As the schools chancellor joined in the announcement of a federal grant to test whether merit pay can lift performance in charter schools, a spokeswoman for the Department of Education confirmed that an investigation of test results was under way in a high-profile school in which the principal benefited from such a merit pay program.

The school is P.S. 33 in the Bronx. Mayor Bloomberg and Chancellor Klein traveled to the school in 2005 to announce their “historic” gains on the fourth-grade reading tests. That year P.S. 33 experienced a one-year gain of nearly 50 points; 83% of the students there were, according to the mayor, then reading at or above grade level. This not only helped the mayor win re-election but it won a $15,000 bonus for the school’s principal, Elba Lopez.

Since that triumphant press conference, things have taken a turn at P.S. 33. Ms. Lopez retired, her bonus figured in to raise her annual pension by an estimated $12,000 a year for the rest of her life. Last year, the fourth-grade scores dropped to 47.5%, and the fifth-graders, the same children who achieved 83% proficiency the previous year, dropped to 41.1%. This year, the fourth-grade results plummeted even further by 11.2 points, down to 36.3%, or almost exactly where they were in 2004.

These roller coaster test scores, combined with the merit pay bonanza for Ms. Lopez has, according to a Department of Education spokeswoman, Julia Levy, resulted in the matter being referred to the Special Investigator for the New York City School District, Richard Condon.

I raised questions about this school in these pages in September, as did Sol Stern in the fall 2006 number of City Journal. Here in Gotham we have been providing bonuses for principals, assistant principals, and superintendents for years. This program goes back to the Giuliani administration, before Mr. Bloomberg won control of the public schools. Hundreds of principals and administrators, including Ms. Lopez, have received bonuses of up to $15,000.

Under the federal pilot program for the charter schools announced last week, administrators will receive bonuses of up to $8,000, teachers up to $6,000 and school aides, up to $2,000. These bonuses will be based on student gains on standardized tests, and therein lies the rub.

I’m a believer in the power of the market to influence outcomes, but this type of program, unless subjected to rigorous scrutiny and security, is nothing more than an invitation to cheat.

Late last month, the Dallas Morning News reported widespread cheating on the Texas Assessment of Knowledge and Skills, a testing regimen that the state administers in grades three through 11. Answer sheets were analyzed by computer, and patterns of answers were found that could only be explained as the result of cheating.

This type of sophisticated analysis is widely accepted and used to identify suspicious patterns on tests such as the SAT and ACT. Some of the cheaters are the students themselves. But there is evidence that much of the cheating is done by teachers and administrators.

Students in Texas cannot graduate high school unless they pass the 11th-grade TAKS, and cheating appears to be more rampant among these juniors. The Dallas Morning News reported that “at more than 100 high schools at least one in 10 juniors was flagged for having extremely suspicious answer patterns on the TAKS graduation tests.” The paper also found that cheating was more prevalent in low-performing schools in danger of being sanctioned under the federal No Child Left Behind law and also in charter schools.

The Dallas paper also reports that the cheating rate is four times higher in charters than in conventional public schools. It could be that administrators worry that if scores aren’t high they will have trouble attracting students or even lose their charter. Teachers, usually without union protection, may feel that their jobs could be on the line if their scores don’t rise. The Dallas Morning News also suggests that Texas charters typically don’t get a high level of oversight by state testing authorities, another incentive for hanky panky.

The Texas test situation is a reprise of similar results of a study in Chicago several years ago. As recounted in the best-selling book Freakonmics, the chief executive officer of the Chicago school system, Arne Duncan, faced the problem head on. Confronted with computer analysis that disclosed probable cheating in 2002, he decided to retest 120 of the classrooms, a mix of suspected cheaters and a control group. Testing officials administered the retests themselves, while the classroom teachers, although allowed to remain in their rooms with the proctor during the exam, were not permitted to touch physically the exam papers.

As predicted, pupils in the classrooms where cheating was suspected did a lot worse the second time around, and those in the control classes replicated their original results. A number of teachers lost their jobs.

Regardless of the outcome of the current investigation here in New York, this is a tragedy for the children of P.S. 33, and an embarrassment to the mayor and chancellor. Did something fishy go on at P.S. 33? I have no direct evidence of this, but certainly there is enough here to warrant the same kind of computer analysis on test papers performed in Texas and Chicago, and I suggest that this kind of analysis be performed routinely throughout New York State, in all schools.