Did you know that if you take any non-negative integer, then subtract the sum of its digits, the answer will always be divisible by 9?
For example, today's date is 11/06. 1106-(1+1+6) = 1098, and 1098/9 = 122.
Curious why? Here's a more general proof [pdf], that the difference between a number and the sum of its digits (if written in base b) will always be divisible by (b-1).
2009-11-06
2009-09-25
Michigan Updates
Alright, I've finally decided to sit down and write in more detail about my Michigan experience.
Living in Ann Arbor is a little strange to me, as it's the first time I'm further removed from a large city. Being in Chicago for four years, visiting San Francisco, LA, and Seattle during the summers, have gotten me used to there being interesting "cultural" events around. I put cultural in quotes because there is of course an Ann Arbor culture, but what I'm talking about is museums and history and architecture. Seattle and San Francisco were great in this respect, where as Ann Arbor is a college town, and thus is dominated by eateries. The university and the town developed together, so only a few blocks from campus the streets become much quieter, and within 15 minutes drive it quickly turns into farmland. Although Detroit is only an hour or so away, I know of no quick/cheap way to get there, and even then I doubt there's much that would interest me. As a result most of my free time is spent reading or climbing, which is a saving grace of sorts. Michigan has a bouldering wall on South Campus, which is across the city from where I live, and so I commute there at least twice a week. It is also one of the few ways I've met people outside of engineering, as North Campus is dominated by engineers. So I've gotten a bit better at bouldering.
As for classes, I'm taking three, and I'll go through them below. As a final though, I will talk about my experience as a Graduate Student Instructor (TA)
Introduction to AI
I've already done a lot of the things on the syllabus, such as search algorithms, inference, and Bayesian networks. All this stuff, however, was done in different classes, and I later decided that this is because a Michigan semester is longer than the Northwestern quarter. I think I could have gotten an equivalency for the course if I wanted to, but I'm considering doing research with the professor, and it has been a while since I did most of the Good Old Fashioned AI (GOFAI) stuff, so I might as well sit in. So far the course has not been surprising, and I'm rather glad I'm in it, as it's my single "easy" class for the semester.
Machine Learning
Although I've also taken a machine learning course before, my previous work was very implementation biased. This course, on the other hand, is based entirely on statistics and linear algebra. I've only taken one course in both subjects, and linear algebra in my freshman year. The good thing is that I've been teaching linear algebra through the years (as it is part of the course I peer tutor), so the knowledge I retained from that is very helpful. To be honest, I'm not sure I will find the mathematical background to these methods helpful. I did read a paper where principal component analysis was used before the course covered it, so it was exciting to know a concrete example.
Computational Complexity
My background for this course is even stranger. Michigan has an undergraduate course on the theory of computation, which I have obviously never taken. Northwestern used to have a similar course, but the only place I've found it referenced was in the course catalog. So most of what I know about Turing Machines come from recreational reading. And it turns out that it was enough: books on Turing and Godel, together with what I picked up in my programming languages and compiler courses, gave me enough background to take the course. I like the course a lot; the professor has a nice way of putting everything in narrative and historical perspective. If I wasn't so interested in AI, theory would definitely be an area I would look into. A system of logic is just so... elegant.
Graduate Student Instructor (for Programming and Intro Data Structures)
Ah, teaching. I'm always surprised by how much teaching I've done already. I was involved with the GSW for all four years, one of them as a student. And I've done two summers of CTY. Still, I expected doing discussion sections and office hours to be different. But it wasn't; after the first day, when I think back to see what I could improve, I didn't see anything that I needed to adapt to the new format. Actually, this is now not entirely true - I think I need to do a better job of emphasizing why these concepts are important, in the world of computer science. It's much harder to keep a room of 30 college students than a room of 14 6th graders engaged, especially when you don't have much flexibility on what to teach.
Anyway, I'm definitely enjoying being a GSI. At least one student have told me that what I do is helpful, and several others have been asking me questions on computer science concepts outside of the course. Yeah. Now the hard part: keeping it up.
Living in Ann Arbor is a little strange to me, as it's the first time I'm further removed from a large city. Being in Chicago for four years, visiting San Francisco, LA, and Seattle during the summers, have gotten me used to there being interesting "cultural" events around. I put cultural in quotes because there is of course an Ann Arbor culture, but what I'm talking about is museums and history and architecture. Seattle and San Francisco were great in this respect, where as Ann Arbor is a college town, and thus is dominated by eateries. The university and the town developed together, so only a few blocks from campus the streets become much quieter, and within 15 minutes drive it quickly turns into farmland. Although Detroit is only an hour or so away, I know of no quick/cheap way to get there, and even then I doubt there's much that would interest me. As a result most of my free time is spent reading or climbing, which is a saving grace of sorts. Michigan has a bouldering wall on South Campus, which is across the city from where I live, and so I commute there at least twice a week. It is also one of the few ways I've met people outside of engineering, as North Campus is dominated by engineers. So I've gotten a bit better at bouldering.
As for classes, I'm taking three, and I'll go through them below. As a final though, I will talk about my experience as a Graduate Student Instructor (TA)
Introduction to AI
I've already done a lot of the things on the syllabus, such as search algorithms, inference, and Bayesian networks. All this stuff, however, was done in different classes, and I later decided that this is because a Michigan semester is longer than the Northwestern quarter. I think I could have gotten an equivalency for the course if I wanted to, but I'm considering doing research with the professor, and it has been a while since I did most of the Good Old Fashioned AI (GOFAI) stuff, so I might as well sit in. So far the course has not been surprising, and I'm rather glad I'm in it, as it's my single "easy" class for the semester.
Machine Learning
Although I've also taken a machine learning course before, my previous work was very implementation biased. This course, on the other hand, is based entirely on statistics and linear algebra. I've only taken one course in both subjects, and linear algebra in my freshman year. The good thing is that I've been teaching linear algebra through the years (as it is part of the course I peer tutor), so the knowledge I retained from that is very helpful. To be honest, I'm not sure I will find the mathematical background to these methods helpful. I did read a paper where principal component analysis was used before the course covered it, so it was exciting to know a concrete example.
Computational Complexity
My background for this course is even stranger. Michigan has an undergraduate course on the theory of computation, which I have obviously never taken. Northwestern used to have a similar course, but the only place I've found it referenced was in the course catalog. So most of what I know about Turing Machines come from recreational reading. And it turns out that it was enough: books on Turing and Godel, together with what I picked up in my programming languages and compiler courses, gave me enough background to take the course. I like the course a lot; the professor has a nice way of putting everything in narrative and historical perspective. If I wasn't so interested in AI, theory would definitely be an area I would look into. A system of logic is just so... elegant.
Graduate Student Instructor (for Programming and Intro Data Structures)
Ah, teaching. I'm always surprised by how much teaching I've done already. I was involved with the GSW for all four years, one of them as a student. And I've done two summers of CTY. Still, I expected doing discussion sections and office hours to be different. But it wasn't; after the first day, when I think back to see what I could improve, I didn't see anything that I needed to adapt to the new format. Actually, this is now not entirely true - I think I need to do a better job of emphasizing why these concepts are important, in the world of computer science. It's much harder to keep a room of 30 college students than a room of 14 6th graders engaged, especially when you don't have much flexibility on what to teach.
Anyway, I'm definitely enjoying being a GSI. At least one student have told me that what I do is helpful, and several others have been asking me questions on computer science concepts outside of the course. Yeah. Now the hard part: keeping it up.
2009-09-09
Spiral Staircases
The new Computer Science and Engineering building has a nice spiral staircase that rises prominently from the main hall. It connects all four floors of the building, and is the most convenient way to get directly up; there is at least one other staircase (probably more; I haven't found any emergency staircases), but that has significant horizontal translation.
I thought a spiral staircase was pretty cool when I first saw it, but as I'm using it more often, I realized how stupid an idea it really is.
