Most US children attend public schools, which are free and run by local officials.
A common misconception is that the federal education department operates US schools and sets curriculum, but that is primarily done by states and local districts.
A relatively small percentage of funding for primary and secondary schools - about 13% - comes from federal funds. Most of the money comes from state and local taxes.
Established in 1979, the department administers student loans and runs programmes to help low-income students.
But Trump has accused it of indoctrinating young people with racial, sexual, and political material.
Surrounded by children seated at school desks in the White House on Thursday, Trump said "the US spends more money on education by far than any other country", yet he added that students rank near the bottom of the list.
The Unesco Institute for Statistics said the US spends roughly 5.4% of its GDP on education, which is higher than many countries but not all.
The department's budget last year was $238bn (£188bn), which is less than 2% of federal spending.
The White House stated that his administration would move to cut parts of the department that remain within legal boundaries.
The executive order is likely to face legal challenges, like many of the Trump administration's efforts to shrink the size of the federal government.
At the signing ceremony, Trump praised Linda McMahon, whom he appointed to lead the department, and expressed his hope she would be the last secretary of education.
He said he would find "something else" for her to do within the administration.
After Trump signed the order, Louisiana Republican Senator Bill Cassidy announced plans to bring legislation aimed at closing the department.
But Republicans hold a slim 53-47 majority in the Senate, and closing a federal department would require 60 votes, making such a goal a longshot.
But even if the department is not formally closed, the Trump administration could decimate its funding and staff as it has done with the US Agency for International Development (USAID), which subsequently stopped many of its programmes and humanitarian work.
The text of the executive order does not include specifics on what actions the administration will take and which programmes might be axed.
It orders McMahon to "take all necessary steps to facilitate the closure" of the department and give authority of such matters to state and local governments.
It also directs her to ensure "the effective and uninterrupted delivery of services, programs, and benefits on which Americans rely".