once you’ve done that, then there’s the computation step. Turn it from that into some answer in a mathematical form. And of course, math is very powerful at doing that. And then finally, turn it back to the real world. Did it answer the question? And also verify it — crucial step. Now here’s the crazy thing right now. In math education, we’re spending about perhaps 80 percent of the time teaching people to do step three by hand. Yet, that’s the one step computers can do better than any human after years of practice. Instead, we ought to be using computers to do step three and using the students to spend much more effort on learning how to do steps one, two and four — conceptualizing problems, applying them, getting the teacher to run them through how to do that.
See, crucial point here: math is not equal to calculating. Math is a much broader subject than calculating. Now it’s understandable that this has all got intertwined over hundreds of years. There was only one way to do calculating and that was by hand. But in the last few decades that has totally changed. We’ve had the biggest transformation of any ancient subject that I could ever imagine with computers. Calculating was typically the limiting step, and now often it isn’t. So I think in terms of the fact that math has been liberated from calculating. But that math liberation didn’t get into education yet. See, I think of calculating, in a sense, as the machinery of math. It’s the chore. It’s the thing you’d like to avoid if you can, like to get a machine to do. It’s a means to an end, not an end in itself, and automation allows us to have that machinery. Computers allow us to do that — and this is not a small problem by any means. I estimated that, just today, across the world, we spent about 106 average world lifetimes teaching people how to calculate by hand. That’s an amazing amount of human endeavor. So we better be damn sure — and by the way, they didn’t even have fun doing it, most of them — so we better be damn sure that we know why we’re doing that and it has a real purpose.
I think we should be assuming computers for doing the calculating and only doing hand calculations where it really makes sense to teach people that. And I think there are some cases. For example: mental arithmetic. I still do a lot of that, mainly for estimating. People say, “Is such and such true?” And I’ll say, “Hmm, not sure.” I’ll think about it roughly. It’s still quicker to do that and more practical. So I think practicality is one case where it’s worth teaching people by hand. And then there are certain conceptual things that can also benefit from hand calculating, but I think they’re relatively small in number. One thing I often ask about is ancient Greek and how this relates. See, the thing we’re doing right now is we’re forcing people to learn mathematics. It’s a major subject. I’m not for one minute suggesting that, if people are interested in hand calculating or in following their own interests in any subject however bizarre — they should do that. That’s absolutely the right thing, for people to follow their self-interest. I was somewhat interested in ancient Greek, but I don’t think that we should force the entire population to learn a subject like ancient Greek. I don’t think it’s warranted. So I have this distinction between what we’re making people do and the subject that’s sort of mainstream and the subject that, in a sense, people might follow with their own interest and perhaps even be spiked into doing that.
So what are the issues people bring up with this? Well one of them is, they say, you need to get the basics first. You shouldn’t use the machine until you get the basics of the subject. So my usual question is, what do you mean by “basics?” Basics of what? Are the basics of driving a car learning how to service it, or design it for that matter? Are the basics of writing learning how to sharpen a quill? I don’t think so. I think you need to separate the basics of what you’re trying to do from how it gets done and the machinery of how it gets done and automation allows you to make that separation. A hundred years ago, it’s certainly true that to drive a car you kind of needed to know a lot about the mechanics of the car and how the ignition timing worked and all sorts of things. But automation in cars allowed that to separate, so driving is now a quite separate subject, so to speak, from engineering of the car or learning how to service it. So automation allows this separation and also allows — in the case of driving, and I believe also in the future case of maths — a democratized way of doing that. It can be spread across a much larger number of people who can really work with that.
So there’s another thing that comes up with basics. People confuse, in my view, the order of the invention of the tools with the order in which they should use them for teaching. So just because paper was invented before computers, it doesn’t necessarily mean you get more to the basics of the subject by using paper instead of a computer to teach mathematics. My daughter gave me a rather nice anecdote on this. She enjoys making what she calls “paper laptops.” (Laughter) So I asked her one day, “You know, when I was your age, I didn’t make these. Why do you think that was?” And after a second or two, carefully reflecting, she said, “No paper?” (Laughter) If you were born after computers and paper, it doesn’t really matter which order you’re taught with them in, you just want to have the best tool.
