I’m no professional philosopher, still less a mathematician, but I understand just enough of Alex Ryan’s paper to see a little ways into the depth of this definition:

“Emergence is the process whereby the assembly, breakdown or restructuring of a system results in one or more novel emergent properties.”

Assembly, breakdown, restructuring: it seems to me that Web 2.0, like education, invites and expects these activities. (So does life, but don’t let on to the folks with good window seats; it will only upset them.) Of course, the definition does not say that the assembly, breakdown, or restructuring of a system inevitably results in one or more novel emergent properties. Indeed, it seems to anticipate that these activities will often not result in novel emergent properties. I note that Ryan’s definition does not give a name to what happens when the novel properties do not emerge. Chaos? Failure?

It seems to me that within the assembly, breakdown, or restructuring of a system, the teacher’s role, perhaps her or his primary role, is to shape and support the process of emergence. The activities must be authentic (real assembly, real breakdown, real restructuring–things could get broken) so that they have their best chance of resulting in emergence, which means there will always be the risk of flying apart into chaos and outer darkness. The other side of this idea is that not engaging in processes that can lead to emergent properties reduces both the risk of chaos and the chances of significant innovation–and understanding can be understood as a kind of cognitive innovation–to near zero.

On Monday I’ll be thinking about these issues, and others, in relation to using Web 2.0 in teaching and learning. I hope to throw some new thought-ingredients into the well-stirred Web 2.0 stew … or at least contribute an old boot and parsnips. I promise to talk about practical stuff, too. 🙂