What kinds of problems are these, can you give an example or two? One alternative would be first to offer him challenges along the lines of:
"Explain why [answer to ... is ...]."
such that he very clearly cannot do the question unless he can explain, because the question *is* to explain. If he genuinely can't answer that kind of question, it's interesting, and worrying. If he can, the next step is to tell him that when he can work out the answer to the actual question in his head, he should set himself a question of the above form and write the answer to that as his answer.
We've explained to our DS that in research mathematics, where you are writing about a problem nobody has ever solved before, there is almost no point in stating an answer: the content of the job is to explain why that is the answer clearly enough that your colleagues can understand. Even for professionals, it can be hard to decide exactly which steps need to be explained and which don't, given the particular expected audience, and it is never too soon to start practising this, but at the very least, you should explain enough that someone who knows as much as you did when you started thinking about the problem but who has not studied the problem can follow your argument easily. DS sometimes complains about writing because he dislikes writing, but seems to accept the necessity. I think they key thing is to get over that nobody is disbelieving that he can get the answer without writing working - rather, writing the working is the point.