So another one that comes up is “Computers dumb math down.” That somehow, if you use a computer, it’s all mindless button-pushing, but if you do it by hand, it’s all intellectual. This one kind of annoys me, I must say. Do we really believe that the math that most people are doing in school practically today is more than applying procedures to problems they don’t really understand, for reasons they don’t get? I don’t think so. And what’s worse, what they’re learning there isn’t even practically useful anymore. Might have been 50 years ago, but it isn’t anymore. When they’re out of education, they do it on a computer. Just to be clear, I think computers can really help with this problem, actually make it more conceptual. Now, of course, like any great tool, they can be used completely mindlessly, like turning everything into a multimedia show, like the example I was shown of solving an equation by hand, where the computer was the teacher — show the student how to manipulate and solve it by hand. This is just nuts. Why are we using computers to show a student how to solve a problem by hand that the computer should be doing anyway? All backwards.
Let me show you that you can also make problems harder to calculate. See, normally in school, you do things like solve quadratic equations. But you see, when you’re using a computer, you can just substitute. You can make it a quartic equation. Make it kind of harder, calculating-wise. Same principles applied — calculations, harder. And problems in the real world look nutty and horrible like this. They’ve got hair all over them. They’re not just simple, dumbed-down things that we see in school math. And think of the outside world. Do we really believe that engineering and biology and all of these other things that have so benefited from computers and maths have somehow conceptually gotten reduced by using computers? I don’t think so — quite the opposite. So the problem we’ve really got in math education is not that computers might dumb it down, but that we have dumbed-down problems right now. Well, another issue people bring up is somehow that hand calculating procedures teach understanding. So if you go through lots of examples, you can get the answer, you can understand how the basics of the system work better. I think there is one thing that I think very valid here, which is that I think understanding procedures and processes is important. But there’s a fantastic way to do that in the modern world. It’s called programming.
Programming is how most procedures and processes get written down these days, and it’s also a great way to engage students much more and to check they really understand. If you really want to check you understand math then write a program to do it. So programming is the way I think we should be doing that. So to be clear, what I really am suggesting here is we have a unique opportunity to make maths both more practical and more conceptual, simultaneously. I can’t think of any other subject where that’s recently been possible. It’s usually some kind of choice between the vocational and the intellectual. But I think we can do both at the same time here. And we open up so many more possibilities. You can do so many more problems. What I really think we gain from this is students getting intuition and experience in far greater quantities than they’ve ever got before. And experience of harder problems — being able to play with the math, interact with it, feel it. We want people who can feel the math instinctively. That’s what computers allow us to do.
Another thing it allows us to do is reorder the curriculum. Traditionally it’s been by how difficult it is to calculate, but now we can reorder it by how difficult it is to understand the concepts, however hard the calculating. So calculus has traditionally been taught very late. Why is this? Well, it’s damn hard doing the calculations, that’s the problem. But actually many of the concepts are amenable to a much younger age group. This was an example I built for my daughter. And very, very simple. We were talking about what happens when you increase the number of sides of a polygon to a very large number. And of course, it turns into a circle. And by the way, she was also very insistent on being able to change the color, an important feature for this demonstration. You can see that this is a very early step into limits and differential calculus and what happens when you take things to an extreme — and very small sides and a very large number of sides. Very simple example. That’s a view of the world that we don’t usually give people for many, many years after this. And yet, that’s a really important practical view of the world. So one of the roadblocks we have in moving this agenda forward is exams. In the end, if we test everyone by hand in exams, it’s kind of hard to get the curricula changed to a point where they can use computers during the semesters.
And one of the reasons it’s so important — so it’s very important to get computers in exams. And then we can ask questions, real questions, questions like, what’s the best life insurance policy to get? — real questions that people have in their everyday lives. And you see, this isn’t some dumbed-down model here. This is an actual model where we can be asked to optimize what happens. How many years of protection do I need? What does that do to the payments and to the interest rates and so forth? Now I’m not for one minute suggesting it’s the only kind of question that should be asked in exams, but I think it’s a very important type that right now just gets completely ignored and is critical for people’s real understanding.
