Test administrators in four classrooms at four D.C. schools appear to have violated rules on standardized tests last year by helping students arrive at correct answers, according to a city report.

An annual review, conducted by the consulting firm Alvarez & Marsal, found less-serious violations of test security at 13 other schools. Those offenses included unauthorized use of cellphones, inconsistent monitoring of test materials and missing test-security documents.

Jesus Aguirre, the District’s state superintendent of education, said that despite the problems, there is no evidence of systemic cheating on the citywide tests, known as the D.C. Comprehensive Assessment System, or D.C. CAS. Aguirre’s office issued its report on the tests Tuesday night.

“The latest results show that the overwhelming majority of District educators are committed to maintaining the integrity and security of our DC CAS process for our students,” Aguirre said in a statement.

In the city’s traditional public schools, students’ D.C. CAS scores play a key role in teacher and principal evaluations, and charter schools can be closed for failing to show adequate achievement or progress on the test. That so many people have a stake in test results has stoked suspicions of cheating in the District and other cities across the country. In response, the superintendent’s office commissioned an annual test-integrity review in recent years.

The four schools cited for “critical” violations during testing in spring 2013 were flagged in part because of a high number of wrong-to-right erasures. Two were part of the traditional D.C. Public Schools system.

To avoid conflicts of interest, the school system prohibits teachers from administering exams to their own students, but at both schools — Plummer Elementary and Oyster-Adams Bilingual — investigators found that test administrators assisted students by explaining questions and urging students to go back and check certain answers.

School system officials said they are reviewing the findings and deciding whether personnel action is warranted. Individuals implicated in testing impropriety will not participate in administering the 2014 D.C. CAS, which begins in two weeks.

“We take any incident of impropriety very seriously and will work to hold any person responsible accountable for their actions,” Schools Chancellor Kaya Henderson said in a statement. “We are proud to see that our stringent test security protocols are working and that nearly every single one of our impressive, talented teachers and school-based staff are following the rules.”

Test administrators provided similarly inappropriate assistance to students at two charter schools cited for critical violations: Ideal Academy and the Parkside Middle School campus of the Cesar Chavez Public Charter School for Public Policy.

Test scores from the four classrooms with critical violations will be invalidated, and the schools will be subject to additional monitoring during the tests this year.

D.C. Public Charter School Board officials said they take test integrity seriously and will take action on the violations after the superintendent’s office recalculates the schools’ proficiency and growth rates.

Six additional schools were found to have “moderate” violations, and seven were found to have “minor” violations. All schools identified in the report will be reprimanded and required to submit a corrective-action plan.

The annual review has consistently reported isolated problems. Investigators do not examine every test or every classroom; instead, they focus on a small subset of classrooms whose results have been flagged for extra scrutiny because of an unexpectedly large improvement by students, a high number of wrong-to-right erasures or some other anomaly.

For the first time, the superintendent’s office randomly chose some classrooms for the review of 2013 testing — a move required under a new city law. Of the 17 randomly chosen classrooms, none were found to have the kind of critical violations that amount to test-tampering, but about one-third were found to have minor or moderate violations.

Altogether, the superintendent’s office flagged 45 classrooms out of the 2,032 in which testing took place. Investigators followed up by interviewing school personnel and students.