An elementary school in East Harlem that has defied the odds on a shoestring budget could soon be rewarded after years of scarcity.

It is among a handful of highperforming schools with a majority of poor students and a tiny share of the tax levy — which pays for things such as teacher salaries, but not for building expenses or food — that could receive a windfall under the mayor’s plan to address funding imbalances among city schools using a new funding formula.

Yet the budgets of several poorly performing schools that are among the richest in the city when it comes to their share of tax levy will remain untouched because of a “hold harmless” provision the mayor announced last week.

The odds-defying school, the Bilingual Bicultural School in East Harlem, has a population that is 83% poor and 90% Hispanic, and receives only $2,200 a year in tax levy aid per pupil. That is less than a third of the tax levy received by another Manhattan school with 79% of its mostly minority students living in poverty, the Hernandez-Hughes Learning Academy.

The Bilingual Bicultural School brought up the percentage of students passing math and reading tests 20 percentage points over three years, while the Hernandez-Hughes school lags behind similar schools in the percentage of students that read proficiently by 17 percentage points — at 37% in 2005.

The president of the United Federation of Teachers, Randi Weingarten, noted that Hernandez-Hughes used to be even worse before it was incorporated into the “chancellor’s district.” Schools in the district received extra funding which she said has allowed Hernandez-Hughes to double its scores. The district was dismantled under the Bloomberg administration.

“It would be incorrect to say that money spent wisely does not make a difference,” Ms. Weingarten said.

At another school that has been beating the odds, P.S. 24 in Sunset Park, the principal, Christina Fuentes, pulled up the percentage of her students reading at grade level 20 percentage points in one year. She said she is hopeful that the formula could increase the budget for her school, which has a student body made up of 45% English language learners and 20% special education students.

Her school receives $2,458 per student in tax levy money, one of the lowest amounts in the city.

“Do we need more? Absolutely,” she said. “There’s never enough for children.”

She said she would spend the money on more library books, field trips, and training for teachers.

Schools will find out how much they get under the formula, if anything, as soon as next week, when the Department of Education is expected to announce the amount of extra funding, or “weights,” it will attach to certain needy students starting this year.

How well the school performs will not factor in to how much money the schools receive, although the department has said it will give middle schools and high schools extra money for poorly performing students when they first enter the school.