It's all over the map, and there are hardworking teachers.

I can tell you about my experience in the 90's. There were exceptions, but generally teachers I had would hand out worksheets and assignments, and then class time would be spent doing what was effectively homework. Very rarely would there be an actual lecture. I had several completely incompetent teachers as well, who were completely tolerated by the schools administration.

One teacher, Mrs. Rushing, was completely incompetent. During the lesson on vector addition, she claimed that if you added a bunch of vectors together, it was the same as taking a vector from the beginning of the first vector to the end of the last vector, if you put the source of each vector at the end of the previous one. Well, that's what she was meant to say, she actually insisted that the length of the paths was the same, and she argued for it despite it being obviously wrong. She had at best a weak and often incorrect understanding of the material she was meant to be teaching. She also used her entire planning period each day to sell Avon or Mary Kay or something, which I witnessed every day as I was an aid in the math department and was in the planning room during her planning period. Every day some random lady would come in to the school and chat with her for an hour and try cosmetics during the time she was meant to be preparing for classes. During class she would often get stuck and go ask other teachers questions mid class.

So it would have been great if they had tested the outcomes of the students who were in her class, and compared them to the several wonderful teachers teaching the same subject at the same school. Instead, she is still there.

Standard teaching methods for science and math don't work by many measures. That's not the fault of poor teachers; even well-rated teachers do poorly at improving student understanding.

This is largely the fault of our notion that teachers are explanation delivery devices and students explanation receptacles, where the only improvements can be found in better explanations and better student engagement. The notion is wrong. Students need to actively test their understanding by making predictions and failing, and no courses I've ever experienced attempt to do this.

If you're interested in the mounds of research:

http://www.refsmmat.com/articles/shutup.html

"Students need to actively test their understanding by making predictions and failing, and no courses I've ever experienced attempt to do this."

Shouldn't a good teacher prod students in this direction?

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.