CHICAGO — Raising U.S. educational expectations through national goals was a priority for Republican President George W. Bush. But many of his would-be successors in the Republican are calling for just the opposite of government-set rules, and it’s splitting the party as the Republican class of 2016 presidential hopefuls takes shape.

Just six years after Bush left office, Kentucky Sen. Rand Paul referred last week to a set of state-created standards, called Common Core, as a national “curriculum that originates out of Washington.” That kind of statement stokes outrage among grass-roots conservatives, who are still incensed with the Obama administration over the 2010 health care law.

It also happens to be untrue: Forty-four states voluntarily participate in Common Core standards developed in part by Republican governors. And some other potential Republican presidential candidates support the standards and are objecting to the red-meat rhetoric designed to fire up the party’s most fervent supporters.

“We cannot expect our children to compete with the best in the world when we have no standards or dumbed-down standards,” former Florida Gov. Jeb Bush, the former president’s brother, said at an education conference in Arizona last week.

In the meantime, education is rising as a Republican priority, if only as a proxy for a larger internal party debate over government’s proper scope.

“This is a microcosm of the heart and soul of the Republican Party,” said Chad Colby, a former top Republican National Committee spokesman who is now with the pro-Common Core group Achieve. “High education standards are too important to our economy and international standing to be derailed by ideological purists with no alternative plan.”

Five years ago, a bipartisan group of governors and staff of the National Governors Association began collaborating with the Council of Chief State School Officers on shared higher standards, as a political alternative to the Bush administration’s No Child Left Behind law.

No Child Left Behind, Bush’s signature domestic policy achievement won congressional approval with bipartisan support. It requires annual testing, publication by districts of performance data of student subgroups, and increasingly tough consequences for schools that don’t meet the bar.

But Congress never fully funded it, and 10 years later it’s become synonymous with unrealistic expectations and an overemphasis on testing at the expense of other educational efforts.

Like No Child Left Behind, Common Core focuses on reading and math. However, its standards are voluntary and in effect in 44 states today.

Common Core standards lay out specific skills in reading and math that students should master by the end of each grade level. For instance: All third-graders should know how to find the perimeter of a shape. How the teacher pursues the goal is up to each school’s curriculum.

President Barack Obama’s administration embraced the standards early on, listing them in 2009 as acceptable for the $4.35 billion Race to the Top grant program. The readiness of the standards and the availability of federal money in the midst of the economic downturn prompted most states to adopt Common Core. Some states, such as Virginia, didn’t adopt them because they had already established their own similar standards.

When asked about his position on them this week, Paul referred to them as derived from the federal government. Former Republican Govs. Mitch Daniels of Indiana and Tim Pawlenty of Minnesota have been advocates and assisted in the standards’ drafting. Paul also implied the standards were mandatory, included specific teaching methods and covered more subjects.

“How we teach history, how we teach world civilizations, there’s a lot of input of philosophy that goes into that. I would prefer it not come out of Washington,” Paul told reporters when asked about his position on Common Core last week after visiting a private school in Chicago. “I would rather not see a national curriculum.”