President Reagan said yesterday that the nation's colleges have gained far more from the economic recovery than they will ever lose in budget cuts, and called on educators to give children "a picture of America that is balanced and full" by teaching good things about the country as well as bad.

In a speech that ranged over some of the touchiest issues in American education, Reagan declared, "We cannot allow our curricula to be determined by narrow interest groups."

Children should learn that air and water pollution have decreased, he said, and "our children should know that, because Americans abhor discrimination, the number of black families living in our suburbs has grown more than three times the rate of white families living in the suburbs, and that, between 1960 and 1982, the number of black Americans in our colleges more than quadrupled."

Reagan said the economic recovery has produced the largest one-year increase in 17 years in the value of college endowments, to $29.6 billion in 1983. He also said that, thanks to the decline in inflation, the purchasing power of total U.S. spending on education has increased $18 billion during his administration even with cuts in federal aid. During the Carter administration, he said, when inflation reached double-digit levels, this purchasing power decreased $17 billion.

Addressing the National Association of Independent Schools, Reagan also defended his budget proposals to cut college student aid. Education Secretary William J. Bennett fueled the fight over that issue two weeks ago when he acknowledged that the cuts might be a hardship for some families, but said they might simply force some students to give up cars, stereos and vacations.

Reagan said the cuts are tilted so the neediest would not suffer. He called the trims "prudent, reasonable and just." He opened his speech with several humorous asides to the combative new education secretary, calling him "an authority on rock 'n' roll" and chiding him for "mincing your words" in interviews.

In other remarks the president:

* Decried a "learning gap" between students in this country and in the Soviet Union, where he said children are taught algebra and geometry in elementary school. He called for a back-to-basics curriculum.

* Called for a return to "discipline" in classrooms, saying, "There's no need to call in a grand jury every time a principal needs to check a student locker." He said he was instructing Bennett and Attorney General Edwin Meese III to review federal laws and suggest changes that might help state and local school officials "maintain effective discipline."

* Renewed his call for tuition tax credits and educational vouchers as two proposals to "expand parental choice" and "foster greater diversity" in the education system.

Reagan's speech was aimed partly at quelling the brushfire of criticism over administration proposals to cut student college aid by about 25 percent while knocking an estimated 1 million students off the federal aid rolls. That plan has been attacked by the higher education community and by both parties on Capitol Hill, and yesterday appeared headed for drastic revision.

Shortly after Reagan's speech, Sen. Robert T. Stafford (R-Vt.), chairman of the Senate Education subcommittee, told a separate conference of trade and technical schools that Senate Republican leaders are weighing an alternative "freeze" in spending on all education programs, with a modest 7 percent reduction in student loan funds that could be achieved mostly through administrative changes.

Earlier yesterday, Bennett came under sharp criticism from the House Committee on Education and Labor. Bennett told the panel that the loan program had provided "a windfall" for many banks while many students were falsely calling themselves independent of their parents to qualify for loans.

Reagan picked up on that theme in his speech. "In our proposal," he said, "we have recommended reserving aid for the needy, limiting aid per student to a level we can afford, closing loopholes that lead to abuse and error, and cutting excessive subsidies to banks and others."

Reagan criticized the current system, which he said gives federal aid to some students from families earning more than $100,000 a year. "This defies common sense, insults simple justice and must stop," Reagan said.

Reagan's proposals include an income ceiling of $32,500 a year for access to the popular guaranteed student loan program. Critics have said that limit would result in a "redistribution" of students from more expensive private colleges into public universities.

Reagan did not address the issue of whether his programs would deny students the choice of attending a more expensive private college. But he did advocate choice on the elementary and secondary level by making a strong push for tuition tax credits.

"Parents should have greater freedom to send their children to the schools they desire," he said, "and to do so without interference by local, state or federal levels of government."

Later, John C. Esty, president of the National Association of Independent Schools (NAIS), said he is concerned that the Reagan budget cuts might hurt independent schools.

"Parents who have made considerable sacrifices to send children to NAIS schools may not be able to in the future because they may have to defer any educational expenditures until the college level," he said. "And we are especially concerned that the years of progress in increasing low income and minority enrollment in NAIS schools could be reversed."