When math teacher Laura Mourino saw how the Common Core standards explained what students should know about algebraic functions, she was confused.

So she rewrote them, picking out parts she found more appropriate for advanced algebra and using more specific language. Now, Mourino’s ideas could have statewide influence.

The United Federation of Teachers has been organizing meetings of a couple dozen educators to discuss the academic standards, which New York adopted in 2010 and lay out what students are expected to learn in math and English at each grade level. Mourino and the other teachers are now working on recommendations meant to benefit members of the state’s next official task force — setting city educators, and the union, up to influence how the Common Core standards are reshaped in New York.

“We are working at the UFT at kind of understanding and unpacking standards,” said Kishayna Hazlewood, a third-grade teacher at Brooklyn’s P.S. 156 who served on the governor’s Common Core task force in the fall. “We will be ready if we are asked for certain things.”

The union is repeating a set of moves it made last year. When Governor Andrew Cuomo appointed a task force to review the standards then, the UFT organized its own group of teachers who developed suggestions and then passed them to Hazlewood.

The committees also reflect teachers unions’ close involvement in New York’s Common Core debates. Last year, the state teachers union convened a task force that reviewed the standards and conducted a survey of over 400 educators.

The UFT supported the move to the standards in 2010, and President Michael Mulgrew has forcefully defended them since then. In one widely-shared 2014 speech addressing hypothetical opponents of the standards, a fired-up Mulgrew threatened to “punch you in the face and push you in the dirt.”

But New York’s unions continue to walk a fine line as they figure out their role in reshaping the standards. Though most of the results of a statewide survey about the standards were positive, some educators have been frustrated with the standards, a lack of support as they grapple with changing their teaching methods, or the way the standards were rolled out in conjunction with new teacher evaluations and state tests.

In January, the UFT spent $1.4 million on ads in support of the recommendations made by the governor’s task force, and suggested the union was ready to dive into adjusting the standards.

“The unions are involved in the whole Common Core revision process in New York State to a degree that is very unique,” said Tom Loveless, an education researcher at the Brookings Institution.

That’s because the unions are more powerful in New York than in other states, he said. But it’s also because the standards are a part of a broader conversation about how to transition the state into a new era of education policy. Over the next several years, the state is set to revisit its entire system of standards, assessments, and teacher evaluations. Reviewing and revising the standards is the first step.

“In New York, the Common Core battle is part of the much larger battle,” Loveless said.

So, what are the teachers fighting for?

Educators on the UFT’s new committee say they are thinking about a number of tweaks. They want to make the standards more appropriate for a range of students, particularly English learners and students with disabilities, but also keep them rigorous.

Several teachers talked about the need remove jargon so that the standards make more sense to parents and are more instructive to teachers. The math standards often need to be “unpacked,” or split into sections that give teachers more explicit direction, said Mourino, who serves as the math department head at Harvest Collegiate High School in Manhattan.

That criticism is consistent with a survey commissioned by the state that solicited feedback about each standard. There is confusion over when algebra and geometry standards should be taught, State Education Commissioner MaryEllen Elia explained to the Board of Regents in February.

But teachers on the UFT’s committee also say there is danger when the standards are too prescriptive, and some worry they are unrealistic for students in younger grades or those with special needs.

That has become a problem in Hazlewood’s third-grade reading class. It is impossible to teach the concept of a main idea using a text too complicated for students to read, she said. The same issue comes into play at the higher grades with English learners, said Jeremiah Robey, who teaches seventh-grade social studies in Brooklyn and is also on the union’s task force.

“If I just had a student that just came from Yemen and he speaks little to no English, how is he expected to write an essay with an argument and a supporting claim?” Robey asked.

Those concerns get at the heart of what kinds of changes the teachers are looking to make, and bring up a number of thorny questions. Are differentiated standards still standards? And would different standards for students who are behind do anything to help teachers catch them up?

For now, educators on the UFT’s task force are still asking those questions. Other states that have tried to overhaul the Common Core standards, including Florida and Indiana, have struggled to make more than superficial changes as they created their own versions.

“What they replaced Common Core with was a set of standards that looked very much like Common Core in the end,” Loveless said of other states.

But Mourino hopes that New York’s process, starting with the teachers’ brainstorming, will have a real impact on classrooms throughout the state.

“I think every single teacher wants joy in the math classroom,” she said. “Some are reaching with limited success.”