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Viliam_Bur comments on Learning by Doing - Less Wrong Discussion
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Spot on. This is a big problem is mathematics education; prior to university a lot of teaching is done without paying heed to the fundamental concepts. For example - here in the UK - calculus is taught well before limits (in fact limits aren't taught until students get to university).
Teaching is all about crossing the inferential distance between the student's current knowledge and the idea being taught. It's my impression that most people who say "you just have to practice," say as such because they don't know how to cross that gap. You see this often with professors who don't know how to teach their own subjects because they've forgotten what it was like not knowing how to calculate the expectation of a perturbed Hamiltonian. I suspect that in some cases the knowledge isn't truly a part of them, so that they don't know how to generate it without already knowing it.
Projects are a good way to help students retain information (the testing effect) and also train appropriate recall. Experts in a field are usually experts because they can look at a problem and see where they should be applying their knowledge - a skill that can only be effectively trained by 'real world' problems. In my experience teaching A-level math students, the best students are usually the ones that can apply concepts they've learned in non-obvious situations.
You might find this article I wrote on studying interesting.
When the specific inferential distance is really really small, people can cross it by doing. This is how things were invented for the first time. And repeating this discovery on your own can be a great feeling that gives you confidence and motivation. So it could be a good teachning technique to do this... as long as you have a sufficiently good model of your student, so you know what exactly is the "really small distance", and if you later check whether the new concept was understood correctly.
So I imagine that while some teachers may really use this as an excuse when they don't know how to teach, I would be charitable and say that a lot of them probably do not have correct understanding of how exactly this works (that very small inferential distances can be crossed easily, but large ones cannot), so they just try copying someone else's style and fail. Actually, sometimes they randomly succeed, because once in a while they have a student who happens to be really close to the new concept, and this prevents them from giving up their wrong ideas about teaching.