Do schools help or hinder social mobility ?

TLDR : both, depending on the details. See also https://plus.google.com/u/0/+RhysTaylorRhysy/posts/HdZD1FMBn4K

Even if they can't make up for all inequalities, at least we might expect them to make the playing field more level. But a major international study on social mobility from the OECD economics think tank shows a more sobering picture. Each year that a child spends in education, the gap between rich and poor grows wider.

On average, across more than 60 countries, that difference between the richest and poorest is the equivalent to three years of schooling by the age of 15. Only about one in 10 children from poor backgrounds will achieve the same results at those from wealthy background.

According to the study, on average by the age of 15 about 13% of the variation in students' performance will be determined by their social background. This varies between countries. In the UK, it's below average at 11%, with Norway and Estonia lower at 8%. In France it's 20% and in Germany and Switzerland it's 16%.

But it's not all pessimism. The OECD's head of education Andreas Schleicher, argues there is also plenty of evidence to say that "poverty need not be destiny". There are school systems where many more disadvantaged children do well.

In countries such as Singapore, Japan and Finland, the test results of the poorest 20% are higher than the richest 20% in the Slovak Republic, Uruguay, Brazil and Bulgaria.

Hang on. Off the top of my head, those first three countries are all very rich, whereas the second set are all rather poor. So the poorest students in very rich countries do better than the richest students in poor countries. Rather than indicating good teaching methods raise people up, that seems to me to simply suggest that economics dominates at all levels. Of course they might have corrected for that, but if so, the article doesn't mention it.

The UK does quite well on this measure, with the median point for UK students being above the wealthiest 20% in Italy and not far behind those similarly advantaged students in Spain. "It shows that students from very similar backgrounds can have very different outcomes," says Mr Schleicher. He says it's a cause for optimism that some countries have made sure that "excellent teaching" is available for rich and poor pupils.
https://www.bbc.com/news/business-46013665