In the story "Thank you, M'am," why does Roger sit so that Mrs. Jones can see him?

In the short story, “Thank you, M’am,” Langston Hughes tells us exactly why Roger sits in such a way that Mrs. Jones can see him.  Hughes tells us that Roger “did not want to be mistrusted now.”  He sits so that Mrs. Jones can see him so that she will know that she can trust him.  This is important to the story as it shows that Roger has come to care about what Mrs. Jones thinks of him.
“Thank you, M’am” is a story about how we can be affected by how people think of us.  It is a story about how one person’s opinion can matter tremendously to another person, particularly if the other person has not had many/any people truly care about him.  Roger does not appear to have anyone in his life who cares about him.  There is no one at his house to feed him or make sure his face is clean.  Perhaps because of this, he goes out and commits petty crimes.  When he tries to snatch Mrs. Jones’ purse, she stops him and drags him home with her.
As the story goes on, Mrs. Jones shows that she trusts Roger and Roger desperately wants to be worthy of that trust.  He wants someone to have a good opinion of him.  Mrs. Jones seems to know this.  She deliberately leaves her purse where he can get it and does not watch him to be sure he does not take it and run off.  She is showing him some amount of trust.  Once she does this, Roger wants more.  He wants to continue to be trusted.  Therefore, he is careful to sit where she can still see him.  For the first time in his life, someone who matters is treating him with trust and respect.  He wants this to continue, which is why he sits so that she can see him.