When Columbia University opened a private elementary school, the vision was bold: By hiring the most talented educators in the business, the school would be a model of best practices. It would also be a model of diversity, taking both neighborhood and university children.

Today, the School at Columbia University is ending its fourth year further from this dream than many who started out there would have wanted.

Parents heap praise on the diverse student body, which is split 50-50 between the children of Columbia faculty and children in the surrounding neighborhoods of Morningside Heights, Harlem, and the Upper West Side. Yet some have also been soured by a change in the financial aid allocations two years ago that led to an exodus of about a dozen parents, all middle-class New Yorkers with no Columbia affiliation — “community” people, in the parlance of the school.

A Democratic Assemblyman of Manhattan, Daniel O’Donnell, said yesterday that after the exodus, he wrote several letters calling the change a betrayal of the university’s commitment to include both neighborhood and faculty children. He is the one who provided the dozen parents figure.

Much diversity remains, yet parents said that, although the younger children embrace it, parents are slower to form a cohesive community.

One parent, Lysa Vanible, said race and class differences sometimes cause discomfort, such as when friends of her children inquire about their fathers or make references to African Americans’ history as slaves. She said that she and other parents — black parents as well as parents of children with disabilities and other minority groups — are forming an independent committee to discuss sensitivity issues next year.

“We have to find out how to get along,” she said.

Teacher turnover is another concern. Of about 100 teachers this year, roughly two dozen will not be returning in the fall, the head of school told teachers in an end-of-year memo this week that listed departing staff members. The memo was shown to The New York Sun.

A parent who asked not to be named said that while teachers have overall been of excellent quality, the ritual of turnover is becoming worrisome.

“We’ve always ended every year with anxiety,” the parent said. “Five years later the school is still like a new school. It’s still creating itself.”

In a series of e-mail messages, the head of school, Annette Raphel, described the School at Columbia University as a thriving community where spots are greatly coveted. More than 80% of current staff are returning in the fall, she said.

Ms. Raphel said the financial aid issue was not a policy change but an effort to correct a discrepancy; Almost 90% of families not affiliated with the university receive financial aid, she said.

The third head of school in four years, Ms. Raphel came to the school after spending two decades at the prestigious Milton Academy.

A Columbia professor whose sons attend the school, Cory Abate-Shen, praised the school’s diversity, describing a recent playdate as an example: Her twin sons, the children of professors, invited as their guests a boy from Turkey, a boy from Israel, and two boys from Harlem.

Another parent, Delphine Durugordon, said the school has been a gift.

“It’s the kind of school, when you walk in, you are happy walking into it,” she said.

Ms. Vanible, a single mother of seven children, said she is grateful too, but also careful not to become complacent.

“I’m not going to accept everything that’s given because I’m poor,” she said. “I push the envelope a little bit, because I have black males, and I don’t want them to grow up to be in jail or to do crimes or to be mixed up.”