Speaking in a subdued, almost hushed tone, Mr. Trump also devoted some time to attacking Mrs. Clinton’s vote as a senator to support the invasion of Iraq, and to defending his own frequent assertions that he had always opposed the Iraq War, despite comments he made in 2002 to Howard Stern in support of the invasion.

Returning to education, Mr. Trump echoed a common Republican refrain about the importance of school choice, saying students should be able to attend a magnet school, a charter school, or a public or a private school.

Mr. Trump’s previous comments on education had been scant and were usually tossed off: American schools were no better than those in a developing country, he has said, and Common Core standards are a “disaster.”

On Thursday, adding a bit of policy meat to this rhetorical skeleton, Mr. Trump said the $20 billion in grants for poor students would come from existing federal spending.

Rather than sending federal education dollars to schools, as the existing system does, Mr. Trump proposed giving block grants to states, which would have the option of letting the dollars follow students to whichever school they choose, including a charter, private or online school.

Funding schools this way, known in education circles as portability, is popular with Republicans as a way to broaden school choice. More choice, reformers believe, introduces competition to the marketplace of schools and raises student learning.