Children learn more in school when parents read to them, share hobbies and discuss current events at home, according to a Reagan administration report on education.

The report, "What Works," is a follow-up to the widely read 1983 report "A Nation at Risk," on the problems of America's schools, which began an education reform movement. The new study, to be unveiled at a White House ceremony next week, offers some "common sense" prescriptions for the problems outlined in the 1983 report.

Unlike the earlier report, which was aimed at education researchers and policy-makers, this one is written primarily for parents, teachers and members of school boards.

The report emphasizes the importance of the home in education, and follows a Reagan administration philosophy of reduced federal government involvement in schools. It also asserts that "what parents do to help their children learn is more important to academic success than how well-off the family is."

"Parents can do many things at home to help their children succeed in school," it said. "Unfortunately, recent evidence indicates that many parents are doing much less than they might . . . . American mothers, on average, spend less than half an hour a day talking, explaining, or reading with their children. Fathers spend less than 15 minutes."

Much of the report draws on previous research. Its conclusion that children read more when they are read to by parents at an early age was the basic finding last year of another education study, "Becoming a Nation of Readers."

Chester E. Finn Jr., assistant secretary for educational research and improvement, said yesterday: "A lot of it looks common-sensical . . . . But ordinary people often don't feel secure in their common sense unless the experts say the same thing. This buttresses common sense."

Despite the report's "back-to-basics" tone, some findings indirectly refute the Japanese-style method of rote memorization that has been mentioned favorably by some educators. The report said, for example, that children learn science best when it is accompanied by hands-on experimentation and does not come not exclusively from a teacher lecturing from a textbook.