Last week, I invited my team to bring in theirs and their friends' school children to our office. The idea was a Skype Connecting Classrooms Session. I am a Skype classroom connector, shown in this video in the very beginning itself.
You can see me at 16th second as you play this video, on the very first page of the "Connecting Classrooms" search, in this video by Skype.
Gopan, CUSAT, brought his daughter Theerdha and her mother Lekha. There were teachers and students from other schools as well.
Children enjoyed their chat with Anne Mirtschin, a very prominent leader in the field of education. Anne was the Chair person of Global Education Conference, Tech Talk Tuesdays and many many platforms.
Fr. Felix, Manager of St Pauls College is keen on taking the college to 21st century skills, he told me recently at a meeting. Hence, I plan to Connect St. Pauls Classrooms to Global Classroom
Listen to this TED video, presenting the history of computers, and how science hobbyists are recreating Charles Babbage's machine to help us see, touch and smell computers.
Here is the transcript
The transcript helps you develop an ear to hear English the way it is spoken by native speakers. As an English lesson is based on this, you achieve multidisciplinary learning.
So the machine I'm going to talk you about is what I call the greatest machine that never was. It was a machine that was never built, and yet, it will be built. It was a machine that was designed long before anyone thought about computers.
If you know anything about the history of computers, you will know that in the '30s and the '40s, simple computers were created that started the computer revolution we have today, and you would be correct, except for you'd have the wrong century. The first computer was really designed in the 1830s and 1840s, not the 1930s and 1940s. It was designed, and parts of it were prototyped, and the bits of it that were built are here in South Kensington.
That machine was built by this guy, Charles Babbage. Now, I have a great affinity for Charles Babbage because his hair is always completely unkempt like this in every single picture. (Laughter) He was a very wealthy man, and a sort of, part of the aristocracy of Britain, and on a Saturday night in Marylebone, were you part of the intelligentsia of that period, you would have been invited round to his house for a soiree — and he invited everybody: kings, the Duke of Wellington, many, many famous people — and he would have shown you one of his mechanical machines.
I really miss that era, you know, where you could go around for a soiree and see a mechanical computer get demonstrated to you. (Laughter) But Babbage, Babbage himself was born at the end of the 18th century, and was a fairly famous mathematician. He held the post that Newton held at Cambridge, and that was recently held by Stephen Hawking. He's less well known than either of them because he got this idea to make mechanical computing devices and never made any of them.
The reason he never made any of them, he's a classic nerd. Every time he had a good idea, he'd think, "That's brilliant, I'm going to start building that one. I'll spend a fortune on it. I've got a better idea. I'm going to work on this one. (Laughter) And I'm going to do this one." He did this until Sir Robert Peel, then Prime Minister, basically kicked him out of Number 10 Downing Street, and kicking him out, in those days, that meant saying, "I bid you good day, sir." (Laughter)
The thing he designed was this monstrosity here, the analytical engine. Now, just to give you an idea of this, this is a view from above. Every one of these circles is a cog, a stack of cogs, and this thing is as big as a steam locomotive. So as I go through this talk, I want you to imagine this gigantic machine. We heard those wonderful sounds of what this thing would have sounded like. And I'm going to take you through the architecture of the machine — that's why it's computer architecture — and tell you about this machine, which is a computer.
So let's talk about the memory. The memory is very like the memory of a computer today, except it was all made out of metal, stacks and stacks of cogs, 30 cogs high. Imagine a thing this high of cogs, hundreds and hundreds of them, and they've got numbers on them. It's a decimal machine. Everything's done in decimal. And he thought about using binary. The problem with using binary is that the machine would have been so tall, it would have been ridiculous. As it is, it's enormous. So he's got memory. The memory is this bit over here. You see it all like this.
This monstrosity over here is the CPU, the chip, if you like. Of course, it's this big. Completely mechanical. This whole machine is mechanical. This is a picture of a prototype for part of the CPU which is in the Science Museum.
The CPU could do the four fundamental functions of arithmetic -- so addition, multiplication, subtraction, division -- which already is a bit of a feat in metal, but it could also do something that a computer does and a calculator doesn't: this machine could look at its own internal memory and make a decision. It could do the "if then" for basic programmers, and that fundamentally made it into a computer. It could compute. It couldn't just calculate. It could do more.
