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My u.s. history teacher showed us Matewan in class, which was pretty cool.
Personally, I'm against using movies as teacher's aides, by which I mean using them at face value to tell a "historicy". Partly this is because "historical" movies are generally pretty propagandist about their given topic, but more generally part of what movies aim to solve in telling a story is how to pare down all the complex and ephemeral links of causation into a pure and coherent vehicle. Even the best movies do this to some extent, and it's just bad history. On the other hand there are plenty of movies that would be good to use as historical artifacts, some of which are also pretty unavoidable in that movies are actually a driving force of much of 20th century historical consciousness. I can't remember the names in particular, but I mean to show things like how the U.S. defense establishment and hollywood used movies to rebuild europe (and basically invented the notion of Paris as "the city of romance'n'love" to attract tourists) after ww2, or using the birth of a nation to show some of the notions and arguments about blacks, and how it was used to reinvent the long-dead kkk as a mass movement (of course teaching it in the context of how that came about, how and why it was different from other incarnations the klan took at different times and different places). Gabriel Over the Whitehouse is a good 30s movie to show as part of a discussion of the ways in which the popular (and practical) idea of what the presidency should be changed, how it's different and how it's the same as today or at other times, and why. I really think that as long as you're carefully using films as artifacts or primary sources rather than as secondary sources (that is, tools to inform your own explanation of history), pretty much anything is fare game.