At a Park Slope elementary school on Brooklyn’s Fifth Avenue, popular book bag themes include Mickey Mouse and Dora the Explorer. “Norbit” is a favorite film. The preferred morning greeting on a recent Thursday: Kalimera.

At the Hellenic Classical Charter School, Modern Greek — in which kalimera means “good morning” — is a required part of the curriculum. As one of the 11 culturally themed charter schools to open in the city since 2002, so are Greek history, Greek traditions, and even Greek dance.

The theme schools were put under a spotlight this spring when the city announced plans to open an Arabic-themed school, the Khalil Gibran International Academy. While some praise Khalil Gibran’s global approach, critics say the school threatens public education’s mission: to build American citizens unified by a single American culture.

The Hellenic School offers a glimpse into how such a balance can play out. Parents praise a rigorous curriculum that will eventually teach Latin as well as Modern Greek, while concerns that the school might be too closely tied to the Greek community have plagued its charter application. Funds from Greece directly pay the salaries of five teachers, an in-kind donation worth $275,000 this year, and a Greek minister of education helps develop curricula, the chairman of the school’s board, Charles Capetanakis, said.

The school’s relationship with a Greek parochial school has been even more polarizing, nearly jeopardizing Hellenic’s charter application in 2004. The school, Soterios Ellenas, shares the building with Hellenic, and several students and teachers who had been at the parochial school have transferred to the charter school. Soterios Ellenas’s priest, Father Damaskinos Ganas, has no formal relationship with Hellenic, but educators there refer to him as Hellenic’s “spiritual leader”; on a recent visit students waved enthusiastically when he passed them in the hall.

Hellenic’s leaders steadfastly defend their cultural model. Not only is the school inclusive — just 30% of the students are Greek; 50% are African-American and 15% are Hispanic, according to its director of operations, Joy Petrakos — it also produces results. This year, 92% of third-graders met state math standards, compared with 82% citywide, according to state data.

Benefits to Greek families are the most straightforward. A parent, Irene Misiriotis, said she feels lucky her son, Kostas, can get a Greek education without having to endure Saturday school. Kostas, one of several students to transfer from Soterios Ellenas, said he enjoys the extra resources: a stronger English program, computers that work, and textbooks that don’t have the answers scribbled in.

School leaders say non-Greek children also benefit.

Rayhana Alhanafi, a second-grader who is African American and Muslim, felt bored at her neighborhood public school. At Hellenic, instead of lessons on 5+5 = 10 — “kindergarten stuff” — she was working on three-digit subtraction. She also can recite the numbers in Greek, and she talks knowledgeably about the gender politics of ancient Athens, such as whether girls could attend school.

The Greek aspects make Rayhana’s mother, Shara Martinez, wary. Ms. Martinez did not take her daughter to a Greek Independence Day parade that other children attended. A holiday performance of Greek plays, performed in Greek, left her feeling at sea.

“I just don’t like the fact that Greek is the main language,” she said. “It should be different languages. Let them do black history plays and things like that.”

Hellenic administrators and parents say their school may not be the last with a Greek theme. Community leaders in Queens and the Bronx, they say, have expressed interest in applying for their own charters.