6 year old boy
Oh, my heart goes out to you and your boy! I, too, have a 6 year old boy, only child. We are seldom apart. I homeschool him, have always stayed at home with him (no outside job is what I mean). He goes through times when he clings so much to me I freak out a little! He is very independent, but at times just will not let me go physically. Like at night when i tuck him in, sometimes he grabs hold of me and says, "Mommy, don't leave me, don't leave me!" It warms and breaks my heart a little at the same time, if you know what I mean :)
My first thought in reading your post, though, was the possibility of some sort of trauma he has recently experienced? He's in first grade, so I assume he went through kindergarten with no major separation issues?
On the other hand, if the teacher says she has seen similar things in other students over the years, maybe just go with her gut? Unless in your heart you feel like something else might be going on? Have you tried asking him what is going on inside his head when he does this?
IS there a big change that your son is about to go through? I can understand that he's still adjusting to the new school, but that's a big change that's past, that he's assimilating, not a new change he's bracing for.
He sounds anxious to me. My son has been almost like this sometimes, and it's always been at times when I was very stressed by things that had nothing to do with him (for example, having a lot of migraines, or upset about being betrayed by a friend) and this apparently was his way of expressing his worry that all was not well with me. I was a chronically anxious child, and the times when I worried particularly about being apart from my parents were when I had encountered (from someone else's experience, TV, or my own wild imagination) a very disturbing idea of something that might happen either to my parent or to me if I were away from my parents' protection. So it might be useful to evaluate what could be worrying your son--even if it seems unrelated, this might be the way he's expressing it.