Her behavior sounds almost symptomatic of ADD/ADHD. A classic feature of people who have ADD/ADHD is that they can't wait for the punchline, so they tend to walk all over other people's sentences. We're not saying you should run off and get her tested, but it might be something to keep in mind in case you notice any other behaviors related to attention.
Perhaps you could help your daughter displace some of that intense focus she has onto something else. For instance, while she's listening to someone talk, maybe she could wear a rubber band on her wrist and snap it, just to help her disperse some of her energy. (You could even get her one of those Silly Bandz that are popular right now.) Or you could recommend that she recite the ABCs in her head or think of a tune while she's listening. It's possible that little distractions like that will trouble her focus just enough to help her calm herself a little.
If this doesn't work, you could consider talking to her pediatrician about the possibility of something like ADD/ADHD, or you could work with her teacher on ways to help her socialize more appropriately. The teacher obviously would be a very helpful person if she's acting up in school.
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