The problem with a spiral staircase is that the steps are non-uniform. Since people's gait depends on their height, and their height is a random variable, people have preferences as to how wide a step should be. With a circular staircase, the steps are obviously longer towards the outside and shorter towards the inside. This means people can pick where they walk, right? Except, of course, when there's two way traffic, so people are forced to one side of the staircase. With normal stairs, moving to one side doesn't change your gait, and so you can continue walking. With spiral staircases though, you have to constantly adjust how far you're stretching your legs just to keep going.
Besides that, Michigan is going well. By virtue of it being a public university, the classes are quite a bit bigger than those at Northwestern, even for relatively obscure classes like machine learning. I think that's the only reason why professors seem a little more distant here than at NU. On the other hand, I have two discussion sections to lead next week, as well as however many office hours, and this is also with the largest number of students I've dealt with yet. It'll be fun.
I thought a spiral staircase was pretty cool when I first saw it, but as I'm using it more often, I realized how stupid an idea it really is.
The problem with a spiral staircase is that the steps are non-uniform. Since people's gait depends on their height, and their height is a random variable, people have preferences as to how wide a step should be. With a circular staircase, the steps are obviously longer towards the outside and shorter towards the inside. This means people can pick where they walk, right? Except, of course, when there's two way traffic, so people are forced to one side of the staircase. With normal stairs, moving to one side doesn't change your gait, and so you can continue walking. With spiral staircases though, you have to constantly adjust how far you're stretching your legs just to keep going.
Besides that, Michigan is going well. By virtue of it being a public university, the classes are quite a bit bigger than those at Northwestern, even for relatively obscure classes like machine learning. I think that's the only reason why professors seem a little more distant here than at NU. On the other hand, I have two discussion sections to lead next week, as well as however many office hours, and this is also with the largest number of students I've dealt with yet. It'll be fun.
2009-09-01
Writing About Writing
I have been writing recreationally for a while - I've been writing in my journal for close to 7.5 years, and this blog has been going for 2 years as well. Before that, I used to have a LiveJournal account, which was mostly used to keep my high school friends up to date with what I was doing. This blog stands out though, because it can be said that I'm doing a lot for a very small audience.
I recently read Paul Graham's essay on essays though, and I found it interesting that the word "essay" comes from the French verb/noun essayer/essai, meaning to try/an attempt. A lot of my blog posts are planned before hand. I have a running list of topics I want to write about, and while I find the time and mood to write them, I collect ideas and quotes in bullet-point form. Often times I don't actually know what I want to write, just want I want to write about. For example, I knew that I would do a post on The Fountainhead, but I didn't know what I want to say about it. Even for this short post, I'm not sure what my final point is, if I have one. Writing, then, is a way for me to figure out my own ideas. It's not just a tool for me to express my ideas to other people, but also for my ideas to become clearer in my head.
My friend Genia also wrote something about writing a little while back.
I thought it would be interesting to show the notes I have collected before writing this too. They're below:
I recently read Paul Graham's essay on essays though, and I found it interesting that the word "essay" comes from the French verb/noun essayer/essai, meaning to try/an attempt. A lot of my blog posts are planned before hand. I have a running list of topics I want to write about, and while I find the time and mood to write them, I collect ideas and quotes in bullet-point form. Often times I don't actually know what I want to write, just want I want to write about. For example, I knew that I would do a post on The Fountainhead, but I didn't know what I want to say about it. Even for this short post, I'm not sure what my final point is, if I have one. Writing, then, is a way for me to figure out my own ideas. It's not just a tool for me to express my ideas to other people, but also for my ideas to become clearer in my head.
My friend Genia also wrote something about writing a little while back.
I thought it would be interesting to show the notes I have collected before writing this too. They're below:
Paul Graham on essays
http://www.paulgraham.com/essay.html
the french essayer, to try
I have a goal, but I don't know how it turns out
I'm not sure what's the point I want to make in this essay
more to write thoughts down, to externalize and make concrete my thinking
to clarify ideas
http://petdinosaur.wordpress.com/2009/05/25/write-a-story-write-a-book/#comment-31
show notes for this essay
2009-08-29
Do Schools Kill Creativity?
I just watched this, and despite wanting to be the "whole purpose of public education throughout the world" that is the university professor, I have to agree with him.
The TED talk can be found here:
http://www.ted.com/talks/ken_robinson_says_schools_kill_creativity.html
I'm also putting the transcript up, if reading is more your thing.
Do Schools Kill Creativity?
Ken Robinson
Good morning. How are you? It's been great, hasn't it? I've been blown away by the whole thing. In fact, I'm leaving. There have been three themes, haven't there, running through the conference, which are relevant to what I want to talk about. One is the extraordinary evidence of human creativity in all of the presentations that we've had and in all of the people here. Just the variety of it and the range of it. The second is that it's put us in a place where we have no idea what's going to happen, in terms of the future. No idea how this may play out.
I have an interest in education -- actually, what I find is everybody has an interest in education. Don't you? I find this very interesting. If you're at a dinner party, and you say you work in education -- actually, you're not often at dinner parties, frankly, if you work in education. You're not asked. And you're never asked back, curiously. That's strange to me. But if you are, and you say to somebody, you know, they say, "What do you do?" and you say you work in education, you can see the blood run from their face. They're like, "Oh my God," you know, "Why me? My one night out all week." But if you ask about their education, they pin you to the wall. Because it's one of those things that goes deep with people, am I right? Like religion, and money and other things. I have a big interest in education, and I think we all do. We have a huge vested interest in it, partly because it's education that's meant to take us into this future that we can't grasp. If you think of it, children starting school this year will be retiring in 2065. Nobody has a clue -- despite all the expertise that's been on parade for the past four days -- what the world will look like in five years' time. And yet we're meant to be educating them for it. So the unpredictability, I think, is extraordinary.
And the third part of this is that we've all agreed, nonetheless, on the really extraordinary capacities that children have -- their capacities for innovation. I mean, Sirena last night was a marvel, wasn't she? Just seeing what she could do. And she's exceptional, but I think she's not, so to speak, exceptional in the whole of childhood. What you have there is a person of extraordinary dedication who found a talent. And my contention is, all kids have tremendous talents. And we squander them, pretty ruthlessly. So I want to talk about education and I want to talk about creativity. My contention is that creativity now is as important in education as literacy, and we should treat it with the same status. Thank you. That was it, by the way. Thank you very much. So, 15 minutes left. Well, I was born -- no.
I heard a great story recently -- I love telling it -- of a little girl who was in a drawing lesson. She was six and she was at the back, drawing, and the teacher said this little girl hardly ever paid attention, and in this drawing lesson she did. The teacher was fascinated and she went over to her and she said, "What are you drawing?" And the girl said, "I'm drawing a picture of God." And the teacher said, "But nobody knows what God looks like." And the girl said, "They will in a minute."
When my son was four in England -- actually he was four everywhere, to be honest. If we're being strict about it, wherever he went, he was four that year. He was in the Nativity play. Do you remember the story? No, it was big. It was a big story. Mel Gibson did the sequel. You may have seen it: "Nativity II." But James got the part of Joseph, which we were thrilled about. We considered this to be one of the lead parts. We had the place crammed full of agents in T-shirts: "James Robinson IS Joseph!" He didn't have to speak, but you know the bit where the three kings come in. They come in bearing gifts, and they bring gold, frankincense and myrhh. This really happened. We were sitting there and I think they just went out of sequence, because we talked to the little boy afterward and we said, "You OK with that?" And he said, "Yeah, why, was that wrong?" They just switched, that was it. Anyway, the three boys came in, four-year-olds with tea towels on their heads, and they put these boxes down, and the first boy said, "I bring you gold." And the second boy said, "I bring you myrhh." And the third boy said, "Frank sent this."
