The president of the National Education Association, the nation's largest teachers' union, opened the group's convention here yesterday by declaring that she will be "pulling out all the stops" to defeat parts of President Reagan's tax plan, which she said will undermine the funding of public education in America.

In a press conference, Mary Hatwood Futrell, president of the 1.7 million-member NEA, also announced a plan to collect $1.7 million to fight illiteracy and the dropout problem. She said she would push NEA delegates to support "the toughest possible standards" for teachers and expressed support for yearly teacher evaluations, but not the kind of standardized test recently given to teachers in Arkansas.

Futrell's main points yesterday were:

*Announcement of a plan to set aside $1 from each NEA member's dues -- for a total of $1.7 million -- to go into a special endowment to combat the twin problems of dropouts and illiteracy. Futrell said she can do this without a formal vote of the assembly, but will seek delegates' approval.

* Declaration of a strong teacher-training plan. She advocated a tougher program for potential teachers, urging that candidates complete two years' of liberal arts education, pass an entrance exam to a teachers'college, maintain a 2.5 grade-point average, and serve an induction period of at least three years before becoming fully certified.

She repeated her call for a national exam for teaching graduates to test their subject matter and professional skills before they are certified.

On the issue of tax reform and educational funding, Futrell said the Reagan plan to eliminate the federal deduction for state and local taxes "would undermine financing for public education."

The White House considers the elimination of that deduction to be an essential feature of the administration's tax plan, because it would raise as much as $40 billion by 1990 -- enough to offset the cost of lowering tax rates for individuals. But a coalition of labor unions and local officials say the elimination of that deduction would weaken local tax bases and make it more difficult to fund public services.

Futrell's opposition adds the NEA's powerful lobbying machinery to the coalition already opposing that part of the Reagan plan. She said the union's 8,000 delegates will write to Congress this week and next, while local affiliates run telephone banks to lobby against it.

Futrell said she will make a formal call for tougher teacher-education standards when she gives her keynote remarks Sunday to the teacher-delegates at the Washington Convention Center. How the delegates respond could significantly affect the debate over educational reform in America.

Futrell's pitch for tougher standards for teacher colleges is partly an effort to deflect the growing national sentiment that current teachers be tested for minimum competency. As the national call for educational reform has found its echo in state capitals around the country, the push for better performance from schools has often taken an anti-teacher tone.

Arkansas became the first state to subject its practicing teachers to a competency test; Georgia and Texas have passed bills to test teachers.

The NEA and its state affiliates have traditionally opposed standardized tests for teachers as well as students. Futrell said yesterday that the union's longstanding opposition was based on how such tests historically have discriminated against minorities. But the NEA's position against testing current teachers put the union in opposition to one of the most popular elements of educational-reform packages. To blunt criticism on this point, Futrell repeatedly called for tougher standards while opposing the Arkansas test and others like it.