He always calls them ladies and gentlemen, and speaks so softly that they must be quiet to hear him; even a little noise sounds loud in Mr. Williams’s room.

Last week, during a lesson on common denominators, a new boy began tapping on his desk. Mr. Williams ignored it and kept teaching. The boy sat on the floor, twirled a ruler and wandered around talking to other students. Mr. Williams kept teaching. When the boy could no longer be ignored — he knocked over a chair — Mr. Williams made eye contact with a special education teacher, who took over the class. Mr. Williams went and sat by the boy.

In a voice so quiet that Citlaly Reynoso, who was sitting next to them, could not hear, he talked to the boy for several minutes. Then Mr. Williams took over the class again, and the boy pulled out a workbook and started answering questions.

Later Mr. Williams, who has spent 14 years teaching poor children, said: “I want to do everything I can to keep that child in class. If he’s sitting in the principal’s office, he’s not learning.”

In 1993, when Mr. Williams graduated from high school in Goldsboro, N.C., with an A average and a 1,320 on his SATs, he had many options, but he chose the North Carolina Teaching Fellows Program. The idea is simple: the state pays top academic students to attend a public college, and in return they spend at least four years teaching in a public school.