Two principals defended a former Atlanta public schools administrator in court Tuesday, saying she passed out notes labeled “go to hell” as a stress-relief exercise — not as an attempt to stonewall investigators looking into widespread cheating.

Their testimony contradicted the story of other principals in the same meeting who have said Tamara Cotman, a former school system area director, allegedly asked them to use their notes to tell cheating investigators and the GBI to “go to hell.”

Tuesday’s testimony came as Cotman’s side began to make its case in the first trial of an educator facing criminal charges related to cheating on standardized tests in Atlanta Public Schools. If convicted of influencing a witness, Cotman faces a sentence of up to five years in prison.

In all, 35 former teachers and administrators were indicted. The outcome of Cotman’s trial could influence whether other defendants enter into plea negotiations or fight their charges in a trial scheduled for next year.

Former F.L. Stanton Elementary School Principal Esther Weems said Cotman never told the principals to direct their notes at the GBI during a meeting on Nov. 17, 2010.

“I just know that she did not tell us not to cooperate with anyone. That was not shared with us,” Weems said. “As far as writing a letter to the GBI, that’s something she did not say.”

Weems said she wrote “our children do erase” on her memo in an attempt to explain why there was a high number of erasures on standardized tests. The erasures of incorrect answers indicated to state investigators that educators had corrected wrong answers on the 2009 Criterion-Referenced Competency Test.

Another former principal, Debra Dixon of Usher-Collier Heights Elementary School, said she wrote the name of her mortgage company on her “go to hell” note.

“I do not recall Ms. Cotman mentioning the GBI,” Dixon said.

The prosecution closed its case after calling on Atlanta Superintendent Erroll Davis to testify about his experience with cheating. Davis took leadership of the school system just days before a state investigation concluded in July 2011 that 185 teachers and administrators participated in cheating or should have known about it.

Davis said it quickly became clear cheating had taken place in Atlanta schools.

“What occurred could not have occurred without human intervention. It was not random,” Davis said.

Davis said school system leaders failed to enact safeguards that would have prevented cheating, and he removed them from their positions. Cotman oversaw 21 elementary and middle schools across the northern arc of Atlanta, and 15 of them were flagged in the erasure analysis.

“I believe that it’s their responsibility for what happens on their watch,” Davis said.

The prosecution on Tuesday survived what could have been a misstep.

After the prosecution rested, Cotman’s lawyer, Benjamin Davis, asked Superior Court Judge Jerry Baxter to grant a directed verdict of acquittal — dismissing the case before it got to the jury.

Prosecutors, Davis said, had failed to prove one fundamental and essential fact: that the alleged crime had been committed in Fulton County. Criminal convictions have been overturned and directed verdicts have been granted when prosecutors neglect to prove venue.

Assistant District Attorney Fani Willis said she believed a witness had testified about Fulton, but Baxter said he was concerned that had not happened. The judge then took the unusual step of allowing the prosecution to reopen its case and call a witness, Weems, who provided the necessary testimony.

Davis said Cotman hasn’t decided whether she will testify in her own defense.