THOUGH AMERICAN colleges and universities retain their reputation as the best in the world, some representatives of higher education have begun to sound like off-campus critics who argue that many college graduates don't know enough of the right stuff. There is uneasiness, especially among presidents and administrators of large universities, that their central mission of educating undergraduates has suffered too long from neglect because of the higher priority placed on faculty research. In a spirit of self-criticism, these college officials are pondering tough questions about what is being taught, how well and by whom; what undergraduates ought to know; and how best to guide students through voluminous course offerings so that they get an education that is both broad and deep.

Statistical evidence of academic problems is limited, and there is considerable disagreement about how to measure the results of higher education. Nonetheless, college administrators have been moved to ask these questions because of their own impressions and observations of student trends on campus.

The few concrete pieces of evidence that there may be something lacking in American higher education include a 1989 Gallup survey done for the National Endowment for the Humanities. The survey showed serious deficiencies in what college seniors know about literature and history. For example, almost a quarter of college seniors surveyed did not know when Columbus landed in the Americas and thought that a Karl Marx quote was from the U.S. Constitution. In addition, a 1989 study of transcripts at 30 selected public and private institutions showed most graduates received neither broad exposure to mathematics and science nor in-depth instruction in the humanities.

So far most campus debates about improving undergraduate education have been conducted without dire words of crisis. Few believe that America's colleges have slipped as far as its public elementary and secondary schools, which once were also considered the world's best. Leaders of various institutions have moved to address the academic problems in the slow, deliberate pace of higher education -- making speeches, appointing faculty committees and studying their recommendations.

The proposed solutions, already implemented on some campuses, have focused on curriculum, academic advising and teaching. Changes in curriculum include requiring all students to take the common courses of a "core curriculum" or tightening general education requirements. Some schools are hiring professional counselors or students as advisers. And attempts are being made to get senior faculty members to teach more undergraduates and better prepare graduate students to be teaching assistants.

Those efforts notwithstanding, the underlying source of the concern about undergraduate education remains unresolved. The conflict between research and teaching endures at four-year colleges, with the exception of small liberal arts colleges that have always concentrated on teaching undergraduates. In a 1985 report, the Association of American Colleges described the prevailing attitude in this way: "Professors speak of teaching loads and research opportunities, never the reverse."

Last April, Donald Kennedy, president of Stanford University, talked bluntly about some academic issues that have been worrying college administrators. Kennedy's critical remarks drew attention because they focused on the state of undergradute study at Stanford, one of the country's foremost private universities.

"There is a suspicion that we have lost focus in designing and delivering a well-planned, challenging and inspiring education to our undergraduates," Kennedy told a faculty council. First among the "troubling" signs that Kennedy cited was professors' teaching fewer courses in order to have more time for research.

"The result is that too many of Stanford's courses are taught by visitors or temporary faculty members," he said. ". . . Junior faculty members who show outstanding teaching ability fail at the tenure line too often, to the dismay of students who understandably wonder about Stanford's values."

Kennedy said the university needs "to talk about teaching more, respect and reward those who do it well, and make it first among our labors." He announced that he and other administrators would also seek ways of "reducing the competitive dichotomy between research and teaching."

Another prominent university president, Howard T. Shapiro of Princeton, disputes that such a conflict exists but nonetheless sees the increasing specialization of faculty research as posing a problem in instruction.

"Countless distinguished researchers are devoted to teaching and do a marvelous job of transmitting the knowledge of their discipline," Shapiro said last fall. "The problem is they are transmitting what they know -- and love -- with little awareness of what the student needs to learn."

A similar conclusion was reached by a study group drawn from several colleges, cochaired by education consultant Ursula Wagener and Mary Patterson McPherson, president of Bryn Mawr College. "With the increasing specialization of knowledge in all fields, the gap between teaching and research appears to be growing, making it even harder to shape teaching as an extension of one's scholarship," reported the study group, part of the Pew Higher Education Research Program in Philadelphia.

Like Kennedy, the group recommended that colleges "value and reward teaching for its own sake."

Hearing that kind of self-criticism from college officials pleases Lynne V. Cheney, chairwoman of the National Endowment for the Humanities. She was among early critics, mostly outside academia, who questioned how much undergraduates were learning and whether they knew enough about traditional Western culture.

