I've observed the classroom and he, as well as many other boys in particular, seem to be aimlessly walking around. I'm not sure if he is bored or overwhelmed by the demands even if he is capable of the work. His math and reading have not suffered, but his teacher said she is concerned that they will in time. How can I help him?
Few first-graders are truly aware of exactly what is expected of them at school. Don't nag your son about messy work. Instead, look over his work each day and applaud how much he does neatly. From time to time, you should point out the importance of his writing so others can read it.
It isn't easy for many first-graders to do neat work. Some simply don't have the small muscle skills needed for writing. This could be true for your son. Encourage him to spend time playing with action figures, small blocks, clay, and other objects that he would manipulate with his fingers to build this skill.
Organizational skills are not inborn. They need to be taught by both teachers and parents. Some classrooms are highly structured, which makes it easy for children to understand what they are expected to do at all times. It sounds like your son's classroom is less structured. He is probably uncertain at times about what he is expected to do.
Try to find out from his teacher exactly how and when your son is disorganized. Then ask her how the two of you can work together to give him better organizational skills. At home, give him the responsibility of organizing small tasks with minimal help from you. Good luck.