Teacher quality and teacher pay: The hole in the bucket problem?

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Ever hear the classic song, the Hole in the Bucket? Its catchy, ironic logic applies to lots of situations, including this one:

Teachers don't get paid enough to attract the best and the brightest, SO
we want to pay teachers more, BUT 
it's hard to justify higher salaries, in the face of flat student achievement results, SO 
the overall quality of the teacher corps continues to be too weak, BECAUSE
we aren't attracting the best and the brightest, SO 
we want to attract better talent and do a better job training them, BUT 
we can't attract our best and brightest, BECAUSE
teachers don't get paid enough.

Well, the Finns provide us with evidence, dear Liza, that the common formulation is wrong.