Here is something that seriously cracks the “bell curve” theory for measuring the potential of children for learning. A “mathematical note” in Wikipedia’s article on the “Pareto principle” has HUGE implications for why the way we do K-12 school fails:
The Pareto Principle is an illustration of a “Power law” relationship, which also occurs in phenomena such as brush-fires and earthquakes. Because it is self-similar over a wide range of magnitudes, it produces outcomes completely different from Gaussian Distribution phenomena. This fact explains the frequent breakdowns of sophisticated financial instruments, which are modeled on the assumption that a Gaussian relationship is appropriate to—for example—stock movement sizes. (Bell curves are Gaussian.)
Think about this: Network science has shown that the internet follows what math calls the power law and Chris Anderson calls the long tail. Ant Wrangler Jake McKee illustrates that when people play in community spaces online, the 90-9-1 principle describes their participation: the power law again. Jakob Nielsen tells us: “In most online communities, 90% of users are lurkers who never contribute, 9% of users contribute a little, and 1% of users account for almost all the action.” AND: The knowledge education is meant to teach is a small world network, as such obeying the power law, as illustrated in Los Alamos’ new Map of Science.
Kids do not all have abilities in the same subjects at the same time. My hunch is that there are 20% of children who are good at each of the things we try to teach them, so we should find out what each child is good at and deliver enough of that to make him or her rise to the top 9% or even 1% in that subject. Doing that is operating within power law. Instead, by using the bell curve, our schools have frequent breakdowns because the Gaussian relationship is not appropriate.
Our grade level and standards model of schooling cannot operate by the power law, but long tail online learning is natural and will thrive in the open internet.
I will be writing much more about this soon.
