Question

kate: but does that—
(she imitates with her fingers.)
—mean that to her?
annie: no. no, she wont know what spelling is till she knows what a word is.
kate: yet you keep spelling to her. why?
annie cheerily: i like to hear myself talk!
kate: the captain says its like spelling to the fence post.
annie a pause: does he, now.
kate: is it?
what does the dialogue reveal about kate?
she is eager to befriend annie.
she is kind to her children.
she is curious about annies methods.
she is well - educated about sign language.

Explanation:

Kate asks Annie multiple questions about spelling to the girl (who can't understand yet). This shows she is curious about Annie's teaching methods (spelling as a method here). She's not showing eagerness to befriend (no friendly - overture signs), there's no mention of her children's kindness context, and it's about the method of spelling (not sign language in general as the focus is on the act of spelling in this context).

Answer:

She is curious about Annie's methods.