The well-oiled volunteer network of parents involved in their local PTAs sprung into action after Sandy to put their fund-raising and outreach expertise to good use, often miles beyond the boundaries of their local schools.

Discord between parents and the principal at the New Explorations Into Science, Technology and Math High School reached a discomfiting peak this week when more than 500 parents and faculty members signed an online petition that criticized the principal, Olga Livanis, as overly punitive in this year’s rating of several well-liked teachers, failing to share important budgetary information with parents, and setting the wrong tone at the school, which is on the Lower East Side.

UPDATED | In a ruling announced on Thursday, Judge Ellen M. Spodek of State Supreme Court in Brooklyn wrote that the city’s decision this year to revoke Williamsburg Charter High School’s charter, despite having renewed it in 2009, was “arbitrary and capricious” and “not corroborated by any policy, regulation or protocol established by the D.O.E.”

Many public schools incorporate food — its production, nutritional value and place in the larger culture — into their curriculums, And at certain private schools lunchtime can include braised meats and Korean meatloaf. But at P.S. 150, a school of fewer than 200 students in TriBeCa, an appreciation for food is an integral part of student life, interwoven into the culture of the school and shared by the families who send their children there, many of whom have sophisticated palettes themselves.

According to Department of Education officials, attendance on Wednesday was at 79.4 percent, a mere .2 percentage points lower than the rate for the last day of school in 2011 — despite the fact that many schools had canceled classes on Monday and Tuesday because the city had clocked none of its allotted snow days this year.

For students, being part of a new school meant designing the student council, instituting annual traditions during the school year, deciding on school colors, school cheers and events. It also meant major preparations for the first graduation, with the added responsibility of setting the tone for younger classmates by coming up with specific ideas that could set their school’s event apart from others. And of course there were a few pitfalls — like, in the case of Pan American International High School, discovering that if you order the yearbook in May, it won’t be there on time for graduation day.

Despite the long-held ideal that public education should be free, parents in New York City are finding themselves paying for an increasing number of things, like class trips and basic supplies.

In an interview in April to mark his first anniversary as chancellor, Chancellor Dennis M. Walcott said the Fund for Public Schools can be an equalizer when it comes to disparities in parent fund-raising. Meanwhile, he said, one thing he is not going to do is discourage parents from raising money for their children’s schools.

There is no centralized accounting of how many New Yorkers owe their livelihood to public school PTAs. But parent association Web sites — which often include lists of the activities parent dollars are now responsible for — suggest that if you are an actress with an appetite for history, an entrepreneurial bongo drummer, a yoga instructor O.K. with teaching downward dog to 6-year-olds, even a skateboard champion looking to earn some extra cash, currying favor with the city’s better-off PTAs is just good business.

In all the sound and fury over Chancellor Dennis M. Walcott’s demand for more power to fire teachers for sexual misconduct, there is little likelihood that Albany will be addressing the matter any time soon — or that the matter will be resolved without legislative intervention, given the heated tension between the city and the union, according to people familiar with the issue.