Dr Gary Stager and the new, now, wow in technology

Transcript

Colin Chapman:

Hi everyone. My name is Colin Chapman and I am one of the master teachers for mathematics at the Academy.

Today we're joined by Dr. Gary Stager, whose internationally recognized work has been helping school leaders and teachers embrace technology, and whose book Invent to Learn is considered the Bible of the Maker movement in schools. Today we are discussing the variety of exciting new computational environments that may be used to support learning ,and engage in project-based approaches for students. This is a great episode for school teachers and leaders to better understand and address the challenges of teaching mathematics. So thanks for joining us, Gary, and-

Dr. Gary Stager:

Great to be here.

Colin Chapman:

... and we'll kick it off. So one of the things that is important to your work is this concept of physical computing. Would you be able to expand on what you mean by that?

Dr. Gary Stager:

Quite simply, physical computing is the addition of interactivity and intelligence to everyday objects. It's commonly thought of as robotics, but it could be wider than that, that you can make something and you can make something do something, and you do that by programming it. And when we think about kids, it's giving us the affordance of having new colors in a crayon box, adding to the breadth and depth and range of projects that are possible. So if you could in the past make a dinosaur out of cereal boxes, but now your cereal box dinosaur can sing dance or send a text message to your grandmother. Why wouldn't you let kids do that? Maybe the dinosaurs could have a conversation with one another. Maybe they could be searching for food, and when they find some stimuli report to the other dinosaurs who come running. It just allows for a greater range of expression than has ever been possible before.

Colin Chapman:

So it seems to be a different environment when we have screen-based outputs, and then we have physical environment outputs, or even inputs for that matter. There's a certain uncertainty with regard to physical computing, isn't there? Because the thing is acting in the world.

Dr. Gary Stager:

And the world's messy.

Colin Chapman:

Yes.

Dr. Gary Stager:

And it has friction and carpet,

Colin Chapman:

A bit of talcum powder, the wheel slip, why isn't it going to where we said it should go and so on? And it brings to mind that acronym that anything that we design, it's volatile, it's uncertain. There's ambiguity and there's complexity. And there's a certain beauty in physical computing in that we can design something in response to a challenge, but the environment may have other ideas. In fact, the apparatus itself may have other ideas. Have you got some vignettes throughout your experience where students have engaged in this messy environment, and what sort of learning they might've taken from that?

Dr. Gary Stager:

Well, sure, I'll give you a simple one. Kid builds a little vehicle that has a motor or two on it, and you push a go button and it goes. And then I'm involved with other kids in the classroom and I notice that he's changed the program so that when he collapse his hands, it'll go and he claps his hands again, it'll stop. So he's dealing with some sensor feedback. And then I observed from a distance that he went to get a meter stick and a stopwatch, and actually didn't need a stopwatch. He programmed the vehicle now to go forward for 10 seconds or one second or some unit of time, and measured how far it traveled with the meter stick. And I instantly knew what he was up to. He wanted to know how fast it goes.

And centimeters per second isn't a very satisfying unit for a kid who's building a car. They want to know kilometers per mile. And that's traditionally where the fun and games ends and several years of tedious, often inaccurate, cumbersome unit conversions begin. And this is maybe 10 years ago already at this point. I pointed the kid to Wolf from Alpha, and he was able to type X number of centimeters per second, and it immediately converted it to all sorts of units, including kilometers per hour or miles per hour. And then one of the things we hadn't anticipated was it was some percentage of the average human walking speed.

And it just gave us this little bit of trivia that we didn't know would appear in this list of units. It was 0.76 of the human walking speed, if I remember correctly. So now we're dealing with fractions and decimals, which is certainly in the syllabus. And there's great motivation now to do something with that, because obviously you want to make your car faster than a human walks. So now this is an invitation to deal with mechanical advantage and gearing and see what he could do to the actual physical thing to make it perform at a higher level of performance than it was naturally.

