Dear Distressed, Start by separating the child's behavior (being mean) from attitude (arrogance). Ask yourself:
Why arrogance? Often an attitude of superiority is a clue that a person is protecting herself from the opposite -- inferiority! It's possible that Abby is thinking, "I don't know how to get them to play with me" or "I don't know how to do that" or "They won't like me." Try assuming that this is true, and then have a talk with her. Choose a private, quiet time to sit together and talk.
Work it out together. If you think Abby was being mean because she didn't know how to say "I want to play," try these ideas:
Cite specifics: "Remember this morning when you saw Carla and Ralph building and you said they were..." (Use the words Abby used.)
Interpret: "I think maybe when you want to play, you say mean words."
Brainstorm: "Let's think of better ways you could tell them you'd like to play." Enlist Abby's energy and imagination in listing positive approaches.
Put Abby in charge: "I've got a great idea! Let's get these guys, and you can tell them all the new ways you're going to..."
Involve the others: Role-play. "Abby, let's pretend you want to play with these children. What could you say?" Encourage Abby to practice her new "lines," and the others to respond kindly.
Look for other reasons. It could be that Abby's behavior has to do with needing to feel proud or be in the limelight. Try giving her a few weeks to use her new bag of tricks, and then have another conference. Begin by complimenting her on any improvement you've noticed. Then educate her on ways to make gracious comments when others are pleased with themselves or are getting attention. Follow the same format as before, eliciting Abby's ideas and those of her classmates.
Ask yourself: Why else might Abby be behaving the way she does? Could she be copying other people in her life? Even if this is so, I suspect that underlying feelings of "I'm not as good as they are" account for the persistence of her behavior. If Abby felt comfortable with herself, I doubt that she would be compelled to put her peers in their place.