A lobster-quadrille is a type of dance that they do at there school. I think that the lobster-quadrille is actually standing for some one getting discipline. The reason i think the mock turtle is crying is cause he is all alone and has nobody to talk to. The reason they are singing is so Alice can hear what the song sounds like. Cause she does not know what a Lobster-quadrille is. I think Alice is having a problem remembering things is cause she has been away from real life so long.The reason they are fighting about the dance is cause one does not remember the dance and the other one does. But they don't agree with each other on the dance.