I find that investing lots of energy in wondering about a specific behavior is often less productive than thinking about a category of behavior. What umbrella would you put mimicking under? I'd guess pestering or teasing. Siblings are especially famous for intentionally, provocatively, and repetitively annoying each other while parents tear their hair out! Which leads us to another mystery: What is so much fun about bugging another child?
Mimicking for Personal Power
I suppose the glee displayed by the child who is pestering (in this case pestering by mimicking) is the result of having the power to manipulate the emotions and behavior of another person. Personal power feels good. I would be interested to know: Is Miriam more an insider or outsider socially? Is she a magnet for other children, one whom children seek to play with, or is she more frequently the one who wants to play but finds that the children she wants to play with are already absorbed in something? Typically, the child who mimics or in other ways provokes peers just for the fun of it is a child who wants the other child's companionship more than the other child wants hers.
What You Can Do
Here are some things you can do to lessen the frequency of Miriam's behavior:
1. Observe Miriam closely. Does she have one or more friends with whom she plays reasonably well? Do the children she mimics often reach out to Miriam to include her in their activities?
2. Meet with Miriam and the children she mimics. Ask if they like it when Miriam mocks them, copying everything they say and do. Say something like, "It sounds to me as if Miriam likes you; she certainly tries to be with you a lot. Maybe she could let you know that she wants to play with you in a way that you would like better."
3. Ask the victims of Miriam's mimicking to suggest friendly ways that she could show she wants to join them, including coming over and watching what they're doing. Then ask Miriam if she could do that. Ask the others if they would sometimes invite her to play. Tell them you understand that sometimes another child cannot be added to the play, but when this happens, you can say, "I can't play with you right now, Miriam, but I will later."
4. Describe the social problem Miriam is having at school to her parents, and ask if anything like this goes on between Miriam and any siblings at home. Explain how crucial you think successful interpersonal relations are in young children's development.
5. Share your ideas and plans about helping Miriam, and encourage her parents to let you know if they have additional thoughts.
The important lesson to be learned from this situation is that any attention is better than no attention, so we all need to help children get the attention they need in positive ways.