We owe a debt of gratitude to Virginia Gov. Robert F. McDonnell for showing us exactly how NOT to try to compensate teachers based largely on student test scores — AND how to waste $3 million in public funds.

A number of states, with the encouragement of the Obama administration, have recently passed laws that do just that, over the objections of assessment experts who say that it is not a reliable and fair way to evaluate teachers.

Yet the method is viewed by proponents as “objective” (though its actually not), and now, McDonnell is getting in on the act by offering up a pool of $3 million to distribute among school districts that would conduct a one-year experiment implementing performance pay for teachers.

The evaluation will be done, according to an article by my colleague Kevin Sieff, with a new formula to measure a teacher’s effectiveness by their students’ standardized tests scores. The metric also will factor in criteria including professional knowledge and instructional planning. But let’s be clear: The tests are the main metric.

McDonnell dangled the cash in front of 169 schools but, as it turned out, only 10 decided to participate, none of them in Northern Virginia. Still, the governor has decided not to reduce the amount for the project, so all $3 million will be used.

Meanwhile, the districts that opted out said the metrics weren’t clear, and, anyway, some already have successful teacher evaluation models that don’t include test scores.

Jack Dale, superintendent of Fairfax County public schools, the largest system in Virginia, has made it clear that these evaluation systems known as “performance pay” have been tried and don’t work, and he isn’t interested.

Arlington public schools also has its own teacher evaluation program that somehow manages to get the job done without student test scores.

Over the Potomac River in Maryland, a related story is unfolding.

Montgomery County public schools, ranked along with Fairfax among the best in the country, also has its own teacher evaluation system in which teachers are involved in the process and, again, test scores aren’t part of the equation. The process is detailed, but teachers say it is fair, and hundreds of teachers have been let go under the system.

Soon to be departing Superintendent Jerry Weast declined to participate in Maryland’s successful application for $250 million in federal Race to the Top funds in which state officials promised to require that test scores be part of evaluation. He knew it wasn’t a good idea.

Here are four reasons why, as explained in an article I recently published by John Ewing, president of Math for America, a nonprofit organization dedicated to improving mathematics education in U.S. public high schools by recruiting, training and retaining great teachers:

1. Influences. Test scores are affected by many factors, including the incoming levels of achievement, the influence of previous teachers, the attitudes of peers, and parental support. One cannot immediately separate the influence of a particular teacher or program among all those variables.”

2. Polls. Like polls, tests are only samples. They cover only a small selection of material from a larger domain. A student’s score is meant to represent how much has been learned on all material, but tests (like polls) can be misleading.

3. Intangibles. Tests (especially multiple-choice tests) measure the learning of facts and procedures rather than the many other goals of teaching. Attitude, engagement, and the ability to learn further on one’s own are difficult to measure with tests. In some cases, these “intangible” goals may be more important than those measured by tests. (The father of modern standardized testing, E. F. Lindquist, wrote eloquently about this [Lindquist 1951]; a synopsis of his comments can be found in [Koretz 2008, 37].)

4. Inflation. Test scores can be increased without increasing student learning. This assertion has been convincingly demonstrated, but it is widely ignored by many in the education establishment [Koretz 2008, chap. 10]. In fact, the assertion should not be surprising. Every teacher knows that providing strategies for test-taking can improve student performance and that narrowing the curriculum to conform precisely to the test (“teaching to the test”) can have an even greater effect. The evidence shows that these effects can be substantial: One can dramatically increase test scores while at the same time actually decreasing student learning. “Test scores” are not the same as “student achievement.”

But none of this stopped a council of Maryland educators and policy makers this week from approving a new model for evaluating teachers and principals.

As reported by my colleague Michael Chandler, the system will tie 50 percent of future teacher evaluations to student test scores or other student growth measures, and will be tried out in seven schools systems starting this fall (including Prince George’s County).

The council made the decision because test-driven evaluation is part of what the state promised to do when it applied for Race to the Top funds.

Before it applied, you might think that Maryland — considered a public education juggernaut — would have considered Montgomery County’s lauded example and decided that sticking with something that works extremely well makes more sense than trying something unproven and controversial.

But officials are plowing ahead, planning to institute this scheme statewide after a year of working out the kinks.

It’s unfortunate that this will be among the last things that occurred in the tenure of Nancy S. Grasmick, the powerful state schools superintendent who is retiring at the end of this month after two decades. Misusing standardized tests to decide the fate of teachers, students and schools will only wind up hurting her legacy.

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