The Trump Administration says it hopes to return education authority to individual states, arguing it will help students in the long run.
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Critics argue the move will gut public education funding.
The Department of Education is responsible for enforcing laws against discrimination, providing funding for low-income students and special education and overseeing college financial aid.
The President said certain functions would be transferred to other federal agencies, but he did not specify which ones.
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Republican Congressman David Valadao released a statement, saying in part, "I'll keep working to make education more affordable and ensure vital programs, including Title 1 funding, TRIO, Pell Grants, and resources for children with disabilities, continue to support our schools and equip our students with the tools they need to succeed."
Democratic Congressman Jim Costa also released a statement, saying in part, "This reckless executive order threatens vital K-12 funding, financial aid for college students, and protections for students with disabilities and special needs. The Constitution is clear: the President cannot abolish a department created by Congress."
The Education Secretary says that the full dismantling of the Department of Education will require action by Congress.
Republicans have said they will introduce a bill to achieve the President's vision.