Geography
Although this is a common subject that all schools still teach, I'm sure the subject matter must have been very different. It's similar to how history classes change inevitably over time to constantly update with current events as well as new discoveries about previously "known" facts. Considering the Louisiana Purchase being only 15 years old at this point, geography must have been quite an important field of study. Today we learn from texts compiling ages of knowledge acquired over many lifetimes of contributing people. Perhaps "geography" was a skills-based class as opposed to a purely information-based one. Some people had to go out and chart good maps. If property lines were disputed a cartographer would have been sent in. Today the profession exists (with satellite and computer assistance), but is very different in main goals and intentions.