Retired Adm. Hyman G. Rickover, long known for his dim view of American education, today offered Virginia officials a stringent, if somewhat unorthodox, prescription for improving the state's schools:

Television sets should be smashed.

High school sports programs should be abolished.

Parents who fail to teach their children should be jailed.

"Drag them parents up before the court if they don't educate their children properly," barked the 83-year-old admiral to Margaret Marston, a member of the state Board of Education.

His ideas on television--offered to the board today in a colorful 20-minute dissertation--were equally draconian. Television, he said, has become a "plug-in drug" that was distracting youths from the serious business of expanding their minds.

"My advice on the television issue is, take a hammer in your right hand, if you're right-handed, or in your left hand, if you're left-handed, and swing it at the damn thing," Rickover said.

Students, the admiral said, should be in class longer.

"Keep them there," he said, "they'll be better off . . . than with their lousy parents."

Board members seemed bemused but generally approving. "I agree with everything he said," said board President Thomas R. Watkins of Hampton.

Spurred in part by a recent national commission that found a "rising tide of mediocrity" in the public schools, the board is expected to vote Friday on a controversial set of proposals for more rigorous academic standards in Virginia high schools.

Although he principally is known as the architect of the nuclear Navy and for his acerbic tongue-lashings of naval officers, Rickover has been speaking out for years on education.

Marston, who served on the national commission, said she was at her home in Arlington last month when Rickover, who lives in Alexandria, "called me up out of the blue.

" 'Are you the Marston lady on the national commission?' " Marston said Rickover asked her.

When Marston told him she was, the admiral replied: "Well, let's get going on this. I'll do anything I can."

Shortly thereafter, Rickover, who was forced to retire last year, accepted Marston's invitation to address the state board. He showed up today with Joann DiGennaro, executive director of the newly created Admiral Rickover Foundation in McLean, and quickly began tangling with Gov. Charles S. Robb over lunch at the Executive Mansion.

"They were arguing like cats and dogs," said Watkins. "They were needling each other."

At one point, Watkins said, Robb, who served in the Marine Corps, disputed Rickover on a matter relating to the teaching of Navy engineers. Rickover fired back at Robb: "What school did you go to, to learn to be governor?" Watkins said.

When the luncheon was finished, Rickover strolled to the General Assembly building where a crowd of legislators, reporters, and state officials had assembled for the Board of Education's meeting.

Rickover did not disappoint them, delivering a historical treatise on the roots of the country's educational problems, quoting from a medieval Russian work called "The Emerald," a 15th century papal charter, Thomas Huxley, the Talmud, and Davey Crockett.

The admiral also stirred a bit of controversy, lashing out at the National Education Association (NEA) for a recently devised curriculum on nuclear conflict. "In an era when our youth are increasingly found deficient in basic subject matter," Rickover said, "it is not comforting to know that our tax dollars are being spent instead to teach kindergartners about nuclear warfare."

"He's totally off base," replied NEA spokesman Lin Stafford, when asked for comment. The curriculum, entitled "Choices: A Unit on Conflict and Nuclear War," was proposed for junior high school--not kindergarten--and "tax dollars have nothing to do with it," he said.

Many of Rickover's other education proposals were more in the mainstream. Saying poor student performance was a product of "mediocre teachers" and useless school electives, he called for more mathematics and science courses, tougher standards and higher teacher pay.

High school football and basketball programs, Rickover said later, might as well be abolished. "After you've seen one football game, you've seen them all," he said.

By the time Rickover was through, Marston was so excited she dashed over and asked if she could have her picture taken with him. Rickover, however, was more disturbed by the pack of reporters that surrounded them. He would agree to the picture, he said, "if you'll get these plebeians out of the way."