TV: homework help for students

''Hello. You're on the air. What's your name and your question?''

''My name is Steven from Syosset High School. In one of the past Regents' essays they asked about foreign policy. How was the United States affected by the actions of any European countries during the 19th century?''

This dialogue is repeated about 40 times each night on Channel 12, a community channel sponsored by Cablevision. Since 1976, ''Extra Help'' has been offered to junior and senior high school students who want a ''one-on-one'' relationship outside the classroom. Students pose questions over the telephone and receive their answers from certified teachers over television.

Since all students in New York State are required to take social studies exams in June, Channel 12 in Woodbury, Long Island, has added Social Studies Regents Review to its ''Extra Help'' classes in math, science, and health.

The new course presents special problems because the line between fact, opinion, and interpretation often blurs. Furthermore, there are multifaceted answers with varying shades of correctness.

On one recent program, for example, the unit on economics was being developed. Questions were asked about the reasons for inflation, the effectiveness of supply-side economics, and the merits of the New Deal. Although economic analysts and political pundits have hotly debated such concerns for years, students expect clear, concise, definitive answers. When responding, teachers remind inquirers that value judgments and opinions are best left to the network commentators and newspaper editorials.

Unlike most educational programs offered on public broadcasting stations, there are no prepared scripts, no videotapes, no audiovisual materials. As in the early days of television, all action is live, with neither visual nor sound delays. Backed by a chalkboard, facing a battery of cameras and klieg lights, the instructor is alone, having only his years of experience and memory to rely on. He works without a ''net,'' moving quickly from one subject to another. In this setting it is the message that really counts - the answers to students' questions.

Lacking the time to establish rapport with students as in a regular classroom , the television teacher must quickly project himself on screen as a confident and knowledgeable person. The teacher's presence, his body movements, vocal quality, and ability to respond quickly and accurately, spell success or failure in this new venture.

''Extra Help,'' conceived six years ago by Charles Dolan, the present board chairman of Cablevision, has served to reinforce the learning process and not to replace the classroom teacher. Producer Robert de Poto commented that ''this format has a single function - to allow youngsters the means to request information in a variety of subjects, on things which have been puzzling in class or questions on their homework.''

Televised three hours daily, four days a week, during the school year, ''Extra Help'' enables thousands of students in this Long Island community to get answers to their factual questions and acquire the knowledge they need to improve their grades.