The Obama administration’s Race to the Top Fund, which was designed to use federal grant money as an incentive for states to replicate programs shown to improve student performance, has been a mixed bag. For one thing, what began as incentives for states to adopt common standards in English and math has risen to the level of what may well be illegal coercion.

But the program also has prompted a number of states to lift arbitrary caps on charter schools and, perhaps most important, has gotten 36 states and the District of Columbia to introduce more rigorous teacher-evaluation systems.

There is no factor within the four walls of a school that affects student performance more than teacher quality. Research by former University of Tennessee professor William L. Sanders found that the effects of a poor third-grade teacher were still measurable on a student’s fifth-grade math scores, regardless of the quality of subsequent teachers. Conversely, academic growth in students who had highly effective teachers three years in a row resulted in scores that were dramatically higher than those unlucky enough to have had ineffective teachers.

Given the importance of teacher quality, few would disagree that we need to attract and retain the very best teachers. But knowing who those teachers are requires rigorous evaluations.

Current systems clearly aren’t working. A 2010 study commissioned by the Massachusetts Business Alliance for Education found that over two school years, half of Boston’s public-school teachers had never been evaluated, while one-quarter of the city’s schools hadn’t turned in a single evaluation.

But there is profound disagreement over how teachers should be evaluated, especially since the results of those evaluations will be central to their compensation and job security. Ground zero for the controversy is the role student test scores should play in the evaluations. The issue was at the heart of the recent Chicago teachers strike, and negotiations with Boston’s teachers union dragged on for years before the sides finally came to an agreement.

Standardized tests routinely attract a torrent of criticism, but the work of noted educational-standards expert E.D. Hirsch is instructive here. Hirsch found a high correlation between standardized reading test results and the likelihood of economic success, adaptability to retraining, civic integration and even the probability of not being incarcerated.

Standardized-test results certainly are not perfect, and they should not be the only measure by which teachers are evaluated. But there is clear evidence that the rate of student improvement on the tests should be a very significant part of those evaluations.

Money isn’t everyone’s primary motivator, but the almost total disconnect between teacher performance and compensation is one cause of our failure to attract more of the best and brightest to work in our public schools. Rigorous evaluation systems that reward teachers who consistently improve student achievement and encourage those who don’t to seek a different career are one important way to make teaching more appealing to talented, ambitious young people.