Two decades after being taken over by Boston University, the schools in Chelsea, Mass., now sparkle instead of crumble. Students are more likely to graduate from high school than to drop out. Elementary and middle schools now have art and music programs, and high school students can now take a plethora of Advanced Placement classes. And yet, problems persist in this district of 5,500 students. Despite an increased focus on early childhood education, just a third of third-graders scored proficiently on a state reading test last year. In middle school, 58 percent of eighth-graders failed the state math test. Less than 30 percent of high school graduates say they plan to attend a four-year college. These are the challenges that the Chelsea School Committee will face when it regains control of its schools July 1.