What these things have in common is that kids will take a chance. If they don't know, they'll have a go. Am I right? They're not frightened of being wrong. Now, I don't mean to say that being wrong is the same thing as being creative. What we do know is, if you're not prepared to be wrong, you'll never come up with anything original. If you're not prepared to be wrong. And by the time they get to be adults, most kids have lost that capacity. They have become frightened of being wrong. And we run our companies like this, by the way. We stigmatize mistakes. And we're now running national education systems where mistakes are the worst thing you can make. And the result is that we are educating people out of their creative capacities. Picasso once said this: he said that all children are born artists. The problem is to remain an artist as we grow up. I believe this passionately: that we don't grow into creativity, we grow out of it. Or rather, we get educated out if it. So why is this?
I lived in Stratford-on-Avon until about five years ago. In fact, we moved from Stratford to Los Angeles. So you can imagine what a seamless transition that was. Actually, we lived in a place called Snitterfield, just outside Stratford, which is where Shakespeare's father was born. Are you struck by a new thought? I was. You don't think of Shakespeare having a father, do you? Do you? Because you don't think of Shakespeare being a child, do you? Shakespeare being seven? I never thought of it. I mean, he was seven at some point. He was in somebody's English class, wasn't he? How annoying would that be? "Must try harder." Being sent to bed by his dad, you know, to Shakespeare, "Go to bed, now," to William Shakespeare, "and put the pencil down. And stop speaking like that. It's confusing everybody."
Anyway, we moved from Stratford to Los Angeles, and I just want to say a word about the transition, actually. My son didn't want to come. I've got two kids. He's 21 now; my daughter's 16. He didn't want to come to Los Angeles. He loved it, but he had a girlfriend in England. This was the love of his life, Sarah. He'd known her for a month. Mind you, they'd had their fourth anniversary, because it's a long time when you're 16. Anyway, he was really upset on the plane, and he said, "I'll never find another girl like Sarah." And we were rather pleased about that, frankly, because she was the main reason we were leaving the country.
But something strikes you when you move to America and when you travel around the world: every education system on earth has the same hierarchy of subjects. Every one. Doesn't matter where you go. You'd think it would be otherwise, but it isn't. At the top are mathematics and languages, then the humanities, and the bottom are the arts. Everywhere on Earth. And in pretty much every system too, there's a hierarchy within the arts. Art and music are normally given a higher status in schools than drama and dance. There isn't an education system on the planet that teaches dance every day to children the way we teach them mathematics. Why? Why not? I think this is rather important. I think math is very important, but so is dance. Children dance all the time if they're allowed to, we all do. We all have bodies, don't we? Did I miss a meeting? Truthfully, what happens is, as children grow up, we start to educate them progressively from the waist up. And then we focus on their heads. And slightly to one side.
If you were to visit education, as an alien, and say "What's it for, public education?" I think you'd have to conclude -- if you look at the output, who really succeeds by this, who does everything that they should, who gets all the brownie points, who are the winners -- I think you'd have to conclude the whole purpose of public education throughout the world is to produce university professors. Isn't it? They're the people who come out the top. And I used to be one, so there. And I like university professors, but you know, we shouldn't hold them up as the high-water mark of all human achievement. They're just a form of life, another form of life. But they're rather curious, and I say this out of affection for them. There's something curious about professors in my experience -- not all of them, but typically -- they live in their heads. They live up there, and slightly to one side. They're disembodied, you know, in a kind of literal way. They look upon their body as a form of transport for their heads, don't they? It's a way of getting their head to meetings. If you want real evidence of out-of-body experiences, by the way, get yourself along to a residential conference of senior academics, and pop into the discotheque on the final night. And there you will see it, grown men and women writhing uncontrollably, off the beat, waiting until it ends so they can go home and write a paper about it.
Now our education system is predicated on the idea of academic ability. And there's a reason. The whole system was invented -- around the world, there were no public systems of education, really, before the 19th century. They all came into being to meet the needs of industrialism. So the hierarchy is rooted on two ideas. Number one, that the most useful subjects for work are at the top. So you were probably steered benignly away from things at school when you were a kid, things you liked, on the grounds that you would never get a job doing that. Is that right? Don't do music, you're not going to be a musician; don't do art, you won't be an artist. Benign advice -- now, profoundly mistaken. The whole world is engulfed in a revolution. And the second is academic ability, which has really come to dominate our view of intelligence, because the universities designed the system in their image. If you think of it, the whole system of public education around the world is a protracted process of university entrance. And the consequence is that many highly talented, brilliant, creative people think they're not, because the thing they were good at at school wasn't valued, or was actually stigmatized. And I think we can't afford to go on that way.
In the next 30 years, according to UNESCO, more people worldwide will be graduating through education than since the beginning of history. More people, and it's the combination of all the things we've talked about -- technology and its transformation effect on work, and demography and the huge explosion in population. Suddenly, degrees aren't worth anything. Isn't that true? When I was a student, if you had a degree, you had a job. If you didn't have a job it's because you didn't want one. And I didn't want one, frankly. But now kids with degrees are often heading home to carry on playing video games, because you need an MA where the previous job required a BA, and now you need a PhD for the other. It's a process of academic inflation. And it indicates the whole structure of education is shifting beneath our feet. We need to radically rethink our view of intelligence.
We know three things about intelligence. One, it's diverse. We think about the world in all the ways that we experience it. We think visually, we think in sound, we think kinesthetically. We think in abstract terms, we think in movement. Secondly, intelligence is dynamic. If you look at the interactions of a human brain, as we heard yesterday from a number of presentations, intelligence is wonderfully interactive. The brain isn't divided into compartments. In fact, creativity -- which I define as the process of having original ideas that have value -- more often than not comes about through the interaction of different disciplinary ways of seeing things.
The brain is intentionally -- by the way, there's a shaft of nerves that joins the two halves of the brain brain called the corpus callosum. It's thicker in women. Following off from Helen yesterday, I think this is probably why women are better at multi-tasking. Because you are, aren't you? There's a raft of research, but I know it from my personal life. If my wife is cooking a meal at home -- which is not often, thankfully. But you know, she's doing -- no, she's good at some things -- but if she's cooking, you know, she's dealing with people on the phone, she's talking to the kids, she's painting the ceiling, she's doing open-heart surgery over here. If I'm cooking, the door is shut, the kids are out, the phone's on the hook, if she comes in I get annoyed. I say, "Terry, please, I'm trying to fry an egg in here. Give me a break." Actually, you know that old philosophical thing, if a tree falls in the forest and nobody hears it, did it happen? Remember that old chestnut? I saw a great t-shirt really recently which said, "If a man speaks his mind in a forest, and no woman hears him, is he still wrong?"
And the third thing about intelligence is, it's distinct. I'm doing a new book at the moment called "Epiphany," which is based on a series of interviews with people about how they discovered their talent. I'm fascinated by how people got to be there. It's really prompted by a conversation I had with a wonderful woman who maybe most people have never heard of, she's called Gillian Lynne, have you heard of her? Some have. She's a choreographer and everybody knows her work. She did "Cats," and "Phantom of the Opera." She's wonderful. I used to be on the board of the Royal Ballet, in England, as you can see. Anyway, Gillian and I had lunch one day and I said, "Gillian, how'd you get to be a dancer?" And she said it was interesting, when she was at school, she was really hopeless. And the school, in the '30s, wrote to her parents and said, "We think Gillian has a learning disorder." She couldn't concentrate, she was fidgeting. I think now they'd say she had ADHD. Wouldn't you? But this was the 1930s, and ADHD hadn't been invented at this point. It wasn't an available condition. People weren't aware they could have that.
Anyway, she went to see this specialist. So, this oak-paneled room And she was there with her mother, and she was led and sat on a chair at the end, and she sat on her hands for 20 minutes while this man talked to her mother about all the problems Gillian was having at school. And at the end of it -- because she was disturbing people, her homework was always late, and so on, little kid of eight -- in the end, the doctor went and sat next to Gillian and said, "Gillian, I've listened to all these things that your mother's told me, and I need to speak to her privately." He said, "Wait here, we'll be back, we won't be very long." and they went and left her. But as they went out the room, he turned on the radio that was sitting on his desk. And when they got out the room, he said to her mother, "Just stand and watch her." And the minute they left the room, she said, she was on her feet, moving to the music. And they watched for a few minutes and he turned to her mother and said, "Mrs. Lynne, Gillian isn't sick, she's a dancer. Take her to a dance school."
