Back in 1974 my family spent nine months in a Munich suburb while I was on sabbatical there. Our two youngest children attended the local elementary school. Early on, big news was a report of a formal action by the German equivalent of the American Medical Association proclaiming that the "New Mathematics" (which was then also the fashion in the U.S.) caused serious damage to the human brain. My wife (who has a PhD in mathematics) cleared up my puzzlement about this as follows: German children (and ours) went to school very early in the morning and returned home after the end of the school day about 1:00 pm. The afternoon was devoted to music lessons, athletics, and homework. In the households of German physicians, they were supervised by very competent well educated mothers. (Then, and perhaps now, German women remained more domestic than those in other countries.) This gave the children of physicians an intellectual advantage, and they moved on to universities in higher proportions than children of lesser parents. The problem with the "New Math" was that the physicians and their wives had no clue about it, so their relative advantage was obliterated. Hence the action of the German AMA.
In my experience, parent teaching (and hiring of tutors) is an unacknowledged source of a great deal of within-group inequality in high-performing districts.
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