Jean Anyon's work is really the baseline[0] and describes just how fundamentally different the schooling process experienced by the privileged and less privileged is. She looked entirely at public schools.
>In the two working-class schools, work is following the steps of a procedure. The procedure is usually mechanical, involving rote behavior and very little decision making or choice. The teachers rarely explain why the work is being assigned, how it might connect to other assignments, or what the idea is that lies behind the procedure or gives it coherence and perhaps meaning or significance. ...Work is often evaluated not according to whether it is right or wrong but according to whether the children followed the right steps.
>In the executive elite school, work is developing one's analytical intellectual powers. Children are continually asked to reason through a problem, to produce intellectual products that are both logically sound and of top academic quality. A primary goal of thought is to conceptualize rules by which elements may fit together in systems and then to apply these rules in solving a problem.
[0]https://www1.udel.edu/educ/whitson/897s05/files/hiddencurric...