I said, "What happened?" She said, "She did. I can't tell you how wonderful it was. We walked in this room and it was full of people like me. People who couldn't sit still. People who had to move to think." Who had to move to think. They did ballet, they did tap, they did jazz, they did modern, they did contemporary. She was eventually auditioned for the Royal Ballet School, she became a soloist, she had a wonderful career at the Royal Ballet. She eventually graduated from the Royal Ballet School and founded her own company, the Gillian Lynne Dance Company, met Andrew Lloyd Weber. She's been responsible for some of the most successful musical theater productions in history, she's given pleasure to millions, and she's a multi-millionaire. Somebody else might have put her on medication and told her to calm down.
Now, I think -- What I think it comes to is this: Al Gore spoke the other night about ecology, and the revolution that was triggered by Rachel Carson. I believe our only hope for the future is to adopt a new conception of human ecology, one in which we start to reconstitute our conception of the richness of human capacity. Our education system has mined our minds in the way that we strip-mine the earth: for a particular commodity. And for the future, it won't serve us. We have to rethink the fundamental principles on which we're educating our children. There was a wonderful quote by Jonas Salk, who said, "If all the insects were to disappear from the earth, within 50 years all life on Earth would end. If all human beings disappeared from the earth, within 50 years all forms of life would flourish." And he's right.
What TED celebrates is the gift of the human imagination. We have to be careful now that we use this gift wisely, and that we avert some of the scenarios scenarios that we've talked about. And the only way we'll do it is by seeing our creative capacities for the richness they are, and seeing our children for the hope that they are. And our task is to educate their whole being, so they can face this future. By the way -- we may not see this future, but they will. And our job is to help them make something of it. Thank you very much.
The TED talk can be found here:
http://www.ted.com/talks/ken_robinson_says_schools_kill_creativity.html
I'm also putting the transcript up, if reading is more your thing.
Do Schools Kill Creativity?
Ken Robinson
Good morning. How are you? It's been great, hasn't it? I've been blown away by the whole thing. In fact, I'm leaving. There have been three themes, haven't there, running through the conference, which are relevant to what I want to talk about. One is the extraordinary evidence of human creativity in all of the presentations that we've had and in all of the people here. Just the variety of it and the range of it. The second is that it's put us in a place where we have no idea what's going to happen, in terms of the future. No idea how this may play out.
I have an interest in education -- actually, what I find is everybody has an interest in education. Don't you? I find this very interesting. If you're at a dinner party, and you say you work in education -- actually, you're not often at dinner parties, frankly, if you work in education. You're not asked. And you're never asked back, curiously. That's strange to me. But if you are, and you say to somebody, you know, they say, "What do you do?" and you say you work in education, you can see the blood run from their face. They're like, "Oh my God," you know, "Why me? My one night out all week." But if you ask about their education, they pin you to the wall. Because it's one of those things that goes deep with people, am I right? Like religion, and money and other things. I have a big interest in education, and I think we all do. We have a huge vested interest in it, partly because it's education that's meant to take us into this future that we can't grasp. If you think of it, children starting school this year will be retiring in 2065. Nobody has a clue -- despite all the expertise that's been on parade for the past four days -- what the world will look like in five years' time. And yet we're meant to be educating them for it. So the unpredictability, I think, is extraordinary.
And the third part of this is that we've all agreed, nonetheless, on the really extraordinary capacities that children have -- their capacities for innovation. I mean, Sirena last night was a marvel, wasn't she? Just seeing what she could do. And she's exceptional, but I think she's not, so to speak, exceptional in the whole of childhood. What you have there is a person of extraordinary dedication who found a talent. And my contention is, all kids have tremendous talents. And we squander them, pretty ruthlessly. So I want to talk about education and I want to talk about creativity. My contention is that creativity now is as important in education as literacy, and we should treat it with the same status. Thank you. That was it, by the way. Thank you very much. So, 15 minutes left. Well, I was born -- no.
I heard a great story recently -- I love telling it -- of a little girl who was in a drawing lesson. She was six and she was at the back, drawing, and the teacher said this little girl hardly ever paid attention, and in this drawing lesson she did. The teacher was fascinated and she went over to her and she said, "What are you drawing?" And the girl said, "I'm drawing a picture of God." And the teacher said, "But nobody knows what God looks like." And the girl said, "They will in a minute."
When my son was four in England -- actually he was four everywhere, to be honest. If we're being strict about it, wherever he went, he was four that year. He was in the Nativity play. Do you remember the story? No, it was big. It was a big story. Mel Gibson did the sequel. You may have seen it: "Nativity II." But James got the part of Joseph, which we were thrilled about. We considered this to be one of the lead parts. We had the place crammed full of agents in T-shirts: "James Robinson IS Joseph!" He didn't have to speak, but you know the bit where the three kings come in. They come in bearing gifts, and they bring gold, frankincense and myrhh. This really happened. We were sitting there and I think they just went out of sequence, because we talked to the little boy afterward and we said, "You OK with that?" And he said, "Yeah, why, was that wrong?" They just switched, that was it. Anyway, the three boys came in, four-year-olds with tea towels on their heads, and they put these boxes down, and the first boy said, "I bring you gold." And the second boy said, "I bring you myrhh." And the third boy said, "Frank sent this."
What these things have in common is that kids will take a chance. If they don't know, they'll have a go. Am I right? They're not frightened of being wrong. Now, I don't mean to say that being wrong is the same thing as being creative. What we do know is, if you're not prepared to be wrong, you'll never come up with anything original. If you're not prepared to be wrong. And by the time they get to be adults, most kids have lost that capacity. They have become frightened of being wrong. And we run our companies like this, by the way. We stigmatize mistakes. And we're now running national education systems where mistakes are the worst thing you can make. And the result is that we are educating people out of their creative capacities. Picasso once said this: he said that all children are born artists. The problem is to remain an artist as we grow up. I believe this passionately: that we don't grow into creativity, we grow out of it. Or rather, we get educated out if it. So why is this?
I lived in Stratford-on-Avon until about five years ago. In fact, we moved from Stratford to Los Angeles. So you can imagine what a seamless transition that was. Actually, we lived in a place called Snitterfield, just outside Stratford, which is where Shakespeare's father was born. Are you struck by a new thought? I was. You don't think of Shakespeare having a father, do you? Do you? Because you don't think of Shakespeare being a child, do you? Shakespeare being seven? I never thought of it. I mean, he was seven at some point. He was in somebody's English class, wasn't he? How annoying would that be? "Must try harder." Being sent to bed by his dad, you know, to Shakespeare, "Go to bed, now," to William Shakespeare, "and put the pencil down. And stop speaking like that. It's confusing everybody."
Anyway, we moved from Stratford to Los Angeles, and I just want to say a word about the transition, actually. My son didn't want to come. I've got two kids. He's 21 now; my daughter's 16. He didn't want to come to Los Angeles. He loved it, but he had a girlfriend in England. This was the love of his life, Sarah. He'd known her for a month. Mind you, they'd had their fourth anniversary, because it's a long time when you're 16. Anyway, he was really upset on the plane, and he said, "I'll never find another girl like Sarah." And we were rather pleased about that, frankly, because she was the main reason we were leaving the country.
But something strikes you when you move to America and when you travel around the world: every education system on earth has the same hierarchy of subjects. Every one. Doesn't matter where you go. You'd think it would be otherwise, but it isn't. At the top are mathematics and languages, then the humanities, and the bottom are the arts. Everywhere on Earth. And in pretty much every system too, there's a hierarchy within the arts. Art and music are normally given a higher status in schools than drama and dance. There isn't an education system on the planet that teaches dance every day to children the way we teach them mathematics. Why? Why not? I think this is rather important. I think math is very important, but so is dance. Children dance all the time if they're allowed to, we all do. We all have bodies, don't we? Did I miss a meeting? Truthfully, what happens is, as children grow up, we start to educate them progressively from the waist up. And then we focus on their heads. And slightly to one side.
