Said another way, children of higher-IQ professionals are more likely to be high-IQ themselves, and thus able to score high on standardized tests.
The one thing that few people are willing to voice, is that the real problem is not low-quality schools, but low-quality students.
That said, one thing that would lift up scores, would be better competence tests for teachers. At the very least, they should be able to score in the top 10% on the tests that are administered to their students. Any unable to score high on tests of their subject matter should be fired.
No one reading this ever sat in a class-room, where his or her equal sat on either side, unless it was his or her twin or triplet! Whether the subject for comparison was academic, in general, physical in general; or confined to a particular discipline, a particular social attribute, etc., etc.; we all differ.
Now that does not mean that a good teacher cannot enhance performance; but that pursuit of enhancement must be directed at the unique personalities with which that teacher has to interact. That interaction, in turn, is an immediate, local interpersonal dynamic. Sweeping pronouncements by agenda seeking egalitarians contribute absolutely nothing worthwhile to a discussion of the process.
William Flax