Such results have spooked teachers watching from afar, particularly as more states are moving to evaluate teachers in part on student test scores.

“Looking at the types of questions on these tests, I’m scared for my kids,” said Lisa Mims, a fifth-grade teacher at Pleasantville Elementary School in New Castle, Del. “It just seems to me that it’s what they’re asking us to do in such a little bit of time, and then saying we’re going to test this.”

In an interview, Mr. Duncan acknowledged that the transition would be difficult. “It’s easier to keep saying everything’s looking great,” he said. “Potemkin village, whitewash the walls. That’s the easy way to do it, but I’m not quite sure that changes kids’ lives or helps our country remain competitive economically.”

According to a report from the Center on Education Policy at George Washington University, teachers in 30 states are already teaching some lessons based on the standards. But only 10 states reported that more than three-quarters of teachers had received any Common Core training in the most recent school year.

Supporters of the new standards say critics are too impatient.

“It’s going to take time, and it’s going to take a lot of work,” said David Driscoll, former commissioner of education in Massachusetts, which raised its own standards in the late 1990s and faced a falloff in state test scores before seeing them steadily climb. Today, Massachusetts leads the country in scores on exams administered by the federal Department of Education and ranks close to some countries frequently cited as world leaders in academic performance.

Several states have conducted teacher training as well as public outreach. In Tennessee, state education officials offered sessions to about 30,000 teachers this summer, and in Delaware, Mark Murphy, the secretary of education, said that school districts would be hosting “back to school” nights where legislators can “take part in a Common Core lesson to see and experience the type of learning that the students will be getting.”

Some critics say the new standards are simply unrealistic. “We’re using a very inappropriate standard that’s way too high,” said Diane Ravitch, an education historian who served in President George W. Bush’s Education Department but has since become an outspoken critic of many education initiatives. “I think there are a lot of kids who are being told that if they don’t go to college that it will ruin their life,” she said. “But maybe they don’t need to go to college.”