Some additional thoughts on analyzing something like graduation/dropping out: if one looks at the transitions between attendance and nonattendance as generally clear but not always, there should be no surprise that we don't have great tools to predict whether someone is going to graduate or not from high school. That's because those tools are poor in many fields. An article in Nature last year discussed one way to look at so-called "state transitions" in dynamic systems in terms of early-warning signs, and at least at a first glance it's almost straight from the chaotic-systems literature. As a result, my attitude was grit teeth,* then see if there's anything that isn't a horrid application of the concept when it comes to non-physical-science areas.
And after thinking about it at the time, and some time to digest it since, I think some of the ideas may apply in a broader range of systems that have sets of fairly stable constellations of behavior (such as regular school attendance and consistent nonattendance). The idea is that if someone (or something) is close to some tipping edge/cliff, you might see some evidence in less resilience to external shocks. Good news: we don't have to talk about schools as dynamical systems that are chaotic (because you don't have any evidence of such a claim*). But that good news is pretty abstract and hard to work with in an institution where the level of detail is "we get you data every year."
Again, I suspect someone may be much more clever than I and figure out how to look at this. I just am not aware of anyone doing it successfully.
* Brief explanation of my gritted-teeth skepticism towards applying chaos notions to human behavior: the existence of so-called strange attractors can only be demonstrated by repeated observations of a dynamic system from almost-identical initial conditions. You don't get that experimental setup with markets or other parts of society. Anyone telling you otherwise is blowing some serious smoke.
Sherman, are you familiar with Guastello and his numerous collaborators?
Managing emergent phenomena : nonlinear dynamics in work organizations
by Stephen J Guastello.
He has other books out, and there are conferences and journals if you are interested.
Cusp catastrophe model is also in wide circulation, and I’ve seen it applied to faculty job satisfaction/nonlinear DISsatisfaction, (i.e., unexpected departures).
The problem may be in the problem you are trying to solve, not the models.
In fact, this may not be a problem at all — educational processes sort and certify students, they distinguish between those that pass and those that fail. Self-selection only validates this.
Attendance is concrete. A degree is a credential. “Dropping out” is a constructed label. They’re related but not identical.
I have to check, but I think Guastello is one of those who thinks that the specifics of chaos literature, including fractals, is applicable to organizational theory and other human institutions. That’s the stuff that sets my baloney alarm system ringing. It’s one thing to say that you can apply some general dynamics systems models to the weirdness of human behavior. But to claim something as specific as strange attractors? I’ve never read anything that persuaded me you could test that claim.
The catastrophe modeling applications in Nature were, well, naturally occurring, not the results of artifically maintained environments.
I don’t know if you had a chance to look at Wahl’s faculty satisfaction model, which I added to. See link. Wouldn’t this apply to drop-outs too?
Glen,
There are several experimental studies of the bifurcation-approach hypothesis, including some invertebrates. And since the literature in the area is broader than strange attractors–I think the term is basins of attraction–it doesn’t set off my “jargon nonsense” alarm bells.
No, I haven’t read Wahl’s dissertation. Given the nature of surveys, the data tend to be too sparse to fit complex models with much confidence.
http://home.earthlink.net/~fheapblog/id33.html
Hey, try it. Maybe you will like it.
Zeeman, Thom’s disciple, included organizational behavior — including stock market crashes — in his repertoire of cusp applications. I was commenting that the Nature article was dominated by natural world applications.
Mathematical models are only as good as those handling them, as George Lakoff suggests, right?
Mathematical models are only as good as those handling them.
Yep. And most of “those” in EdLand are smart fools–as exemplifed by the Rand stooge hired by Hechinger for the LATimes.
But I digress.
Thom’s cusp notion makes a lot of sense to me, but I don’t think it applies to “graduation/dropout” rate. Oh sure, there are a few kids who are “born again” at a later age and see the light and become successful in school.
But school achievement can be predicted pretty well at the end of K as demonstrated by ECLS-K data. the common belief is that this is due to “poverty.” Wrong! It’s in the instruction, stupid. With few exceptions kids come to school well motivated and with the minimal prereqs to be taught how to read–to handle text in the same way they handle spoken language.
Schools inadvertently disadvantage kids by focusing on their “deficits” rather than upon their academic assets. If a kid hasn’t been taught/learned how to read by grade 3, “dropout” risk is high, unless the kid is docile and can tolerate “special education.”