Colin Chapman:

And isn't it wonderful to see the mathematics that's in there? So even just doing that calculation for speed, taking at the meter stick, and trying to get an idea of how fast the machine is going, is an understanding of the idea of rate of change, which is so important to our science endeavors. It's a step towards calculus eventually, isn't it?

Dr. Gary Stager:

No, I have a photo of this, because I was so taken by the kid going to get a piece of paper, a pencil, a clipboard and a meter stick, and I just let it go, because I knew exactly what he was doing and he was on the right track, and he didn't need anyone to interrupt him. This was just something natural to him that if I make a car, I want to know how fast it is. And then when I find out how fast it is, I might want to make it faster.

Colin Chapman:

And that idea of ratio that we talked about just moments ago, that applies to mechanical advantage.

Dr. Gary Stager:

Of course.

Colin Chapman:

And then you've got these other concepts which come out of that, which is the work principle. You don't get anything for nothing. So you can be fast, but low torque, high torque, slow, there's always a trade-off and so on. So you're getting all these rich ideas, which brings me to something you quoted the other day by Kay. And he was talking about the apparent failure of our interventions computationally in the classroom. And the suggestion was, no, there's been no failure. It's we don't understand the mathematics that these students are doing.

Dr. Gary Stager:

Well, I'll get to the actual quote in a moment, but I think it's representative of this fool's errand that we're always engaged in of scale. We have to make sure that everyone is doing this at scale, instead of letting a thousand flowers bloom instead of creating compelling models that a variety of people could be inspired by that move all of us in a forward direction. So every movement in education, every intervention that achieves any kind of popularity immediately becomes self-conscious and starts talking about, "Well, we're just preaching to the converted." Well, there are institutions that do quite nicely preaching to the converted. And there's an importance of having a community around a set of ideas that can nurture one another and challenge one another and learn and grow. And beginning in late 1960s when LOGO was developed, originally coming out of the artificial intelligence laboratory at MIT, the idea was that if kids were thinking about thinking and thinking about how to communicate their thinking and their mathematical ideas to the computer, they would become better thinkers or better mathematicians.

By the advent of a personal computer in the early eighties, LOGO was primarily the thing you could do with computers in schools. My friend Dan Watt wrote a book called Learning with LOGO that around 1983, 84 sold a hundred thousand copies. So it was a book for teachers on how to teach programming to children, that a hundred thousand teachers had a copy of at a time where there may have been half that number of computers in schools. It was kind of extraordinary. Creative Computing magazine had 400,000 subscribers in 1984. This was a recreational computer programming magazine that had Cosmopolitan or Vanity Fair subscription numbers. So there's been these ebbs and flows of interest in computation formally and informally in the hobbyist community over time and in education. And so by the late eighties when lots of schools were doing LOGO, people started demanding evidence.

And the evidence is almost always in the form of something to disprove that what you know is good for kids is good for kids, to justify not doing it to move on to some other whim or to go back to basics or whatever. And Alan Kay, who coined the term personal computer and sketched the Dynabook on his flight home from visiting Seymour Papert and Cynthia Solomon in 1968, and was so excited by the mathematics he saw kids engage in getting LOGO, thought, "Oh my god, we need a children's machine. We need a computer for everyone." And if you look at... Google Dynabook, the picture of the Dynabook that he sketched looks remarkably like everything we have today. He was inspired to create the personal computer because of the work that he had seen children doing with it in this context. And he said, as a mathematician himself, to the extent that we want to declare LOGO a failure, it was a failure because the teachers didn't understand the mathematics that the children were naturally engaged in while communicating with the computer.

Just one more thought, when my partner, Sylvia Martinez, worked at the company that made software Math Blaster, you remember Math Blaster was drilling practice software, where you had to kill aliens with fractions or something. It was dreadful stuff. It was also the only piece of educational software that ever made a billion dollars. The marketing people in the company used to refer to Walk Behind Maths, which meant when mom or dad who spent 49.95 on the software walked behind Johnny or Susie using the software, what was on the screen needed to look like the stuff they hated in school. So you couldn't actually innovate in mathematics, educational software, no matter how good it was for the kids, because the market had such low expectations for what mathematics was.

