Context: a math course at an American research university.

The problem: I have a course assistant assigned to help me, whose duties include running weekly problem sessions and grading. It is a moderately difficult course, and he is not particularly experienced in the subject. Each week after I've assigned the homework he will come to my office so I can tell him how to do the problems. Of course, it would be nicer if he had the interest and ingenuity to do them himself, but it takes me ten minutes to indicate the solutions and from my point of view, what I expect him to do is accurately and correctly lead the problem session. That means he is supposed to give some general hints on solutions, and it requires a very good understanding of a problem to give the right hints.

However, his lack of security in the subject has the following unintended consequence. He really wants to prove himself to the students. He cares to show them that he's smart. As a result, I keep discovering that he has essentially solved the homework for the students in problem session. He doesn't do it directly, of course. He just makes offhand remarks to show off and which contain the essence of the proof.  Now, this is a proof-based course. It is intended to develop mathematical creativity and facility in a particular field. Most of the homework problems require a basic insight, a more substantial insight, and then working through details of the proof. To my mind, telling the students the answer deprives them not only of a certain pleasure, but also significantly detracts from their education.

I've tried explicitly telling him "Do not solve this for them" (by trying to impress them with what I explained to him an hour before!) and given my pedagogical reasons above but it doesn't help. I don't think he does it consciously on purpose. But it is annoying, and damaging just the same.

Has anyone dealt with a similar situation, or can anyone give advice on how best to handle this?