This is a tale of good deeds gone unrequited. And of city officials unable to nourish the good fortune they find in their midst.

I’m getting ahead of myself, however.

Let’s walk into Public School 19, a brick fort of a school that sits alongside a hillside road in West Brighton on Staten Island.

Jeanne Raleigh, 50, who greets me at the door, vibrates like a tuning fork. Sardonic, passionate and funny all at once, she teaches fourth grade. She also runs the Penny Harvest for this school, made up of working-class Yemenis and Mexicans, Ecuadoreans and Sri Lankans.

Each year, P.S. 19’s children collect piles and piles of pennies, plopping them in buckets. Then Ms. Raleigh convenes her executive team (which is to say 15 fourth and fifth graders) and the team telephones the C.E.O.’s of foster care agencies and pediatric wards and interviews them. The committee picks finalists and the student body votes. Then the children hand over their great haul — $2,243 last year — and give scholarships to foster care children, and Xboxes to cancer wards.