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JACKSON, Miss. — About 3,000 more Mississippi third graders passed a toughened reading test on the second try in May, the Mississippi Department of Education said Tuesday, cutting the number of public school students in danger of not advancing to fourth grade.

Of 35,000 third graders, nearly 9,000, or 25%, failed the test the first time. The department said about 7,500 of those students were retested and 2,900 passed, leaving 17% of third graders still at risk of failing. Students will get a third chance to pass the test in June and July, after many districts complete summer school. Final numbers won’t be published until this fall, and about 3% of students were allowed to advance last year without passing for various reasons.

Mississippi is one of 16 states that demand third grade students pass a reading score threshold or flunk, with Nevada and Michigan imposing such requirements in the next two years. Mississippi raised its threshold this year, mandating students reach the middle of five scoring levels, which officials describe as “approaching grade level expectations.” From 2015, the first year the requirement was implemented, until last year, students only had to reach the second lowest achievement level, called “basic.”

State Superintendent Carey Wright helped persuade the Legislature to increase the threshold in 2016. She was uncomfortable that students were allowed to advance even though they remained far from proficient: the second-highest level on Mississippi’s test.

“The passing score was raised to get closer to measuring proficiency,” Wright said in a statement. “Once we raised expectations, students and teachers have proven, once again, they can meet higher academic standards.”

Department spokeswoman Jean Cook says district and school passing rates aren’t available for the second round. The districts that performed the worst in the first round were typically small, rural, poor and overwhelmingly African American, places that struggle to attract highly credentialed teachers.

Officials predicted passing rates would drop from last year’s 94%, when students had to reach the second level.

By comparison, 15% of students failed the first round of testing in 2015, with 8% ultimately forced to repeat third grade. Students repeating third grade are supposed to receive intensive tutoring from highly qualified teachers. Mississippi is paying for literacy coaches to help improve instruction in 182 of 420 schools statewide with a third grade. The state also has provided training on teaching reading to 13,000 people, and provides extra money for summer schools for struggling readers.

The Republican policymakers who adopted Mississippi’s plan from Florida support it, also pointing to improvements in performance on a nationwide test. At least one independent study of Florida has found benefits uncertain.