And there were software like Rocky's Boots where you built Logic gates and did really fun profoundly complex things, and the logical journey of the [inaudible 00:11:50] And I can tell you inside the industry those were mocked as prima facie evidence of what you never do as a software company. You never produce anything where kids are actually learning or loving mathematics. You have to make things that when parents walk behind them, they'll recognize it as something they hated. So Papert dedicated his life to the notion of instead of sugarcoating maths that kids hate, why don't we invent a mathematics diet that kids can love?

Colin Chapman:

And that's wonderful too because that sensibility of course is now through the idea of gamifying things rather than saying, "Let's get a concept and put it into a game," but gamifying the experience itself. It's a really-

Dr. Gary Stager:

Right, it's sort of a dishonest trivialization of the actual domain.

Colin Chapman:

So what is it that... So as Kay was developing the personal computer and he was imagining children using this computer and doing mathematics, what was it that he could see when the children weren't in front of him? What mathematics could he see that we don't seem to be able to see ourselves when the students are actually in front of us working with these machines? What did he imagine that we could see mathematically?

Dr. Gary Stager:

Well, he was inspired by what LOGO could do, and even just the total geometry of communicating geometric ideas to the computer or arithmetic or algebraic ideas to the computer and having it manifest themselves and manifest itself on the screen. And I ran a workshop for 55P to six kids and their parents of family maths and art night the other night at Spensley Street Primary School here in Melbourne. And I was introducing TurtleArt, which is a dialect of LOGO. It has a very small skillset, it's block based, so I can provide a minute of instruction, and with forward and back, you can draw anything in the universe. And it's like learning to paint or use any kind of powerful, extensible, open-ended tool. The kids immediately have an idea, and each idea either generates a larger idea to embellish, to improve, to decorate. They discover something cool and they want to run with it, or they have to engage in some debugging processes where the question isn't, am I right or wrong, but is it fixable?

How do I solve that problem? How do I go around it? How do I modify my expectations or change my goal in order to achieve what I'm capable of doing? And what he sketched looked a lot like the iPad, but he's not a big fan of the iPad, because the iPad is a consumptive device as opposed to a constructive one. It's not something you make anything on. Now, are there exceptions? Are there people drawing cartoons on an iPad and stuff? Yes, sure. But by and large, it's a way of delivering things to a passive user as opposed to using it as a knowledge machine, an intellectual laboratory and vehicle for self-expression.

Colin Chapman:

So that's really interesting because him imagining the sorts of mathematics one could do, informed his key ideas with regard to the software or the package. The device has to have interactivity. That's essential. It has to be modular, it's got to be extensible, and it's got to be flexible with regard to data types.

Dr. Gary Stager:

Affordable, portable, adorable. Right. And the iPad's really interesting because you may remember HyperCard, HyperCard was software that allowed lots and lots of people to make software who could never have been software developers before. And in a lot of ways, HyperCard was the iPad, it was software before we had iPads. And for whatever reason, Apple didn't even do the obvious thing of making HyperCard run on the iPad.

Colin Chapman:

And that fits to the modularity aspect of it. But let's think about the extensibility. What did he mean by that?

Dr. Gary Stager:

Oh, from the very early days... I just published a book called 20 Things to Do with the Computer Forward 50, that was commemorating a paper that Cynthia Solomon and Seymour Papert wrote in 1971, where they shared 20 ideas for projects that kids could do with computers. And the 20th was, Think up 20 more things. It was called the Recursion Line. And one of the stunning aspects of this 1971 paper is not only that most schools can achieve a lot of the objectives today, more than 50 years later, but that they had said that most of these things had already been done in classrooms. They talked about every kid having a computer. They actually said if computers were to be cheap enough for every child to be given access to a computer, computers would be cheap enough for every child to be given access to a computer.