If you were to visit education, as an alien, and say "What's it for, public education?" I think you'd have to conclude -- if you look at the output, who really succeeds by this, who does everything that they should, who gets all the brownie points, who are the winners -- I think you'd have to conclude the whole purpose of public education throughout the world is to produce university professors. Isn't it? They're the people who come out the top. And I used to be one, so there. And I like university professors, but you know, we shouldn't hold them up as the high-water mark of all human achievement. They're just a form of life, another form of life. But they're rather curious, and I say this out of affection for them. There's something curious about professors in my experience -- not all of them, but typically -- they live in their heads. They live up there, and slightly to one side. They're disembodied, you know, in a kind of literal way. They look upon their body as a form of transport for their heads, don't they? It's a way of getting their head to meetings. If you want real evidence of out-of-body experiences, by the way, get yourself along to a residential conference of senior academics, and pop into the discotheque on the final night. And there you will see it, grown men and women writhing uncontrollably, off the beat, waiting until it ends so they can go home and write a paper about it.
Now our education system is predicated on the idea of academic ability. And there's a reason. The whole system was invented -- around the world, there were no public systems of education, really, before the 19th century. They all came into being to meet the needs of industrialism. So the hierarchy is rooted on two ideas. Number one, that the most useful subjects for work are at the top. So you were probably steered benignly away from things at school when you were a kid, things you liked, on the grounds that you would never get a job doing that. Is that right? Don't do music, you're not going to be a musician; don't do art, you won't be an artist. Benign advice -- now, profoundly mistaken. The whole world is engulfed in a revolution. And the second is academic ability, which has really come to dominate our view of intelligence, because the universities designed the system in their image. If you think of it, the whole system of public education around the world is a protracted process of university entrance. And the consequence is that many highly talented, brilliant, creative people think they're not, because the thing they were good at at school wasn't valued, or was actually stigmatized. And I think we can't afford to go on that way.
In the next 30 years, according to UNESCO, more people worldwide will be graduating through education than since the beginning of history. More people, and it's the combination of all the things we've talked about -- technology and its transformation effect on work, and demography and the huge explosion in population. Suddenly, degrees aren't worth anything. Isn't that true? When I was a student, if you had a degree, you had a job. If you didn't have a job it's because you didn't want one. And I didn't want one, frankly. But now kids with degrees are often heading home to carry on playing video games, because you need an MA where the previous job required a BA, and now you need a PhD for the other. It's a process of academic inflation. And it indicates the whole structure of education is shifting beneath our feet. We need to radically rethink our view of intelligence.
We know three things about intelligence. One, it's diverse. We think about the world in all the ways that we experience it. We think visually, we think in sound, we think kinesthetically. We think in abstract terms, we think in movement. Secondly, intelligence is dynamic. If you look at the interactions of a human brain, as we heard yesterday from a number of presentations, intelligence is wonderfully interactive. The brain isn't divided into compartments. In fact, creativity -- which I define as the process of having original ideas that have value -- more often than not comes about through the interaction of different disciplinary ways of seeing things.
The brain is intentionally -- by the way, there's a shaft of nerves that joins the two halves of the brain brain called the corpus callosum. It's thicker in women. Following off from Helen yesterday, I think this is probably why women are better at multi-tasking. Because you are, aren't you? There's a raft of research, but I know it from my personal life. If my wife is cooking a meal at home -- which is not often, thankfully. But you know, she's doing -- no, she's good at some things -- but if she's cooking, you know, she's dealing with people on the phone, she's talking to the kids, she's painting the ceiling, she's doing open-heart surgery over here. If I'm cooking, the door is shut, the kids are out, the phone's on the hook, if she comes in I get annoyed. I say, "Terry, please, I'm trying to fry an egg in here. Give me a break." Actually, you know that old philosophical thing, if a tree falls in the forest and nobody hears it, did it happen? Remember that old chestnut? I saw a great t-shirt really recently which said, "If a man speaks his mind in a forest, and no woman hears him, is he still wrong?"
And the third thing about intelligence is, it's distinct. I'm doing a new book at the moment called "Epiphany," which is based on a series of interviews with people about how they discovered their talent. I'm fascinated by how people got to be there. It's really prompted by a conversation I had with a wonderful woman who maybe most people have never heard of, she's called Gillian Lynne, have you heard of her? Some have. She's a choreographer and everybody knows her work. She did "Cats," and "Phantom of the Opera." She's wonderful. I used to be on the board of the Royal Ballet, in England, as you can see. Anyway, Gillian and I had lunch one day and I said, "Gillian, how'd you get to be a dancer?" And she said it was interesting, when she was at school, she was really hopeless. And the school, in the '30s, wrote to her parents and said, "We think Gillian has a learning disorder." She couldn't concentrate, she was fidgeting. I think now they'd say she had ADHD. Wouldn't you? But this was the 1930s, and ADHD hadn't been invented at this point. It wasn't an available condition. People weren't aware they could have that.
Anyway, she went to see this specialist. So, this oak-paneled room And she was there with her mother, and she was led and sat on a chair at the end, and she sat on her hands for 20 minutes while this man talked to her mother about all the problems Gillian was having at school. And at the end of it -- because she was disturbing people, her homework was always late, and so on, little kid of eight -- in the end, the doctor went and sat next to Gillian and said, "Gillian, I've listened to all these things that your mother's told me, and I need to speak to her privately." He said, "Wait here, we'll be back, we won't be very long." and they went and left her. But as they went out the room, he turned on the radio that was sitting on his desk. And when they got out the room, he said to her mother, "Just stand and watch her." And the minute they left the room, she said, she was on her feet, moving to the music. And they watched for a few minutes and he turned to her mother and said, "Mrs. Lynne, Gillian isn't sick, she's a dancer. Take her to a dance school."
I said, "What happened?" She said, "She did. I can't tell you how wonderful it was. We walked in this room and it was full of people like me. People who couldn't sit still. People who had to move to think." Who had to move to think. They did ballet, they did tap, they did jazz, they did modern, they did contemporary. She was eventually auditioned for the Royal Ballet School, she became a soloist, she had a wonderful career at the Royal Ballet. She eventually graduated from the Royal Ballet School and founded her own company, the Gillian Lynne Dance Company, met Andrew Lloyd Weber. She's been responsible for some of the most successful musical theater productions in history, she's given pleasure to millions, and she's a multi-millionaire. Somebody else might have put her on medication and told her to calm down.
Now, I think -- What I think it comes to is this: Al Gore spoke the other night about ecology, and the revolution that was triggered by Rachel Carson. I believe our only hope for the future is to adopt a new conception of human ecology, one in which we start to reconstitute our conception of the richness of human capacity. Our education system has mined our minds in the way that we strip-mine the earth: for a particular commodity. And for the future, it won't serve us. We have to rethink the fundamental principles on which we're educating our children. There was a wonderful quote by Jonas Salk, who said, "If all the insects were to disappear from the earth, within 50 years all life on Earth would end. If all human beings disappeared from the earth, within 50 years all forms of life would flourish." And he's right.
What TED celebrates is the gift of the human imagination. We have to be careful now that we use this gift wisely, and that we avert some of the scenarios scenarios that we've talked about. And the only way we'll do it is by seeing our creative capacities for the richness they are, and seeing our children for the hope that they are. And our task is to educate their whole being, so they can face this future. By the way -- we may not see this future, but they will. And our job is to help them make something of it. Thank you very much.
