Ms. Dillon said that even within gifted classes there was a spectrum of ability, and that she commonly arranged pupils into small groups, according to their abilities, for reading, writing, math and the like.

This fall, in studying the branches of the federal government, about a third of her students understood that some concepts of power also extended to the states and that there was an interplay between state and federal powers.

“The general education students might not have all covered this topic,” said Ms. Dillon, whose class is more diverse than most of the gifted and talented rooms, with five black and eight Hispanic children among the 26 students.

Sara K. Bloch’s triplets are all in different programs at the school. Leon is in Ms. Dillon’s gifted class; Jason is in general education; and Felix is in what is known as an integrated co-teaching class, which mixes special education students with general education children like Felix. “To be completely honest, we feel that this class is probably similar to a regular fifth-grade class,” she said on the day she visited Leon in Ms. Dillon’s class. “Math is the same; all three — they have the same book.”

But Leon does seem to be pushed harder, Ms. Bloch said. He is asked to think of things in complex ways, not just to memorize dates of the American Revolution or names like John Adams, for instance, but also to understand relationships between events and people, or to explain possible motives or forces behind certain events, like the Boston Tea Party. She also said that the relationship between the parents and the teachers was more intense at the gifted level, with an expectation of parent involvement and connectedness.

“There is none of that in the other classes,” Ms. Bloch said.

In her experience in teaching those who teach gifted children in New York City’s public schools, Christy T. Folsom, a professor at Lehman College and a former board member of Advocacy for Gifted and Talented Education in New York State, said gifted children got a “much deeper experience and, in some cases, more advanced curriculum.”

“In the gifted classrooms that I’ve been in, the majority of kids are reading at grade level or beyond, and they can write well, and then so much time is not spent on basic skills so they can spend more time on content and on comparing historical eras,” Professor Folsom said. “They are then able to do the more deep thinking work because less time has to be spent on the fundamental skills.”