And they talked about their vision of the school computer laboratory. They were still using the word laboratory, not as a place you visited every fortnight, like a excursion to Sovereign Hill, where you meet a person who has primitive tools and tells you about them, but as a place where you had access to stuff you wouldn't have access to normally. They didn't envision that it would be in our pockets perhaps. But they explicitly said in their vision of a computer laboratory, there would be motors, lights, sensors, things you could connect to the computer to extend the range and breadth and depth of projects, or possibly to collect data from the world and interpret it on the computer to make a physical control or for something that's simulated on the screen for data logging and interpretation and analysis, et cetera. So that was right there in 20 things to do with the computer in 1971.

Colin Chapman:

And that concept or that idea of extensibility seems to be a pivotal aspect, to be able to act computationally in the world, which is also Steven Wolfram's project. This idea that computation isn't just a screen-based, very private idea, it's directed towards the world itself. And Steven would say that his objective is to make the world computable. This extensibility allows for teachers as well as students to do the sorts of research that you would say was in the past, just a province of the university.

But now students can do research in their own classrooms, they can invent devices, they can attend to people's needs, and they can respond to community situations and all sorts of things. In fact, we've had students in the school that I work in who are working on projects for their physics year 11, 12, and they're building their own apparatus in order to do the investigation, and having to deal with all that messiness of what it means to actually develop apparatus that can measure something reliably and so on. This idea of extensibility and portability and so on is so central to being able to act in the world.

Dr. Gary Stager:

But I think we have to keep in mind child development as well. That dinosaur that sings and dances might have all the engineering principles of a first year university engineering course embedded in it, but it's also something that's appropriate for a seven-year-old. And one of the things I learned from the great educators of Reggio Emilia is if you ask preschoolers to build a park for the birds who come to visit, they know what that means. And then some kid says, "Hey, I've got an idea. Why don't we make it an amusement park?" And a teacher says, "Well, what's in amusement park?" And they brainstorm rides, places to eat, places to rest, places to get food. The kids immediately know what to do, and they can go back and modify their project and enhance it, embellish it, make it more complex or sophisticated.

And what the incredibly beautiful, humane, subtle educators at Reggio Emilia point out is, they've made their little corner of the world a better place, which by extension makes the world a better place. As opposed to starting with how do we change the world? When you ask kids to do that, all you get is a brochure. You just get pablum, you just get talking points that'll make the teacher nod as opposed to actually throwing your whole self into something that you're capable of doing. And physical computing and programming languages developed for children allow kids to be bigger and better versions of themselves.

Colin Chapman:

And that's really interesting because we know that Seymour Papert was a colleague of Piaget, and he had those sensibilities about people working in the world, that they have their immediate environment, and that that environment keeps expanding as one gets older. And you make a really, to me, an important point that we can romanticize this idea that a child can change the world, but they need to change their world as it is at the moment and then extend out outwards.

Dr. Gary Stager:

Yeah, it's okay. Papert used to say, I think he cribbed this from his student [inaudible 00:21:18] but it's okay for teachers to worry about what they're going to do Monday, as long as what they do Monday points in the direction of what they hope to do someday.

Colin Chapman:

I like that idea of signaling.

Dr. Gary Stager:

Well, Paolo Ferri had a different version, which was, you want to keep your tactical foot inside the circle and your strategic foot outside of it, and by circling that system.

Colin Chapman:

And that's this idea of working on personal projects, but we have to live in the world of our immediate person as well as our future person.

Dr. Gary Stager:

Let me share an example. I visited a school here in Australia, I can't even remember where at this point, where they wanted me to meet these year seven kids who had just engaged in these pneumatic projects. And I looked at what they had done. And they brainstormed all the things you needed to know about pneumatics and what kinds of things we might want to make. And they learned all the vocabulary for dealing with pneumatics. And they were doing all this sort of schooly kind of stuff, and it was maybe following the design cycle from the Stanford D school or something. And then they handed the kids pneumatic kits that had step-by-step instructions and parts to build a model.

