I disagree slightly (explanation below), but whether you take "educate" to mean some sort of deep exploration or just rote repetition, I think the the point still stands.
The disagreement comes from n=1 anecdata drawn from my own education, but after 8th grade or so nearly all my homework was designed to complement rather than reinforce in-class instruction. Picking on mathematics as one of the things you mentioned, the in-class instruction would introduce a concept, and the homework would give you the opportunity to flounder a bit and probe the bounds of that concept. I particularly enjoyed questions like "the author made a mistake in this question; how would you correct it to be answerable?" In some sense that's repeating a concept, but when you're doing something more than repeating the same technique over and over there's a sense in which it's different too.
The disagreement comes from n=1 anecdata drawn from my own education, but after 8th grade or so nearly all my homework was designed to complement rather than reinforce in-class instruction. Picking on mathematics as one of the things you mentioned, the in-class instruction would introduce a concept, and the homework would give you the opportunity to flounder a bit and probe the bounds of that concept. I particularly enjoyed questions like "the author made a mistake in this question; how would you correct it to be answerable?" In some sense that's repeating a concept, but when you're doing something more than repeating the same technique over and over there's a sense in which it's different too.