The new president of the National Education Association, showing an emphasis different from that of her predecessors, yesterday stressed the importance of high academic standards and firm discipline to improve achievement in American schools.

Mary Hatwood Futrell, a business teacher from Alexandria, told a press conference that one of the "mistakes" schools made over the past two decades "was to lower the standards, especially for minority kids" in an effort to expand educational opportunity.

"What we should have done is raise the students to meet the standards," declared Futrell, who is black and taught in both segregated and integrated schools.

Over the past decade NEA has strongly criticized standardized achievement tests for students and minimum competency exams for high school graduation. It also has given more emphasis to fairness in discipline than to firmness.

Those positions put it at odds with a trend toward stiffer standards in schools nationwide, which has been strongly backed by NEA's rival, the American Federation of Teachers, and, in recent months, by the Reagan administration.

Yesterday Futrell said she supported standardized tests as long as teachers were involved in selecting them and students were taught the material they cover. She said this was the case with most of the achievement tests and minimum competency exams now in use.

On discipline, she said, "I was a no-nonsense teacher. I suppose some of the kids thought I was mean, but they come back to me and say they really learned something . . . . Now I think there is a tightening up on discipline and attendance around the country. We want principals and administrators to give us their support."

Futrell said NEA's positions were changing "as the situations have been changing in the schools." She said her own views reflect policy statements adopted over the past few years, but added: "I'm saying it in a more positive way."

In a major shakeup in its leadership, NEA also has a new executive director, Don Cameron, replacing Terry Herndon, who resigned in June after 10 years in the post. Herndon had led NEA into heavy involvement in national politics.

Futrell said the NEA planned to endorse a presidential candidate again, but she had conciliatory words about President Reagan and said her organization "will be putting education issues back up front."

Futrell also urged teachers to give more homework and said she opposed "social promotions" for students "who cannot really read, write, or calculate."