I've visited Montessori classrooms that did some of that. But I think that kind of engagement is contingent on good student/teacher ratios and a fair bit of unstructured time.

Standardized testing pushes in the opposite direction, alas. It encourages teachers to push for the sort of rote learning that is instantly forgotten when the test is past.

Yes, but they often don't. We usually think of good teachers as people who give clear explanations and keep the students interested. Attacking student misconceptions tends to confuse them, even if it improves their understanding in the end, so people are reluctant to do it.

Funny. We call that process the "scientific method," yet it is hardly applied when it comes to actually learning anything. It should be a student's goal to strike out and fail, to discover that he does not know things about the world. But this isn't the environment that is fostered in classrooms - it is compliance and memorization that is taught.