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.
This is the approach that I've used with both my daughter and my students. With my students (middle and high school), I usually give them the line that I need to be sure that they are not doing math that I don't know, or don't remember.
What sometimes helps kids who are getting use to showing all of their work is to allow diagram-ing or "backwards" work to be shown.
For example: solve 3x+10 = 28
answer: 6, because 3 goes into 18 6 times
(which can then be used to get them to answer the question where did the 18 come from?)
18 is 10 less than 28
then I repeat their steps in the conventional order of solving problems.
It takes a few times of doing this before the student eventually feels confident/comfortable enough to do this themselves. However, most of the time these kids can break down the process backwards more rapidly than forwards and it is actually really cool to see their order of operations.
Just warn the teacher before he turns in the first assignment with the work done out "backwards"
since many middle and high school math teachers will freak out when presented with work done out this way. (I'd explain it as the first step to getting him to do math the teacher's way and ask for understanding as you work towards what is required by the class.)