So I believe [there is] critical reform we have to do in computer-based math. We have got to make sure that we can move our economies forward, and also our societies, based on the idea that people can really feel mathematics. This isn’t some optional extra. And the country that does this first will, in my view, leapfrog others in achieving a new economy even, an improved economy, an improved outlook. In fact, I even talk about us moving from what we often call now the “knowledge economy” to what we might call a “computational knowledge economy,” where high-level math is integral to what everyone does in the way that knowledge currently is. We can engage so many more students with this, and they can have a better time doing it. And let’s understand: this is not an incremental sort of change. We’re trying to cross the chasm here between school math and the real-world math. And you know if you walk across a chasm, you end up making it worse than if you didn’t start at all — bigger disaster. No, what I’m suggesting is that we should leap off, we should increase our velocity so it’s high, and we should leap off one side and go the other — of course, having calculated our differential equation very carefully.
(Laughter)
So I want to see a completely renewed, changed math curriculum built from the ground up, based on computers being there, computers that are now ubiquitous almost. Calculating machines are everywhere and will be completely everywhere in a small number of years. Now I’m not even sure if we should brand the subject as math, but what I am sure is it’s the mainstream subject of the future. Let’s go for it, and while we’re about it, let’s have a bit of fun, for us, for the students and for TED here.
Thanks.
(Applause)
Well, that’s kind of an obvious statement up there. I started with that sentence about 12 years ago, and I started in the context of developing countries, but you’re sitting here from every corner of the world. So if you think of a map of your country, I think you’ll realize that for every country on Earth, you could draw little circles to say, “These are places where good teachers won’t go.” On top of that, those are the places from where trouble comes. So we have an ironic problem — good teachers don’t want to go to just those places where they’re needed the most.
I started in 1999 to try and address this problem with an experiment, which was a very simple experiment in New Delhi. I basically embedded a computer into a wall of a slum in New Delhi. The children barely went to school, they didn’t know any English — they’d never seen a computer before, and they didn’t know what the internet was. I connected high speed internet to it — it’s about three feet off the ground — turned it on and left it there. After this, we noticed a couple of interesting things, which you’ll see. But I repeated this all over India and then through a large part of the world and noticed that children will learn to do what they want to learn to do.
This is the first experiment that we did — eight year-old boy on your right teaching his student, a six year-old girl, and he was teaching her how to browse. This boy here in the middle of central India — this is in a Rajasthan village, where the children recorded their own music and then played it back to each other and in the process, they’ve enjoyed themselves thoroughly. They did all of this in four hours after seeing the computer for the first time. In another South Indian village, these boys here had assembled a video camera and were trying to take the photograph of a bumble bee. They downloaded it from Disney.com, or one of these websites, 14 days after putting the computer in their village. So at the end of it, we concluded that groups of children can learn to use computers and the internet on their own, irrespective of who or where they were.
At that point, I became a little more ambitious and decided to see what else could children do with a computer. We started off with an experiment in Hyderabad, India, where I gave a group of children — they spoke English with a very strong Telugu accent. I gave them a computer with a speech-to-text interface, which you now get free with Windows, and asked them to speak into it. So when they spoke into it, the computer typed out gibberish, so they said, “Well, it doesn’t understand anything of what we are saying.” So I said, “Yeah, I’ll leave it here for two months. Make yourself understood to the computer.” So the children said, “How do we do that.” And I said, “I don’t know, actually.” (Laughter) And I left. (Laughter) Two months later — and this is now documented in the Information Technology for International Development journal — that accents had changed and were remarkably close to the neutral British accent in which I had trained the speech-to-text synthesizer. In other words, they were all speaking like James Tooley. (Laughter) So they could do that on their own. After that, I started to experiment with various other things that they might learn to do on their own.
I got an interesting phone call once from Columbo, from the late Arthur C. Clarke, who said, “I want to see what’s going on.” And he couldn’t travel, so I went over there. He said two interesting things, “A teacher that can be replaced by a machine should be.” (Laughter) The second thing he said was that, “If children have interest, then education happens.” And I was doing that in the field, so every time I would watch it and think of him.
(Video) Arthur C. Clarke: And they can definitely help people, because children quickly learn to navigate the web and find things which interest them. And when you’ve got interest, then you have education.
Sugata Mitra: I took the experiment to South Africa. This is a 15 year-old boy.
(Video) Boy: … just mention, I play games like animals, and I listen to music.
