I am no expert, but there's one little addition:
In situations like these, make sure he is sufficiently rewarded for his effort when he finally makes sounds.
I remember when I was little, I was discouraged from speaking when people tried to constantly correct me on sounds I made "No, no" and the like, so some tutors simply learned to encourage me regardless of how bad I was, and remembered to reward me when I did a good job. But that's well past J.K. though.
Make sure your son doesn't hate the J.K. teacher. There's a possibility that specific mannerisms of the J.K. teacher is so different from the mom and dad, that your son is so frightened of the J.K. teacher and refuses to speak. Or maybe the son is so scared of the other kids. If your son has a history of being constantly scared of strangers, then you may need to research on these "side-matters" because another problem may be at hand, that needs to be solved before encouraging the son to speak.
One way is to ease him into strangers by going to kid-meets of sorts with other parents, and "ease" him into stranger kids in smaller groups, in precense of comforting parents, before he goes to J.K. Sometimes J.K. is just too much and there needs to be a step before J.K. for certain people. Can be as simple as a neighbourhood meet of 4 or 5, or perhaps a parents-day at the daycare center, or something else....where parents are with their kids, and the groups are smaller than a J.K.
If your son is comfortable with strangers (i.e. loves to play with other kids he doesn't know) then that might not be the problem, but it bears worth mentioning...
(Profound deaf here.)
