Thanksgiving (Photo credit: Pictoscribe – Home again)
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 I’ve been thinking about in #moocmooc, the MOOC about MOOCs. Saari’s 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 don’t 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 Arrow’s 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.
It’s 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. It’s 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?
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Liberation Math 
A good question because the amount known and needed to process is getting larger all the time. Education though should be about method, that you have the ability to seek knowledge effectively (and recognize an educational opportunity) and then apply it to real world situations. So really isn’t it about building an effective scaffold for knowledge from birth to death? No need to drill down if the base layers are solid. So a long, big picture view of the formal education requirments based on a linked curriculum is essential for K-12 for instance.
Yes, and we could do everything right on the detail level and still screw it up on the larger level. Combine that with the inability to keep up with the knowledge in the world and frankly it seems hopeless! We need that big picture.
Hi!
I liked your post so much, I can’t stop brainstorming about it.
One thing I completely forget to mention in my post is that I doubt learning is just solving problems. Sometimes, learning is creating problems, questioning them and even ignoring them.
About the method of breaking the issue into parts, I would like (again!) to make a metaphor with the game of chess. In chess, we usually must think strategically besides tactically. In chess, tactics are the short run actions. When one player does not have strategy and only play little threats moves, we use to say he/she is playing isolated moves, he/she has no plan. So, I believe that sometimes the quick, local and short actions are needed. But there are times when thinking more globally, more strategically, more deep is needed.
Great analogy, since we can’t just look at every future option with chess, so we have to chunk our ideas together to make that plan. How do we learn to do that? I feel like an idiot in chess (which my daughter is learning right now) because I don’t feel like I understand strategy. Since we can’t teach strategy exhaustively, how do we teach people how to think in these ways?