One idea for mid-level college math classes (i.e. after calculus, before highly proof based courses) which I've seen people speak very positively of is to have a portion of the course consist of students producing conjectures on their own by coming up with examples and counterexamples until they have a viable conjecture.
This sounds like a great fit with, for instance, a discrete math course, where engaging with lots of examples is important to grasping the topic.
However every time I've tried this, I find myself serving as an oracle, because there's no "stopping point" if they get the answer right: if there's a counterexample, they might be able to find it if they looked harder, but once they have a right conjecture, the only tool they have for verifying it is asking me whether or not it's right. So every time they have a new conjecture, they ask me if it's right. (And, at its worst, we alternate between me giving a counterexample and them producing a new conjecture taking into account that one additional counterexample and then asking again.)
One thing I like about the concept is that it starts to move away from "professor as arbitrary decider of right and wrong" which many of my students have internalized. But when the definition of correct conjecture is "professor says you can stop now", it ends up reinforcing that notion instead.
My question is how to avoid this: for students who can't be asked to prove their conjectures, how do they know when to stop looking for counterexamples?