It is as though the neighborhood were divided by an invisible wall.

On one side, children attend a public elementary school where test scores are high, the students are mostly white and well off, and the parent-teacher organization can raise $800,000 a year to pay for things like a resident chef.

On the other side, children attend a public elementary school where 87 percent of the students are black or Hispanic and 84 percent receive some form of public assistance. Just over a tenth pass the state reading and math tests. There is no library or art teacher.

The first school, Public School 199 on West 70th Street in Manhattan, is also seriously overcrowded, with a waiting list of nearly 100 children for kindergarten in recent years. The second, P.S. 191 on West 61st, has many empty seats.

Now, to address the overcrowding at P.S. 199, the New York City Education Department is proposing to redraw the line, transferring to P.S. 191 several blocks of apartment buildings where children are currently zoned for P.S. 199. The change would be controversial under any circumstances, but it is particularly so because the state this year put P.S. 191 on its list of “persistently dangerous” schools.