Reflections on Teaching
I'm not sure when it became apparent to me that liked teaching. I
remember helping other people with math and biology back in ninth
grade, but I don't think I had that much self-understanding at the
time. I helped with some (in reality, a minimal amount) of peer
tutoring in high school through the math center, where students can
drop in and ask questions about their math work. Not too many students
used that though, and I maybe helped three students in the two years I
was there. Freshman year in college, I was a student in theGateway Science Workshop (GSW)
peer tutoring program at Northwestern. I think that was the first time
I really woke up to the idea that I want to teach. I remember that my
facilitator was really not very good at the whole facilitation thing,
and often I would be explaining things to other people in the session,
if other people were there at all. I stayed in the program because I
was bored (the things boredom make you do!), and I stayed with the same
facilitator because it was easy (the things comfort makes you do!). But
by the last quarter of that year, I had made up enough of my mind to
apply to be a GSW facilitator next year, which I got.
For the next three years, I was first a facilitator, then a senior facilitator, and finally just filling in sessions as necessary. This means I've been involved with the program for all four years of college, and of course I did two summers of CTY as well. In the next two weeks I will be a Graduate Student Instructor (GSI) at Michigan, my "fourth" year of teaching.
It is therefore unfortunate that this last year, if not more, of GSW was horrible.
By this statement I don't mean that I grew to hate GSW, or indeed that GSW was something I had to tolerate. No, I still enjoyed every session of GSW; I just wasn't convinced my students enjoyed it. When I think back over successive years of GSW, I can see that I have gotten complacent about teaching and have relaxed how I think about it. Let me give some examples.
Although the GSW facilitator orientation at the start of the year recommends doing ice breakers during the first session (or two) of each quarter, I gave up doing those around the middle of junior year. During the first year of GSW, I had a couple students follow me for the entire year. Since students can get priority to follow the same facilitator through the school year, this means that the students found what I said useful. I had some students join me the second quarter, who stayed for the final quarter too. But each quarter there were also new students, and so despite it being awkward for the people who I already know and who already know each other, I continued to do ice breakers. The second year, no one from my first quarter stayed, but a number from my second quarter stayed for the third. I didn't intend to skip ice breakers - I remember coming prepared to do them, but there were only two students in the first session of the quarter, and it seemed silly to do games with just two people.
I could blame the decreasing number of students in GSW for that, but while that does contribute to the situation, it is my attitude which changed. Simply put, I became more focused on what an ideal session is like than on how to foster such an ideal session. For peer tutoring (and I think teaching in general), it's best if the students talk to each other and exchange ideas. Not because there's a barrier, however small, between facilitator and student, but also because students are much closer in mindset than the facilitator. Sharing how they approach problems allows everyone to reformulate the question, and perhaps find a perspective which helps them most easily understand. And therefore, in an ideal session (I remember I had one absolutely perfect session back in my first year), the facilitator mostly listens while the students teach each other, only stepping in if everyone is stuck.
My mistake is that I allowed my non-participation become status quo, without adapting to whether the students were discussion. This turns what should be a discussion into something worse than a lecture - it turns into a self study. I forgot that getting that initial engagement takes work, and an ice breaker - even if it seems silly - is part of that work. Instead of leading the students through problems until they have developed the confidence to discuss among themselves, I have just been letting them work.
I just finished Ken Bain's What the Best College Teachers Do, and while it wasn't a ten point plan to better teaching (which would have been bound to failure), I did get some insight into what I've been neglecting. The main thing I learned is that even though you may be going through the same motions, your relationship with you students depends as your attitude as well, and without that the same motion just doesn't work. My personal example of that is offering to stay after the session to help. The first year, I've had students ask me more questions afterwards, and that had led me to know more about them and their background as well. Lately though, although I still make the same offer, no students take me up on it. This is because I haven't gained their trust (note: this is different from them not trusting me enough). When I started GSW, I cared a lot more about what the students are thinking and how they are feeling about the material and the session itself. In my personal journal I have written short evaluations of the students after the first couple sessions, noting how they're reacting to me, and how I can draw them out more. I actually cared about their answer to the customary "how was your week?" - it wasn't just a greeting, but a semi-serious attempt to know more about the students. This mutual understanding and trust, although not reflected in the students' attendance records or grades, paves the way to the autonomous learning I described.
The other big mistake I made is not leading them through the questions anymore. This applies whether or not that trust is established, although if the students are actively discussion the problem at hand it is more permissible to step back. What I realized is that talking them through the question (note: not through the solution) shows them more than how to arrive at the answer. It also shows them how to approach these types of questions, and what kind of thinking the student is supposed to have. After all, the material is only part of what we care about as teachers. Equally as important, if not more so, is that the students can think within the discipline. For computer science, for example, that means the ability to break down a complex procedure into simple steps, evaluating whether that solution is cost-effective, and so on. For Newtonian mechanics, that means seeing the forces acting on objects and knowing how the forces interact. Whether they can use big-O descriptions or integral calculus to find the answer is something else, but getting that thinking there takes precedence. If I lead the students through the question, letting them make mistakes and questioning them on why their solution does or does not work, I am changing ever so slightly the way they see the world.
The last mistake I made, this one somewhat less apparent but equally influential, is that I stopped thinking about what the students are learning. This seems silly, especially since GSW has all the worksheets made for us. But without a goal, without consciously trying to lead the students into the way of thinking, it is too easy to simply go for the answers. I am robbing the students of their opportunity to look at the larger questions. Again, it's not the questions on the worksheet which are the most important, but the concepts behind it. The successful completion of the worksheet is merely a proxy to what the students learned. Bain brought up studies where the students can ace a Newtonian physics final, but still hold some naive, intuitive beliefs about motion. Part of it is certainly how the final was designed, but part of it (a larger part, I would argue) is that the teacher has not thought about how to bring it above just plugging and chugging.
If I had to summarize Bain's book in one sentence, it's this: The goal of teaching is for students to not just learn the material, but to understand it's implications. This necessarily means changing (or at least adding to) how students think. Ways of thinking, unfortunately, are pretty resistant to change, and so to accomplish that the teacher needs to be prepared. I want to give three examples of good teaching, all of which I have personally experienced as a TA to the course.
The first is from CTY, where once a week during lunch my instructor will give a student a dollar if they can give the pronunciation and meaning of a word (limited to a collegiate dictionary) which he couldn't spell. The result is that the day before and the day of, the students will spend a lot of their free time looking at a dictionary. Think about it: if a teacher's job, in general, is to spark people's desire to learn, then he has achieved this beyond measure. No children of twelve will willingly spend hours looking at a dictionary, but giving them this challenge drives them to do so. Whether they learned anything by looking at the dictionary is arguable, but it did inspire an educational fervor.
The second example is from compilers. The professor consistently brought up books and papers which were not included in the textbook. These books were not necessarily related to compilers, although they were all relevant to the topic under discussion at the time. This has the same effect as the spelling challenge - it draws the students deeper in to the subject, while making them aware of the larger context of what they're studying. The best thing is that, at least for me, I really get the sense that the professor is really bringing up the books because he wants to invite the students to share his curiosity and interest in those subjects, and not just to impress students by how much he knows.
The last example is by the same professor. I mentioned that exams and most homework being just a proxy to measure how much a student understands. So the "final" for the compilers course (in addition to a working compiler, of course), instead of being a paper, was a "code walk". That means the student/group comes in to meet the professor for an hour, during which the student walks the professor through their code. This is done in an informal fashion - it's not a powerpoint presentation - but it allows the student to let the professor know, with the highest "bandwidth" possible, what they have learned. And although there are "points" awarded through the quarter for sections of a finished compiler, that merely influences the final grade. If a student did poorly before, but have improved as the quarter went on (each assignment is cumulative, and previous test cases are run again) with the final result of presenting a well organized code walk at the end, then they get a good grade. That is, the students are graded on what they understand, both about compilers and about programming in general, and not just whether they can answer questions about compilers in general.
So to put this into practice, I'm writing my own CTY robotics curriculum (like I did last year) with all this in mind. I will post the result here when I'm done. To close though, I want to pull a totally unrelated quote. I feel this should be how assignments given to students should be viewed, as:
For the next three years, I was first a facilitator, then a senior facilitator, and finally just filling in sessions as necessary. This means I've been involved with the program for all four years of college, and of course I did two summers of CTY as well. In the next two weeks I will be a Graduate Student Instructor (GSI) at Michigan, my "fourth" year of teaching.
