ATLANTA — Nearly 20 elementary schools across Georgia would be scrambling to cope with a cheating scandal had the state used a more common standard for spotting problems, according to the head of the investigation.

Kathleen Mathers, executive director of the Governor’s Office of Student Achievement told members of the State Board of Education today that her office only looked at the most extreme instances of scores that were outside the range of statewide averages for improvement, a statistical tool called 3.5 points of standard deviation. Since this was the first cheating investigation, she said she decided to only look at cases where the evidence was overwhelming and that next time her staff would use 2 points of standard deviation.

Had she used the stricter standard in the current investigation, she said about 20 of the state’s 600-plus elementary schools offering the retest would have come under suspicion. As it was, only four did.

“In subsequent investigations, I don’t anticipate that our starting point will be as generous,” she said.

State Board member Larry Winter, a forensic accountant by profession, said he often uses such statistical tools in rooting out fraud.

“The evidence is extremely compelling,” he said.

Four Georgia elementary schools caught cheating on a 2008 standardized math test will be punished as the result of a decision today by the State Board of Education.

The scores will be invalidated, parents will get letters detailing the incident, and educators will tailor a math-instruction plan for each of the students.