Get him a speech therapist now. He will most likely continue to stutter, but the speech therapy will give him many useful techniques to manage his stuttering. I was in the exact same situation as your son when I was at his age. My mother was told the exact same thing as you, that it's a childhood thing, but in my case, it was absolutely not. Keep on pushing to get him a speech therapist, it's very important to start as early as possible and I cannot stress this enough.