SM: And I asked him, “Do you send emails?” And he said, “Yes, and they hop across the ocean.” This is in Cambodia, rural Cambodia — a fairly silly arithmetic game, which no child would play inside the classroom or at home. They would, you know, throw it back at you. They’d say, “This is very boring.” If you leave it on the pavement and if all the adults go away, then they will show off with each other about what they can do. This is what these children are doing. They are trying to multiply, I think. And all over India, at the end of about two years, children were beginning to Google their homework. As a result, the teachers reported tremendous improvements in their English — (Laughter) rapid improvement and all sorts of things. They said, “They have become really deep thinkers and so on and so forth. (Laughter) And indeed they had. I mean, if there’s stuff on Google, why would you need to stuff it into your head? So at the end of the next four years, I decided that groups of children can navigate the internet to achieve educational objectives on their own.
At that time, a large amount of money had come into Newcastle University to improve schooling in India. So Newcastle gave me a call. I said, “I’ll do it from Delhi.” They said, “There’s no way you’re going to handle a million pounds-worth of University money sitting in Delhi.” So in 2006, I bought myself a heavy overcoat and moved to Newcastle. I wanted to test the limits of the system. The first experiment I did out of Newcastle was actually done in India. And I set myself and impossible target: can Tamil speaking 12-year-old children in a South Indian village teach themselves biotechnology in English on their own? And I thought, I’ll test them, they’ll get a zero — I’ll give the materials, I’ll come back and test them — they get another zero, I’ll go back and say, “Yes, we need teachers for certain things.”
I called in 26 children. They all came in there, and I told them that there’s some really difficult stuff on this computer. I wouldn’t be surprised if you didn’t understand anything. It’s all in English, and I’m going. (Laughter) So I left them with it. I came back after two months, and the 26 children marched in looking very, very quiet. I said, “Well, did you look at any of the stuff?” They said, “Yes, we did.” “Did you understand anything?” “No, nothing.” So I said, “Well, how long did you practice on it before you decided you understood nothing?” They said, “We look at it every day.” So I said, “For two months, you were looking at stuff you didn’t understand?” So a 12 year-old girl raises her hand and says, literally, “Apart from the fact that improper replication of the DNA molecule causes genetic disease, we’ve understood nothing else.”
(Laughter)
(Applause)
(Laughter)
It took me three years to publish that. It’s just been published in the British Journal of Educational Technology. One of the referees who refereed the paper said, “It’s too good to be true,” which was not very nice. Well, one of the girls had taught herself to become the teacher. And then that’s her over there. Remember, they don’t study English. I edited out the last bit when I asked, “Where is the neuron?” and she says, “The neuron? The neuron,” and then she looked and did this. Whatever the expression, it was not very nice.
So their scores had gone up from zero to 30 percent, which is an educational impossibility under the circumstances. But 30 percent is not a pass. So I found that they had a friend, a local accountant, a young girl, and they played football with her. I asked that girl, “Would you teach them enough biotechnology to pass?” And she said, “How would I do that? I don’t know the subject.” I said, “No, use the method of the grandmother.” She said, “What’s that?” I said, “Well, what you’ve got to do is stand behind them and admire them all the time. Just say to them, ‘That’s cool. That’s fantastic. What is that? Can you do that again? Can you show me some more?'” She did that for two months. The scores went up to 50, which is what the posh schools of New Delhi, with a trained biotechnology teacher were getting.
So I came back to Newcastle with these results and decided that there was something happening here that definitely was getting very serious. So, having experimented in all sorts of remote places, I came to the most remote place that I could think of. (Laughter) Approximately 5,000 miles from Delhi is the little town of Gateshead. In Gateshead, I took 32 children and I started to fine-tune the method. I made them into groups of four. I said, “You make your own groups of four. Each group of four can use one computer and not four computers.” Remember, from the Hole in the Wall. “You can exchange groups. You can walk across to another group, if you don’t like your group, etc. You can go to another group, peer over their shoulders, see what they’re doing, come back to you own group and claim it as your own work.” And I explained to them that, you know, a lot of scientific research is done using that method.
