The mixed feelings reflect deep and widespread anxiety among parents as they approach the end of a summer break that has produced no national consensus on how to balance the risks of the virus against the academic, social and economic impacts of keeping schools closed.

Given three options for the fall, a plurality of parents — 44 percent — want their schools to offer a mix of online and in-person classes, an idea that has been considered by many school districts and adopted by some. In a close second place is all-virtual education, favored by 39 percent of parents.

Fully in-person school, the approach pushed by President Trump and his allies in Congress, comes in a distant third, with 16 percent favoring it for their children. A separate question finds that two-thirds of parents oppose requiring all public schools to open for in-person classes five days a week, with one-third supporting it.