Several weeks into his first year of teaching math at the High School of Arts and Technology in Manhattan, Austin Lampros received a copy of the school's grading policy. He took particular note of the stipulation that a student who attended class even once during a semester, who did absolutely nothing else, was to be given 45 points on the 100-point scale, just 20 short of a passing mark.
Mr. Lampros's introduction to the high school's academic standards proved a fitting preamble to a disastrous year. It reached its low point in late June, when Arts and Technology's principal, Anne Geiger, overruled Mr. Lampros and passed a senior whom he had failed in a required math course.
That student, Indira Fernandez, had missed dozens of class sessions and failed to turn in numerous homework assignments, according to Mr. Lampros's meticulous records, which he provided to The New York Times. She had not even shown up to take the final exam. She did, however, attend the senior prom.
Through the intercession of Ms. Geiger, Miss Fernandez was permitted to retake the final after receiving two days of personal tutoring from another math teacher. Even though her score of 66 still left her with a failing grade for the course as a whole by Mr. Lampros's calculations, Ms. Geiger gave the student a passing mark, which allowed her to graduate.
Ms. Geiger declined to be interviewed for this column and said that federal law forbade her to speak about a specific student's performance. But in a written reply to questions, she characterized her actions as part of a ''standard procedure'' of ''encouraging teachers to support students' efforts to achieve academic success.''
The issue here is not a violation of rules or regulations. Ms. Geiger acted within the bounds of the teachers' union's contract with the city, by providing written notice to Mr. Lampros of her decision.
No, the issue is more what this episode may say about the Department of Education's vaunted increase in graduation rates. It is possible, of course, that the confrontation over Miss Fernandez was an aberration. It is possible, too, that Mr. Lampros is the rare teacher willing to speak on the record about the pressures from administrators to pass marginal students, pressures that countless colleagues throughout the city privately grumble about but ultimately cave in to, fearful of losing their jobs if they object.
Mr. Lampros has resigned and returned to his home state, Michigan. The principal and officials in the Department of Education say that he missed 24 school days during the last year for illness and personal reasons. He missed two of the three sets of parent-teacher conferences. He also had conflicts with an assistant principal, Antonio Arocho, over teaching styles. Mr. Lampros said all of this was true.
Still, Mr. Lampros received a satisfactory rating five of the six times administrators formally observed him. He has master's degrees in both statistics and math education and has won awards for his teaching at the college level.
''It's almost as if you stick to your morals and your ethics, you'll end up without a job,'' Mr. Lampros said in an interview. ''I don't think every school is like that. But in my case, it was.''
The written record, in the form of the minutely detailed charts Mr. Lampros maintained to determine student grades, supports his account. Colleagues of his from the school -- a counselor, a programmer, several fellow teachers -- corroborated key elements of his version of events. They also describe a principal worried that the 2006 graduation rate of 72.5 percent would fall closer to 50 or 60 percent unless teachers came up with ways to pass more students.
After having failed to graduate with her class in June 2006, Miss Fernandez, who, through her mother, declined to be interviewed, returned to Arts and Technology last September for a fifth year. She was enrolled in Mr. Lampros's class in intermediate algebra. Absent for more than two-thirds of the days, she failed, and that grade was left intact by administrators.
When second semester began, Miss Fernandez again took the intermediate algebra class, which fulfilled one of her graduation requirements. According to Mr. Lampros's records, she missed one-third of the classes, arrived late for 20 sessions, turned in half the required homework assignments, failed 11 of 14 tests and quizzes, and never took the final exam.
Two days after the June 12 final, Miss Fernandez told Mr. Lampros that she had a doctor's note excusing her from school on the day of the exam, he said. On June 18, she asked him if she had failed the class, and he told her she had. The next day, the principal summoned Mr. Lampros to a meeting with Miss Fernandez and her mother. He was ordered, he said, to let her retake the final.
Mr. Arocho, the assistant principal, wrote in a letter to Mr. Lampros that Miss Fernandez had a doctor's note, issued March 15, permitting her to miss school whenever necessary in the spring. Mr. Arocho did not respond to telephone and e-mail messages seeking comment.
There is such a note, issued by Dr. Jason Faller, but it excused absences ''over the last three months'' -- that is, the period between mid-December and mid-March. In a recent interview, Dr. Faller said he saw Miss Fernandez only once, in March, and confirmed that his excuse note covered absences only before March 15.
For whatever reason, school administrators misinterpreted the note and told Mr. Lampros that Miss Fernandez would be allowed to retake the final -- and to retake it after having two days of one-on-one tutoring by another math teacher, an advantage none of Mr. Lampros's other students had, he said.
Mr. Lampros, disgusted, did not come to school the next two days. Miss Fernandez meanwhile took the test and scored a 66, which still left her far short of a 65 average for the semester. Nonetheless, Mr. Arocho tried to enter a passing mark for her. When he had to relent after objections by the teachers' union representative, Mr. Lampros was allowed to put in the failing grade. Ms. Geiger promptly reversed it.
Samantha Fernandez, Indira's mother, spoke on her behalf. ''My daughter earned everything she got,'' she said. Of Mr. Lampros, she said, ''He needs to grow up and be a man.''
From Michigan, Mr. Lampros recalled one comment that Mrs. Fernandez made during their meeting about why it was important for Indira to graduate. She couldn't afford to pay for her to attend another senior prom in another senior year.