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. 

In William Gibson's play The Miracle Worker, Kate Keller is Helen Keller's mother and the second wife of Arthur Keller. She loves her daughter fiercely and is willing to do anything it takes to provide her a chance at a normal life.

When Helen is a baby, Kate is the first one to notice her physical disabilities. As Helen grows older, though Kate loves her, she is unable to adequately care for her. A naturally kind and sweet-tempered woman, Kate is hesitant to discipline Helen, because she fears that Helen won't understand what is happening to her. She champions her daughter's independence and fights to keep her from being sent to an institution.

Kate is also the member of the Keller family who is most interested in trying whatever it takes to help Helen. While Arthur and Helen's half-brother James become dismissive of the various treatments presented to aid Helen, Kate is relentlessly optimistic and persevering. She encourages Arthur to write to different specialists and seek out help wherever it can be found, despite his reluctance.

Keller. Katie. How many times can you let them break your heart?
Kate. Any number of times.

Annie Sullivan is just the latest in a series of attempts to give her daughter a better life. This is part of why she is so supportive of Annie's methods even when her husband disagrees with them. Though she still struggles to discipline her daughter, she believes Annie is the best chance of Helen learning to live with her disabilities.

The Miracle Worker is based on true events in the life of Helen Keller.  When she was very young, Helen became blind and deaf.  Her parents, unsure of how to help her, raised Helen with little structure and no formal education.  They hired a teacher, Anne Sullivan, to come to their home to help Helen.  Anne found Helen to be a lost and "wild" child, who did almost anything she wanted in the Keller home.  Anne did what everyone thought was impossible.  She taught Helen to communicate.  She did this after many attempts.  Over and over, she signed words into Helen's palm.  Helen did not understand that each word was for a certain thing.  Then one day, Helen held her hand under a water pump.  As the water flowed into Helen's hand, Anne signed the letters "W-A-T-E-R."  Suddenly, Helen understood that "water" was the cool liquid flowing onto her hand.  After that, she became an eager learner.  Anne was Helen's teacher for years, and she taught her to read and write.  Mark Twain later called Anne Sullivan a "miracle worker," which is where the title of the play came from.

The Miracle Worker by William Gibson was originally written for television and was adapted for the stage, opening on Broadway in 1959. It is based on the true story of Annie Sullivan's attempts to teach the blind and deaf Helen Keller when Helen was seven years old. Kate Keller is Helen's mother, the second wife of Captain Arthur Keller. Kate is much younger than her husband and is also step-mother to James, Helen's half brother.

Kate is a loving, indulgent mother but this has allowed Helen to become unruly and basically unmanageable. She is anxious to try anything to help her daughter and manages to persuade Helen's dominant father that Annie Sullivan, whom he is inclined to dismiss, should be given a chance because she knows that Helen has potential, desperately mentioning that "It’s still in her, somewhere, isn’t it?" (Act II) . It is very difficult for Kate to relinquish control of Helen to Annie but she knows that, otherwise, Helen will no doubt be sent to an institution, "an asylum."

Helen touches her cheek to indicate that she is looking for her mother but Annie insists that the only way to help Helen is to not give in to her all the time and so Kate agrees because she recognizes the truth in Annie's words - "I don’t think Helen’s worst handicap is deafness or blindness. I think it’s your love. And pity." She is encouraged by Helen's folding of her napkin, a huge step forward for the otherwise petulant child. Despite the many setbacks, she believes in Annie and Helen's development is phenomenal.      

An inspiring drama of courage, persistence, and faith, The Miracle Worker by William Gibson presents an interesting interplay of characters.  Here is a discussion of the salient characteristics of the main characters:

Captain Arthur Keller

The patriarch of the Keller family, Captain Keller is accustomed to having the final word on all household decisions.  He has "stopped believing in wonders" regarding his child, Helen.  Although he indulges Helen, after a while he decides that it may be better to put her into an institution.  However, he does love his wife and agrees to write to The Perkins Institute in order to learn if anything can be done for Helen.  When Anne Sullivan arrives, Captain Keller regards her assertiveness as offensive and unbecoming of a woman; thus, he is in constant conflict with her as he is skeptical of her abilities.

Mrs. Keller [Kate Keller]

The main characteristic of Mrs. Keller is her overwhelming guilt over what has happened to her daughter.  As a result of this guilt, she spoils her child, who acts like a feral animal.  As opposed to her husband, Kate refuses to give up hope that something can be done; thus, she begs her husband to not fire Anne when he becomes angry with her and to allow Anne to isolate Helen from them in the garden house for a week. It is Kate Keller's enduring love for her daughter and hope that she will be able to learn that supercedes all else.

James Keller

The son of Captain Keller, James is rather unmotivated, often sarcastic, and especially jealous of all the attention given to Helen.  However, he becomes the champion of Anne Sullivan, supporting her efforts to teach Helen. In Act III, for example, he argues with his father to allow Anne to make Helen fill the pitcher that she has flung at Anne. With this show of inner strength, James wins some respect from his father.

Anne Sullivan

A child of the slums who herself has been blind, Anne has learned to endure.  She has the inner strength to insist that Helen learn and behave properly. In addition to her fortitude, Anne believes in the power of the soul, persisting in tapping this soul of Helen.  Driven by this belief and her guilt over the death of her brother, Anne finally breaks through to Helen and becomes "the miracle worker."  Her victory is both one for Helen and for herself as she has conquered her inner demons and the forces of Captain Keller's disapproval of her as well as having helped Helen.

Helen Keller

Helen, of course, is the main character of this play. Her handicaps notwithstanding, Helen is obviously a girl of high intellect and cleverness as evinced in her locking Anne in her room and her other devious acts.  Indeed, her brillance is the key to her breakthrough to the world of learning since she was only six months when she learned to say "wa-wa," the key to her awakening.  Her strong will, then, is turned to her great success as Anne Sullivan helps her make the definitive transtition. 

Anne Sullivan (the protagonist) was shaped by her childhood. Born in poverty to an Irish Catholic family, she was sent to a mental hospital and was raised among the mentally ill. With her brother Jimmy, Anne survived the horrible conditions until her brother’s died from tuberculosis. After she became legally blind, Anne was sent to a school for the blind to complete her education. Upon graduation, she accepted a position as a teacher for Helen Keller in Tuscumbia, Alabama. Anne explains her background to Helen’s step-brother, Jimmy, in an effort to make him understand why she will not give up.

Anne’s strength of character guided her in facing the conflict from the Keller family as a Northerner and Irish (the Irish were discriminated against during this time in American history). She persevered in spite of Captain Keller’s antagonism, Mrs. Keller’s interference, and Helen’s animosity. Determined to reach Helen in the same way she herself was reached and rescued, Anne managed to lead Helen out of the darkness of ignorance.