The story of Helen Keller is well-known and Helen Keller remains an inspiration to many who are awe-struck by her unswerving faith in the future. The play The Miracle Worker reveals the influence, dedication and purpose of Annie Sullivan when she arrives at the Keller's home where she cares for and assists the family in coping with Helen's debilitating condition, Helen having been left blind and deaf after an illness as a baby. 

1. The most obvious similarity between Kate Keller, Helen's mother, and Annie Sullivan is their love of Helen. The most obvious difference is their methods of helping Helen to thrive.  

The play starts just as Helen has made it through the worst of her illness. It is Kate who notices Helen's lack of response to movement or talking and the audience knows that the difficulties are just beginning. Five years later, Annie arrives. Kate has changed from a spirited young woman into one "steeled in grief" (Act 1, scene 3). She has not changed in her resolve, however, and wants to keep trying to find a doctor or specialist who can help Helen.

2. This will be revealed as a similarity between Kate and Annie later when the audience sees Annie's perseverance and intent. It also reveals a difference between the two as Kate is tired and worn whereas Annie is more determined than ever, especially as she has had to battle her own disabilities during her childhood and, even now, only has partial vision. 

Annie is not what the family expected; she strong-willed and, according to Captain Keller, Helen's father, seemingly disrespectful with no concept of her status in the family environment. 

3. Both Kate and Annie have an awareness of Helen that the others do not share. They are both patient with her but they have very different natures which contribute to their different styles of educating and furthering Helen's education and improvement. Kate sees Helen as "an afflicted child" (Act 1, scene 3) who needs to be pampered to at every turn but Annie sees Helen as an obstinate and difficult child. Kate pities Helen and sets no boundaries but Annie does not pity her and insists on defined levels of behavior which is why she would rather take Helen out of her immediate environment so that Helen can learn to trust others and find independence whilst developing respect. 

4. Kate and Annie are both at the mercy of Captain Keller, the head of the household but they respond very differently to him. Kate is largely controlled by her husband although she will sometimes stand up to him when she thinks it will benefit Helen whereas Annie refuses to be controlled at any time, anywhere, by anyone (especially Captain Keller) or anything.

5. Annie and Kate like each other and Kate is interested in how Annie speaks to Helen by signing on Helen's hand. Kate wonders how to communicate because Helen is "impaired" but Annie soon points out that "there's nothing impaired in that head. It works like a mousetrap" (Act 2, scene 1). Kate wants to learn this method too but when she gives Helen a sweet "for stabbing" Annie with a needle, the differences between the two women are obvious.

When Helen learns to spell water, the world opens up ahead of them and the play ends on this note of unity whereas the family had before been divided and almost broken. Kate and Annie can now imagine a future for Helen.

How do Captain Keller and Annie Sullivan compare and contrast in The Miracle Worker?

In The Miracle Worker, Annie Sullivan and Captain Arthur Keller, Helen's father, are both similar and different.  If we look at the similarities, both love Helen, though the captain hides his feelings more than Annie does.  Having Helen, both are determined to help her make progress as Miss Sullivan and Captain Keller want her to be able to help herself.  Both want success.

These two dominant figures in Helen's life are also very different.  Miss Sullivan is determined to bring Helen into some kind of calm and to follow what Miss Sullivan is asking her to do.  Helen has long been able to bully anyone into doing as she wants including eating off the plates of anyone at the table.  Annie must fight both the determined Helen and Helen's father as he would indulge his daughter.  As a captain during the Civil War, he is used to giving orders and having them followed, but he cannot seem to get control of Annie as she does what is best for Helen and defies the Captain.  Leading to constant conflict on how to handle Helen, Annie finally has to appeal to Helen's mother, Kate, for help.  The father wants to help his daughter learn, but totally disagrees with Annie's methods as he is required to learn to say no to the child.

Eventually, the breakthrough is made with Helen's sharp mind, and Annie and Captain Sullivan can work together to help Helen learn.

What are the differences and similarities between Annie Sullivan and Kate Keller in The Miracle Worker?

I can't even tell you what fun I had answering your question!  I love this play and know most of it by heart, but never really explored these two characters as a pair.  What an interesting set of characters to compare!  There are many more differences than similarities in these two characters, so let me begin with the similarities and end with the all-important differences.

Both of these women want to help Helen and serve as a mother-figure in some way.  Yes, it is redundant to say that the two are both women, but that is the first (and the most obvious similarity).  They also both serve as a mother figure in some way.  Kate, of course, is Helen's real mom.  Annie, of course, is Helen's teacher, but especially when she spends a few months apart from the family in the small cottage adjoining the property, Helen has to learn to depend on Annie for the necessities of life.  The most important similarity that both women share is the desire to help Helen.  I will go even further and say that it is an INTENSE desire to help Helen.  This is where the similarities end and the differences begin.  The differences arise in exactly WHY and HOW they intend to help Helen.

