Sorry 22B - I've explained it badly. As best as I can understand, some people learn best by building up smaller tasks into a larger picture (most teachers work this way), from simpler to more complex. Others (my DH and DS among them) learn best by starting with a big, general concept, and then trying to fit facts in/ derive the specifics from it. If they start with the simpler facts, they seem to have nothing to attach them to, and struggle to hang on to them. Most people probably benefit from working both directions, but some seem to work much better from one end over the other. Having a family split between the extremes, that Mom's words in the review really resonated for me.
With AoPS, I agree, it builds up incrementally, and certainly expects no epiphanies! I guess for us it feels more like a tendency to start with, for example, a larger concept like "we're trying to solving this kind of problem, but we seem to need a way to turn any number into "1", and since we don't have one, let's invent one and call it a reciprocal. OK, so now what can we do with this thing?" Instead of the way I was taught, more like "a reciprocal is 1 over a number, and here's how you use that in increasingly complex ways". Perhaps it would make more sense to say they have a tendency to start with the conceptual idea, and then see how it can be used to help deal with specific tasks and problems? Ah, probably just digging myself in deeper...
