Final answer:
Structural-Functional Analysis is the approach that examines how education supports societal stability by teaching social roles and preparing individuals for economic roles.
Step-by-step explanation:
Structural-Functional Analysis looks at ways in which formal education supports the operation and stability of society. Structural functionalism, a major sociological theory, describes how various aspects of a society, like education, fit together to contribute to the integrated whole of culture. This perspective sees education as one of the more important social institutions that serves both manifest and latent functions in maintaining the operation of society.
Functionalists argue that education equips people to perform different functional roles within society. By teaching children how to socialize and preparing them for adult economic roles, education is seen as a key part of maintaining societal stability. According to the functionalist perspective, elements of culture such as schools, classrooms, and textbooks exist to fulfill society's needs, particularly in the transmission of knowledge and values.