D.C. School Superintendent Vincent E. Reed last night proposed eliminating driver education courses and all free field trips for students, a curtailment in the number of assistant principals in elementary schools and a reduction in the number of shop teachers in the system.

Reed, who has already proposed cutting back significantly in the school system's administration and teaching staffs and its prekindergarten and adult education programs, recommended the additional cuts so that fewer teaching positions would have to be eliminated next year. The moves are designed to cope with an expected $27 million deficit in the 1980-81 school budget.

Reed initially proposed increasing the pupil/teacher ratio in the elementary schools from 26 to 1 to 28 to 1 to save about $6 million. But some school board members objected to this proposal and asked Reed to come back to the board with an alternative.

Last night, Reed said that the current 26 to 1 ratio could be maintained in grades 1 to 6 and the school system would still save about $3 million. This is because there will be about 7,500 fewer students in the public school system next year, he said.

Because many board members favor even further lowering of the pupil-teacher ratio in elementary grades, Reed submitted some additional data that showed that if the board decreased the ratio to 23 to 1, it would cost an additional $1.9 million.

The school system has asked the City Council to approve a budget for the coming school year of $279 million. But the council has approved only $252 million.

The school board's finance committee, which received these proposals last night, took no action.

According to the new proposals, the school system could save $1.7 million by reducing the number of shop teachers from 145 to 73; $618,106 by eliminating driver education courses, and $15,000 by ending the free field trip program.

Reed also proposed reducing the number of assistant principals on the elementary school level from 34 to 22 to save $375,576.