If I had to choose one of the elements of fiction that was the most important in "The Lesson," it would be point of view.
The story is told from Sylvia's viewpoint and the story's focus, of course, is Miss Moore's lesson. Had the story been told from the third person, its impact on the reader would not be as powerful; we would not have been able to follow the uneasy progression of Sylvia's thoughts. With the first person point of view, we know exactly how Sylvia feels.
The group of students Miss Moore has chosen to try to teach are either unaware, disinterested, or—as is the case with Sylvia—opposed to her attempts. Miss Moore is not trying to teach all these children a lesson; she is speaking to an audience that does not welcome her intent. The essence of "The Lesson" is Miss Moore's hope to reach past the naiveté of someone (anyone) in the group, and open his or her eyes to a more sophisticated view of the world of which they are a part—and in doing so, motivate that person to take a personal interest in his or her life, with positive results.
It is easy to perceive through Sylvia's internal dialogue that she feels disdain and resentment about most things. She is an angry girl. If we could speak to Sylvia, she would probably know some of the reasons why she is angry, but probably not all. It is to this second aspect of Sylvia's intellect that Miss Moore's words find purchase, and take root.
Can we, as the reader, know that Miss Moore is specifically speaking for the sake of reaching Sylvia in particular? There is no indication from Sylvia to support this kind of conjecture, though we find out that Miss Moore is very quick to notice Sylvia's grasp of the "lesson." Miss Moore probably throws her ideas out, like seeds, to see with which youngster (if any) the ideas "find fertile ground" and start to grow.
Sylvia is enlightened when she learns of the foolish way people with money can spend it even while other people are struggling daily to make ends meet. As she processes this, we can almost see Sylvia wrinkling her forehead as she tries to make sense of this seemingly nonsensical "truth."
Sylvia was unaware (as were the other kids) that this kind of store—and this kind of disparity between those who "have" and those who "have not," existed. The unfairness of it jolts Sylvia's social awareness awake enough to know that something is seriously wrong (though we can also tell that she would not thank Miss Moore for providing Sylvia with this new insight).
As Sylvia follows some distance behind Sugar at the end, she has new food for thought. As Sylvia tells it, Sugar momentarily seemed to grasp the situation at the toy store, but then the "light went out" and she let the idea go. And although Sylvia does not seem to completely understand the enormous significance of what she has learned, her awareness has been tapped. We can assume that she will never let go of this new world view, and will never be the same person. We are able to get a precise sense of Sylvia's state of mind with the use of the first person point of view.