The first difference Kate and Annie have is a difference in their pasts.  Kate had an easy past with "old money" and riches.  Kate is the wife of a very prominent "Captain Keller."  They live on a vast plantation with many servants and much land.  There is nothing to indicate the Kellers are a rags-to-riches story.  They are simply the outcome of society in the old South.  This life of luxury in the old South unfortunately led to a weak woman.  Kate, quite simply, is ruled by her husband.  Luckily, she is wise enough to know how to get her way (as in hiring Annie).  Annie, on the other hand, had an extremely difficult past full of poverty and illness.  She was blind and can only see with much difficulty because of an operation and glasses.  No life of luxury for Annie, ... ever!  Annie describes these effects here:

Annie.  ... The youngest were in another ward to have babies they didn’t want, they started at thirteen, fourteen. They’d leave afterward, but the babies stayed and we played with them, too, though a lot of them had—sores all over from diseases you’re not supposed to talk about, but not many of them lived. The first year we had eighty, seventy died. The room Jimmie and I played in was the deadhouse, where they kept the bodies till they could dig—

Kate (closes her eyes). Oh, my dear—

Annie. —the graves. (She is immune to KATE’S compassion.) No, it made me strong. But I don’t think you need send Helen there. She’s strong enough. (She waits again; but when neither offers her a word, she simply concludes.) No, I have no conditions, Captain Keller.

The next difference has to do with WHY the two women want to help Helen.  Kate wants to help Helen because Kate has PITY on Helen.  Of course, Helen is Kate's own child and, as such, has much compassion due to her (thinks Kate). 

[HELEN is back at AUNT EV, fingering her dress, and yanks two buttons from it.] 

Aunt Ev. Helen! My buttons. 

[HELEN pushes the buttons into the doll’s face. KATE now sees, comes swiftly to kneel, lifts HELEN’S hand to her own eyes in question.] 

Kate. Eyes? (HELEN nods energetically.) She wants the doll to have eyes.

Watching the unruly Helen live in her own world of darkness is a sadness for Kate.  She wishes to have peace in the household and a child who will not harm the little ones nor disturb the older ones.  Standing as a complete opposite to Kate here is Annie who wants to help Helen because Annie wants to prove her success as a teacher.  This doesn't necessarily mean that Annie doesn't "like" Helen or "feel for" Helen, but that is not her main impetus.  Annie, due to her situation in life, is forced to make a way for herself and, due to her disability, must teach others who are in the same situation as herself.  Before this time, Annie was at a collective school and this is her very first position.  Her failure at this position may nix her career entirely.

Perhaps an even more important difference is in HOW the women plan to help Helen.  Kate has two methods:  coddle and ask for help.  Thank God for the latter!  Coddling Helen, due to Kate's pity, has made Helen into a monster.  Annie says so herself. 

Annie. I know an ordinary tantrum well enough, when I see one, and a badly spoiled child—

James. Hear, hear. 

Keller (very annoyed). Miss Sullivan! You would have more understanding of your pupil if you had some pity in you. Now kindly do as I—

Annie. Pity? (She releases HELEN to turn equally annoyed on KELLER across the table; instantly HELEN scrambles up and dives at ANNIE’S plate. This time ANNIE intercepts her by pouncing on her wrists like a hawk, and her temper boils.) For this tyrant? The whole house turns on her whims. Is there anything she wants she doesn’t get? I’ll tell you what I pity, that the sun won’t rise and set for her all her life, and every day you’re telling her it will. What good will your pity do her when you’re under the strawberries, Captain Keller?

Luckily, Kate does have the gumption to ask for help for Helen and makes sure her husband acquires that help for the family.  In regards to Annie, the HOW of helping Helen has to do with being stubborn (and often downright abrasive) with her own tried and true teaching tactics.  Although the above quote serves as a perfect support for this argument, there is another near the conclusion of the play:

[KELLER shoots a glare at him, as HELEN plunges her other hand into ANNIE’S plate. ANNIE at once moves in to grasp her wrist, and HELEN, flinging out a hand, encounters the pitcher; she swings with it at ANNIE; ANNIE, falling back, blocks it with an elbow, but the water flies over her dress. ANNIE gets her breath, then snatches the pitcher away in one hand, hoists HELEN up bodily under the other arm, and starts to carry her out, kicking. KELLER stands.] 

Annie (savagely polite). Don’t get up! 

Keller. Where are you going? 

Annie. Don’t smooth anything else out for me, don’t interfere in any way! I treat her like a seeing child because I ask her to see, I expect her to see, don’t undo what I do! 

Keller. Where are you taking her? 

Annie. To make her fill this pitcher again!

The irony is, it is precisely HERE that Helen has her breakthrough and learns that every word has meaning.  Annie's stubbornness and grit pay off.  Helen learns, ... and eventually hands "the key" of learning to "teacher."

I guess you could say, in conclusion, that Kate and Annie serve as foils to one another where one remains static (Kate) while the other is dynamic (Annie).  Kate continues with her compassion and pity for Helen.  I can't forget the actress when she finally welcomes Helen back into her arms after the months apart.  Kate, there, doesn't give a care what has happened, she just wants her child back.  Annie, however, goes from a stubborn teacher who doesn't care about Helen to a dedicated mentor who cares VERY MUCH about Helen.  In fact, Annie cares SO much that the two spend the rest of their lives together having many  more adventures.