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My guess here is that I'm being asked if I go to a private or state university, but I don't know what 「どっちに 」 means. 「いってるの」 is something I've never seen before, either. Also, is か a particle used to say "or?"
I just want to clarify one thing here. 「日本では」 is using two particles, correct? One to mark Japan as the topic and the place?
「自分」 - I understand this, with the help of a dictionary, to mean myself and other similar words. But I don't understand the use of で. 「勉強するのと」 - I don't know what のと means here, either. 「教えてもらうのは」 - This part is a little confusing, too. I'm not completely sure if it's part of どちら or not since I don't know what どちら means. But I think 「教えてもらうのは」 has something to do with receiving instruction (teaching), but I don't know what the のは is for. My guess is that は is for marking it the topic...but の...?
My overall guess for what the last sentence means is: "You study (to teach) yourself, but is the instruction you receive at college good?"
Thanks for the help.