Very well put. > it’s not easy or typically very efficient It is also very possible for folks to think they have it right, and go off in entirely wrong direct

Very well put. > it’s not easy or typically very efficient It is also very possible for folks to think they have it right, and go off in entirely wrong directions. In my experience it is likely, even in quite good and hard-working students. I teach an inquiry-based proofs class and so I sit through the students's discussion. Even on material that would be considered trivial in many of the books mentioned here, there are people saying aloud things in that discussion that are just simply wrong. It is not that these folks are dummies, it is that this stuff is hard. I'm not a people person but one thing I've seen from this class is that a lot of learning is about community. It makes a big difference.