The Miracle Worker by William Gibson is a play about Helen Keller and Annie Sullivan, particularly the influence Annie has on Helen and her family. Helen Keller was left blind and deaf after an illness as a baby and the play starts with that event. Having survived, Helen must learn to communicate but her efforts are mostly unsuccessful and her family's pity means that Helen is allowed to behave inappropriately. Annie's first hurdle is to teach Helen some manners.
Dynamic characters are those who undergo significant change. The most significant of these would be both Annie and Helen who change and develop throughout the play which makes them dynamic characters. Annie teaches Helen and reveals her enormous compassion and patience, even though she is quite headstrong. She is determined not to let Helen down, especially as she feels a burden of guilt for the circumstances surrounding her own (late) brother, Jimmie. Kate Keller does come around to Annie's methods and eventually reveals herself as a dynamic character even if, at first, it seem unlikely. By the end she is ready to learn how to help Helen. She knows that pity is not the answer and understands that Helen's willingness to fold her napkin is a huge step forward.
Static characters refer to those characters who are much the same at the end (of the play) as they are in the beginning. Keller would be the most obvious as from the beginning he has been skeptical. In Act I, he reveals that he is resigned to accepting Helen just the way she is no matter how inappropriate her behavior, suggesting that it would be pointless "rushing up and down the country every time someone hears of a new quack." He does not feel that anything else can be done. By Act III, he still has little faith in Annie's abilities to teach Helen anything. He comments that "you're the difficulty, Miss Annie" revealing his mistrust of Annie's methods or even her suitability for the task.
James remains a static character in terms of is relationship with his father and although there are instances when he defends Annie or Helen, he does not expect anything to change. He says "I think we've started all over" when Helen has a temper tantrum at the table in Act III and his father simply dismisses his opinion when he tries to state one.