I just went to a talk by Don Saari here at the Joint Mathematics Meetings in San Diego, and the first 3 minutes blew my mind by connecting the mathematics to the things Ive been thinking about in #moocmooc, the MOOC about MOOCs. Saaris point was that we often used a reductionist method to solve problems in many areas. We take big problem, break it down into parts, solve the parts, and then put the parts back together into a whole. His first example of this? The university! We break knowledge into disciplines, majors, and courses. We teach in those parts to solve the problem represented by the need for learning, and then we try to put the ideas back together to make sense of the world.
The trouble with reductionist techniques is that, very often, the dont work. You can solve the parts, but when you try to put things back together, you get a mess. A good example of this is Arrows Impossibility Theorem. If we try to make decisions in large groups, we have to break this problem down into smaller problems meeting certain criteria, and putting the parts together leads to difficulty, hence there is no perfect system of voting.
Its the same in education. Supposing that we do a good job of drilling down, teaching students how to understand language, math, science, sociology, etc., we are still left with the problem of how we put together all the knowledge widgets into something meaningful. Its a hard problem, and course requirements that take care of the learning widgets become checklists, turf wars erupt over which widgets are most important, and the big picture gets lost. In other words, once we cut the elephant up into pieces to try to understand it, it ceases being an elephant.
But what other way is there? Saari contents that we need a kind of reductionist coordination, a theory of how the parts get put back together. It seems to me that the #moocmooc is operating in another way throw all the ingredients together and let the crowd sort it out, with groups self-organizing to coordinate pieces, and trees of thought growing and getting pruned all the time. Do folks have any ideas about this?