Like many this past week I have found myself extremely impressed by Vi Hart and Nicky Case’s “Parable of the Polygons.” It is basically an interactive simulation that introduces students to an old game from Thomas Schelling that demonstrates how small biases individually can aggregate up into much larger biases overall. If you have not taken a look at the Hart-Case treatment, check it out here.
What interests me is how this represents the evolution of a piece of knowledge into ever improving teachable chunks. Schelling, who won a Nobel prize for his contributions to game theory, came up with the original idea in a paper in 1971. On the scale of readable academic papers, this one already rates close to a 10 (out of 10 on some strange subjective scale I have in my mind). I would feel comfortable giving it to an undergraduate student. But it is long (some 40 pages) and while a student may get the main idea from this, they are on their own to process it.
Fast forward to 1978 when Schelling published a series of lectures entitled Micromotives and Macrobehavior. Chapter 4 explores the 1971 paper in a far more readable form; this was essentially Schelling taking his idea and putting it into a lecture. And it is a gifted lecture rating close to a 10. The whole book is like that and influenced many of us. Suffice it to say, if I were teaching this I would cast aside the 1971 reading and put this in instead. It is aimed at teaching and it shows. There is less processing required for the student but it is still somewhat static.
Dynamism comes in 2009 when economics journalist, Tim Harford, writes about Schelling’s model in his book, The Logic of Life, but, more importantly, produces a video illustrating the segregation model. It is nicely produced, explains the concept in 2 minutes but it only touches on the main point. But it does have dynamics.
If you want to see this in MOOC form you can look to Scott Page and his Powerpoint with the lecturer in a box model. It is 11 minutes long but you can see the model genesis, its abstract form, and watch Page manipulate a simulation to see how it all works. This is as good as it gets for lectures online.
Which is why the Hart-Case approach is so compelling. It is not a video. It is an interactive page. And, moreover, it is not obviously about racial segregation. Indeed, it starts with a parable – a model – which, when you think about it, is all Schelling was doing. The allusion to segregation and this being a mechanism to explain it was just labeling the terms. The model is mathematics and is true. The interpretation for segregation is theory and may not be true in reality.
But the page does a perfect job of giving students a feel for what is going on. It starts with a generic model and you can see how it plays out dynamically. Then it adds parameters you can adjust and then play with. It is a sandbox and eventually, with a staged introduction, the student learns what to do and is encouraged to predict behavior before checking it with the mathematics. As a teaching device it completely displaces Schelling’s original approach and all those before it.
Herein lies the lesson for online education. Hart and Case put an enormous effort into this. They are not ‘star professors.’ They are not experts in this area. They just explored the knowledge and acted as the translators. And there are similar efforts going on around the world.
This means something for online education. These chunks are the components. All of the efforts, the experts or professors are putting into courses with videos etc are mere place-holders until the true best-practice mode of expression is created. In the end, we will have to think of online education as a vetting and then curation of these components to give students an education. Suffice it to say, we are surely still in the Wild West of doing this.
Digitopoly 
Great stuff. And I’d also say, the associated tools improving is important, the ability to make an interactive sandbox more easily, better, and with less time and training by teachers, due to greatly improved software. Even blogs, which I think have helped learning, have been hugely made possible by this recent software, like the free Blogger, which makes it so much easier to start and maintain a high quality blog.
“Suffice it to say, we are surely still in the Wild West of doing this.”
Not at all. I wrote a similar (not as sophisticated) simulator on the PLATO educational computer network in 1977 for a Law and Economics professor. And I wrote a very successful pacemaker/patient simulator for training cardiologists a couple of years later.
The reason we don’t see this often is that skilled educational design using simulation works for relatively few, easily modeled subjects and is much more costly up front than other modes of instruction. The skilled design can be from brilliant/well-trained designers or it can come through an iterative, experimental approach: both are quite expensive.
And even this brilliant lesson is incomplete: real education requires at least four tasks: reading, writing, speaking and listening. And in this case, also doing. Online education has no cost advantage for the writing and speaking tasks yet.
I took Scott Page’s class on coursera.org – Model Thinking. The whole class is excellent and accessible to anyone who can handle college-level material. These paradigms need to be introduced at the high school level, in my opinion.
As you attempt to process more and more information for your students, looking for ways of making the information manageable for them is the whole idea behind chunking. As you break down your course materials into more manageable chunks of information, you will find that your students will have an easier time of processing the information and retaining it for a longer period of time.
My first Impression of Page’s presentation was, like everyone else’s, I thought it was strikingly excellent and I saved the original email with plans to encourage other people to watch it. But with some mulling, I’ve realized I’m not so satisfied. There are, I think, some complications in the real world that make his results less interesting than I at first thought. Is the question: “like me/not like me” sufficient? If there is a hierarchy, such as wealth? Might the question be “equal to or better than me/less than me?” And would the desire to move to a potential new location increase depending on how much better than me? And, still considering wealth, the cost of moving to the more desirable locations is higher as the wealth of the people already there is higher. So, not everyone has the same ability to choose among the ‘more desirable’ potential new locations. Some people cannot afford to move at all. Those people just stay and may be forced out later if their location becomes too expensive to afford.
Well, you must see my point by now. In some situations it’s wealth, in other situations it may be skin color. In others it may be sexual orientation. In real situations, there may be multiple factors in the decision. For that matter, not everybody will have the same threshold for deciding to move. The model is just too simple to account for people’s actual decision to move and I’m not sure Schelling’s approach can handle the reality well enough to be applicable.