With a 92 average in her classes and two passing scores on Regents exams last year, Jacalyn Swintelsky had reason to be optimistic on her way to pick up her report card at Midwood High School this morning.

But when she got there, Swintelsky was stunned to see that she had failed the Global Studies Regents exam. Her score was two points shy of the 65 required for graduation and well below her marks on the three other Regents exams she took this year.

“I was really shocked,” said Swintelsky. “I expected to pass, that’s for sure.”

The outlier on Swintelsky’s report card stood out for another reason: It was the only test she took that was graded using the city’s new online scoring system that CTB/McGraw-Hill developed for four frequently taken Regents exams.

Serious glitches in the scoring system caused delays in getting grades and introduced concerns that scores might be artificially diminished. Now, students such as Swintelsky and their teachers are crafting plans to appeal lower-than-expected scores.

“We had a lot of kids who should have passed who had less than a 65,” said an English teacher in a Queens high school.

Students, parents, and administrators can appeal low grades and ask for exams to be regraded by hand. It’s a high-stakes gamble, because if the third grader awards a lower score, that’s the one students will end up with. But the option allows students to be sure they’ve had the fairest shot possible at clearing hurdles to graduation.

Many educators do not know about the option. When Swintelsky asked her guidance counselor about appealing her score, the counselor first handed her a form that would let her appeal her graduation status. “Then she said, ‘Wait, this is just for the seniors,'” Swintelsky recalled.

But educators are quickly learning, and many say they intend to use the appeals process in a way they never have before. The Department of Education distributed information about appealing low scores to principals on Tuesday evening.

At Forest Hills High School, administrators are preparing to appeal all failing scores, said Adam Bergstein, an English teacher and the school’s union chapter leader. Benjamin N. Cardozo High School plans to review all grades and appeal the most abnormal ones, according to Dino Sferrazza, the chapter leader there.

The city will have to ask the State Education Department for permission to regrade exams when appeals include more than 5 percent of test-takers at a single school, under state rules.

Schools have a strong incentive to get scores right. Schools and principals are rated by the city in part by their Regents pass rates, and while this year’s scores won’t factor into teachers’ evaluations, they will in the future. And, of course, students use the scores to rack up graduation credentials and place into college classes.

Bergstein said one student with a 94 in his English class received a 74 on the Regents exam. He said he might push to appeal all scores under 75, a benchmark that city colleges use to decide if a student needs to take remedial courses.

“It could directly cost them courses in college if you were banking on that 75 or above in English or that 80 in math,” Bergstein said.

Appeals can be filed only by students, parents, and school administrators, who must send a written letter to the superintendent asking for regrading. But several teachers told GothamSchools that they planned to encourage students whose scores seemed deflated to appeal.

A Queens history teacher said he is reaching out to students and their parents this week to let them know about the option to appeal. He said about a fifth of his students had received scores that did not seem right, based on their past performance. And a Brooklyn teacher said he planned to scrutinize the essays his students wrote, once McGraw-Hill delivers promised scans of the papers, to make sure that their scores are accurate.

Some teachers have already started spreading the word. “When my English teacher saw my grade … she told me that my grade could’ve been a mistake,” a student wrote in a panicked note to GothamSchools today. “When my earth science teacher also saw my Regents score, he also told me that I should get it checked because it could’ve also been a mistake. Please help me and tell me what I should do.”