My colleague Bill Turque had an intriguing story recently about an attempt by Bruce-Monroe Elementary School in the District to raise achievement through the popular Singapore math program.

It hasn’t worked so far, Turque reported. The math proficiency rate at the school declined from 49 percent in 2009 to 23 percent in 2010. Reading proficiency at Bruce-Monroe also dropped from 39 to 24 percent.

The educators and experts Turque consulted gave many possible reasons for this. There was too much staff turnover. The school lacked enough funds for teacher training. The school was distracted by a merger with Park View Elementary School.

Nobody offered the reason that first came to my mind. I wonder whether the school’s test security suddenly improved.

A series on cheating nationally by USA Today earlier this year (conceived and edited by my wife, Linda Mathews) revealed widespread wrong-to-right erasures on D.C. Comprehensive Assessment System tests. Those exams are used to judge the city’s schools under the federal No Child Left Behind law. The newspaper found 103 D.C. schools with above-average erasures. In a few classes the average was more than 10 wrong-to-right erasures per child on a single exam.

I don’t know what the erasure rates were at Bruce-Monroe. The Office of the State Superintendent of Education told me it will take at least 15 business days to provide that information. But I know from official documents acquired by USA Today that four Bruce-Monroe classrooms in 2009 were flagged for having an above-average rate of wrong-to-right erasures. That is enough to have a significant impact because only 141 students were tested at that school.

Bruce-Monroe Principal Marta Palacios, who has not been accused of any wrongdoing, declined to comment.

Acting Schools Chancellor Kaya Henderson has asked the D.C. inspector general to investigate possible cheating on the DC-CAS tests. I will be surprised if much comes of that. There still appear to have been no interviews of any of the children who allegedly changed so many wrong answers to right.

The Inspector General is supposed to review the erasure investigation submitted by the Caveon data analysis firm. That contractor accepted without a trace of skepticism the explanations from several educators that better teaching explained their students’ high rate of wrong-to-right erasures. This ignores the fact that if students are well taught, they will mark the right answer the first time, not have sudden flashes of insight that lead to many corrections .

I have sought other explanations. To me, an obvious question is whether administrators in charge of the tests (or maybe well-educated burglars, if you want to be fair) took the answer sheets out of the locked school cabinets where they were kept and changed the answers long after the children went home.

I attended last week’s confirmation hearing for Henderson, a good person who knows schools. No one asked her any detailed questions about how she planned to address this embarrassment. The question has been pushed so far into the background that otherwise intelligent commentators have suggested that Henderson’s recent announcement of minor sanctions at three schools for testing irregularities meant the problem was solved, even though her actions had nothing to do with erasure rates.

Administrators don’t want the system’s reputation further tarnished. Henderson doesn’t want to hurt teacher morale. But our schools’ success or failure is going to be judged by those test results. If the scores are the product of cheating rather than genuine student achievement, we are lost. School decisions about which students need extra help and which teachers should seek other employment would be based on lies, and our schools would be in even worse shape in the future than they are now.