Whether school culture exert different degree of influence between children of higher Socio-Economic Status(SES) and lower Socio-Economic Status families?
I suggest looking into Doug Foley's Learning Capitalist Culture: Deep in the Heart of Tejas who adapts the approach of Paul WIllis Learning to Labour. These are both ethnographies of English based school systems. For a pointed ethnographic snapshot of New York City under Giuliani rule of metal detectors in schools, please read Maximum Security, https://www.publishersweekly.com/978-0-226-14387-3
These all employ anthropological ethnography and are somewhat dates. Anthropology of Education research is more in this informal mode. Educational Anthropology research is more policy oriented and can be seen in the work of Henry (Enrique) Trueba and George Spindler and Louise Spindler. Then there are the theoretical treatments of Michael Apple applying Foucault's theories to public education. Richard Valencia's Educational Psychology approach develops Deficit Thinking Theory into a interdisciplinary psychology, sociology, and anthropology approach to his longitudinal work Chicano School Failure and Success - https://searchworks.stanford.edu/view/8933285
The American Indian Boarding School experience described by K Tsianina Lomawaima provides reflects similarities with colonial education and mission education systems. All of the works on minority student experience in the US assumes a dominant group imposition of curriculum and instruction but may not discuss the direct interaction of lower class and higher class students. However, Foley's study is a great investigation into issues of gender, racial, and ethnic class status as what today is called "Intersectional" aspects of social analysis.