The higher classes also are likely to learn the language of school - the extended code, the ability to think and speak abstractly, the ability to think beyond your own circumstances, the ability to put yourself in the position of a quite different Other. It is the language in which this blog is written. They come to school with a hidden advantage. Their primary habitus matches the school habitus.
Bourdieu's signal contribution to sociology is the idea that cultural capital is the way that the richer classes can turn their economic capital into a productive social advantage. And when they teach that cultural capital to their children, the children reap that advantage. Part of the advantage comes in their greater ease in school. Their primary habitus matches the school's habitus, which is normally the authorized habitus of the dominant culture.
Beyond their greater ease with what the school does teach, advantaged kids come to their school years at ease with important cultural knowledge that the school does not teach. Their primary habitus is full of all the cultural knowledge that involved, informed parents drag their kids too. Beyond that, the primary habitus of the most advantaged children has an attitude toward learning culture that makes school success and social success much easier.To really succeed in school, you need a code that the school does not teach.