When J.P. Cotton began teaching at Davis Elementary School in Southeast Washington in August 2010, he puzzled over the scores of his fifth-graders on the previous spring’s D.C. tests. They were doing poorly in his class, as were most of the children at a school long plagued by low expectations and teacher turnover.

Yet several of them had scored proficient as fourth-graders on the D.C. Comprehensive Assessment System exams. How could that be?

The answer, several colleagues told Cotton, was that at least one school staffer handling the exams had found ways to help students change their wrong answers into right ones. An administrator told him that one of his students’ former teachers was no longer at the school because of a lapse of integrity. Still the new principal, Maisha Riddlesprigger, told Cotton and other young teachers she had hired that they would turn Davis around.

That hasn’t happened. In fact, Cotton was dismissed last summer as the result, it seems to me, of events he had nothing to do with. Many incidents of possible test manipulation in the District — as indicated by large numbers of wrong-to-right erasures detected by the test company, CTB/McGraw Hill — have gone mostly uninvestigated and unpunished. These questions are poisoning the system.

A few teachers such as Cotton are speaking up about this. Fifth-grade teacher Sarah Wysocki did so in my Post colleague Bill Turque’s recent examination of the D.C. teacher evaluation system. If more educators reveal what they know, school district leaders may be shamed into finally launching a deep, aggressive investigation into the corruption that threatens to ruin their heartfelt efforts to save the city’s kids.

Cotton worked hard at Davis. He said his evaluations from classroom observers got better as the year went on. But his students failed to outdo their suspiciously high fourth-grade scores to save his job. Those test results counted 50 percent in Cotton’s final evaluation. He was not allowed to come back this year despite what he said were Riddlesprigger’s efforts to save him. Riddlesprigger did not respond to a request for comment.

D.C. schools spokeswoman Melissa Salmanowitz said “we take potential cheating very seriously. . . The picture you appear to want to draw is just not supported by the facts.”

School leaders continue to quote a CTB/McGraw Hill report that found unusual numbers of wrong answers erased in favor of right ones in more than 100 schools on the D.C. CAS test, but concluded the erasures “may be simply coincidental and do not necessarily indicate inappropriate behavior.” They have cited no research buttressing the bizarre notion that children changing as many as a dozen answers each from wrong to right — an impossibility to veteran educators I have consulted — could be the result of anything but tampering by adults.

I have asked Schools Chancellor Kaya Henderson for some alternative, innocent explanation that makes sense to a seasoned classroom teacher like herself. So far, neither she nor her staff has answered that question.

Cotton said other Davis teachers and parents have useful information. But under the narrow rules that D.C. officials have imposed on their latest testing probe, Davis will not be investigated because it had no unusual gains in individual student scores from 2010 to 2011.

Has it occurred to those running the city’s schools that if Davis’s 2010 scores were inflated, then they would have gone down, not up, in 2011? That is what happened — from 23 to 15 percent in math proficiency and from 25 to 24 percent in reading. But no investigator has called on Cotton for leads.

The vast majority of possibly tainted test scores have been ignored. The new teacher evaluation system could be using distorted numbers.

A school system desperate for a jolt of honesty gets officially sanctioned cowardice instead.