Teachers in three District classrooms cheated last year on high-stakes standardized tests, according to the results of an investigation released Friday morning by the Office of the State Superintendent.

Superintendent Hosanna Mahaley said the probe’s findings show that the vast majority of the city’s school staff and students are “playing by the rules” on the D.C. Comprehensive Assessment System — the standardized test used to measure student achievement and teacher effectiveness.

“Widespread cheating was not found,” Mahaley added.

D.C. test scores have come under increasing scrutiny since USA Today published a March 2011 investigation showing an unusually high number of erasures from wrong to right answers in more than 100 D.C. public schools between 2006 and 2010.

In response, Chancellor Kaya Henderson asked D.C. Inspector General Charles J. Willoughby to examine the newspaper’s findings. U.S. Education Department officials have since joined the review.

Some observers said that suspicions about the city’s test scores will not be settled until the results of that longer-term investigation are made public. At stake is the public’s confidence not only in the test scores themselves, but in education reforms ushered in by Henderson and her predecessor, Michelle A. Rhee.

“Cheating can be covered up quite effectively when multiple persons at a school are involved,” said Bob Schaeffer of FairTest, a Boston-based advocacy group that is critical of standardized testing. “Without a thorough investigation, you don’t know if what we’re looking at is the tip of the iceberg, most of the iceberg or the entire iceberg.”

District school officials say that the investigation released Friday is the most exhaustive to date.

For the first time, the state superintendent’s office hired an outside firm — Alvarez and Marsal, a New York-based management consulting firm — to review potential cheating citywide. The investigation cost about $400,000, Mahaley said.

Tests were administered in 5,089 classrooms last year. Of those, a total of 70 classrooms at 38 schools were flagged for investigation because they had some combination of suspicious wrong-to-right erasure marks, unusually big gains in students’ scores or unusual score patterns in a classroom.

Alvarez and Marsal reviewed forms and protocol at each school and interviewed more than 300 teachers, students and administrators, asking each whether they cheated or knew of someone else who did.

Students in three classrooms said their teachers had coached them toward correct answers. District officials have invalidated those classrooms’ test scores.

One of the teachers found to have cheated was a third-grade teacher at Hyde Leadership Academy, a public charter school now known as Perry Street Prep. Officials at the school said that the teacher — along with a proctor who was in the room during testing — left the school at the end of the 2010-11 school year before any investigation was initiated.

The other two teachers, employed by D.C. public schools, worked in 2011 at Langdon Education Campus and Martin Luther King Elementary.

The latter case came to light because a parent — “a huge hero,” Mahaley, the state superintendent, said — was suspicious of her child’s high test scores. D.C. public school officials said they are pursuing termination of both teachers.

Nine schools were found to have “moderate” violations that fell short of test-tampering — a proctor using a cellphone, for example, or leaving students briefly unattended. Another 11 had “minor” violations, including missing paperwork.

Fourteen schools were found to have no violations, but one of them — Raymond Education Campus — is still under review for an incident that occurred in 2010. In that previously unreported case, a staff member is alleged to have repeatedly pointed at a student’s answer sheet.

Finally, one school flagged for review, Nia Community Public Charter, closed before it could be investigated.

Last year, OSSE invalidated 2010 test scores in three classrooms after evidence of cheating was found by Caveon, a firm hired by D.C. public schools. Critics questioned whether that investigation was rigorous enough to root out the truth after Caveon officials said they had not been asked to use all the forensic tools at their disposal.

Henderson said she hopes this new investigation puts skepticism about the District’s test scores to rest and gives the community “a renewed sense of confidence in the work that we are doing here.”

Critics said the new probe is still not enough, in part because Alvarez and Marsal did not have subpoena power — unlike investigators in Atlanta, who last year reported a cheating scandal involving more than 170 teachers and principals at almost half the system’s schools.

“To send an investigator out that doesn’t have any kind of authority to do a searching investigation is kind of a waste of everybody’s time,” said Gregory Cizak, a professor at the University of North Carolina at Chapel Hill who assisted with the Atlanta probe. “It’s feckless.”

Meanwhile Mary Lord, who represents Ward 2 on the D.C. Board of Education, said the city’s scrutiny of testing irregularities has improved every year and “should inspire confidence.” But, she said, school officials now need to grapple with another issue: whether the emphasis on and worry over standardized testing is actually helping kids learn.

“I hope we go and say, ‘Why are we investing so much time and money in these tests?' ” she said, “and is this really a good use of our money and time?”