I've been a college prof, undergrad and grad classes. It was a breeze. I've been a high school teacher in a suburban school. It was tougher but not too bad. I was a high school teacher at an inner city school. It was a nightmare. I taught in each situation but got different outcomes in each. What made the inner city job a nightmare was that teachers are held accountable for the behaviors of over a hundred students many of whom had no desire to be there and a few who were actively hostile to it. That was much less the case in the suburban school, you were held accountable for a similar number of students and more of them saw value in getting a degree, but even there you had many kids who were only there because they had to be.
You taught at an Ivy League school? That's quite an accomplishment but it in no way positions you to understand what public school teaching is like and your suggestion that the US move to "rigorous testing to separate the wheat from the chaff" shows that you have a very poor understanding of the reality of public school teaching. Do that, separate the wheat from the chaff and you know who will make up most of the chaff? Minority kids, not entirely, not by a long shot, but well out of proportion to their overall numbers. And there will be political hell to follow. Yes, do something like that and you'll start seeing much better scores on standardized tests given to public school students because you'll have stopped testing the kids who are dragging the overall scores down. But that is simply not going to happen in the US.
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But once more, if you think it's so easy and that you can do so much better than the people doing it now, there is no time when the doors to the profession are more open. I assume you really don't want to be a public school teacher and don't care to step through those doors. But you really should come up with an answer to a question like, "If it's such an easy job why can't they get enough people to do it?"