Now, if we look at this, and we stop for a minute, and we think about chips today, we can't look inside a silicon chip. It's just so tiny. Yet if you did, you would see something very, very similar to this. There's this incredible complexity in the CPU, and this incredible regularity in the memory. If you've ever seen an electron microscope picture, you'll see this. This all looks the same, then there's this bit over here which is incredibly complicated.
All this cog wheel mechanism here is doing is what a computer does, but of course you need to program this thing, and of course, Babbage used the technology of the day and the technology that would reappear in the '50s, '60s and '70s, which is punch cards. This thing over here is one of three punch card readers in here, and this is a program in the Science Museum, just not far from here, created by Charles Babbage, that is sitting there — you can go see it — waiting for the machine to be built. And there's not just one of these, there's many of them. He prepared programs anticipating this would happen.
Now, the reason they used punch cards was that Jacquard, in France, had created the Jacquard loom, which was weaving these incredible patterns controlled by punch cards, so he was just repurposing the technology of the day, and like everything else he did, he's using the technology of his era, so 1830s, 1840s, 1850s, cogs, steam, mechanical devices. Ironically, born the same year as Charles Babbage was Michael Faraday, who would completely revolutionize everything with the dynamo, transformers, all these sorts of things. Babbage, of course, wanted to use proven technology, so steam and things.
Now, he needed accessories. Obviously, you've got a computer now. You've got punch cards, a CPU and memory. You need accessories you're going to come with. You're not just going to have that,
So, first of all, you had sound. You had a bell, so if anything went wrong — (Laughter) — or the machine needed the attendant to come to it, there was a bell it could ring. (Laughter) And there's actually an instruction on the punch card which says "Ring the bell." So you can imagine this "Ting!" You know, just stop for a moment, imagine all those noises, this thing, "Click, clack click click click," steam engine, "Ding," right? (Laughter)
You also need a printer, obviously, and everyone needs a printer. This is actually a picture of the printing mechanism for another machine of his, called the Difference Engine No. 2, which he never built, but which the Science Museum did build in the '80s and '90s. It's completely mechanical, again, a printer. It prints just numbers, because he was obsessed with numbers, but it does print onto paper, and it even does word wrapping, so if you get to the end of the line, it goes around like that.
You also need graphics, right? I mean, if you're going to do anything with graphics, so he said, "Well, I need a plotter. I've got a big piece of paper and an ink pen and I'll make it plot." So he designed a plotter as well, and, you know, at that point, I think he got pretty much a pretty good machine.
Along comes this woman, Ada Lovelace. Now, imagine these soirees, all these great and good comes along. This lady is the daughter of the mad, bad and dangerous-to-know Lord Byron, and her mother, being a bit worried that she might have inherited some of Lord Byron's madness and badness, thought, "I know the solution: Mathematics is the solution. We'll teach her mathematics. That'll calm her down." (Laughter) Because of course, there's never been a mathematician that's gone crazy, so, you know, that'll be fine. (Laughter) Everything'll be fine. So she's got this mathematical training, and she goes to one of these soirees with her mother, and Charles Babbage, you know, gets out his machine. The Duke of Wellington is there, you know, get out the machine, obviously demonstrates it, and she gets it. She's the only person in his lifetime, really, who said, "I understand what this does, and I understand the future of this machine." And we owe to her an enormous amount because we know a lot about the machine that Babbage was intending to build because of her.
Now, some people call her the first programmer. This is actually from one of -- the paper that she translated. This is a program written in a particular style. It's not, historically, totally accurate that she's the first programmer, and actually, she did something more amazing. Rather than just being a programmer, she saw something that Babbage didn't.
Babbage was totally obsessed with mathematics. He was building a machine to do mathematics, and Lovelace said, "You could do more than mathematics on this machine." And just as you do, everyone in this room already's got a computer on them right now, because they've got a phone. If you go into that phone, every single thing in that phone or computer or any other computing device is mathematics. It's all numbers at the bottom. Whether it's video or text or music or voice, it's all numbers, it's all, underlying it, mathematical functions happening, and Lovelace said, "Just because you're doing mathematical functions and symbols doesn't mean these things can't represent other things in the real world, such as music." This was a huge leap, because Babbage is there saying, "We could compute these amazing functions and print out tables of numbers and draw graphs," — (Laughter) — and Lovelace is there and she says, "Look, this thing could even compose music if you told it a representation of music numerically." So this is what I call Lovelace's Leap. When you say she's a programmer, she did do some, but the real thing is to have said the future is going to be much, much more than this.