(Laughter)
(Applause)
The children enthusiastically got after me and said, “Now, what do you want us to do?” I gave them six GCSE questions. The first group — the best one — solved everything in 20 minutes. The worst, in 45. They used everything that they knew — news groups, Google, Wikipedia, Ask Jeeves, etc. The teachers said, “Is this deep learning?” I said, “Well, let’s try it. I’ll come back after two months. We’ll give them a paper test — no computers, no talking to each other, etc.” The average score when I’d done it with the computers and the groups was 76 percent. When I did the experiment, when I did the test, after two months, the score was 76 percent. There was photographic recall inside the children, I suspect because they’re discussing with each other. A single child in front of a single computer will not do that. I have further results, which are almost unbelievable, of scores which go up with time. Because their teachers say that after the session is over, the children continue to Google further.
Here in Britain, I put out a call for British grandmothers, after my Kuppam experiment. Well, you know, they’re very vigorous people, British grandmothers. 200 of them volunteered immediately. (Laughter) The deal was that they would give me one hour of broadband time, sitting in their homes, one day in a week. So they did that, and over the last two years, over 600 hours of instruction has happened over Skype, using what my students call the granny cloud. The granny cloud sits over there. I can beam them to whichever school I want to.
(Video) Teacher: You can’t catch me. You say it. You can’t catch me.
Children: You can’t catch me.
Teacher: I’m the gingerbread man.
Children: I’m the gingerbread man.
Teacher: Well done. Very good …
SM: Back at Gateshead, a 10-year-old girl gets into the heart of Hinduism in 15 minutes. You know, stuff which I don’t know anything about. Two children watch a TEDTalk. They wanted to be footballers before. After watching eight TEDTalks, he wants to become Leonardo da Vinci.
(Laughter)
(Applause)
It’s pretty simple stuff.
This is what I’m building now — they’re called SOLEs: Self Organized Learning Environments. The furniture is designed so that children can sit in front of big, powerful screens, big broadband connections, but in groups. If they want, they can call the granny cloud. This is a SOLE in Newcastle. The mediator is from Pune, India.
So how far can we go? One last little bit and I’ll stop. I went to Turin in May. I sent all the teachers away from my group of 10 year-old students. I speak only English, they speak only Italian, so we had no way to communicate. I started writing English questions on the blackboard. The children looked at it and said, “What?” I said, “Well, do it.” They typed it into Google, translated it into Italian, went back into Italian Google. Fifteen minutes later — next question: where is Calcutta? This one, they took only 10 minutes. I tried a really hard one then. Who was Pythagoras, and what did he do? There was silence for a while, then they said, “You’ve spelled it wrong. It’s Pitagora.” And then, in 20 minutes, the right-angled triangles began to appear on the screens. This sent shivers up my spine. These are 10 year-olds. Text: In another 30 minutes they would reach the Theory of Relativity. And then?
(Laughter)
(Applause)
SM: So you know what’s happened? I think we’ve just stumbled across a self-organizing system. A self-organizing system is one where a structure appears without explicit intervention from the outside. Self-organizing systems also always show emergence, which is that the system starts to do things, which it was never designed for. Which is why you react the way you do, because it looks impossible. I think I can make a guess now — education is self-organizing system, where learning is an emergent phenomenon. It’ll take a few years to prove it, experimentally, but I’m going to try. But in the meanwhile, there is a method available. One billion children, we need 100 million mediators — there are many more than that on the planet — 10 million SOLEs, 180 billion dollars and 10 years. We could change everything.
Thanks.
(Applause)
Can I ask you to please recall a time when you really loved something — a movie, an album, a song or a book — and you recommended it wholeheartedly to someone you also really liked, and you anticipated that reaction, you waited for it, and it came back, and the person hated it? So, by way of introduction, that is the exact same state in which I spent every working day of the last six years. (Laughter) I teach high school math. I sell a product to a market that doesn’t want it, but is forced by law to buy it. I mean, it’s just a losing proposition.
So there’s a useful stereotype about students that I see, a useful stereotype about you all. I could give you guys an algebra-two final exam, and I would expect no higher than a 25 percent pass rate. And both of these facts say less about you or my students than they do about what we call math education in the U.S. today.
To start with, I’d like to break math down into two categories. One is computation; this is the stuff you’ve forgotten. For example, factoring quadratics with leading coefficients greater than one. This stuff is also really easy to relearn, provided you have a really strong grounding in reasoning. Math reasoning — we’ll call it the application of math processes to the world around us — this is hard to teach. This is what we would love students to retain, even if they don’t go into mathematical fields. This is also something that, the way we teach it in the U.S. all but ensures they won’t retain it. So, I’d like to talk about why that is, why that’s such a calamity for society, what we can do about it and, to close with, why this is an amazing time to be a math teacher.
