A microcomputer might make a student put in a little overtime

The blond head of Matthew Sieber and the dark head of Phi Thanh almost touch as they bend over the Apple computer keyboard in the corner of the classroom. Sieber enters a simple trigonometric equation, and both students stare intently as a luminous, yellow line traces the function's scalloped shape on the screen.

Meanwhile, their trigonometry classmates here at Prospect High School work on problems, talk quietly, or try to attract the attention of their teacher, Polly Tamura, who moves about the room answering questions.

This is just one example of how computers are being used to teach mathematics and science here in Silicon Valley. Prospect High has been using them for four years now, making it a pioneer in this effort.

''We've gotten most of our stumbling over with,'' says the school's computer coordinator, Alice Mitchell. Despite all the debate over computers in the classroom, the experience here suggests that these machines can play a positive role in math and science instruction at the high school level.

Today, Prospect's computers are put to all sorts of uses. They provide visual aids to supplement teachers' lectures. In remedial classes, they drill students in basic math skills. Computer simulations mimic classical physics experiments and reinforce what students learn in the laboratory. And programming courses are used not only to teach about computers, but to reinforce basic skills in math, science, and other subjects.

The school has clearly benefited from its strategic location in the microcomputer industry heartland. Last year it received a grant of $55,000 worth of computer equipment and programs from the Hewlett-Packard Company. But what has been achieved here has come primarily from the dedicated efforts of educators like Mrs. Mitchell and Mrs. Tamura.

Mrs. Tamura's students are just being introduced to trigonometry and, in some cases, computers.

In trigonometry, the computer's greatest virtue is that it ''helps students generalize,'' Mrs. Tamura explains. Then she adds emphatically, ''But I make sure they can still do the problems, and the graphing, by themselves.''

When they first began using computers, Prospect's administrators and faculty drew a clear distinction between computer-aided instruction of the type Mrs. Tamura is using and instruction in computer programming. ''Our most surprising discovery has been that kids learn more mathematics in programming than in regular math class,'' Mrs. Mitchell reports.

The reason for this, she says, is that programming both motivates students and forces them to learn basic mathematical concepts.

Writing a program to solve a math problem requires a solid understanding of the concepts involved. So programming can serve as a powerful math-learning tool. And the same thing goes for other subjects.

Of course, there is sometimes a problem with students who get hooked on programming and tend to ignore other studies. Mrs. Mitchell had one such student four years ago. She finally told him that he could not use the computers after school until he had finished his calculus homework. ''There are decisions you just have to make for the kids,'' she explains. This boy wrote and sold a popular game for the Apple computer, making $40,000 in royalties his first year out of high school, she reports.

While at Prospect, this same student wrote a program for the social studies teacher which drills students on the geography and economies of European nations. This illustrates one of the most innovative aspects of the school's computer program: use of student programmers to create custom software for teachers.

These efforts are part of the final semester of the programming course. Teachers draw up a detailed description and students convert this into software.

Perhaps the most telling point of all is one of Mrs. Mitchell's observations: ''Of all the subjects we teach, computer courses are the only ones where the students do more than you assign.''