Mark Zuckerberg has been denounced after a school he and his wife established for children from low-income families in East Palo Alto announced in April that it will be shutting down, leaving students and their parents confused and angry.

But it turns out that a mile away, behind a high wall of hedges, the billionaire and his wife, Priscilla Chan, were running a private school out of a house at their Palo Alto compound for two of their daughters and a dozen other children. And they were doing it in violation of city code.

Residents in the Crescent Park neighborhood started noticing during the pandemic that one of Mr. Zuckerberg’s homes on Hamilton Avenue had school-style rhythms, with families dropping off their children each morning and picking them up in the afternoon. Sometimes, they saw big vehicles with darkened windows pick up the children to take them on outings.

They suspected the house was being used as a school, and they were right.

A private school called BBS, formerly named Bicken Ben, has been operating at that property, according to state documents and city officials.

Private schools must file affidavits providing basic information with the California Department of Education. Documents filed with the state agency for the past three years describe BBS as a coed day school that enrolls 14 children in kindergarten through fourth grade. It employs three full-time teachers, one part-time teacher, one administrator and one other staff member.