Education Secretary William J. Bennett, saying that the typical secondary school curriculum is inadequate and incoherent, yesterday urged American high schools to adopt a rigorous course of study that requires more basic academic subjects and allows fewer electives.

Bennett said 15 percent of the nation's 12 million high school students are receiving what he considers an appropriate curriculum: four years of English; three years each of social studies, mathematics and science; two years each of foreign language and physical education/health and one year of fine arts.

Students should be required to master these basic courses, even if it takes five or six years of high school, Bennett said. Under his proposal, about a quarter of the schedule would remain free for electives.

"There's so much academic clutter, so many electives," Bennett said, "sometimes the core curriculum gets lost . . . . You have to guide kids toward the real stuff."

Bennett's recommendations -- he is prohibited by federal law from establishing a national curriculum -- represent the first effort by the Education Department to specify in detail what students should be learning. The report, outlining the ideal curriculum at a mythical "James Madison High School," not only suggests which courses should be offered but also what the courses should contain.

"It says our children should know about continental shift and quadratic equations, about Gothic architecture and the Gettysburg Address, about what a symphony is and about who Shakespeare was and what he wrote," Bennett said at a news conference.

The report, published as a booklet by the Education Department, follows by four years a highly publicized study, "A Nation at Risk," that was a scathing critique of U.S. education. According to that document, "secondary school curricula have been homogenized, diluted and diffused to the point that they no longer have a central purpose. In effect, we have a cafeteria-style curriculum in which the appetizers and desserts can easily be mistaken for the main courses."

In a movement away from the less structured curriculum that was popular in the 1960s and 1970s, "A Nation at Risk" recommended that students take four years of English and three years each of social studies, mathematics and science. Bennett said that since 1983, nearly all states have taken steps to require these courses. But the curriculum studied by most American students, he said, still falls far short of the ideal.

To support his criticism of American schools, Bennett cited several statistics in the new report: Only about 5 percent of American 17-year-olds have advanced reading skills; the average high school student takes only 1.4 years of history; American 18-year-olds finished last when competing in mathematics against students from nine other nations.

Bennett named several high schools with model curricula -- such as A. Philip Randolph Campus in New York City, James A. Garfield in Los Angeles and CAL in Latimer, Iowa -- saying the common element is the schools' high expectations for all students, regardless of economic or racial background. "What characterizes these schools is not carelessness or apathy but a real sense of activity and conviction," he said.

Education groups supported Bennett's call for a core curriculum, but offered some criticism. The Association for Supervision and Curriculum Development said the recommendations could exacerbate the dropout problem because they do not meet the needs of students who are likely to fail in school.

Other groups said the report relies too heavily on Western civilization and does not go far enough in suggesting how students can be motivated.

"It would be shortsighted to believe that by simply adding new courses, or requiring that students take them, achievement will increase," said Scott D. Thomson, executive director of the National Association of Secondary School Principals.