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My two cents is that there are Marxist, and "Annales" type longue durée people, and some World Systems people who try to basically mix the two. There are also a fair number of feminist historians. I think there are relatively few people in history who would call themselves "positivists". However, for the most part, these sort of ideo-esptimo-methodological categories don't mean all that much in the sense that most historians wouldn't fit themselves into ANY of the above camps. Instead, the meaningful things that cut across time and space are subfields: "social history", "cultural history", "political history", "intellectual history", "environmental history", "women's history", "world history", "economic history", etc. That's how people identify themselves more, that's more telling of approach, than anything else, at least in my experience. Because things like "social history" and "economic history" and perhaps especially "world history" are as more distinct approaches as they are studies of distinct objects.

I cannot really say what the schools are for the whole of American history, but I can say that in the study of the American Revolution there are (probably more accurate to say were) two opposite schools: The Whigs and the Progressives. There are of course several others but I know little about them.

The Whigs argue that the Revolution was all about benevolence, the Rights of man, progress, liberty et cetera. Think the stereotype of American Patriot/Tea Partier to get a general (though incomplete and biased) idea of the kind of rhetoric i'm talking about here. Whigs see the Revolution as a genuine rebellion by libety-minded patriots against the evils of monarchism and the old world. This school is obviously a bit old fashioned and out of favor in modern historiography, but it was a huge influence at one point. Charles Beard, who would go on to "found" the Progressives, wrote about the Whigs in An Economic Interpertation of the Constitution that they "[explain] the larger achievements in our national life by reference to the peculiar moral endowments of a people acting under divine guidance." (Pg. 1) Disparaging and Biased, but you get the idea.

I've already touched on the Progressives, which got started with Charles Beard's work An Economic Interpertation of the Constitution of the United States, which basically said that the Founding Fathers wrote their own economic interests into the Constitution. Beard, I believe, has also been highly discredited in modern historiography (his work is from the early 20th century), but his ideas kind of got the ball rolling on the study of "other" (i.e. economic) causes of the Revolution rather than just the desire for freedom and liberty on the part of the patriots.

Unfortunately, I have reached the limits of the historiography paper I wrote last semester. You can see this link for more information. The first part of Charles Beard's Economic Interpertation is a summation of American historiography up until he began writing, although you should probably take it with a grain of salt.