Thursday, January 3, 2013

On the Conservation of Pedagogical Energies

My physics textbook this past semester introduced the concept of energy and energy conservation by way of an analogy to money. Money can be stored in a variety of different forms (cash, deposits, coins) and, as long as you don't spend any money or have any income (do work), your money is conserved. That is to say, energy was presented as a means of accounting for change in a physical system.

I thought this was a useful analogy as far as it goes, although my text and professor were both of the attitude that energy, framed this way, is just a tool humans use to describe systems and not something fundamental to the stuff of the universe. What energy truly represents is a bit more philosophical than I want to be right now, so I'll just get to the point.

If we turn this analogy around, it's easy to think of other systems as being governed by the exchange and conservation of energy. Take education, for example.

This was, in fact, a point my professor made, albeit in an entirely different context. He was trying out a new "active learning" approach to teaching based on findings that most students don't actually learn much from the traditional lecture format. The idea is that students learn primarily through interaction with their textbook, so class time is best used merely to reinforce what is learned by way of the text.

Interestingly, it turns out that I've spent almost no money on textbooks so far. Because Amazon will almost always buy back used textbooks for credit, my textbooks for next semester turn out to be free, and this process can hopefully continue indefinitely. So I've put very little (zero, in the limit) financial energy into my textbooks, where I've extracted the greatest amount of pedagogical energy, and I've put a great deal of financial energy into tuition, where my return has been somewhat more modest.

So what happens to all the money I pump into my community college? Does it leave the system entirely and thus not contribute to the school's pedagogical energy? In that case I might suggest some form of insulation to slow the rate of loss. This would have the added benefit of keeping the classroom warmer during the winter.

More to the point, what's the point of class? Why not just have an assigned textbook and a set of problems with periodic assessments to determine progress?

Now, I'm not saying this is the way things should be. There is clearly some reason why we have the setup we do, and I imagine that reason is something other than pure tradition.

To wit, I took an online World Lit class this past semester that worked more or less as I just described. We had selected readings, occasional tests, and perfunctory discussions. I got an A in the class, but I learned virtually nothing. There was almost no participation from the professor and the assignments required no deep understanding of the material.

This could, of course, just be the result of a bad professor, but it could also be symptomatic of that style of learning.

On the other hand, I did get something out of my physics class -- taught in the active learning style -- and my calculus class -- taught in the traditional lecture style. But what was it?

Most of the Calculus 2 curriculum was a review of material I'd inadvertently taught myself while brushing up on Calculus 1 stuff, yet I feel significantly more confident in my math skills after the semester than before. Similarly, my physics class touched on very few principles that I hadn't encountered elsewhere in one form or another, yet I'm more capable of doing physics problems than I was previously.

Returning to the original analogy, what subtle form is the classroom's pedagogical energy taking, and how can I account for it? Perhaps it is interaction with other students and the professor. Even if I'm not directly learning anything from them, maybe merely being around talk of physics encourages my brain to be more receptive to knowledge about physics. (We might call this convective learning.)

I've also heard that there is a benefit to having your errors pointed out in public. Doing so forces you to reexamine your understanding of an issue -- something that might not necessarily happen just by checking your answers in the back of the text.

So, what have we learned from this investigation of pedagogical energies? I'm not sure, honestly. I know plenty of people brag about never having to show up to class and still acing the exams at the end of the semester. I was more or less that type of person way back in high school, and I probably could have been this past semester as well, but my intuition tells me that, going forward, such an approach isn't going to be feasible.

The material will be getting more abstract and less intuitive, for one, but there's another factor at play. I think that by showing up to class and doing the work, I am committing myself to learning the material. The act of commitment is probably valuable in and of itself, apart from any specific learning I do in class.

Oh, and what accounts for the relative abundance of pedagogical energy liberated from textbooks? Very little goes in, but a lot comes out. Why, textbooks must be radioactive! Perhaps I can get them banned.

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