So my first question was, "Why'd you do all that other stuff then if you were just going to follow instructions to build a kit?" And then the kids made these machines, that I still was unclear on the relevance of them, or if the kids understood any key principles. But the kids had made a brochure. Because you always have to have a brochure. That's proof they learned something. And you have to name the thing, and you have to say how much you're going to charge for it. And one of the things that I observe all the time is from the time I was a little kid is I know when something's inauthentic. The kids giggle through those presentations. They don't care what this thing is, they don't care what they call it. Why are we putting a price on something that doesn't exist and we're not selling?

We like to teach entrepreneurship, which is just a way of talking about commerce and selling something. Why don't we teach kids how to do something, and then the commerce takes care of itself? But we like to talk about things we like to teach, Alan Kay used to say, maths appreciation as opposed to mathematics, art appreciation as opposed to kids being artists. And after the kids made their presentations, I said to them, "That's terrific kids. If you don't mind, I want to beat up on your teachers for a moment." And I shared with them some of my concerns that I just shared with you. And then it occurred to me that if I wanted kids to understand pneumatics, I could have put four scraps of paper in a hat and had each group of kids pull one of the scraps of paper out of the hat, and the scraps of paper would've said, "Push something, pull something, lift something, throw something."

And I could have put the materials on a table and the kids would have learned a lot more about pneumatics and a lot more about a lot of other concepts by having invented something, as opposed to following either this dogmatic design cycle, which I'm sure was aborted because teachers always emphasize the part of the cycle they like. They never actually go through the whole cycle. Or building a puzzle. And so I really like the idea of generative projects, and I'm consistently challenging myself with the question of what's the smallest seed I can plant that generates the most beautiful blossom or the largest garden? What's the least that I could do to set the students do the most? And then pneumatic example really solidified that for me, because I literally could have taught a much more effective unit by putting four scraps of paper in a hat and having kids pull them randomly, than going through this elaborate scheme that no one could still justify the time that was invested in the first place.

Colin Chapman:

And what's compelling about that is that we are really looking for us to work at a higher cognitive level. So designing things or building things, justifying, explaining and so on. But when we take that descriptive route, we're down at the low level listing, identifying and those sorts of things. You call it generative processes, I've heard also it being described as emergent processes. So just by doing, can you then develop some ideas about concepts of mechanical advantage, or if I have different size pistons, what does that mean with respect to, first of all, how fast the system will work, what the throw is, how much force magnification, all those sorts of really important and interesting things?

Dr. Gary Stager:

I don't care if a kid calls the thing the thingy, if he doesn't know the word piston. Once he has some experience with it, I'll say, "Oh, by the way, it's called a piston." And then they know it for the rest of their life.

Colin Chapman:

And isn't that interesting too because... And it goes back to this, we don't understand the mathematics the students are doing. Our job is to be really attentive to the mathematics they're doing. And when the students use their everyday language to be able to describe things, then to map that to what it might be. And those mappings can be to physical things, names of things, but it can also be to conceptual ideas. So if they say something like, "I notice that I'm getting a larger force at this end compared to this end," so you can map that to, "Well, that's mechanical advantage."

Dr. Gary Stager:

And a teacher should be keeping track of all that to justify it in terms of the curriculum. If you make your primary objective to be the understanding of the thinking of each kid to make private thinking public, invisible thinking visible, as opposed to having some rigid top-down approach or a bottom up approach. I'm not an expert in this, and I wish I had had the time to spend more time discussing with Seymour Papert, but he dismissed the idea that Piaget was all that wedded to the stages, and points out just an obvious empirical fact, which is almost, or the vast majority of Piaget's research was at the concrete stage. And it just so happened that when he was doing his work in epistemology, evolution was hot and things were being presented in stages, and just that kind of work and it was available.

Papert's interpretation of Piaget is, "Anytime you learn anything new, you return to a level of concreteness." So the goal wasn't to become abstract as quickly as possible, it was a recognition that when you learn something, you have to construct the mental structures for understanding it based on previous experience and current context and such, perhaps in a social milieu. And that's very different from the sort of ways in which we design curriculum and school to win the race, get there faster, be better than someone else, hierarchical. And that leads to all the ranking and sorting and other nonsense that we don't need to engage kids in.

