This is a minor point, but I found understanding the "discourse" behind a field super helpful. In abstract algebra my professor spent a lot of time why we study certain structures (groups, commutative rings, modules, fields) more than others. One time he was making this super frustrated remark that our book (Dummit&Foote) calls ring a non-unitary ring whereas in class he'll call ring as a ring with unity (i.e. a ring that has 1). He was frustrated because for him this was not an interesting distinction and "to have interesting results you need to introduce a 1 anyway". I think this sort of emotional and human responses emphasizes what is important to understand in that field and what is not. Some people saw algebra as a laundry list of structures with axioms, whereas it's just another way of solving problems and structure is the approach, so finding useful structures for the problem in hand is more important than studying all those structures, as if memorizing the periodic table.
