Andrea Byrd, mother of two boys, had enough with her son’s school. After she and her older son, Andrae, moved from Mississippi to Memphis a year ago, the formerly straight-A student “started dumbing himself down,” she says, to fit in with the other boys at his new school.

“I needed to get my child into a school where there were high expectations,” Ms. Byrd says. A charter school had recently opened nearby, but the 34-year-old single mom hesitated over getting an application since Tennessee law required her son to either be considered low-performing—which he wasn’t—or attend a low-performing school—which he didn’t—in order to get in. But all that changed a few weeks ago, when the state enacted a law for charter schools to also include students from low-income families. Two weeks ago, Ms. Byrd went into the Power Center Academy for an application. Later that same day, she got a call to say Andrae had been accepted.