Three words

[GonzoStyle]

Only because I’m a history/education major I can explain 2 of them.

Hegemony is the study of theories and explanations of dominant social classes, groups, cultures, etc, over another class, group, etc. The main aspect is the study of how the one group achieved and maintained dominance over the other. So it's not just a study of a dominant group, you need to have both groups. Modern America as hegemony is a widely debated topic because the consensus if fairly split on the subject. The split is similar to the question of America as a modern empire (imperialistic), some even saying it never existed at all, it can be argued well on both sides.

Pedagogy encompasses many aspects of theories in education; in essence it is the philosophy of education. How one approaches education and what values they place on the function of teaching, whether it be teaching style, theories of curriculum, relationship between student and teacher, etc.