I think that Oates' real power lies in the first sentence. In this opening, we are naturally introduced to the character. At the same time, we also gain insight into Connie. The preoccupation with her appearance ("glance into mirrors or checking other people's faces to make sure her own was all right.") At the same time, we also see someone who is driven by her own sense of self. The idea of opening with "Her name was Connie" almost constructs the idea that she was the center of the universe, something that Connie believed as a teenager. At the same time, the use of the past tense brings to light that this is someone of the past, literally and figuratively. We are almost reading an obituary of someone. With this introduction into the self indulgent nature of Connie, Oates also helps to facilitate the change in the character. Contrast the vision of Connie in the first paragraph, after the opening sentence. Her mother is criticizing her, while she is apathetic to such critique, with her sense of superiority confirmed. This is nowhere near the character we see at the end of the story. After crying for her mother, she recognizes that her sacrifice will save her family. She is "hollow" with "an emptiness" and she recognizes that she will not see her mother again nor sleep in her bed again. She walks out of the house nowhere like the character she was at the start. The opening line we have at the start brings us to a characterization that is completely divergent from the vision we have at the end fo the narrative.