In the story "The Lesson," what is the lesson that Miss Moore is trying to teach the children?

Miss Moore wants to teach the children that there is "more" in life that what their ghetto neighborhood offers.  In showing them there is "more," she hopes they will reach for "more." However, when the narrator says at the end "There ain't nobody gonna beat me at nuthin," we are not sure if she has learned the lesson or not for throughout their trip to the city she resists what Miss Moore has to say because she doesn't want to appear stupid--she wants to be a tough know-it-all.  Miss Moore is concerned that such an attitude might limit the child rather than expand her possibilities in life.