There are many different types of stuttering such as blocks (cannot physical make the sound and stop maybe hold their breath) repetition, probably the most common. And prolongations of a certain sound ( I usually do this on S sounds) I would consider what you are saying a repetition. I believe most kids outgrow it when they don't know it's there. But when it is constantly brought up by others and causes stress. It's messed with their unconscious mind. When they know that is the reason why people pick on them it becomes a part of them. They are children who are learning and when something is questioned about them that they cannot help. May it be parents telling them to "slow down" or "say is again" it's frustrating. It points out the stutter. When other kids at school ask them "why do you do th-th-that". Kids don't know how to respond. It messes with your psychology. I believe it's best to let it be. I don't believe speech therapy works for stuttering. There is not enough research on it. All they teach you to do is "cope". When I was a around 5 I stopped stuttering then started again less than a year later. I was taken out of speech therapy because the speech therapist said "you cant stop then start again". I didn't get speech therapy again until highschool. I have met a girl who worked with a specialist who figured out the reason for her stutter was gluten. So I suppose a way to test while they are young is taking away bread from their diet and observing any difference. I've never tried this myself.