Today, instead of getting him to explain his thinking in more detail, I got another student to do it for him. One of my ultra-neat, super-organized girls took his scrawling mess of a piece of paper and sat down to try and translate how he had got to the solution. With help from the little boy (it was a great mathematical discussion) she was finally able to organize his work into something coherent.
This was a valuable lesson for both students. For the boy, he had to describe his thinking to another person on a one-on-one basis, without the pressure of the social group staring at him. He knew that the girl was an organized, neat-thinking person, so he had to adapt his style to meet hers.
For the girl, this was a lesson in outside the box thinking. She was able to take something that is completely alien to her (invented strategies in subtraction) and turn it into something that is neat, logical, and works for her. She even commented after they finished that she liked this way of doing it, and she would try it with questions in the future.
This kind of translating thinking is something that I will do again in the future. I think it would work well if you have a mixture of kids in your class who are Kumon-type math kids, and who are more of the invented strategies type.