Carole R. Goshorn is special -- one of 104 high-school science and mathematics teachers who are in Washington this week to receive presidential awards for their excellence in the classroom.

Although she does not look it, the 34-year-old mother of two is one of the front-line fighters in America's battle for survival in the increasingly tough international economic competition. Study after study has shown the United States is doing a worse job on science and math education -- the building blocks for tomorrow's technology and industry -- than Germany, Japan and other competitor nations.

Despite recent moves in many states to require more and tougher science and math courses in high schools, close to one-third of those classes are taughty people with minimal or no qualifications in those subjects. And the proportion is growing.

Science and math majors can double their teaching salaries by moving into industry. Science-minded college undergraduates tend to shun teaching degrees. Colleges complain that high schools are sending them fewer students with good preparation for science, math and engineering courses. And industry says it cannot find the trained technical and scientific people it needs.

Two years ago, after a wave of reports highlighted these problems, the administration reversed course. After reducing to one-tenth the National Science Foundation programs for math and science education in his first two years, Reagan endorsed an expanded program of scholarships and training for teachers in those fields. The annual presidential awards for two top math and science teachers in each state are the public relations frosting on that cake.

They are also a mee of how far most communities in this nation have to go if they are to provide students with the education that results when a gifted teacher such as Carole Goshorn works in a well-equipped school in a community as supportive of education as Columbus, Ind.

Columbus is the international headquarters of Cummins Engine Company, whose management has made this city of 31,000 a showcase of distinguished architecture and a remarkably comfortable place to live. Along with Arvin Industries and other local firms, the Cummins people have spurred the development of high-quality local schools, needed to attract top managers to central Indiana and to educate a skilled work force.

East High, where Goshorn teaches, was designed and built 13 years ago to accommodate and foster team teaching and highly individualized instruction. In the science wing, there are large lecture halls with sophisticated audiovisual equipment, where several classes can get basic instruction at one time. Individual classrooms are very small, holding not more than 20 pupils, so teachers can supervise problem- solving and answer questions on a one- on-one basis. A large, modern lab serves several courses, with a full- time lab attendant and at least one teacher on duty at all times. Between the lab and the classrooms, a science library has desks for individual study.

The 1,600-student school draws from an industrial city and a farm county; it is not elitist, but its standards are tough. The other day, Goshorn, wearing a white lab coat with a button reading "Chemists Have Solutions" on her lapel, and her teaching partner, Jack Young, took perhaps 120 beginning chemistry students through a fast-paced workout on calculating molecular weights of compounds. Her analogies were down-home -- "10 to the 23d power is about as many leaves as you'd find on all the trees in Bartholomew County" -- but the equations flashed on the screen click-click-click. No one had time to daydream.

With a master's degree in biology from Indiana University, Goshorn could probably double her mid-$20,000s salary in industry. But she and her husband, an administrator at North High, have a commitment to education and welcome the chance to work in a community that has demonstrated its dedication to its schools. Despite its small size, Columbus has just hired a superintendent away from a swanky Minneapolis suburb by offering him the second- highest education salary in Indiana and a $100,000 "excellence in education" fund, raised from local business and available for projects he picks.

The recommendations for Goshorn's award, which brings a $5,000 federal grant to her school, noted not only her work on statewide science curriculum development but her skill as a student adviser, her role-model status for young women considering science or other professional careers and her enthusiasm for teaching.

"It's wonderful to work in a school and community like this," she said. It is wonderful to watch her in her superb public school. But you have to remember she stands out as special. America will have to clone her -- and the commitment to education her school and community represent -- many times over to meet the challenges ahead.