Several Prince William County teachers, some of whom were placed on administrative leave, will have to undergo retraining after giving students inappropriate help on state-mandated exams, and students were required to retake tests, according to a school official.

County schools spokesman Phil Kavits said the teachers, who were supposed to interact minimally with students during testing in the spring, were overzealous in offering assistance.

Twenty-eight students had to retake tests, Kavits said. He could not say exactly how many teachers were involved.

The testing problems were first reported Tuesday in the Washington Examiner.

Many of the problems occurred during a third-grade test at Swans Creek Elementary in Dumfries, according to a report by the Virginia State Board of Education. A third-grader told a teacher at recess that the teacher who administered the history and social sciences test had changed some answers on students’ exams .

The teacher denied changing answers, but interviews with students led investigators to conclude that “inappropriate assistance was provided to students,” according to the state report. Investigators weren’t sure whether the teacher’s actions helped or hurt the students’ scores, but they said the 24 students should be tested again to be sure.

At other schools, a math test was given again to a student as a result of the inquiry, and three students had to retake a science test because of problems with the way it was administered.

Kavits said that the teachers involved will be retrained and that the incidents will be a part of their evaluations.

Teachers are supposed to read a script before a test and interact minimally with students during a test, Kavits said. But at Elizabeth Vaughan Elementary in Woodbridge, one teacher indicated correct answers by saying “You go!” and a student’s name or giving a pat on the back. Other answers were confirmed through humming or other nonverbal cues, the state report said, and attention was called to incorrect answers by asking student to try again.

At Cedar Point Elementary, a fifth-grader had to retake a math test after mentioning to a teacher that the person who administered the test provided him with definitions of “mean” and “mode” — or the average and the most frequently occurring number.

Problems at two other schools, Woodbridge Middle and Kerrydale Elementary, were also reported to the state, but they were not deemed serious enough to merit having students retake tests.

Staff writer Emma Brown contributed to this report.