To address Ted's original question; yes, I think it can be taught - although I fear that people without at least some innate (genetic) ability - those relying on what they've been taught alone - are likely to produce merely a succession of 'derivative' images, based on what they have seen or been taught.
I think that might apply to me, especially as I haven't shown much of what I've shot for the last 3 years, nor shot much at all for the last 2, because I don't think they are 'good enough' - but that's another story.
I believe my brain is capable of visualising images before capture (including both the effect of camera settings plus the 3D to 2D aspects), although if I rush, that side suffers and I end up trying to rescue it in Post Production - perhaps that explains my keenness (and hopefully, ability) to help others here at CiC by offering critique and suggestions on their pictures - let others learn by my mistakes
Unfortunately, being able to visualise 'better' images means that I can work out that I am (in many cases) incapable of getting the angle of view a scene requires (for an 'outstanding' composition) due to factors beyond my control - inability to gain access, get the camera to a suitable position, to control the scene, not have time to wait for the best light, not put up with the physical discomforts - the list goes on.
Or perhaps I give up to easily!
Critiquing images is a lot easier than taking them myself and I think I am better at critique than actually taking them. So I tend to stick to what (I think) I am good at.
That said, my life tends to move in phases and I hope that I'll get back in to a 'photos' phase sometime.