Colin Chapman:

And that notion of Seymour Papert's that this idea of staging is an artifact or a legacy from this evolutionary sensibility, is important too because this toing and froing, first of all, they bleed into each other, all these different so-called stages, but also they can be uneven depending on the experience of the student background and the sorts of things they do and-

Dr. Gary Stager:

Time of day, the topic.

Colin Chapman:

Right, and to be attentive to that and to identify it, and also to value, okay, you've had to go, what some people would say, backwards in order to go forwards. That's an important part of the process, isn't it?

Dr. Gary Stager:

I call it riding up to down escalator. Yeah. I've seen this a million times in my summer institute, constructive modern knowledge, where teachers have four days uninterrupted to work on personally meaningful projects with a mountain of materials, and remarkable guest speakers and a terrific faculty who can support them in achieving their goals. And this process emerges... Actually, we took educators one year on a field trip to visit the MIT media lab, and Leah Buechley, who was a professor there at the time, who was a pioneer in wearable technology and bringing robotics into the arts and embedding it in textiles, and she had wallpaper that if you blew on the dandelion on the wall, you would watch the seeds fly across the wallpaper. And one of the teachers came back to CMK the next day and said, "I want to do that." And she wasn't at MIT, she wasn't qualified to be an MIT graduate student.

She didn't have any of the cool stuff they had. We had some conductive tape and some LEDs. And when she described her project, and the processes she went through, she was talking about it in terms of I had this objective that what I saw Professor Buechley doing, and I wasn't clever enough to do that, but I could do this, but I didn't have the materials I needed. So I modulated my expectations a little bit more, a little lower. And then that worked. And that led me to an insight that I could go in this other direction. And I start seeing this process, I called it riding up the down escalator. You have the goal of going to the next floor, Meyer or whatever, but you're going to get there in a route that you're going to take one step forward, three steps back, four steps forward, that it's not quite as linear and sequential as you would think.

Colin Chapman:

And that fits in with our description of computational thinking in Victoria, where we talk about decomposition. And decomposition is essentially, let's find a simpler problem, let's go backwards in order to step forward and generalize. Because generalization is something that is super important too, being able to specific example, generalized to more cases.

Dr. Gary Stager:

I'm finding, just this week with the teachers that we've worked with, an inability to try one thing and then try something else. They want to do 50 things at once. The building something generatively is an experience that's... Something they don't have a lot of experience with.

Colin Chapman:

And that LilyPad platform that you mentioned before, that was an amazing innovation. And I think she developed that when she was first in Colorado and then she went to MIT. But this idea of developing... It was an Arduino based system at the time, I think it still is. And we know that Lady Ada at ADAFruit has made a different version, Flora. But this idea of wearable technology... And it's interesting because it starts off almost as a decorative activity first, flash some LEDs. But if you can flash an LED, you could drive a servo, you could do all sorts-

Dr. Gary Stager:

You could have a push in sensing dress. You could...

Colin Chapman:

And it could change colors according to the pollution levels. You could have a dress that senses social distance if social distance is an issue for you. But just that simple decorative step is a decomposition of a more complex computational environment. And playing with that and then seeing the possibilities afterwards signaling forward is a really important process. And I've always admired her project of the LilyPad because it was outstanding with respect to vision.

Dr. Gary Stager:

And you can make the whole thing. So again, it constructing modern knowledge. A group of teachers, 10 years ago, wanted to make a dress that responded to noise. So it would light up in a dance club and pulse with the music. And again, this wasn't a brochure or a tri fold display at a science fair, an invention convention. They made the dress, and they learned to sew, and they dealt with electronics and the programming and the sensors. They made the whole thing. And by doing so, they learned a zillion curricular objectives plus felt good about what they had done, and they made something beautiful. And it's just worth pointing out for an educational context, I'm not using LilyPad or the Flora stuff anymore because the software wasn't appropriate for kids. The threshold was too high.

