Despite our fierce national argument over whether to use student test scores to rate teachers, most people who care about schools agree that sophisticated, multifaceted assessments of teachers are good. The National Board Certification process sponsored by the Arlington-based National Board for Professional Teaching Standards is an oft-cited example.

Even teacher union leaders, rightly suspicious of teacher-rating schemes, have praised the National Board assessments, which ignore student scores. The evaluation process takes about a year. Applicants must analyze their classroom situations and student needs, submit videos of their teaching, provide student work samples and explain how they would handle difficult moments.

Half of the applicants fail to qualify, giving those who succeed such luster that many states and districts pay them bonuses.

Prince George’s County, eager to attract the best teachers, was one of the first districts a decade ago to promise more money for board-certified teachers. So why did the county teacher union this year agree to cut the bonus for its 300 National Board-certified teachers (NBCTs)?

Prince George’s board-certified teachers were originally promised an extra $8,000 their first year and $7,000 each year after that. When the recession hit in 2009, those teachers got no bonus, but in the past two years some of the money returned: $2,000 from the county and $1,000 from the state. This year, the union, known as the Prince George’s County Educators’ Association, agreed instead to a deal that reduced the county bonus to $1,000. The union wanted to use the money saved to give other teachers some of the raises and stipends they had missed in recent years.

“The union sees the NBCT differential as elitist, and really is uninterested in teacher excellence,” said Jonathan Keiler, the union’s faculty representative at Bowie High School. He is a board-certified teacher of social studies. He objected to the cut at a union meeting Aug. 12, but he was outvoted.

Kenneth B. Haines, the union president, said he supports board certification. He narrowly missed qualifying for the bonus when he taught French at Northwestern High School. But “we have to look out for all 9,000 of our members,” he said. “I wish we could pay all our teachers what they are worth.”

The county is losing some board-certified teachers, school officials said. Haines said good teachers without certification also are being lured away. A teacher who makes $55,000 a year, near the average for the county, would earn $63,000 if the county were able to pay promised raises in the past few years. “We are bleeding teachers everywhere,” Haines said, “and this is a tough call.”

For board-certified teachers, “it is a perfect storm,” Keiler said, “with reduced revenue giving the board reason to cut differentials, and with the union taking an essentially hostile attitude to the differential.” He said younger certified teachers are especially attracted to higher bonuses elsewhere, such as $5,000 in Loudoun County and as much as $4,000 in Anne Arundel County.

Haines said he has seen no sign of teacher resentment toward the bonuses, but I sense such feelings are widespread. I have criticized public bonuses like these because they undermine teacher teamwork, vital to raising achievement. Principals should pay some teachers more than others if that makes their schools work but keep it quiet.

The Prince George’s clash shows that our effort to find some standardized way to identify our best teachers is unlikely to get far. Test scores don’t work. Complex board certification might not work, either. It would be better if we selected and trained principals with great care, made them responsible for their schools’ successes, then let them decide whom to reward and how.

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