Here are two tough questions for D.C. Schools Chancellor Kaya Henderson. They are suggested by a study from TNTP, a nonprofit teacher improvement organization for which Henderson once served as a vice president:

1. Will the chancellor transfer top-performing teachers to low-performing schools, where they are most needed?

2. Will she require principals to do all they can to keep their best teachers?

The study, “Keeping Irreplaceables in D.C. Public Schools: Lessons in Smart Teacher Retention,” was released Thursday and makes the D.C. schools look good in some ways. Predictions that top teachers would abandon the District because of its annoying new evaluation system have proved false. Teachers like the raises and bonuses they are getting for good evaluations. The study says the District leads the nation in keeping good teachers and getting rid of bad ones.

But in other ways, the city is failing its students and its best teachers. “In DCPS,” the study concludes, “highly rated teachers are much less likely to teach in schools with high concentrations of poverty than in other schools, and that disparity is greater than what we found in other districts.”

Top teachers make up 42 percent of the lowest poverty school faculties but only 11 percent in the highest poverty schools.

The study says that either the teacher distribution system or the evaluation system is to blame. I think it’s the former. National research has shown that experienced, effective teachers frequently seek transfers to high-performing schools because they get more support and have fewer difficult students. But maybe the new evaluation system, IMPACT, has a problem. There are indications that it is easier to get a good rating if your class is full of good students.

The D.C. salary system gives top teachers a chance to earn more in low-performing schools. But many prefer the reduced stress of a high-achieving school to a somewhat bigger paycheck.

The study also reveals another startling problem. The researchers surveyed 994 D.C. teachers and 144 D.C. school leaders. Top teachers were more likely to receive positive comments from their principals than low performers were. But they weren’t being recognized publicly or offered leadership opportunities to the extent recommended by previous TNTP reports.

Why? The report says principals showed little interest in keeping their best teachers happy.

“Principals do not consider smart retention a top priority,” the study concluded. “In fact, more than two-thirds of DCPS principals do not consider ‘retaining effective teachers’ one of their top five priorities.” The study suggests that the District provide better training for principals and convince them that their careers depend on keeping their best people.

Henderson’s predecessor as chancellor, Michelle A. Rhee, founded TNTP (formerly known as The New Teacher Project) in 1997. Henderson joined its staff in 2000. Both came to D.C. schools in 2007. TNTP has conducted several studies showing that U.S. school systems rarely differentiate between their most- and least-effective teachers. That has changed in the District, the report says, because under a new contract the best teachers “can earn total compensation of $100,000 after only four years in the classroom and a base salary of $100,000 after only six years.”

In the 2010-11 school year, the study said, D.C. schools kept 88 percent of their top performers as measured by an evaluation system based on classroom observations and test score progress. D.C. schools retained only 45 percent of their lowest performers, while other school districts kept about the same percentage of high- and low-performing teachers.

Spokeswoman Melissa Salmanowitz said Henderson won’t require top teachers to transfer, but she will rely on pay incentives and standards to nudge them and principals in the right direction. That hasn’t worked. To make her dreams a reality, Henderson might have to do more.