When we wrote Invent to Learn, we spent a lot of pages singing the virtues in praise of Arduino, because here was a $25 microcontroller that was being used by hobbyists and professionals alike. And it was allowing us to democratize access to robotics and electronics in ways we had long dreamed of. And we thought, "The only weakness is the software is terrible, but surely someone will fix that." And no one ever did. And your Arduino guys just kept making the hardware more complex and more sophisticated, which was cool, it's fine for them, but it wasn't something appropriate for kids. And the BBC micro bit has been a game changer in that regard. And ADAFruit's version of that, which is the Circuit Playground Express, is essentially the same.

And it can be programmed in a block-based environment that doesn't just allow a couple of kids who can figure out C programming to participate. It allows everyone to participate, and it also changes the quality of the experience. And this is an important distinction. When you were working with Arduino, every project began by finding someone else's code that does something close to what you hope to achieve, and then maybe tweaking it or modifying it a little bit. I never saw anyone do anything with Arduino from a blank sheet of paper or a blank screen. It was always borrowing someone else's code and changing it, which is a way of learning to program. But it doesn't allow for a five-year-old to make wallpaper that sings them a lullaby, because there's no bridge from here to there.

Colin Chapman:

And the neat thing about the micro bit, of course, is you could sew that onto your clothing.

Dr. Gary Stager:

Absolutely. No, it does all the same functionality. And I would say, I think they would admit to it, the make code developers, make code scratch, snap, turtle stitch, micro blocks, beetle blocks, all are part of the LOGO family tree. If we're talking about planting seeds, the seed of LOGO has generated all those variants. It would be nice if there was one environment that could do everything we want, that was the Swiss Army knife. But that doesn't exist. It's not likely to exist for a lot of political and commercial reasons, but it also probably shouldn't exist because it would just add false complexity to a system that would intimidate teachers, in particular, and make it even less likely to be used.

One of the reasons why I love TurtleArt so much is it only has about a dozen primitives in it, meaning words that it knows. And with that, you can create infinite complexity, so it doesn't feel intimidating. It doesn't feel like it's something that you have to teach the kids where all the menu options are. When I hear people talk about AI being added to Photoshop, I think, "Oh, thank God." I can describe what I want Photoshop to do. I could never just do it because I don't remember what they call anything or where the menus are hidden. But if I could communicate the idea to it in a natural way, then it can help me be a better artist, or manipulate the photo that I need to manipulate in the following way, as opposed to me having to phone a friend and email them something and say, "Could you clean this up for me?"

Colin Chapman:

And there are two things I would like to tease out there. So first one is, it is interesting to me that you mentioned earlier on about an activity in LOGO, draw a certain polygon, and that's fairly straightforward. Draw a triangle. It's not long. You turn your back. And one of the students in the class has developed a general purpose polygon drawing application inside LOGO. And so they've generalized the whole process, a deep understanding about regular polygons, a deep understanding about angle, deep understanding about all sorts of important issues that are conceptually based, no longer recall.

Draw a square, recall, draw a triangle, recall. Generalize any polygon, you've got a general understanding of concept. Really deep. And you get a sense also that journey from the simple regular polygon and going through towards a general one, you're getting a story, you're getting a story about how their ideas have changed with respect to this geometric idea. And that story itself is something that can be used to enhance learning later on. You can remind students you've been through this story before while we do. I mentioned that because you're talking about the teachers and the dress, now, I think I know the answer to it, but did the dress work first go?

Dr. Gary Stager:

No.

Colin Chapman:

Yeah, that's right. It didn't work first go, and the teachers start to experience what it's like to have, first of all, the cognitive load of having to work on something they don't know the answer to, but also the absolute joy when it does work or aspects.

