President Trump signed an executive order on Thursday that directs the federal Department of Education to come up with a plan for its own demise.

Only Congress can abolish a Cabinet-level agency, and it is not clear whether Mr. Trump has the votes in Congress to do so. But he has already begun to dismantle the department, firing about half of its staff, gutting its respected education-research arm, and vastly narrowing the focus of its civil rights division, which works to protect students from discrimination.

Mr. Trump’s long history of attacking the Department of Education represents a revival of a Reagan-era Republican talking point. It has unified Democrats in fiery opposition. But is shuttering the department possible? And if not, how has Mr. Trump begun to use the agency to achieve his policy goals?

What does the department do?

The Education Department was founded in 1979. Its main job is distributing money to college students through grants and loans. It also sends federal money to K-12 schools, targeted toward low-income and disabled students, and enforces anti-discrimination laws.

The money for schools has been set aside by Congress and is unlikely to be affected by Mr. Trump’s executive order. But oversight of the funds could be reduced and moved to other federal agencies.

Those federal dollars account for only about 10 percent of K-12 school funding nationwide. While Mr. Trump has said he wants to return power over education to the states, states and school districts already control K-12 education, which is mostly paid for with state and local tax dollars. The federal department does not control local learning standards or reading lists.