The number of New York students passing state reading and math exams dropped drastically this year, education officials reported on Wednesday, unsettling parents, principals and teachers and posing new challenges to a national effort to toughen academic standards.

In New York City, 26 percent of students in third through eighth grade passed the tests in English, and 30 percent passed in math, according to the New York State Education Department.

The exams were some of the first in the nation to be aligned with a more rigorous set of standards known as the Common Core, which emphasize deep analysis and creative problem-solving over short answers and memorization. Last year, under an easier test, 47 percent of city students passed in English, and 60 percent in math.

City and state officials spent months trying to steel the public for the grim figures.

But when the results were released, many educators responded with shock that their students measured up so poorly against the new yardsticks of achievement.