LOS ANGELES — More than 30,000 Los Angeles public-school teachers began a strike on Monday, the first in three decades in the district. Holding plastic-covered signs on rain-drenched picket lines across the city, they demanded higher pay, smaller classes and more support staff in schools.

The strike effectively shut down learning for roughly 500,000 students at 900 schools in the district, the second-largest public school system in the nation. The schools remained open, staffed by substitutes hired by the city, but many parents chose to keep their children at home, either out of support for the strike or because they did not want them inside schools with a skeletal staff.

With negotiations apparently at a standstill, the strike could last days or even weeks.

The decision to walk off the job came after months of negotiations between the teachers’ union, United Teachers Los Angeles, and the Los Angeles Unified School District. Although educators on all sides agree California should spend more money on education, the union and the district are locked in a bitter feud about how Los Angeles should use the money it already gets.

Although district officials have agreed to come closer to meeting some of the union’s demands, they say fulfilling all of them would bankrupt the system, which is already strained by rising health care and pension costs.