Amber Weiss and Sharon Papo, both of Berkeley, Calif., hold hands during their wedding ceremony June 17, 2008, at City Hall in San Francisco. Just what public schools will be required to teach about same-sex marriage has emerged as the central issue in the campaigns against same-sex marriage in both California and Maine.

San Francisco ? Gay marriage opponents pulled off another victory at the ballot box this week by using a tried-and-tested argument: Approve it and children will be taught homosexuality in school.

Voters seemed to be swayed by the message, both in Maine and in last year’s gay marriage battle in California. And it has become an important part of the ever-evolving playbook of gay marriage opponents, who have now won 31 consecutive statewide ballot measures against the issue.

In Maine and California, voters were besieged with ad images of what would supposedly happen if same-sex marriage were legal: students going on a field trip to a lesbian wedding, elementary school kids reading books featuring gay couples, kindergartners learning about homosexuality from their teachers — all without any say from parents.

Critics assailed the messages as blatantly misleading fear-mongering.

“It’s drawing on the fears of the unknown,” said Sandy Maisel, director of the Goldfarb Center for Public Affairs and Civic Engagement at Maine’s Colby College. “There’s no evidence that it’s going to happen, but there’s very clear evidence that it’s an effective campaign tactic.”

Gay marriage opponents discovered the effectiveness in last year’s successful effort to pass Proposition 8 to outlaw gay marriage in California.

After signing up to lead the campaign, political consultants Frank Schubert and Jeff Flint noticed that polls were showing voters tended to not have much of a problem with gay relationships.

With the help of focus groups, surveys and ammunition unwittingly supplied by their opponents, the two soon found a new way to frame the issue, by focusing on education.

It’s not the first time gay marriage opponents have played the education card, but not until the California campaign did it became the preferred strategy. That is a departure from elections in recent years when the focus was almost solely on the argument that marriage is a sacred institution between a man and a woman.

Schubert said he had an ah-ha moment in California when a focus group watched a campaign commercial featuring a Massachusetts couple who described how their 7-year-old son came home from school and explained that a man can marry another man, something he learned in a children’s book.

One of the members of the focus group shook his head, and Schubert asked the moderator to inquire. The participant said he would be angry if something like that happened to his kids.

“So that was sort of a light-bulb moment, that this education issue was really going to be a powerful one for us,” said Schubert, who with Flint was named the “public affairs team of the year” for 2009 by the American Association of Political Consultants.

In California and Maine, gay marriage supporters countered the claims with spots featuring prominent elected officials such as California’s chief of public instruction and Maine’s attorney general, who both insisted that same-sex marriage had nothing to do with schools.

But the issue persisted, according to advocates on both sides, in part because gay marriage supporters failed to discuss a key fact: Many public schools already have lessons that refer to gay families in the younger grades and confront anti-gay discrimination for older students.

Although the topics usually are broached in the context of appreciating diversity and tolerance, for some parents any discussion of gay people is too close to talking about gay sex.

“The trend that we are seeing is homosexuality is being promoted more and more in schools, and the increase in this is creating a hostile environment for kids with Christian or socially conservative viewpoints,” said Candi Cushman, education analyst for the Christian group Focus on the Family.

Cathy Renna, a public relations consultant in Washington who is married to a woman and has a 4-year-old daughter, said that equating references to gay parents with sex is “like saying that introducing someone’s mother and father to a class means you are talking about heterosexual sex.”

But Renna agrees that same-sex marriage supporters need a different comeback to the kids-and-schools argument.

“This idea that gay people are coming to eat your children is a long-standing tactic of the right wing,” she said. “The response to those ads that not only has more truth, but more integrity, is that we live in a diverse world and our kids know that. And it’s irresponsible for us not to talk about the world we live in in age-appropriate ways.”