Dr. Gary Stager:

But I just wonder about all this, oh, risk taking. There was no risk taking here. It's just stuff happens. I mentioned earlier, Papert said it's not failure, it's the best projects push up against the persistence of reality. And we had a project once at CMK where the teachers wanted to build a Lego robot that would fold an origami paper airplane and then launch it. And when they demo it, I've got a video of it somewhere, they say, "Oh yeah, we didn't have the right belt for that, but if we did, it would do this." And they were actually engaged in conceptual engineering. They were completely confident that this thing would work if for I had better bits and I knew more. And I thought that was an interesting project result in and of itself. They were completely confident, they were ultra confident that everything that they had in mind worked perfectly, even though the thing on the table didn't do anything.

And I don't know what to say about that. And I think we need to spend a lot more time talking about those kinds of experiences. You talked about generalized radio polygons. Well, we could also just take that to another discipline or another curricular topic. So the other day I drew stick figures and said, you could reproduce those, or the next slide was a photo I took of a Dreamtime design that was outside the classroom on the walls decorating the school. You could say, "We're going to use those polygons to create a Dreamtime design." Now you're dealing with culture and storytelling and visual imagery, and all the mathematics is in service of that. So I think teachers could be involved in a generative design process as well of, "Oh, the kids have shown me they don't know how to do this, how could I leverage that to do something else?"

Colin Chapman:

And that piece about teachers being a practitioner of the discipline, whatever it might be, to me, seems to be important. Because if they're working on problems where there's no answer, there's always this crashing against, as Papert said, the persistence of reality. That gives a little more truth to their statements. So rather than describe a process, they're actually doing the process. And to me, that seems to be the learning hat the students take away.

Dr. Gary Stager:

Because knowledge is a consequence of the experience. And when I hear people say to me, "Well, the teachers don't like knowing everything." I always ask, "Who told them they do? Well, what class were you in, where you were told you knew everything?" It seems just preposterous to me. I'm profoundly ignorant about an infinite number of subjects. I'm fine with that. Just like I don't believe that I'm entitled to bore children for 40 minutes at a time with a lecture on something that I probably don't know very much about and aren't particularly passionate about.

I pride myself in figuring out what can I do with these 55P to six kids at 6:30 at night that conveys to their parents why we're doing this, and holds their interest long enough to let them do it? And that to me seems like a much greater win. I sometimes want to say to teachers, "You're not Cate Blanchett or Denzel Washington. You're really not that compelling. What makes you think you deserve an audience for that amount of time?" And so I then started thinking about is how do we develop an alternative? So if you're talking for 20 minutes, try 10. If you're talking for 10, try five.

One of the things that came out of the successive Invent to Learn was we started doing a lot of workshops, and we needed portable materials we could bring with us that if we had Makey Makeys and Arduinos and micro bits and TurtleArt and Lilypad, how could we have everyone have a high quality experience with a lot of things happening in the classroom at the same time without us pouring all the information into the heads of the participants? And we created one sheet getting started tutorials for all of those technologies. If it took more than a front and back of the page of a piece of paper, I felt like I had failed. And yesterday I handed teachers something, there was two pages and they all just readily told me, "Yeah, none of us read the second page." So if you're not going to read the second page, how dare you think some kid is going to? So part of the art of teaching is brevity and ambiguity. So brevity in just get to it, and ambiguity in, bring yourself to it.

Colin Chapman:

And ambiguity is a wonderful opportunity for people to express a concept in different environments, be challenged by it, be provoked by it, and so on.

Dr. Gary Stager:

And exceed our expectations.

Colin Chapman:

Indeed. Now, our time is rolling on. So on that note, I think we'll leave the conversation there. I've really enjoyed myself. I'm sure we could keep going for hours. And I'd like to thank you very much, Gary, for this opportunity for you to share some ideas.

Dr. Gary Stager:

It's been a joy.

Colin Chapman:

And it's important to keep thinking that mathematics is happening, and that we need to be attentive to all the possibilities, including those possibilities that we don't necessarily see in ourselves, and to be really surprised by the wonder and creativity of the students we work on. So if you enjoyed this episode, stay tuned because we have another two episodes with Gary.