It's kind of counter-intuitive but it might be better if you treat it as a separate skill to be developed from the grounds up. While I was mildly annoyed at the time (early elementary) at the show work requirements, I have become rather grateful that our schools actively taught this skill from an early age and made it impossible to get an A without mastering it.
It is entirely normal to be disinclined to show work, particularly if you have high ability in math and have to reverse and slow down your thinking processes to provide an intelligible description. However, the fact that your DS' accuracy is not very high should be an additional persuasive argument for showing some of his work. I think there is a wonderful article in the AOPS database by Richard Rusczyk that related to an AIME contestant learning the value of writing down some of his work. I plan to show DS11 when the time is right. At present, he can do most of the AMC8 and much of the AMC10 problems in his head but he does so to his detriment and ends up averaging a couple of careless errors per test. I haven't push this point on multiple choice questions because he tends to make fewer (sometimes none) mistakes on exams that are easier than the AMC exams(county benchmarks, state assessments, MAP, SAT, etc.).
However, DS has mastered the art of showing work in essay type questions and the following has helped: At the early stages, it may be helpful to encourage your DS to do the problems twice and compare the answers - once all in his head and once on paper as if he had to explain to another student. It may also be helpful to show him completely different approaches (pictures, words, number sentences or a combo) to showing work so he can decide which method is least painful to him. Ultimately, he needs scaffolding (such as provided to elementary students) for each problem type. The teacher needs to identify and explain step by step what he needs to write and once he has assimilated the steps, then he needs to apply those exact same steps to another similar problem. For example, if he is given an elementary geometry problem such as find the volume of a rectangular prism, one approach would be to identify the formula (volume = length x width x height), identify the value of each constant/factor (l=9, w=7, h =5), input the values into the formula (v = 9 x 7 x 5), and provide the answer (v = 315 cubic units).
What I am suggesting is to separate out the writing down of steps from math instruction until he has gain some basic skills. Teach him to identify the general steps for particular types of problems. Have him study actual model answers and have him practice on similar problems. Although DS still prefers to do everything in his head, he is able to apply the same technique to new problems and provide written "proof" when called to do so. In fact, I think that this type of training has made writing geometric proofs very natural for him.
