In "Thank You M'am," Mrs. Jones is upset with the boy who tries to steal her purse. No doubt, Mrs. Jones becomes very angry with the boy. As the boy snatches her purse, the strap breaks and the boy falls down. At this moment, Mrs. Jones kicks the boy in the rear. "Then she reached down, picked the boy up by his shirt front, and shook him until his teeth rattled." This quote is just an expression. It exemplifies how hard Mrs. Jones shook the boy. Of course his teeth did not actually rattle. The author just uses this cliche to express Mrs. Jones' agressive behavior toward the boy who stole her purse.
At the time this story was written, corporal punishment was a popular or preferred way of punishing a child for misbehavior. Mrs. Jones was old school. She grew up in a time when children were spanked. Physical punishment was prevalent. Parents would often say that they were going to shake a child until his or her teeth rattled. This is a popular expression which only means that Mrs, Jones punished the boy for stealing her purse. She was angry. She retaliated by shaking the boy in an extremely forceful manner. Mrs. Jones was trying to get the boy's attention. She was trying to teach him how wrong it was to steal:
Pulling the boy up by his shirt and shaking him, the large woman demands that he return her pocketbook.