Reading is still mandatory, I gather that. But writing may have gotten obsolete, so that may no longer exist.
I doubt the art of writing is any more obsolete in the UFP than it is today. Technicaly, we today have no need to write; just to type. Given the UFP's sense of culture and refinement, I can see them hanging onto writing, even if it's not used much.
Mathematics may be downgraded significantly due to the enormous amount of computers that seem to be around.
I think it'll go the opposite way. IIRC, in one TNG episode we saw a ten year old learning calculus. I imagine that it'd get significantly easier as a class as calculators advance, however. I can easily see calculators storing all the required formulae, with the only necessary user input being what number goes where.
topography is going to be a difficult one, as countries no longer exist. Cities may be learned, but they have much less significance as they are probably much more the same by that time. Learing the planets and solar systems gets more important. Which brings about the problem of the third dimension.
Geography/Topography as a subject would still be around. Although Earth is one big happy family, there are still borders between states on the planet. Those will still be important to recognise, as will geographical landmarks and other info.
I can imagine that such a class in an Earth school would also give a brief rundown on major planets in the UFP, and an overview of their location in space and the locations of other races. I doubt they'd pay much attention to it, though. After all, how much importance would a US school place on learning about places in Russia?
Languages may be downgraded significantly as well, due to the presence of a universal translator.
I can easily imagine language classes dissappearing from basic schooling altogether. With the UT, there's no need for it.
I can imagine that you could learn and study other languages in college, however, similar to how you can learn ancient Greek and Latin now.
Economics will have completely transformed due to the replicator.
Aye, the class will be completely different. And if Picard's dialogue and actions in
The Neutral Zone is anything to go by, it may also include a load of pro-communism propaganda villifying other types of economies.
physics an chemistry, the beta section will probably very different as well.
Doubt it. What we teach in schools now are the basics of those subjects. Unless our knowledge of basic physics and chemistry turns out to be completely wrong, that'll stay the same. It'll be the college courses that change.
Education of culture is going to be difficult. While derelicts of the past are still around, and can be replicated en masse, they are sparser because they aren't needed any more, and little seems to have changed since TOS times.
I can't say much on this one. We don't have culture classes over here. Learning about other cultures is included in the various language classes.
History, that's a difficult one. I'd say instead of seeing the progress of how nations and states were formed, history may start at april 5th, 2063.
I seriously doubt that. I can imagine each planet teaching the history of their world up to the point that they joined the UFP, then turning to a joint course on how the UFP was formed and progressed.
In our history, and presumably the histories of other cultures, there is a lot to be learned. Forgetting about such things, particularly lessons such as the Holocaust, would be highly foolish lest we make the same mistakes again.
The rest, fill it in, guys.
Biology:
I imagine the basics of this being the same, with each planet concentrating on the predominant population of the planet in question. Presumably at higher levels there'd be brief rundowns on other races.
Religion:
Not sure how the UFP would handle this. This may be transformed into sort of a general "other cultures" class, which is the direction that most religion classes are heading over here in Ireland.
Art/Music/PE/Etc:
I imagine most other classes would remain the same. Again, there would presumably be brief rundowns on how those subjects relate to other races at higher levels.