James, I think you're missing the context of these sorts of questions, which is open-ended group exploration of a topic in a classroom, rather than students tackling work-sheets, or people trying to solve escape-rooms. It's a very different context! I agree that most of these questions would be very annoying in the latter situation.
What is the answer?
I included that one just to be complete, so as not to imply that ALL questions need to be of non-traditional type. Here "What is the answer?" is intended as a placeholder for the typical sort of question a teacher asks students in the midst of a class. I'm aware that I'm trying to get an answer - this is an infuriating
question.
You can't be aware that you're trying to get an answer if I haven't even asked the question yet. :-)
Does this answer make sense? Folks either do their own standard sanity checks
Most students don't have the habit of doing sanity checks. The mindset is write down an answer --- any answer --- and move on. or need you to point
them toward a check that they haven't thought of. I'd prefer "What's the limiting case of ... " or "WRONG".
But what if the answer is right? I'm just trying to get the students to use common sense as well as the algorithms that they may or may not have learned correctly. In any case, I try to avoid saying "wrong", to say nothing of "WRONG".
What question might this lead us to ask? I think the goal here is to get someone to verbalize their thoughts. Maybe a better way to achieve that is a less interrogative "Talk me through your thoughts on X so I can help"
"Help" is the wrong verb here, since the class is just exploring some ideas together.
Is there a pattern here? "I OBVIOUSLY don't know, or I would have solved it". Give me a hint or leave me alone.
Again, James is assuming a different context for these questions than the one I had in mind. If the class has just figured out the first four terms of a sequence, it's natural to pause to say "Does anyone see a pattern here?"
How convinced are you? AKA "are you sure?" Maybe I'm poorly socialized, but I take this as epistemological. Probably not the discussion anyone wants to have.
After I present a proof, I want the students to think about it critically. Sometimes I'll put in a mistake on purpose. In that case, the answer I'm hoping for is "No, I'm not convinced, and here's why." I should stress that these sorts of questions only make sense in a classroom culture that encourages trying out ideas even if they turn out to be wrong, and figuring things out together. Setting up the social dynamics for this is a tricky business! I do my best, but I still find that fewer than half of my students participate in discussions; the rest just lurk. Work in progress. I measure my success this semester in part by the fearlessness with which one of my favorite students participates. He usually disagrees with the other students about what the right answer is (until they convince him), and he's nearly always wrong, but he still keeps at it. But let me say again that I think I see where James is coming from, and that I agree that in certain contexts (such as helping a student with homework during an office hour), some of these questions would probably be really irritating! Jim