Republican presidential hopefuls Donald Trump and Sen. Ted Cruz (R-Tex.), seen at a Jan. 14 debate, are among the top-tier GOP candidates who want to end Common Core and shrink the federal role in education. (Andrew Harrer/Bloomberg)

To hear the top-tier Republican presidential candidates tell it, on their first day in office, they will shift power over education from the federal government back to states and local communities.

Problem is, Congress already took care of that.

In December, the House and Senate overwhelmingly approved a new law that dials back the power of the federal government when it comes to local classrooms. It marked a profound reset of the relationship between federal and state governments. States, not the federal government, decide curricula, teaching methods, academic standards, what to do about struggling schools and how to define success or failure, among other things.

All but two of the GOP candidates — former Florida governor Jeb Bush and Ohio Gov. John Kasich — are also promising that they will rid the country of Common Core, the K-12 academic standards in math and reading adopted by more than 40 states and the District of Columbia.

The trouble is, the president has no power over the Common Core. States decide academic standards. That has been true for years but was spelled out explicitly in the new federal education law.

Still, that hasn’t stopped Donald Trump, Sens. Ted Cruz and Marco Rubio, or retired neurosurgeon Ben Carson from telling voters that they will reduce the federal role in education while they also mothball the Common Core.

From a 45-second video released by Trump on Wednesday: “I’m a tremendous believer in education, but education has to be at a local level. We cannot have the bureaucrats in Washington telling you how to manage your child’s education. So Common Core is a total disaster. We can’t let it continue.”

Two weeks ago, Cruz posted a video in which he said, “If I’m elected president, I will direct the U.S. Department of Education — which should be abolished — I will direct the Department of Education that Common Core ends today. Instead, I will restore power back to the states and to the local governments and ultimately back to the parents — those closest to our kids who have direct responsibility for raising our children, each and every one of us moms and dads.”

From Rubio’s website: “On Day One, Marco will issue an executive order directing federal agencies to stop any and all activity related to implementing or encouraging Common Core. . . . He will ensure no federal education funding is tied to mandates and prohibit the federal government from forcing states or local districts to adhere to principles or interfere in local education.”

And from Carson’s website: “In recent years, however, the U.S. Department of Education has increasingly tried to dictate how children are educated. . . . This federal intrusion must stop and Common Core must be overturned. Our education system must be run by involved parents and engaged teachers and principals at the state and local levels. Attempts by faceless federal bureaucrats to take over our local schools must be defeated.”