The largest study ever of school cellphone bans finds that they offer decidedly mixed results, with teachers reporting fewer distractions when students lock their phones away during the school day, but little evidence that the bans quickly improve academic achievement or lead to better behavior, as many advocates have hoped. The study, by scholars at Stanford University, Duke University, the University of Michigan and the University of Pennsylvania, compiled data from Yondr, a California startup that makes lockable pouches for schools, businesses and entertainment venues. Published Monday by the National Bureau of Economic Research, it looks at data from about 4,600 schools and is the first nationally representative look at cellphone bans. It’s also the first to rely on actual data tracking locked-up phones, not just school “no-show” policies that ask students to keep phones hidden in backpacks or pockets, said Thomas Dee, a Stanford economist who co-led the study.…