Now, a hundred years later, this guy comes along, Alan Turing, and in 1936, and invents the computer all over again. Now, of course, Babbage's machine was entirely mechanical. Turing's machine was entirely theoretical. Both of these guys were coming from a mathematical perspective, but Turing told us something very important. He laid down the mathematical foundations for computer science, and said, "It doesn't matter how you make a computer." It doesn't matter if your computer's mechanical, like Babbage's was, or electronic, like computers are today, or perhaps in the future, cells, or, again, mechanical again, once we get into nanotechnology. We could go back to Babbage's machine and just make it tiny. All those things are computers. There is in a sense a computing essence. This is called the Church–Turing thesis.
And so suddenly, you get this link where you say this thing Babbage had built really was a computer. In fact, it was capable of doing everything we do today with computers, only really slowly. (Laughter) To give you an idea of how slowly, it had about 1k of memory. It used punch cards, which were being fed in, and it ran about 10,000 times slower the first ZX81. It did have a RAM pack. You could add on a lot of extra memory if you wanted to.
(Laughter) So, where does that bring us today? So there are plans. Over in Swindon, the Science Museum archives, there are hundreds of plans and thousands of pages of notes written by Charles Babbage about this analytical engine. One of those is a set of plans that we call Plan 28, and that is also the name of a charity that I started with Doron Swade, who was the curator of computing at the Science Museum, and also the person who drove the project to build a difference engine, and our plan is to build it. Here in South Kensington, we will build the analytical engine.
The project has a number of parts to it. One was the scanning of Babbage's archive. That's been done. The second is now the study of all of those plans to determine what to build. The third part is a computer simulation of that machine, and the last part is to physically build it at the Science Museum.
When it's built, you'll finally be able to understand how a computer works, because rather than having a tiny chip in front of you, you've got to look at this humongous thing and say, "Ah, I see the memory operating, I see the CPU operating, I hear it operating. I probably smell it operating." (Laughter) But in between that we're going to do a simulation.
Babbage himself wrote, he said, as soon as the analytical engine exists, it will surely guide the future course of science. Of course, he never built it, because he was always fiddling with new plans, but when it did get built, of course, in the 1940s, everything changed.
Now, I'll just give you a little taste of what it looks like in motion with a video which shows just one part of the CPU mechanism working. So this is just three sets of cogs, and it's going to add. This is the adding mechanism in action, so you imagine this gigantic machine.
So, give me five years. Before the 2030s happen, we'll have it.
Thank you very much. (Applause)
Here is the transcript, a lesson worth your time, Maths teachers!
(Of course, we can replace all references to U.S. with India or the school where you work!)
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)
Some parents of GHSS, South Ezhippuram students invited me. They wanted to discuss about my proposal to help the students "Learn English Online". Last week I had attended George Machlan's Karaoke English with their children.
I got some students to listen to a Karaoke English lesson by George Machlan. The young boys and girls found it so much fun. They had never known lessons can be fun!! George's lessons are engaging.
Here is Shiji's testimonial about George and his way of teaching online. Shiji is a Learn English Online teacher, currently polishing her English to get rid of her South Indian accent, to grow into a world class English Teacher online.
I am now teaching some students of Ezhippuram school on GeoGebra. I am a member of Connecting Classrooms on Skype.
I am helping these students learn English language by empowering them to teach Vedic Mathematics to students abroad in English. Cross disciplinary learning, teaching mathematical content, should bring multiple benefits.
Yet another tool to teach Generation Next!
Electronics, Gates, Logic, Logic Gates, game made programmable with electronics... you have to see it to beleieve Makey Makey.
A computer, a plaything, a toy, a technology tool - you can name it anything. Rasperry Pi allows today's Net Generation to learn electronics, programming and everything they need to learn by playing around with this.
I hope the Engineering Colleges in Kerala takes it on as their responsibility to help students use this tool creatively.
I purposefully burn my bridges behind me.
I have announced at an Interview that WE (Wiki Educators) and GeoGebra Institute of Kerala have teamed up with the Smart School to take Kerala to the hyperspace. Once I have announced like this in public, I have to live up to it, lest I lose face and people ridicule me for showing off.
Yes. We are going to do that. I have a great team!