It is therefore unfortunate that this last year, if not more, of GSW was horrible.
By this statement I don't mean that I grew to hate GSW, or indeed that GSW was something I had to tolerate. No, I still enjoyed every session of GSW; I just wasn't convinced my students enjoyed it. When I think back over successive years of GSW, I can see that I have gotten complacent about teaching and have relaxed how I think about it. Let me give some examples.
Although the GSW facilitator orientation at the start of the year recommends doing ice breakers during the first session (or two) of each quarter, I gave up doing those around the middle of junior year. During the first year of GSW, I had a couple students follow me for the entire year. Since students can get priority to follow the same facilitator through the school year, this means that the students found what I said useful. I had some students join me the second quarter, who stayed for the final quarter too. But each quarter there were also new students, and so despite it being awkward for the people who I already know and who already know each other, I continued to do ice breakers. The second year, no one from my first quarter stayed, but a number from my second quarter stayed for the third. I didn't intend to skip ice breakers - I remember coming prepared to do them, but there were only two students in the first session of the quarter, and it seemed silly to do games with just two people.
I could blame the decreasing number of students in GSW for that, but while that does contribute to the situation, it is my attitude which changed. Simply put, I became more focused on what an ideal session is like than on how to foster such an ideal session. For peer tutoring (and I think teaching in general), it's best if the students talk to each other and exchange ideas. Not because there's a barrier, however small, between facilitator and student, but also because students are much closer in mindset than the facilitator. Sharing how they approach problems allows everyone to reformulate the question, and perhaps find a perspective which helps them most easily understand. And therefore, in an ideal session (I remember I had one absolutely perfect session back in my first year), the facilitator mostly listens while the students teach each other, only stepping in if everyone is stuck.
My mistake is that I allowed my non-participation become status quo, without adapting to whether the students were discussion. This turns what should be a discussion into something worse than a lecture - it turns into a self study. I forgot that getting that initial engagement takes work, and an ice breaker - even if it seems silly - is part of that work. Instead of leading the students through problems until they have developed the confidence to discuss among themselves, I have just been letting them work.
I just finished Ken Bain's What the Best College Teachers Do, and while it wasn't a ten point plan to better teaching (which would have been bound to failure), I did get some insight into what I've been neglecting. The main thing I learned is that even though you may be going through the same motions, your relationship with you students depends as your attitude as well, and without that the same motion just doesn't work. My personal example of that is offering to stay after the session to help. The first year, I've had students ask me more questions afterwards, and that had led me to know more about them and their background as well. Lately though, although I still make the same offer, no students take me up on it. This is because I haven't gained their trust (note: this is different from them not trusting me enough). When I started GSW, I cared a lot more about what the students are thinking and how they are feeling about the material and the session itself. In my personal journal I have written short evaluations of the students after the first couple sessions, noting how they're reacting to me, and how I can draw them out more. I actually cared about their answer to the customary "how was your week?" - it wasn't just a greeting, but a semi-serious attempt to know more about the students. This mutual understanding and trust, although not reflected in the students' attendance records or grades, paves the way to the autonomous learning I described.
The other big mistake I made is not leading them through the questions anymore. This applies whether or not that trust is established, although if the students are actively discussion the problem at hand it is more permissible to step back. What I realized is that talking them through the question (note: not through the solution) shows them more than how to arrive at the answer. It also shows them how to approach these types of questions, and what kind of thinking the student is supposed to have. After all, the material is only part of what we care about as teachers. Equally as important, if not more so, is that the students can think within the discipline. For computer science, for example, that means the ability to break down a complex procedure into simple steps, evaluating whether that solution is cost-effective, and so on. For Newtonian mechanics, that means seeing the forces acting on objects and knowing how the forces interact. Whether they can use big-O descriptions or integral calculus to find the answer is something else, but getting that thinking there takes precedence. If I lead the students through the question, letting them make mistakes and questioning them on why their solution does or does not work, I am changing ever so slightly the way they see the world.
The last mistake I made, this one somewhat less apparent but equally influential, is that I stopped thinking about what the students are learning. This seems silly, especially since GSW has all the worksheets made for us. But without a goal, without consciously trying to lead the students into the way of thinking, it is too easy to simply go for the answers. I am robbing the students of their opportunity to look at the larger questions. Again, it's not the questions on the worksheet which are the most important, but the concepts behind it. The successful completion of the worksheet is merely a proxy to what the students learned. Bain brought up studies where the students can ace a Newtonian physics final, but still hold some naive, intuitive beliefs about motion. Part of it is certainly how the final was designed, but part of it (a larger part, I would argue) is that the teacher has not thought about how to bring it above just plugging and chugging.
If I had to summarize Bain's book in one sentence, it's this: The goal of teaching is for students to not just learn the material, but to understand it's implications. This necessarily means changing (or at least adding to) how students think. Ways of thinking, unfortunately, are pretty resistant to change, and so to accomplish that the teacher needs to be prepared. I want to give three examples of good teaching, all of which I have personally experienced as a TA to the course.
The first is from CTY, where once a week during lunch my instructor will give a student a dollar if they can give the pronunciation and meaning of a word (limited to a collegiate dictionary) which he couldn't spell. The result is that the day before and the day of, the students will spend a lot of their free time looking at a dictionary. Think about it: if a teacher's job, in general, is to spark people's desire to learn, then he has achieved this beyond measure. No children of twelve will willingly spend hours looking at a dictionary, but giving them this challenge drives them to do so. Whether they learned anything by looking at the dictionary is arguable, but it did inspire an educational fervor.
The second example is from compilers. The professor consistently brought up books and papers which were not included in the textbook. These books were not necessarily related to compilers, although they were all relevant to the topic under discussion at the time. This has the same effect as the spelling challenge - it draws the students deeper in to the subject, while making them aware of the larger context of what they're studying. The best thing is that, at least for me, I really get the sense that the professor is really bringing up the books because he wants to invite the students to share his curiosity and interest in those subjects, and not just to impress students by how much he knows.
The last example is by the same professor. I mentioned that exams and most homework being just a proxy to measure how much a student understands. So the "final" for the compilers course (in addition to a working compiler, of course), instead of being a paper, was a "code walk". That means the student/group comes in to meet the professor for an hour, during which the student walks the professor through their code. This is done in an informal fashion - it's not a powerpoint presentation - but it allows the student to let the professor know, with the highest "bandwidth" possible, what they have learned. And although there are "points" awarded through the quarter for sections of a finished compiler, that merely influences the final grade. If a student did poorly before, but have improved as the quarter went on (each assignment is cumulative, and previous test cases are run again) with the final result of presenting a well organized code walk at the end, then they get a good grade. That is, the students are graded on what they understand, both about compilers and about programming in general, and not just whether they can answer questions about compilers in general.
So to put this into practice, I'm writing my own CTY robotics curriculum (like I did last year) with all this in mind. I will post the result here when I'm done. To close though, I want to pull a totally unrelated quote. I feel this should be how assignments given to students should be viewed, as:
"A series of great opportunities disguised as insoluble [read: intriguing] problems" - president of Stanford University John Hennessy, on the energy-climate challenge, as quoted in Thomas Friedman's Hot, Flat, and Crowded
2009-08-24
Answers of the Weeks
What is the difference between hurricanes, typhoons, and maelstroms?
Hurricanes are basically large storm systems (aka tropical cyclone). Typhoons are just hurricanes which form in the Pacific ocean; as far as I can tell, it's just a naming difference.
Maelstroms are giant whirlpools; they have nothing to do with the above.
How do 3D glasses work?
3D glasses allow movies to be turned into "stereograms". Humans (and most animals, I assume) have depth perception because each of our two eyes sees slightly different things. This is most clearly demonstrated if you put a finger in front of your nose. If you then focus on something far away, you will have two semi-transparent fingers. This comes from the brain trying to compensate for the blocked view, and piecing information from the two eyes together.
