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WASHINGTON — A study released Tuesday found that offering teachers annual bonuses of up to $15,000 had no effect on student test scores — a result likely to inflame debate about performance-pay programs sprouting in schools nationwide.

The study suggests that teachers already were working so hard that the lure of extra money failed to induce them to intensify their efforts or change methods of instruction. The experiment, in Nashville, Tenn., public schools, calls into question a key aspect of market-driven initiatives to improve schools that have become the vogue in some education circles.

“Pay reform is often thought to be a magic bullet,” said Matthew Springer, a Vanderbilt University education professor who led the study. “That doesn’t appear to be the case here. We need to develop more thoughtful and comprehensive ways of thinking about compensation. But at the same time, we’re not even sure whether incentive pay is an effective strategy for improving the system itself.”

With backing from federal and state governments and private foundations, a growing number of public schools in recent years have embraced determining teachers’ pay at least in part on how much they raise student achievement.

President Barack Obama has encouraged the movement despite skepticism from some teachers unions and from lawmakers within his party. District of Columbia Schools Chancellor Michelle Rhee became a hero to reformers in part because of her insistence on a new teachers’ contract that allows performance bonuses.

Central to such reforms is the notion that teachers should be rewarded when their students achieve outsize gains on standardized tests. That is a major shift from the tradition of determining pay by seniority and credentials such as master’s or doctoral degrees.

But the study from the National Center on Performance Incentives at Vanderbilt casts doubt on hopes that performance pay alone can dramatically improve public schools.

Three-year evaluation

In a three-year experiment backed by federal funding, researchers tracked what happened in Nashville schools when math teachers in grades 5 through 8 were offered bonuses of $5,000, $10,000 and $15,000 for hitting targets in annual test-score gains.

About 300 teachers volunteered, and half were assigned to a control group ineligible for the bonuses.

Researchers designed the bonuses, funded by a private donor, to be large enough to function as a legitimate incentive. There were no additional variables — no professional development, mentoring or other elements in the experiment meant to help elicit better test scores.

On the whole, researchers found no significant difference between the results from classes led by teachers who could receive bonuses and those led by teachers who did not.

Obama administration officials and a wide range of experts were quick to note that the study did not examine the effect of performance pay in combination with other measures to improve teaching.

“While this is a good study, it only looked at the narrow question of whether more pay motivates teachers to try harder,” said Peter Cunningham, assistant U.S. education secretary for communications and outreach. “What we are trying to do is change the culture of teaching by giving all educators the feedback they need to get better while rewarding and incentivizing the best to teach in high-need schools, hard-to-staff subjects. This study doesn’t address that objective.”

Under Obama, officials say, a federal program that backs performance- pay efforts in dozens of school systems has quadrupled to $400 million a year. Federal officials say a number of such efforts have shown positive results; they also are planning a comprehensive review of the program.

A waste of time?

Eric Hanushek, an expert on the economics of education at Stanford University’s Hoover Institution, a conservative-leaning think tank, said that the Vanderbilt study appeared to be sound but that it did not address a key question.

“The biggest role of incentives has to do with selection of who enters and who stays in teaching, . . . how incentives change the teaching corps through entrance and exits,” Hanushek said. “I have always thought that the effort effects were small relative to the potential for getting different teachers. Their study has nothing to say about this more important issue.”

A teachers union leader in Nashville said the study raised significant questions about “the extent to which we spend a lot of time trying to develop complex schemes to measure teacher performance and then reward them based on that performance.”

The leader, Erick Huth, who is president of the Metropolitan Nashville Education Association, said the study’s results indicate that such efforts “may be a waste of time.”