Final answer:
Functionalism is the sociological perspective that views integration in the education system as a means to promote social stability by acculturating children to the dominant culture, thereby strengthening societal functions.
Step-by-step explanation:
The sociological perspective that would argue that the concept of integration in relation to the educational system in the United States promotes overall social stability and social order by way of teaching children to become acculturated to the dominant culture is Functionalism. This perspective views education as essential for the socialization process, teaching children the norms, values, and skills necessary to function in society. Functionalists see education as serving the needs of society by preparing students for later roles, or functions, within the societal structure, thereby contributing to social cohesion and stability.