In Act Three of The Miracle Worker, Anne Sullivan begs Mrs. Keller to allow Helen to remain with her another week because as a teacher Annie has not yet been able to make the action of forming letters into Helen's hand connect Helen to the word that represents something. At this point, Helen merely considers the letter-making in her hand as a sort of game that Annie plays with her.
When Captain Keller returns with the Irish setter, Belle, Helen hugs the dog in delight. Then, she plays with the paws of the dog, making letters with her fingers and demonstrating to the dog by manipulating her claws in imitation of the "game" that Annie has taught her. Her actions suggest that Helen seeks approval from Annie that she has learned the game so well.
In response to Mrs. Keller's questions about these actions, Captain Keller intervenes and comments,
"The dog doesn't know what she means, any more than she knows what you mean, Miss Sullivan. I think you ask too much of her and yourself. God may not have meant Helen to have the --eyes you speak of."
It is only when Helen flings the water from the pitcher upon Annie and Annie takes her outside to the pump that Helen finally learns that the "game" has a tremendous function.
Once the dog is out of the scene though, what does Helen WANT from Annie? Does she want her to teach her? To help her understand? To put her on the right path? Like you said she still doesn't understand what the signs are for so what could she possibly want from Annie then?