NEW ORLEANS — BEFORE Hurricane Katrina, about 74 percent of this city’s schools were considered “failing,” based mainly on their standardized test scores. By 2012, that figure had dropped to 42 percent, even as the bar for passing was raised. Average ACT scores for the city’s public school students have inched up. In 2011, black students in New Orleans outperformed their peers in the rest of Louisiana for the first time since the state test scores have been tracked.