Cute trick - take a hollow, see-through, cylindrical tube (like a used toilet paper roll), and put it up to one eye. Now, take your hand, and put it along the tube in front of the other eye. Open both eyes. If you're doing this correctly, you should see a "hole" in your hand. It's the same principle as the two "fingers" above - your brain fills in the what should be behind the hand, and since it only knows what your other eye can see through the tube, that's the only part it fills in.
Anyway, back to stereograms and 3D movies. In the old days, 3D pictures are created with color-filtered glasses. Two images of different colors are projected onto the movie screen, and when people put 3D glasses on, each eye sees only one of the colored pictures - because the filter blocks out the other color. By presenting each eye with a slightly different image, the illusion of depth is created. In the two images, things that should be "closer" would have more horizontal displacement, while things that should be "further" would have less. This can be demonstrated by moving the finger back and forth, while still staring at something far away. The further you extend your finger, the closer the two "fingers" appear.
What my question was really getting at was the new, polarized, 3D glasses. I watched Pixar's Up in those, and noticed while standing in line that the glasses only darken when paired with one lens and turned to a certain angle, but it would not darken with the other lens at all. We knew it was polarized, but we thought it would be linearly polarized at first. If that was the case though, the lens should darken regardless of which other lens it was paired with. I thought they were circularly polarized, which would explain the odd pairing thing, but I never did find out why it would be darkest at a certain angle.
Does truth exist?
This question was suggested to me by a friend. Clearly, the answer to this one would not be as... objectively truthful most other questions. I can, however, give my personal belief: yes.
I do believe in an objective truth. To me it's simple: either the trees, the mountains, and my laptop all exist, or I'm a brain in a vat and hallucinating all this, or even I'm part of a strange dream of a giant frog. Whichever one of these is true - and I'm not saying that I know which one is - the basic idea remains that one of them is true. Of course, it could be that none of those are correct, but it's hard to imagine a reality where there is no truth at all. It would almost be a paradox to call it a reality at that point.
Whether we, as humans, would ever know the truth is a completely different question.
Why do humans have social needs?
As far as I can tell, it's evolutionary. This section of Wikipedia gives a fairly simple answer.
I actually made a mistake in the list of questions; the question of whether AIs can become a human's best friend should have been under this question of social needs. That was the true point of asking this question: if social needs could be met without physical contact (for example, through the phone, through email, IM, etc.), then it is almost inevitable humans will eventually befriend an AI.
Let me attack the conditions first. Could human social needs be satisfied without physical contact? I think so. In the old days people have pen pals and write letters to family members in far away places. There is satisfaction in doing those things, and it could only be social in nature. Nowadays people have phones, email, IM, Facebook, etc. which makes it even easier to keep up with people without their physical existance.
A deeper question could be asked as to how advanced the AI has to be. Now that people are used to computers and the idea of AI, it would have to be quite advanced. When AI was just being invented, however, people were willing to believe that they were interacting with a human. Just look at the first ELIZA tests. People got attached to the computer, despite being told how it works and that it's just a computer program. That's one of the big downfalls of the Turing test - that people are too willing to believe. For the purpose of meeting social needs, however, this willingness to believe might be exactly what is needed.
On another level, and also speaking personally, the AI would have to be quite advanced for me to be satisfied. I'm interested in people's stories, not just discussions on various topics. Sure, a lot of my conversations with people have a philosophical leaning, but it's interesting because they have experiences which led them to their believes. Without this experience, it's no different from reading a dry book which simply lays out the argument - or it should more properly called the plan of attack, because there wouldn't be any argument at all.
That said, I believe we will eventually have the technology to create AIs which have their own - albeit not physical - histories and stories.
Hurricanes are basically large storm systems (aka tropical cyclone). Typhoons are just hurricanes which form in the Pacific ocean; as far as I can tell, it's just a naming difference.
Maelstroms are giant whirlpools; they have nothing to do with the above.
How do 3D glasses work?
3D glasses allow movies to be turned into "stereograms". Humans (and most animals, I assume) have depth perception because each of our two eyes sees slightly different things. This is most clearly demonstrated if you put a finger in front of your nose. If you then focus on something far away, you will have two semi-transparent fingers. This comes from the brain trying to compensate for the blocked view, and piecing information from the two eyes together.
Cute trick - take a hollow, see-through, cylindrical tube (like a used toilet paper roll), and put it up to one eye. Now, take your hand, and put it along the tube in front of the other eye. Open both eyes. If you're doing this correctly, you should see a "hole" in your hand. It's the same principle as the two "fingers" above - your brain fills in the what should be behind the hand, and since it only knows what your other eye can see through the tube, that's the only part it fills in.
Anyway, back to stereograms and 3D movies. In the old days, 3D pictures are created with color-filtered glasses. Two images of different colors are projected onto the movie screen, and when people put 3D glasses on, each eye sees only one of the colored pictures - because the filter blocks out the other color. By presenting each eye with a slightly different image, the illusion of depth is created. In the two images, things that should be "closer" would have more horizontal displacement, while things that should be "further" would have less. This can be demonstrated by moving the finger back and forth, while still staring at something far away. The further you extend your finger, the closer the two "fingers" appear.
What my question was really getting at was the new, polarized, 3D glasses. I watched Pixar's Up in those, and noticed while standing in line that the glasses only darken when paired with one lens and turned to a certain angle, but it would not darken with the other lens at all. We knew it was polarized, but we thought it would be linearly polarized at first. If that was the case though, the lens should darken regardless of which other lens it was paired with. I thought they were circularly polarized, which would explain the odd pairing thing, but I never did find out why it would be darkest at a certain angle.
Does truth exist?
This question was suggested to me by a friend. Clearly, the answer to this one would not be as... objectively truthful most other questions. I can, however, give my personal belief: yes.
I do believe in an objective truth. To me it's simple: either the trees, the mountains, and my laptop all exist, or I'm a brain in a vat and hallucinating all this, or even I'm part of a strange dream of a giant frog. Whichever one of these is true - and I'm not saying that I know which one is - the basic idea remains that one of them is true. Of course, it could be that none of those are correct, but it's hard to imagine a reality where there is no truth at all. It would almost be a paradox to call it a reality at that point.
Whether we, as humans, would ever know the truth is a completely different question.
Why do humans have social needs?
As far as I can tell, it's evolutionary. This section of Wikipedia gives a fairly simple answer.
I actually made a mistake in the list of questions; the question of whether AIs can become a human's best friend should have been under this question of social needs. That was the true point of asking this question: if social needs could be met without physical contact (for example, through the phone, through email, IM, etc.), then it is almost inevitable humans will eventually befriend an AI.
Let me attack the conditions first. Could human social needs be satisfied without physical contact? I think so. In the old days people have pen pals and write letters to family members in far away places. There is satisfaction in doing those things, and it could only be social in nature. Nowadays people have phones, email, IM, Facebook, etc. which makes it even easier to keep up with people without their physical existance.
A deeper question could be asked as to how advanced the AI has to be. Now that people are used to computers and the idea of AI, it would have to be quite advanced. When AI was just being invented, however, people were willing to believe that they were interacting with a human. Just look at the first ELIZA tests. People got attached to the computer, despite being told how it works and that it's just a computer program. That's one of the big downfalls of the Turing test - that people are too willing to believe. For the purpose of meeting social needs, however, this willingness to believe might be exactly what is needed.
On another level, and also speaking personally, the AI would have to be quite advanced for me to be satisfied. I'm interested in people's stories, not just discussions on various topics. Sure, a lot of my conversations with people have a philosophical leaning, but it's interesting because they have experiences which led them to their believes. Without this experience, it's no different from reading a dry book which simply lays out the argument - or it should more properly called the plan of attack, because there wouldn't be any argument at all.
That said, I believe we will eventually have the technology to create AIs which have their own - albeit not physical - histories and stories.
Subscribe to:
Posts (Atom)
