Two Rivers Public Charter School first-graders listen during the weekly community meeting in this April 11, 2012, photo. One former D.C. teacher says Two Rivers is among city schools with a high proportion of white students. (Mark Gail/The Washington Post)

Erich Martel, a great Advanced Placement history teacher at Wilson High School, was involuntarily transferred to another school and then forced to retire because, I think, he refused to stop investigating alleged D.C. school mismanagement, including his revelation that high schools were graduating students who didn’t meet all of the requirements.

Retirement only gave him more time to delve into suspicious practices. His latest critique involves some of the city’s most successful public charter schools. He wonders how they have such high percentages of white students when just 4.4 percent of students who took the D.C. Comprehensive Assessment System tests last April shared that ethnicity.

The charters with the highest percentages of whites taking the tests, according to Martel’s research, were Washington Latin Lower School (41.7 percent), BASIS Middle School (33.9 percent), Washington Latin High School (23.9 percent), Washington Yu Ying elementary school (22.2 percent), Capital City Lower School (22 percent), Two Rivers elementary and middle schools (19.9 percent) and E.L. Haynes Elementary School (17.1 percent).

“Are we to believe that these percentages are the result of pure chance?” Martel said. He told me those school directors should produce evidence that “their student demographic data are the results of random lotteries” and not caused by sneaking more affluent white kids onto their rolls when the D.C. school admissions officials aren’t looking.

“I have enough experience documenting alteration of records [and] creation of euphemistic proxies of achievement . . . to question the integrity of the charter lotteries and the process of replacing students who have been transferred from charters,” he said.

D.C. charter school board spokeswoman Tomeika Bowden suggested I ask the schools and the My School D.C. office about their admissions procedures, which I will do in a future column. For now I want to address Martel’s view that having some D.C. schools with unusual numbers of middle-class students of any ethnicity is bad for the school system.

He told me he thinks some urban charters with high achievement rates “claim to be meeting the needs of children in poverty, but they are really just skimming off those who have the socialization for success in school and throwing the rest back to” the rest of the D.C. public schools.

This contradicts those who think having significant numbers of middle-class children is a plus for urban schools and should be encouraged. The nation’s leading advocate of giving urban schools a good mix of poor and affluent students is Century Foundation scholar Richard D. Kahlenberg. He has written several books on research showing such balanced enrollment raises achievement for all students. Racial integration is also good, he said, because that reduces racism and teaches students “what they have in common as Americans.”

I have spent much time in charters with almost no middle-class children but impressive achievement rates. The reasons of their success, in my view, are mostly better teaching and more time for instruction. But many educators, including Martel, think their test scores are higher because they attract more children raised with middle-class values, even if their parents don’t have much money.

Martel said he shares Kahlenberg’s integration goal, but notes that in districts with majority poor populations, most impoverished students will still be sitting next to each other. I think whether or not charter school parents are better than regular school parents, their children should not be denied a chance to attend a better-functioning school if their local school is not giving them the education they deserve.

Martel has a point that some of the schools with high white and middle-class percentages have ambitious academic policies — such as heavy use of AP — that alienate parents who think their children can’t handle the strain. Whether something should be done about that will be the topic for a future column on what Martel has discovered.