"When you get insiders talking like that, it's getting to be a crisis," Cheney said. "Solving this is going to be very, very difficult. It's a systemic problem . . . Everyone wants to be a research university, and that's the peak of {academic} prestige."

Asked to identify a research university that truly values and rewards good teaching, Cheney paused and then admitted: "I'm struggling to think of one." ONE COLLEGE THAT has been touting itself as fitting that description is Rice University in Houston. Dennis Huston, who teaches English there, was named professor of the year in 1989-90 by the Carnegie Foundation for the Advancement of Teaching and the Council for the Advancement and Support of Education. A senior faculty member with 20 years at Rice, Huston still teaches freshman English courses, and college officials say it is common for tenured professors like him to handle courses taken by freshmen and sophomores.

"You can actually count on one hand the number of graduate students who teach classes," said William Noblitt, Rice's director of university relations.

At Indiana University, graduate-student instructors of mathematics were replaced with full-time faculty members in 1988. Now all undergraduate math courses, with the exception of remedial classes, are taught by regular faculty members. The changeover required about 15 additional professors and was prompted by student reports of difficulty understanding the accented English of foreign graduate students. Nearly all of Indiana's 35,000 undergraduates are required to take math.

"We may be the only large public university that does all its calculus with regular faculty," said Morton Lowengrub, Indiana's dean of arts and sciences. "It was not difficult to persuade faculty to do this. We have a math crisis in this country."

Other institutions are trying to prepare graduate students better for teaching responsibilities. Harvard's math department, for instance, has an apprenticeship program that pairs each doctoral candidate with an experienced professor who acts as a teaching coach. At the University of Chicago, graduate students in the humanities and social sciences attend weekly workshops where professors discuss teaching issues.

There has been scattered adoption of a "core curriculum," which Cheney and other outside critics advocate. Finn, now an education professor at Vanderbilt University, has called most colleges a "curricular smorgasbord" that "just serve everything and let the students decide what to consume."

While many college officials find the critics' proposed core curriculums too narrow and proscriptive, there is greater acceptance of the charge that course offerings have become confusingly broad. Alternate methods of guiding undergraduates through the course catalog are being explored.

Curricular sprawl can be a problem even at a small liberal arts college like Wesleyan University, which has fewer than 3,000 students. In his inaugural address last fall, president William Chace called the 1,000 courses that Wesleyan offers "a celebration of our intellectual enthusiasm" but "also a glorious way of distracting ourselves from the duty we have, particularly to freshmen, of disclosing . . . what do we know that is essential, what is unmistakably central to the beginning life of an educated person?"

After studying the transcripts of graduates of 30 colleges of various sizes, Robert Zemsky, director of the Institute for Research on Higher Education, last year concluded that "there is a notable absence of structure and coherence in college and university curricula." Zemsky's study, done for the Association of American Colleges, which promotes the liberal arts, reviewed what courses students actually took -- not which were offered.

Zemsky found that "generally experience in the domain of natural sciences and mathematics was lacking" and "the humanities curriculum largely lacked the kind of depth of study conveyed through prerequisites."

At Wesleyan, a faculty committee is studying how to give the freshman curriculum more focus so that, for instance, fewer escape science courses. Stanford's Kennedy is considering "how to improve vital non-classroom types of teaching, like advising." WASHINGTON UNIVERSITY in St. Louis and University of the Pacific in Stockton, Calif., have modified the traditional system of faculty advisers, which students have frequently criticized because professors are said to be often unavailable and tend to take little interest in advising.

At Washington business school, three full-time counselors advise undergraduates, refering detailed questions about courses to professors as needed. Pacific assigns both a professor and a paid upperclassman to advise each freshman or transfer student.

Bill Stott, president of Ripon College in Wisconsin and a former dean of students at Georgetown, believes that advisors have an important role in addition to helping 18-year-old students figure out which courses to take. Good advisors can help students feel connected to big, impersonal institutions and engaged in their own learning.

"What I think has been lost sight of at many colleges and universities is learning is affective as well as cognitive . . . Our institutions have become providers of services to a passive constituency," Stott said. "We have to restore that sense of personal involvement on the part of the student. I think we in the liberal arts colleges do that pretty well."

Kenneth J. Cooper covers education for the National Desk of The Washington Post.