So first, five symptoms that you’re doing math reasoning wrong in your classroom. One is a lack of initiative; your students don’t self-start. You finish your lecture block and immediately you have five hands going up asking you to re-explain the entire thing at their desks. Students lack perseverance. They lack retention; you find yourself re-explaining concepts three months later, wholesale. There’s an aversion to word problems, which describes 99 percent of my students. And then the other one percent is eagerly looking for the formula to apply in that situation. This is really destructive.
David Milch, creator of “Deadwood” and other amazing TV shows, has a really good description for this. He swore off creating contemporary drama, shows set in the present day, because he saw that when people fill their mind with four hours a day of, for example, “Two and a Half Men,” no disrespect, it shapes the neural pathways, he said, in such a way that they expect simple problems. He called it, “an impatience with irresolution.” You’re impatient with things that don’t resolve quickly. You expect sitcom-sized problems that wrap up in 22 minutes, three commercial breaks and a laugh track. And I’ll put it to all of you, what you already know, that no problem worth solving is that simple. I am very concerned about this because I’m going to retire in a world that my students will run. I’m doing bad things to my own future and well-being when I teach this way. I’m here to tell you that the way our textbooks — particularly mass-adopted textbooks — teach math reasoning and patient problem solving, it’s functionally equivalent to turning on “Two and a Half Men” and calling it a day.
(Laughter)
In all seriousness. Here’s an example from a physics textbook. It applies equally to math. Notice, first of all here, that you have exactly three pieces of information there, each of which will figure into a formula somewhere, eventually, which the student will then compute. I believe in real life. And ask yourself, what problem have you solved, ever, that was worth solving where you knew all of the given information in advance; where you didn’t have a surplus of information and you had to filter it out, or you didn’t have sufficient information and had to go find some. I’m sure we all agree that no problem worth solving is like that. And the textbook, I think, knows how it’s hamstringing students because, watch this, this is the practice problem set. When it comes time to do the actual problem set, we have problems like this right here where we’re just swapping out numbers and tweaking the context a little bit. And if the student still doesn’t recognize the stamp this was molded from, it helpfully explains to you what sample problem you can return to to find the formula. You could literally, I mean this, pass this particular unit without knowing any physics, just knowing how to decode a textbook. That’s a shame.
So I can diagnose the problem a little more specifically in math. Here’s a really cool problem. I like this. It’s about defining steepness and slope using a ski lift. But what you have here is actually four separate layers, and I’m curious which of you can see the four separate layers and, particularly, how when they’re compressed together and presented to the student all at once, how that creates this impatient problem solving. I’ll define them here: You have the visual. You also have the mathematical structure, talking about grids, measurements, labels, points, axes, that sort of thing. You have substeps, which all lead to what we really want to talk about: which section is the steepest.
So I hope you can see. I really hope you can see how what we’re doing here is taking a compelling question, a compelling answer, but we’re paving a smooth, straight path from one to the other and congratulating our students for how well they can step over the small cracks in the way. That’s all we’re doing here. So I want to put to you that if we can separate these in a different way and build them up with students, we can have everything we’re looking for in terms of patient problem solving.
So right here I start with the visual, and I immediately ask the question: Which section is the steepest? And this starts conversation because the visual is created in such a way where you can defend two answers. So you get people arguing against each other, friend versus friend, in pairs, journaling, whatever. And then eventually we realize it’s getting annoying to talk about the skier in the lower left-hand side of the screen or the skier just above the mid line. And we realize how great would it be if we just had some A, B, C and D labels to talk about them more easily. And then as we start to define what does steepness mean, we realize it would be nice to have some measurements to really narrow it down, specifically what that means. And then and only then, we throw down that mathematical structure. The math serves the conversation, the conversation doesn’t serve the math. And at that point, I’ll put it to you that nine out of 10 classes are good to go on the whole slope, steepness thing. But if you need to, your students can then develop those substeps together.
