IMO it should be clear when the problem is something 'new' that may not be solvable with techniques already covered in the class.
That's certainly helpful, and I won't argue with the idea that it's sensible for most children most of the time. My reservation is that, of course, in real life problems (of any kind) don't come so labelled - one of the things one has to learn is to tackle something even though to begin with you
just don't know whether you can do it or not.
We haven't done AoPS but my impression is that learning how to solve new/different problems is kind of the point there, right?
Well, yes and no. Yes, because the clue is in the name :-) No, because this is not an add-on, something intended to be presented alongside a "normal" class that does things differently: the idea is that you do AoPS geometry instead of any other geometry class. They do it this way because they think this is the way it should be done (at least for "high performing" students, and I don't think they are trying to be very exclusive here; this ought to apply to anyone who needs to be accelerated in maths, for example). See
here and related pages.
If you still disagree, then I guess I would conclude that we have very different learning styles.
More likely, different ideas of what it means to learn mathematics. I submit that there is practically no point in being able to solve problems only if you know in advance that you can solve them and have been taught a technique to do so. That's not doing mathematics; that's pretending to be a computer, and we have computers for that these days.
