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.