BURLINGTON, Vt. — With schools closed for a third day Monday because of a teachers strike in Vermont’s largest city, working parents scrambled to find child care, a boys and girls club extended its hours and the teachers union and school board agreed to meet again with a mediator Tuesday.

The teachers in Burlington say the issue is scheduling time for teachers to prepare outside the classroom and to work one-on-one with students. The school board says teachers made new, unexpected demands at the last minute.

The strike affecting about 4,000 students has left some working parents scrambling to figure out what to do with their kids, and some calling on grandparents to help.

Parent Linda Debose worked a half day Monday and took advantage of the warm weather by taking her teenage daughter and a friend to North Beach on Lake Champlain while her younger child was with his grandmother.

“I’ve gotten lucky, but for a lot of others it’s been chaos,” she said.

Child care worker and parent Kelly Wells, of Burlington, took 11 kids, including her own twin 14-year-olds, by bus to the beach.

“It’s a challenge for parents, especially when you don’t know day to day,” Wells said.

She said she hopes the strike is resolved soon and teachers and the school board can set an example for students by coming to resolution.

“And these kids are observing that. It’s important,” she said.

Some students affected by the strike said they were happy to have a day or two off but would prefer to get back to school. They believe they will have to tack on days in June to make up for days missed because of the strike. A few other middle schoolers said they were concerned about a lack of sports practice.

Two Republican state lawmakers, Rep. Kurt Wright and Sen. Joe Benning, said they will introduce legislation that would ban teachers from striking and school boards from imposing contracts. It also would require contract negotiations to be open unless both sides agree to have them closed and create a task force to investigate how to resolve an impasse.

The Vermont National Education Association opposes the proposal. Two years ago, Wright proposed a similar measure that was narrowly defeated in the House.

Republican Gov. Phil Scott said he supports the right to impose contracts and the right to strike but understands the concerns the two legislators hope to address. He said if the proposal passes in the Legislature he would give it “fair consideration.”

Meanwhile the Pomerleau Family Boys & Girls Club of Burlington, which provides after-school programming to young children, extended it to all day in response to the strike. The kids who attended Monday had a chance to play tennis, pool and basketball, use computers and participate in reading time.

“When we knew that kids were going to need us, we just put together the plan to make sure that we’d be there,” said club Director Tanya Benosky.