In this TEDxNYED talk, Dan Meyer discusses the particular challenges of math education. Essentially he observes that students are taught to view math as the application of a formula. Indeed they become so inured to that expectation that they view with some suspicion the encounter of math without a formula. As I view it, students come to desire to serve as the meaty end of a calculator. It's an interesting video. I encourage you to watch it. I think it has much to say about the general challenges of teaching.
I would describe this situation in Latourian terms. We tend to view teaching, but especially the content of teaching, as "matters of fact." As matters of fact they are rational objects that can be measured by scientific means, such as multiple choice tests. In other words, there is a "science of learning." It is not only students that come to desire operating as the meaty end of a mechanical process. Teachers also desire formulaic methods. Deny that if you wish, but the internet is replete with lesson plans. The extreme end of that desire is scripted teaching, or what I call "do you want fries with that? pedagogy." I doubt that many teachers wish to be reading scripts all day. But the underlying premise is commonplace: formulae exist for successful teaching.
As Latour observes, the modernist split between nature and society never really happens, but we firmly believe in it. Scientists object when Latour remarks on the processes they employ to construct knowledge, believing that such remarks are meant to suggest that their results are fictions rather than facts. That's not the point at all, of course. Science is supposed to be separate from the political but we know that never is the case from cloning and climate change to DoD research and academic entrepreneurialism. Obviously the same thing is true with teaching: the political and marketplace debates over teaching are endless. And yet we still believe that the content of schooling is factual and the processes of teaching are scientific. Ultimately what gets lost in that modernist view are the roles of students and teachers in the composition of knowledge. Learning is making. Learning is composing. And not just in the sense of composing writing but in the broader sense that we might also say knowledge is composed in a scientist's laboratory.
The obvious difference between the scientist and the 5th grader is that the scientist is an expert. We think of the knowledge she composes as being an original contribution: she learns something that no one else knew before. On the other hand, 5th graders are supposed to learn canned knowledge that we all supposedly know (though that game show about being smarter than a 5th grader belies that supposition). But that's not how either of these processes work. For one thing, science is often about repeating experiments: verifying knowledge composed elsewhere. In addition, scientific discoveries rely upon a great deal of technical problem-solving. In a very different way, as a rhetorician, I also expect to compose new knowledge but spend most of my time solving technical problems from the interstices among the different philosophical concepts I'm using to rhetorical problems of arrangement and style. In other words, experts spend much of their time solving everyday real world problems in their work so that they can create conditions for composing new knowledge.
I would suggest that 5th graders, students of all ages, do the same thing. They have to construct new knowledge for themselves and in doing so they face everyday obstacles to those constructions. They do not encounter the world as a pile of pre-digested matters of fact ready to be consumed by baby-bird students. No one lives in that world, so perhaps we ought to not build pedagogies built on the belief that we do. To be fair, I don't believe anyone would state their beliefs in that way. And yet, we also seem to resist the notion that students must make knowledge for themselves. In part because it is difficult to understand the role of the teacher in the process. Even if we have long understood the "banking" model as bankrupt, we still hold on to the teacher as authority. Of course the teachers are authorities in the sense that they do know more about the subject at hand than the students. I know more about writing and rhetoric than my students. But so what? They still have to make that knowledge for themselves. Every scientist, every researcher, scholar, and academic, knows that there is someone out there in his community that knows something more or other about the work he's doing than he does. No one can read all the possibly relevant research. Nevertheless, we all must compose knowledge from what we have. And in doing so, we can create value. This is what students must do as well.