Schools in the District of Columbia open today for nearly 110,000 pupils and a teaching staff that has yet to vote on a new contract for the school year.

However, the prospects of another teachers' strike, like the one that crippled the system last spring, appear dim. The executive committee of the Washington Teachers' Union voted last week to recommend to its membership that a new two-year contract be ratified.

Harold Fisher, a union official, said yesterday that he expects the 5,000 union members to vote on the contract by the end of the month. Copies of the contract will be sent to the members during the next two weeks. Last week, teachers reported to work as scheduled for general preparation, curriculum development and other business.

The school board is expected to ratify the contract.

School Superintendent Vincent Reed said yesterday he is looking forward to a grand school year. "We're ready for them (the students) . . . We are hoping everybody is ready to work."

Reed has expanded a program called Competency Based Curriculum (CBC), a back-to-basics approach to teaching, to about 120 of the city's 200 schools. CBC, which has a step-by-step manual to teaching each subject, was used last year in about 60 schools.

Reed hopes that the program will show marked improvement in students' learning abilities. So far, CBC as a teaching aid is an unknown quantity.

The schools have become a political issue as the school board members try to convince the public that they are improving the schools, which have long been criticized for the students' poor scores on standardized tests. Six school board seats are up for election in November, a factor contributing to the politicalization.

Teachers and the union, meanwhile, have been trying to convince the public that the school board and the school administration, not them, are responsible for the low scores.

The school board and the union have been feuding since January 1978, when the teachers' 18-month contract expired.

The board contended that that contract gave too much power to the union and required teachers to spend less time in the classroom than they should. The union maintained that the board was trying to break the union and take away gains teachers had won.

Last March, the teachers struck for 23 days. The strike ended only after Superior Court Judge Gladys Kessler met a key union demand and extended the old contract until the summer.

Fisher said the teachers will return to the classroom today under a memorandum of understanding that will serve until the new contract is voted on.