"Parents are their children's first and most influential teachers," concludes the U.S. Department of Education in a new report.

"What parents do to help their children learn is more important to academic success than how well off the family is."

The report, What Works: Research About Teaching and Learning, hailed by President Reagan yesterday, does much more than pat parents on the back. Its 65 pages, uncluttered by jargon, provides a guide for parents to help thei1914708067and assess the schools, based on the most current research on teaching and learning.

In a forward to the report -- which supports such basics as phonics, homework and memorization -- Education Secretary William J. Bennett acknowledges that many of the research findings seem like common sense. "So be it," he declares. "Given the abuse common sense has taken in recent decades . . . it is no small contribution if research can play a role in bringing more of it to American education."

A sampling of some of its teaching endorsements: for science, the use of experiments; for beginning math, the manipulation of tangible objects; for writing, student revision of first drafts.

Running through most of the report are two themes:

*The curriculum should be rigorous and firmly structured, not a catch-all "do your own thing."

*Parents should be involved, not just on the periphery of committees and fund-raising, but in the substance of teaching their children and helping them to develop persistence and responsibility.

"I think it's absolutely sound advice," says Steven Frankel, director of educational accountability for Montgomery County public schools. "Oh, in each of the different areas I'm sure some specialist will say that it's only part of the story. But if parents and school systems go out and do those things, there is no doubt that things will be better."

Among findings and comments:

*Parents should create a "curriculum of the home," which teaches their children that school work matters. "Conversation is important," and so are providing books and a place to study. Parents should read, talk and listen to their children; follow routines for meals, bedtime and homework and help children meet deadlines. TV-watching should be limited.

When parents of disadvantaged children take those steps, says the report, "their children can do as well at school as the children of more affluent families."

*Values matter. Students who believe in hard work, responsibility and the importance of education "are likely to have higher academic achievement and fewer disciplinary problems." Parents can improve their children's chances for success by emphasizing these values and encouraging friendships with peers who share them. The ideals that children and parents hold "are more important than . . . socioeconomic and ethnic background in predicting academic success."

*Reading achievement is tied directly to the amount of reading children do. Parents should read aloud to young children and make sure their older ones read.

Reading books is more valuable than filling out workbooks or performing computer drills.

*Many highly successful individuals have "above-average, but not extraordinary intelligence." Their accomplishments depend more on "hard work and self-discipline" than on IQ's.

*Children who are encouraged to draw and scribble "stories" at an early age will later learn to write more easily.

*Students get a better start in reading if they are taught phonics -- learning the relationship between letters and sounds -- rather than the "look-say" method of whole word instruction. Phonics, however, "should not be over-used" and children should soon move into reading "good stories and poems."

*"Children learn science best when they are able to do experiments, so they can witness 'science in action.'"

*The most effective way to teach writing is as "a process of brainstorming, composing, revising and editing" with lots of prompt feedback from teachers.

*Teachers who set higher expectations obtain higher academic performance. Good teachers know their subjects well and manage their classrooms so time is not wasted on unimportant activities.

*More homework raises achievement. Teachers should explain it carefully in advance, mark it promptly and count it as part of the grade.

*"The best way to learn a foreign language is to start early in elementary school and to study it intensively over many years." Total immersion programs have been highly successful.

*Schools should strengthen the study of history. Unless all students have some common knowledge of the "heritage, institutions and values that draw Americans together," teaching is hindered and social cohesion impaired.

Free copies of "What Works" are available by writing the Consumer Information Center, Pueblo, Colo. 81009. Specific research questions may be asked by phoning 463-0083 in the Washington area or 800-424-1616, a toll-free number for the rest of the country.

Other booklets with detailed suggestions for helping children learn at home may be purchased from the Home and School Institute, a nongovernment organization, at 1201 16th St., NW, Washington, D.C. 20036. (202) 466-3633.

A free packet of pamphlets for parents, called "Parents Are Teachers, Too" is available from the California State Department of Education, P.O. Box 944272, Sacramento, Calif. 94244-2720.