She tore open the envelope, pulled out the test results and held her breath. She was a 32-year-old second-grade teacher with years of experience and a California credential. She had been teaching at a Fairfax County elementary school for two years with good ratings and results. Yet she had to pass this high-school-level mathematics test to keep her job.

She blinked in dismay. The sheet said she scored 176 on the math section of a national teacher qualification test called Praxis I. She needed a 178. It was her third try, the result of weeks of study with a private tutor. By two points, Jennifer Kramer's career as a Virginia public school teacher was over.

Many school districts have become strict about such tests. The Virginia Board of Education decreed its Praxis passing marks would be the highest in the country. Other states, not to be outdone, say they may move the bar even higher.

That leaves no place in the public schools for educators like Kramer. She can make a frightened 7-year-old blossom into an eager reader, but she cannot think fast enough to answer correctly 30 arithmetic, algebra and geometry questions in an hour.

Ordinarily her out-of-state credential would have allowed her to skip Praxis I, which is given mostly to college undergraduates before they start teacher training. But Virginia has not endorsed the test she passed in California, which, unlike Praxis, has a number of essay questions and puts less emphasis on mathematics.

Don't ever ask a teacher about these examinations if you're rushed for time. Chilling tales of wrongheaded questions and bad scoring abound. A summa cum laude physics graduate was surprised to find the new Massachusetts test for physics teachers full of questions she had never seen in high school or college. She nearly flunked. Districts are losing hard-to-find special education teachers -- the educational equivalent of left-handed relief pitchers -- because of low scores on math tests unrelated to their much-needed skills.

Kramer has recovered from her disappointment. She found a job teaching third grade in a private school, taking a pay cut large enough to prove beyond doubt her devotion to teaching. Her new school was more interested in the recommendations she brought from her former bosses than her test scores. But many other teachers are stumbling over this hurdle, exposing a frustrating paradox in the national effort to make teaching a true profession.

Many educators want parents and politicians to put less faith in student test scores and more faith in a teacher's ability to assess each child and apply whatever learning techniques are needed. They want teachers to be licensed like doctors after detailed review of their classroom skills. They long for the day when samples of a student's work and nuanced reports on each child's progress replace standardized tests as the preferred measuring stick.

Yet for that to happen, parents have to be confident of teachers' abilities and judgment -- and one popular way to build this confidence is by requiring teachers to pass tests in English and math. The old Ronald Reagan line "trust but verify" actually means "don't trust." That expresses the view of many parents toward teachers.

School officials are willing to wave goodbye to teachers like Kramer in order to polish the professional image of educators in their states. These policymakers crave the power of fashion and image. It is unlikely that teacher salaries will receive a significant boost, they say, but if academically talented young people come to see teaching as an elite profession, they may be more willing to work in classrooms. Astronomers and poets don't make much money either, but the culture blesses them with an intellectual aura so their spouses can be proud even while shopping for the cheapest brand of peanut butter.

Kati Haycock, director of the Washington-based Education Trust, raises another argument for testing teachers: Brains beget brains. She cites Texas and Alabama studies showing that teachers who scored higher on general math and English tests similar to Praxis I produced students who scored higher on standardized tests.

Policymakers who want to raise standards will often quietly admit that most schools are doing fine. Over the last few decades all the major indicators of educational progress are up, despite larger and more diverse student populations. The new standards, they say, will have the greatest benefit in low-income neighborhoods where the most overburdened teachers and administrators are often found.

Meanwhile, the school board members who have made the new rules usually live in affluent neighborhoods where money and political pressure attract good principals and experienced teachers and success. And if they don't like the public school, they can afford to send their child to a private one.

Whom will they find there? Jennifer Kramer. Once they see how much energy and warmth she devotes to their child, they are not likely to mind so much that her algebra skills are two points below their standard.

Jay Mathews's e-mail address is mathewsj@washpost.com.