Coordinators of the art and music departments for Montgomery County public schools told the Board of Education this week that more supervisors are needed to evaluate the classroom work of art and music teachers because principals do not have a sufficient background in the arts to judge teachers effectiveness.

But members of the school board asked the coordinators to justify the need for more supervisors in light of possible cuts in the school budget if property taxes are reduced.

"You're asking for more supervision, more specialists, more administrators," said board members Roscoe R. Nix. "How do you respond to people who say we have to many administrators and not enough teachers?"

Associate Superintendent Leroy Stern replied that principals themselves have called him "asking us for help in evaluating art and music teachers and programs."

Stern said that if fiscal cutbacks are made and the arts and music departments are not given supervisors, the schools would not know whether "the series of activities that a teacher goes through with students in the classroom are meeting the goals of education."

Under one of Superintendent Charles M. Bernardo's policies, principals must evaluate the classroom performance of teachers.

Schools board member Blair Ewing said the art and music departments in the junior high schools and high schools lack a "coherent policy that says this is what the arts do. We must decide what we want to do and whether we have an adequate staff to do it."

Bernardo replied that the art departments lack a comprehensive plan of their goals because they have not been given the same financial resources as other disciplines.

School board member Marian Greenblatt said she would like the music department to teach elementary school students a classical instrument instead of having them "sing songs, clap their hands and walk around the room."

"The schools should help students develop a lifetime interest in music and generate knowledge of our culture. Where does this come in?" Greenblatt asked.

Phyllis Kaplan, coordinator for elementary school music, replied that guitar instruction is provided in 29 percent of elementary schools. She also said that students need to "experience music at a stage commensurate with their own intellectual development. We whet their appetites for the study of band and orchestral music."

School board member Elizabeth Spencer disagreed, saying "I don't think any children in elementary school are too young for exposure to instruction in an instruments."