The staff of Normandy Crossing Elementary School outside Houston eagerly awaited the results of state achievement tests this spring. For the principal and assistant principal, high scores could buoy their careers at a time when success is increasingly measured by such tests. For fifth-grade math and science teachers, the rewards were more tangible: a bonus of $2,850.

But when the results came back, some seemed too good to be true. Indeed, after an investigation by the Galena Park Independent School District, the principal, assistant principal and three teachers resigned May 24 in a scandal over test tampering.

The district said the educators had distributed a detailed study guide after stealing a look at the state science test by "tubing" it — squeezing a test booklet, without breaking its paper seal, to form an open tube so that questions inside could be seen and used in the guide. The district invalidated students’ scores.

Of all the forms of academic cheating, none may be as startling as educators tampering with children’s standardized tests. But investigations in Georgia, Indiana, Massachusetts, Nevada, Virginia and elsewhere this year have pointed to cheating by educators. Experts say the phenomenon is increasing as the stakes over standardized testing ratchet higher — including, most recently, taking student progress on tests into consideration in teachers’ performance reviews.

Colorado passed a sweeping law last month making teachers’ tenure dependent on test results, and nearly a dozen other states have introduced plans to evaluate teachers partly on scores. Many school districts already link teachers’ bonuses to student improvement on state assessments. Houston decided this year to use the data to identify experienced teachers for dismissal, and New York City will use it to make tenure decisions on novice teachers.

The federal No Child Left Behind law is a further source of pressure. Like a high jump bar set intentionally low in the beginning, the law — which mandates that public schools bring all students up to grade level in reading and math by 2014 — was easy to satisfy early on. But the bar is notched higher annually, and the penalties for schools that fail to get over it also rise: Teachers and administrators can lose jobs and see their school taken over.

No national data is collected on educator cheating. Experts who consult with school systems estimated that 1 percent to 3 percent of teachers — thousands annually — cross the line between accepted ways of boosting scores, like using old tests to prep students, and actual cheating.

"Educators feel that their schools’ reputation, their livelihoods, their psychic meaning in life is at stake," said Robert Schaeffer, public education director for FairTest, a nonprofit group critical of standardized testing. "That ends up pushing more and more of them over the line."

Others say that every profession has some bad apples, and that high-stakes testing is not to blame. Gregory J. Cizek, an education professor at the University of North Carolina who studies cheating, said infractions were often kept quiet. "One of the real problems is states have no incentive to pursue this kind of problem," he said.

Recent scandals illustrate the many ways, some subtle, that educators improperly boost scores:

— At a charter school in Springfield, Mass., the principal told teachers to look over students’ shoulders and point out wrong answers as they took the 2009 state tests, according to a state investigation. The state revoked the charter for the school, Robert M. Hughes Academy, in May.

— In Norfolk, Va., an independent panel detailed in March how a principal — whose job evaluations had faulted the poor test results of special education students — pressured teachers to use an overhead projector to show those students answers for state reading assessments, according to The Virginian-Pilot citing a leaked copy of the report.

— In Georgia, the state school board ordered investigations of 191 schools in February after an analysis of 2009 reading and math tests suggested that educators had erased students’ answers and penciled in correct responses. Computer scanners detected the erasures, and classrooms in which wrong-to-right erasures were far outside the statistical norm were flagged as suspicious.

The Georgia scandal is the most far-reaching. It has already led to the referral of 11 teachers and administrators to a state agency with the power to revoke their licenses. More disciplinary referrals, including from a dozen Atlanta schools, are expected.

John Fremer, a specialist in data forensics who was hired by an independent panel to dig deeper into the Atlanta schools, and who investigated earlier scandals in Texas and elsewhere, said educator cheating was rising.

"Every time you increase the stakes associated with any testing program, you get more cheating," he said.

That was also the conclusion of economist Steven D. Levitt, of "Freakonomics" fame and a blogger for The New York Times, who with a colleague studied answer sheets from Chicago public schools after the introduction of high-stakes testing in the 1990s concluded that 4 percent to 5 percent of elementary school teachers cheat.

Not everyone agrees. Beverly L. Hall, who, as the superintendent of the Atlanta Public Schools has won national recognition for elevating test scores, said dishonesty was relatively low in education.

"Teachers overall are principled people in terms of wanting to be sure what they teach is what students are learning," she said.

Educators ensnared in cheating scandals rarely admit to wrongdoing. But at one Georgia school last year, a principal and an assistant principal acknowledged their roles in a test-erasure scandal.

For seven years, their school, Atherton Elementary in suburban Atlanta, had met the standards known in federal law as Adequate Yearly Progress — AYP in educators’ jargon — by demonstrating that a rising share of students performed at grade level.

Then, in 2008, the bar went up again and Atherton stumbled. In June, the school’s assistant principal for instruction, reviewing student answer sheets from the state tests, told her principal, "We cannot make AYP," according to an affidavit the principal signed.

"We didn’t discuss it any further," the principal, James L. Berry, told school district investigators. "We both understood what we meant."

Pulling a pencil from a cup on the desk of Doretha Alexander, the assistant principal, Berry said to her, "I want you to call the answers to me," according to an account Alexander gave to investigators.

The principal erased bubbles on the multiple-choice answer sheets and filled in the right answers.

Any celebrations over the results were short-lived. Suspicions were raised in December 2008 by The Atlanta Journal-Constitution, which noted that improvements on state tests at Atherton and a handful of other Georgia schools were so spectacular that they approached a statistical impossibility. The state conducted an analysis of the answer sheets and found "overwhelming evidence" of test tampering at Atherton.

Crawford Lewis, the district superintendent at the time, summoned Berry and Alexander to separate meetings. During four hours of questioning — "back and forth, back and forth, back and forth," Lewis said — principal and assistant principal admitted to cheating.

"They both broke down" in tears, Lewis said.

Lewis said that Berry, whom he had appointed in 2005, had buckled under the pressure of making yearly progress goals. Berry was a former music teacher and leader of celebrated marching bands who, Lewis said, had transferred some of that spirit to passing the state tests in a district where schools hold pep rallies to get ready.

Berry, who declined interview requests, resigned and was arrested in June 2009 on charges of falsifying a state document. In December, he pleaded guilty and was sentenced to probation. The state suspended him from education for two years and Ms. Alexander for one year.

Lewis, now retired as superintendent, called for refocusing education away from high-stakes testing because of the distorted incentives it introduces for teachers. "When you add in performance pay and your evaluation could possibly be predicated on how well your kids do testing-wise, it’s just an enormous amount of pressure," he said.

"I don’t say there’s any excuse for doing what was done, but I believe this problem is going to intensify before it gets better."

© 2010 The New York Times Company