If you'd were to teach photography, how would you start, and why?
Would you first teach camera usage, then composition, then exposure?
Or would you start with composition without a camera, then camera usage?
Or just teach camera usage and exposure and leave composition to personal taste?
Please keep in mind, this question is explicitly not about learning photography, but about teaching it.
First a bit of a background to my answer. In the days before digital cameras were widely available (or available at all), people asking "what camera should I get to learn photography", answers would tend to go along the lines "get your self an old, manual camera so that you learn from the ground up". I always found that rather stupid. If you stick a manual camera in the hands of a newbie, chances are that all images come out completely crappy, exposure way off and so on. I can't see a more efficient way of killing and aspiring interest in photography. My advice was always the opposite; get something fully automatic (but with manual capabilities), and focus on the image. The rest will come.
Different people will have to approach the subject in different ways. Photography has two sides; the technology and the image. I have seen plenty of stunning images captured by people of haven't got the slightest clue about aperture, or ISO settings or shutter speeds. All it took was an eye for a good image. I have seen fewer great images from technological virtuosos without an artistic eye. Of course, it helps if you can predict the result in some way by knowing the technology, but I would argue that it is not strictly necessary to know all about how aperture, shutter speed and ISO are chained together.
So, I would say, start off with the image. Dive into composition, what makes an image more or less interesting. These discussions will most likely spawn threads into the technological field (How do I get the background more out of focus in my portraits?" or "How do I get more of this landscape to be in focus?" - start talking about aperture and how it affects depth of field - "Wow, how can I do to capture the feeling of speed when that motorcycle drives by?" - start talking about shutter speeds). When there are specific cases to talk about, it is often easier to learn. When a beginner has captured an image that they feel proud of, but perhaps wonder how it could get even better, there is a hunger for learning that will make things so much easier.
I generally agree with Fredrik, I think with the features of modern cameras a beginner can be overwhelmed and so it's best to let the camera do the work as they begin to understand what makes a good picture. It basically removes distractions and lets them focus, no pun intended, on what they see in the viewfinder or display.
Once they have confidence that they can compose a good picture, they can then start to play with the various options on the camera, especially if they're using an SLR. The single biggest upside to digital is that mistakes don't really cost, except for time that they already want to invest. Got a terrible shot? Delete it and try again. That gives so much freedom as you can experiment with the effects of shutter speed, aperture, and ISO on various subjects and just learn from doing it and without the expense of developing your mistakes.
So, in a sense, I'm suggesting that the best way to teach them is to have them do. Of course, that doesn't mean that you don't start them off with the basics of things like composition, exposure, and such, but that you then encourage them to just do it.
My approach would be a little different. First I wouldn't even break a camera out. Learn to observe and read light first. Then we respond to it with a camera. Then we add controlling and manipulating the light. This would give them the proper fundamentals of how to express themselves through photography.
