LOS ANGELES — In California public schools, students are required to learn about black history and women’s history. And if a bill approved by the State Senate this week becomes law, the state will become the first in the country to mandate that schools also teach gay history.

While the bill does not set specific requirements about what should be taught to students, it does say that contributions of gays and lesbians in the state and country must be included in social science instruction. So Harvey Milk, one of the first openly gay elected officials in the state, and Bayard Rustin, a civil rights activist, may take a prominent place in the state’s history books.

Advocates say that teaching about gay, lesbian, bisexual and transgender people in schools would prevent bullying and shatter stereotypes that some students may harbor. They point to several students who have committed suicide after being taunted by peers for being gay. But the bill has drawn vociferous criticism from opponents who argue that when and how to talk about same-sex relationships should be left to parents.

A similar bill was approved by the Democratic-controlled Legislature in 2006, but vetoed by Gov. Arnold Schwarzenegger, who said that school curriculum should be left up to local schools. But there is a new governor now. And both supporters and opponents of the bill expect it will sail through the heavily Democratic Assembly and be signed into law by Gov. Jerry Brown, a Democrat who has been supportive of gay rights.