The D.C. school board last night voted partial approval of a controversial new program that could allow city teachers to earn master's degrees in 20 weeks and authorized expenditure of $53,000 in school funds for it.

The board's action permits continuation of the first stage of the program, under which teachers may take courses in management and curriculum and up to two courses for graduate credit accredited by the University of Massachusetts. The board, however, did not sanction expenditure of school funds on the most hotly debated part of the program under which the University of Massachusetts would award master's degrees to teachers who complete course work during 20 intensive weekend sessions.

Massachusetts has no license to offer courses in the District, and that has been one of the chief reasons that the program has been opposed by some board members. Teachers have been attending courses offered by the program for the last four weeks, and university officials have said they would apply for the necessary license when they had worked out details of the full degree program with D.C. school officials. The board did not bring up the licensure issue last night.

The program, called the Professional Development Institute, is being run by Rhody A. McCoy, chief assistant to acting schools superintendent James T. Guines.

The board voted 11 days ago to terminate the program as of April 27 and prevent expenditure of school funds for it if Guines and his staff could not prepare a report that answered specific questions on how the institute was to be funded and what specific degree the teachers would be able to get.

At first Guines said salaries for the instructors and other costs for the institute would come out of a $60,000 "food services" fund, but in a report delivered to the board yesterday he said he had uncovered $53,000 available for expenditure on the program in a "superintendent's discretionary fund." Guines said the fund consisted of contributions citizens have made to the school system over the last 13 years but which have never been spent. Guines also reported that more than $3,000 in school system money had already been spent on the program.