Teaching the three R's reading, 'riting and 'rithmetic - remains the most important goal for high school educators, according to a survey of secondary school leaders released Tuesday.

The report from the National Association of Secondary School Principals summarizes the organization's 1987 survey of 1,225 high school principals and assistant principals in 1,544 schools. It is a follow-up to similar surveys in 1965 and 1977.The study indicated the top three goals of school officials - teaching students basic skills, helping them develop positive self-images and furthering intellectual inquiry and problem solving skills - stayed the same as in the 1977 survey.

Teaching basic skills also was the top priority in 1965, but that year the second and third top objectives were, respectively, promoting development of moral and spiritual values, and promoting an understanding of the American system.

Today's high school principals also see a greater need to prepare American youth "for a changing world" - a goal that was fourth in the latest survey, up from eighth in 1977.

The other goals identified in the new survey were, in order: promoting development of moral and spiritual values; providing career planning and training in special entry-level job skills; promoting understanding the American value system; teaching skills needed in a technological society; teaching skills for family life; promoting physical fitness; and offering exposure to the fine arts.

Asked to rate a list of skills and characteristics needed by teachers, the administrators ranked the top five as competence in subject matter; adjusting instruction to students; interpersonal skills with students; competence in methods; and skill in developing positive student self-images.

Asked which of 27 conditions would have an impact on their schools in the next five years, almost half (49 percent) said gang activity would have a strong influence, followed by 39 percent who listed increases in enrollment and 37 percent who identified youth unemployment.