Florida plans to seek a waiver from several fundamental portions of the Every Student Succeeds Act that dictate how schools handle some of the country's most historically underperforming and disadvantaged students.

But the draft request, which seeks to mostly keep intact a state school accountability system that predates the new federal K-12 law, already has inflamed civil rights advocates, and could prove an early test of how the U.S. Department of Education intends to weigh states' bids...