The correct completion of this sentence is as follows:  Kate discovers that Helen is able to learn the gift of language thanks to her teacher, Annie.  We see this in the climactic scene of the play when Helen finally learns the word "water."  After grasping the concept of language, Helen stops long enough to wonder who opened up this world for her.  Annie signs the word "teacher" into Helen's hand.

Helen stands thinking it over, then turns again and stumbles back to her parents.  They try to embrace her, but she has something else in mind. ... Helen spells a word to her.  Kate comprehends it, their first act of verbal communication, and she can hardly utter the word aloud, in wonder, gratitude, and deprivation, it is a moment in which she simultaneously finds and loses a child.

Kate:  Teacher?

Annie turns, and Kate, facing Helen in her direction by the shoulders, holds her back, holds her back, and then relinquishes her. ... Helen slides into Annie's arms, and lifting away her smoked glasses, kisses her on the cheek.  Annie gathers her in.  Kate torn both ways turns from this, ... and makes her way into the house.

Before this moment, Kate secretly hoped that it was a mother's love that would grant Helen the concept of language.  It was not.  It was the harsh hand of a loving teacher.  Even with the epiphany of the day, Kate still has a hard time accepting this, especially the fact that the very first word Helen spelled wasn't "mom" but was "teacher."  Oh, there are many different kinds of love, Helen.  Congrats to you for learning a new way of love that day!