Do you guys see how this, right here, compared to that — which one creates that patient problem solving, that math reasoning? It’s been obvious in my practice, to me. And I’ll yield the floor here for a second to Einstein, who, I believe, has paid his dues. He talked about the formulation of a problem being so incredibly important, and yet in my practice, in the U.S. here, we just give problems to students; we don’t involve them in the formulation of the problem.
So 90 percent of what I do with my five hours of prep time per week is to take fairly compelling elements of problems like this from my textbook and rebuild them in a way that supports math reasoning and patient problem solving. And here’s how it works. I like this question. It’s about a water tank. The question is: How long will it take you to fill it up? First things first, we eliminate all the substeps. Students have to develop those, they have to formulate those. And then notice that all the information written on there is stuff you’ll need. None of it’s a distractor, so we lose that. Students need to decide, “All right, well, does the height matter? Does the side of it matter? Does the color of the valve matter? What matters here?” Such an underrepresented question in math curriculum. So now we have a water tank. How long will it take you to fill it up? And that’s it.
And because this is the 21st century and we would love to talk about the real world on its own terms, not in terms of line art or clip art that you so often see in textbooks, we go out and we take a picture of it. So now we have the real deal. How long will it take it to fill it up? And then even better is we take a video, a video of someone filling it up. And it’s filling up slowly, agonizingly slowly. It’s tedious. Students are looking at their watches, rolling their eyes, and they’re all wondering at some point or another, “Man, how long is it going to take to fill up?” (Laughter) That’s how you know you’ve baited the hook, right?
And that question, off this right here, is really fun for me because, like the intro, I teach kids — because of my inexperience — I teach the kids that are the most remedial, all right? And I’ve got kids who will not join a conversation about math because someone else has the formula; someone else knows how to work the formula better than me, so I won’t talk about it. But here, every student is on a level playing field of intuition. Everyone’s filled something up with water before, so I get kids answering the question, “How long will it take?” I’ve got kids who are mathematically and conversationally intimidated joining the conversation. We put names on the board, attach them to guesses, and kids have bought in here. And then we follow the process I’ve described. And the best part here, or one of the better parts is that we don’t get our answer from the answer key in the back of the teacher’s edition. We, instead, just watch the end of the movie. (Laughter) And that’s terrifying, because the theoretical models that always work out in the answer key in the back of a teacher’s edition, that’s great, but it’s scary to talk about sources of error when the theoretical does not match up with the practical. But those conversations have been so valuable, among the most valuable.
So I’m here to report some really fun games with students who come pre-installed with these viruses day one of the class. These are the kids who now, one semester in, I can put something on the board, totally new, totally foreign, and they’ll have a conversation about it for three or four minutes more than they would have at the start of the year, which is just so fun. We’re no longer averse to word problems, because we’ve redefined what a word problem is. We’re no longer intimidated by math, because we’re slowly redefining what math is. This has been a lot of fun.
I encourage math teachers I talk to to use multimedia, because it brings the real world into your classroom in high resolution and full color; to encourage student intuition for that level playing field; to ask the shortest question you possibly can and let those more specific questions come out in conversation; to let students build the problem, because Einstein said so; and to finally, in total, just be less helpful, because the textbook is helping you in all the wrong ways: It’s buying you out of your obligation, for patient problem solving and math reasoning, to be less helpful.
And why this is an amazing time to be a math teacher right now is because we have the tools to create this high-quality curriculum in our front pocket. It’s ubiquitous and fairly cheap, and the tools to distribute it freely under open licenses has also never been cheaper or more ubiquitous. I put a video series on my blog not so long ago and it got 6,000 views in two weeks. I get emails still from teachers in countries I’ve never visited saying, “Wow, yeah. We had a good conversation about that. Oh, and by the way, here’s how I made your stuff better,” which, wow. I put this problem on my blog recently: In a grocery store, which line do you get into, the one that has one cart and 19 items or the line with four carts and three, five, two and one items. And the linear modeling involved in that was some good stuff for my classroom, but it eventually got me on “Good Morning America” a few weeks later, which is just bizarre, right?
And from all of this, I can only conclude that people, not just students, are really hungry for this. Math makes sense of the world. Math is the vocabulary for your own intuition. So I just really encourage you, whatever your stake is in education — whether you’re a student, parent, teacher, policy maker, whatever — insist on better math curriculum. We need more patient problem solvers. Thank you. (Applause)
Musings of a Mathlete 