R.M.
My suggestion is to try and find out what kind of writing activities the teacher is having them engage in and then try to duplicate it at home. If he has issues with it there too, then you have your first real clue as to what is bothering him. You might try doing more "paper" activities with him at home, coloring, identifying things, just get him more used to doing that type of activity. Personally, I don't think it is as simple as him just having anxiety over the writing exercise, but it will take some detective work on your part to figure out what it is. (It could just be a "phase" too and disappear as mysteriously as it came!!)
Do they have assigned places to sit during these activities? Maybe someone who is sitting near him it pressuring him about his work or being subtly aggressive and hard to deal with. Ask the teacher to move his seat, see if sitting next to someone else will have a positive effect.
If there is a set schedule to the time that things are done in class, trying being there BEFORE he is told to go and sit down for his writing activities, sit with him and see if that helps at all or if you can see something that is upsetting to him in the situation.
Good luck and let us know what you find out.