The Senate may be nearing an agreement on mayoral control, but now there’s a new debate — over how to increase parental involvement, and what involvement means.

At the center of the debate are the two parent groups most actively lobbying Albany, and each has its own slightly different vision.

The Parent Commission on School Governance is pushing for a kind of parent union, which it calls an Independent Parent Organization and Training Academy.

According to Patricia Connelly, a member of the Parent Commission, the organization would act like a think tank-cum-lobbying force for parent advocate groups and would be modeled on the now-defunct United Parent Association.

“It can be a place where people come together and learn from one another,” Connelly said, adding that the group would also do research and train less experienced parents.

“Right now we don’t have an institutionalized role and people say well there’s OFEA [Office of Family Engagement and Advocacy], but that’s just an arm of the Department of Education and it’s more about delivering PowerPoint presentations rather than what we really need to know to be effective advocates,” she said.

The Independent Parent Organization would begin under the aegis of a nonprofit, said Steven Bell, a member of the 3R’s Coalition — a group that’s also backing the proposed organization — but would work toward becoming independent. It would have a chapter in each school district and hold elections to fill its ranks.

According to Bell, Sampson’s staff told the Independent Parent Organization’s supporters that they should aim for funding in the range of $3 to $5 million for the project, which would be paid for entirely through state education money.

Shomwa Shamapande, a spokesman for the Campaign for Better Schools — a group that wants to modify mayoral control — said the Campaign was opposed to the idea of an organization that didn’t have parent training as its central focus.

Tensions between the two groups center on concerns about diversity.

While the Parent Commission maintains that its vision of citywide chapters would attract diversity, the Campaign for Better Schools urges a focus on parents who wouldn’t otherwise get involved.

The Campaign’s own plan calls for the creation of a Citywide Parent & Student Leadership Center, which would offer training for parents and students in navigating the city’s public school bureaucracy.

The Leadership Center would focus on schools with weak or virtually non-existent Parent Associations and schools with a majority of African-American, Latino, low-income, and immigrant students. The Campaign is asking for $5 million in funding for the Center, which would be attached to a nonprofit.

Shamapande said the Center’s training would emphasize ways to get bilingual education and special needs students the proper instruction.

Connelly said the Parent Commission would welcome a training center in addition to the Independent Parent Organization. “I don’t think we’re in contradiction with other plans,” she said. “We’re complementary.”