The functionalist theories believe that authority in education is an important part of teaching children to respect authority figures and thus it is a positive aspect of the schooling system. In Marxist theories, the view of authority in schools is negative because Marxism believes it stems from unjust subordination.
The basic idea of functionalism is that society is an organism and each part of society is a necessary piece, including criminal behavior. The view in Marxism is a theory of class struggle and does not consider the elements of society as necessary or like an organism, but rather a show of how different parts of society struggle.
The Marxist view of education in general starts out similar to the functionalist view in that it is viewed as preparing children for their future. In the Marxist view, the system is seen as creating inequality among children by teaching children in private schools to lead and rule while teaching children in public schools to follow and obey. The functionalist theories take a different perspective by believing that the education system takes the most talented children and prepares them for leadership rather than those in different schools. In functionalism, the qualifications of the children are the reasons for leaders and followers.
The functionalists believe that society is one of shared values; society works together and shares perspectives to reach common ends. The Marxist beliefs differ and, instead, see society as a domination culture where one group stands above the rest. The leaders are not sharing the subordination and misery of the working classes.