ALLENTOWN — Pennsylvania’s charter schools show mixed results in math and reading, with all cyber charter students lagging their counterparts in public schools when it comes to learning, according to a Stanford University study. Authors of the report released in April said comparisons of reading and math test scores between 2007 and 2010 showed that, overall, students at more than one-third of the charter schools trailed those at comparable public schools. But 30 percent of the charter schools outperformed the public schools in reading and 25 percent of the charter schools did better in math. “Elementary school students enrolled in charter schools outperformed their peers in traditional public schools in both math and reading, while those enrolled in middle and multilevel charter schools performed worse in both subjects than their peers at traditional public schools,” the report says. A poor showing by the state’s online charter schools dragged down the overall charter school numbers. Students at online cyber-charter schools, who accounted for 30 percent of the charter students covered by the study, performed significantly worse than students at public schools, the study said. If cyber-charters are excluded, 35 percent of students performed better than their public school counterparts in reading while 34 percent performed worse. Results were not as good in math, with 27 percent of brick-and-mortar charter students performing significantly better and 42 percent performing significantly worse. The study was conducted by Stanford’s Center for Research on Education Outcomes, which has conducted about 20 assessments of charter-school performance, including a national study in 2009.