The survey shows that during the 2020-2021 school year, shortages of key school staff were common — a problem that has continued even after the height of the pandemic.

In the 2020-2021 year, more than a quarter of schools employed uncertified teachers and 24 percent had no counselors.

And of the nation’s 49 million public school students, nearly 1.7 million attended a school with a police officer or security guard but no school counselor, a statistic that Miguel Cardona, the U.S. secretary of education, highlighted on Wednesday. Black, Native American and multiracial students were more likely than white students to attend these schools.

The pandemic amplified the need for highly qualified teachers and health professionals in schools. Students emerged from the lockdown era academically behind and with high rates of anxiety and other mental health challenges.

In the 2020-2021 school year, discipline rates fell. But federal officials cautioned that these figures should not be compared with previous data, because physical school buildings were, in large part, partially or fully closed.

Even so, tough discipline and disparities by race did not disappear, even at the youngest ages.

Nearly 1,000 preschool students were suspended. Though Black children make up 17 percent of the pre-K population, they accounted for 31 percent of those who received out-of-school suspensions.

There were also significant racial disparities in access to advanced coursework, a priority for the Biden administration.

High schools with high enrollments of Black and Latino students were less likely than other high schools to offer calculus and computer science.

And 39 percent of all public middle schools did not offer algebra, which can prevent students from accessing advanced math in later grades.

“We spent years fighting Covid,” Mr. Cardona said. “Now we must fight complacency.”

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