But the squabble isn't limited to the highly-publicized controversy throughout the public school system – it's also taking place in the thousands of American Catholic schools trying to grapple with the same issue.
Although the most-often debated math and English benchmarks are secular, approximately 100 of the nation's 195 Catholic dioceses have taken them on in some form.
"If our academic North Star for our students is college readiness, what we have to do is align ourselves with certain standards that are going to predict our ability for our kids to meet that North Star," says Rick Maya, superintendent of Catholic schools for the Diocese of Sacramento, which is using the standards.
"We look at the standards as what they are – it's the blueprint and tells us what kids should know and by when, and what to do if they don't," he added.
Catholic dioceses that are implementing the standards say they have done so for a variety of reasons. In addition to preparing students for college, they've said aligning with the standards is important because many Catholic school students go on to attend public high schools. In other cases, they've said it is a proactive approach because many textbooks will be aligned to the Common Core.
But the opponents of the new standards have some of the same concerns as those in public schools. They worry that the standards aren't academically rigorous enough, that they standardize education too much and that they appear to be a federal takeover of local education.
Maya, along with the superintendents of California's 11 other dioceses, convened to decide as a state whether or not to bring the Common Core standards into Catholic schools.
Together, they decided to support the Common Core Catholic Identity Initiative, or CCCII – an effort put forth by the National Catholic Educational Association – which seeks to "infuse the standards with the faith, principles, values and social justice themes inherent in the mission of a Catholic school," according to an NCEA statement.
That's why Catholic school leaders say they're "adapting" the standards, rather than "adopting" them.
Adapting Standards Is Nothing New
According to Kevin Baxter, superintendent of elementary schools for the Archdiocese of Los Angeles, building off of secular academic standards is nothing new, at least in California, where Catholic schools have used state standards since the late 1990s.
"We've always used a secular standard as our academic benchmark," Baxter says. "Then our job as Catholic educators is to make sure the faith is infused and the Catholic identity of our schools is strong. That's always been something that we've had to do."
And that's the case even for some states in which Catholic schools have chosen not to adapt the Common Core standards, such as Indiana.
According to Mark Myers, superintendent of the Diocese of Ft. Wayne-South Bend, although the standards are generated from within, they are closely aligned with the Indiana state standards.
"That model has served our children and our Catholic communities very well in regards to academic achievement and Catholic identity," Myers says.
Before making the decision to adapt Common Core, Baxter says the California superintendents looked to the example of other states, including those that followed the CCCII, such as Illinois.
Jean Johnson, superintendent of the Diocese of Springfield, says schools in the diocese are studying the Common Core "through a Catholic lens."
"Our schools have the academic freedom to select what they will adapt from the Common Core State Standards, according to what is supportive to the Catholic mission of the school," Johnson says. Much like California, the superintendents of different dioceses in Illinois banded together in support of the CCCII.