The U.S. Department of Education (ED) was originally created in 1867 and for many years remained a relatively minor agency of the federal government. President Jimmy Carter elevated that department to cabinet-level status with the Department of Education Organization Act in 1979, which divided the existing Department of Health, Education, and Welfare into the Department of Education and the Department of Health and Human Services.
President Carter's action in creating the ED was opposed by many Republicans at the time, who argued that the Constitution did not grant the federal government regulatory authority over education and that Washington would be creating yet another costly bureaucracy to usurp authority better exercised at the local level. Over the ensuing decades, various conservative politicians have advocated cutting or entirely eliminating the ED, but a political alliance of Democrats and teacher's unions has so far been able to keep the department intact.
Republican Presidential candidate Donald Trump's comments about education reform during the 2016 presidential campaign have so far been broad and non-specific. From the start of his campaign he announced opposition to the Common Core State Initiatives Standard, saying that Common Core is a "very bad thing" and a "disaster," one of the programs that "take decisions away from parents and local school boards" and "allow the progressives in the Department of Education to indoctrinate, not educate, our kids."
(The Common Core's Myths vs. Facts web page notes that "Common Core is a state‐led effort that is not part of No Child Left Behind or any other federal initiative. The federal government played no role in the development of the Common Core. State adoption of the standards is in no way mandatory.")
Likewise, Trump has on several occasions during the campaign suggested that the Department of Education should either be eliminated entirely or drastically curtailed in size and scope. His 2015 policy book Crippled America states that "A lot of people believe the Department of Education should just be eliminated. Get rid of it. If we don't eliminate it completely, we certainly need to cut its power and reach. Education has to be run locally."
As well, on the campaign trail Trump has at various times said that "You could cut [the ED] way, way, way down," that "I may cut Department of Education," and that "The Department of Education is massive, and it can be largely eliminated." At one of the Republican presidential debates, he asserted: "Education through Washington, DC, I don't want that. I want local education. I want the parents, and I want all of the teachers, and I want everybody to get together around a school and to make education great."
Based on these general statements of Trump's the Center for American Progress Action Fund (CAPAF), a progressive public policy research and advocacy organization (elsewhere termed a "liberal think tank"), performed an analysis of what the potential effects of eliminating the Department of Education could be. That analysis stated (among other things) that "over 490,000 teacher positions could be eliminated":
Using official budget figures from the Department of Education, CAPAF’s full analysis shows just how far reaching the impact of Trump’s proposals could be on students, teachers, and families. Our analysis examined the largest programs that the agency runs in order to demonstrate what their elimination would mean for the country and for each state. Nationally, according to that analysis:
o 8 million students every year would lose Pell grants
o 490,000 or more teacher positions could be eliminated
o $1.3 trillion in student loans would be at risk
o 9 million low-income students would lose $15 billion of Title I funding annually
o 5 million children and students with disabilities would lose $12.7 billion used every year to ensure that they receive a quality education
o 750,000 or more students from military families, Native American students, students living in U.S. territories, and students living on federal property or Native American lands would lose $1.1 billion per year for their schools
0 4,000 or more rural school districts would lose more than $175 million used annually to help improve the quality of teaching and learning in many hard-to-staff schools
0 $700 million used by states to support the 5 million English language learners currently in public schools — representing close to 10 percent of all students — would be cut
CAPAF's 490,000 figure has now been transformed into a definitive claim by Trump's opponents that the GOP candidate plans to cut nearly half a million teaching jobs. However, like all such analyses, CAPAF's figures constitute a single group's estimates based on current conditions and assumptions about what "could be," and they should therefore be considered in that light.
CAPAF assumes Trump would completely do away with the Department of Education, or at the very least eliminate all of the "largest programs that the agency runs," but Donald Trump hasn't yet articulated his plans for education in sufficient detail for anyone to really know what he plans to do in that regard. The CAPAF analysis also assumes that all of the referenced education-related programs and federal funding would be completely eradicated and not implemented or financed in any other way, something that is difficult to estimate without knowing (and knowing the effects of) what Trump's comprehensive economic and educational plans might be.
Trump's expressing an interest in K-12 public education being locally run, for example, doesn't mean he necessarily seeks to eliminate loans and grants for college students, or expects that the U.S. education system can get along just fine with 490,000 fewer teachers. In Crippled America, for instance, he not only supported the idea of federal student loans but argued that such loans should be made less costly for borrowers:
A four-year degree today can be expensive enough to create six-figure debt. We can't forgive these loans, but we should take steps to help students.
The big problem is the federal government. There is no reason the federal government should profit from student loans. This only makes an already difficult problem worse. The Federal Student Loan Program turned a $41.3 billion profit in 2013.
These student loans are probably one of the only things that the government shouldn't make money from, and yet it does. And do you think this has anything to do with why schools continue to raise their tuition every year? Those loans should be viewed as an investment in America's future.
Finally, that a candidate expresses a particular stance on an issue doesn't mean he can or will be able to implement that position once in office, as CAPAF themselves noted:
Calls to abolish the Department of Education have been made a number of times over the years in the name of both reducing the size of government and fiscal restraint. But, perhaps there is no example more informative to highlight the misguided shortsightedness of such calls than former President Ronald Regan’s attempt — and subsequent reversal — to take an axe to the Department of Education in the early 1980s. During Reagan’s first presidential campaign — and later in his very first State of the Union Address — he called for the abolishment of the U.S. Department of Education. At the time, he and others claimed such a move would be the source of “major savings,” further stating that the department’s existence was a classic case of federal overreach. However, during his time in office, Reagan’s position evolved to the point where he helped broker a deal in 1985 to keep the department, and, during his final year in office, he would propose what were — at the time — record increases to its budget.
Whatever ideas Donald Trump might espouse on the campaign trail, it's exceedingly unlikely that, were he to gain the White House, he could muster nearly enough political or public support to enact a policy that would strip America's educational system of upwards of half a million teachers.