How did Roger change in "Thank You, M'am"?
At the beginning of "Thank You, M'am," Roger is a thief who preys on an older woman. Because he is fairly young and still not very physically imposing, Roger's attempt to mug Mrs. Luella Bates Washington Jones fails, and he finds himself being drug back to her home for a few lessons.
Roger proves that he is capable of change by allowing this older woman to take him home. Although he is fairly small, he is still young and could perhaps have evaded her attempts to capture him. Mrs. Jones uses a maternal stance to convey to Roger that he doesn't have to follow a path of crime in order to achieve his goals. She makes sure that he recognizes his physical disorderliness, offering him a place to wash his face and clean up.
Inside her home, Roger is polite, referring to her as "m'am" at various points in their conversation. He is honest with her about his situation, acknowledging that "there's nobody home at [his] house" to properly care for him. Roger also chooses to stay, ignoring the freedom he has to leave:
After he had dried his face and not knowing what else to do dried it again, the boy turned around, wondering what next. The door was open. He could make a dash for it down the hall. He could run, run, run, run, run!
Because Mrs. Jones presents a sense of maternal compassion and structure that Roger lacks, he follows her directions and remains in her home. Perhaps the moment that demonstrates his greatest change comes when Roger realizes that he could now steal Mrs. Jones's unprotected money:
The woman did not watch the boy to see if he was going to run now, nor did she watch her purse which she left behind her on the day-bed. But the boy took care to sit on the far side of the room where he thought she could easily see him out of the corner of her eye, if she wanted to. He did not trust the woman not to trust him. And he did not want to be mistrusted now.
Roger respects Mrs. Jones, because she has taken the time to care for a young boy who has tried to inflict harm upon her. This impresses him so much that he no longer wants to steal from her and doesn't want to lose her trust. Mrs. Jones has impacted Roger's choices through her kindness and concern.
Understanding that his poor choices lead to consequences, Roger leaves Mrs. Jones with a new understanding of how he can choose a path that doesn't lead to destruction and that doesn't harm others.