The Prince George's County Board of Education last night approved three new programs aimed at improving the quality of mathematics teachers.

The programs, proposed by Superintendent Edward J. Feeney, were in response to the poor showing--fourth worst in the state--by ninth graders on this year's Maryland Functional Math Test.

Under one program, 50 teachers who now teach other subjects will be retrained in mathematics at the University of Maryland, beginning this fall. Their part-time studies will last up to two years before they become secondary math teachers, according to Louise Waynant, coordinating director for instruction for the county schools. That program will cost about $70,000.

In addition, $70,000 will be set aside to pay substitute teachers to free math teachers for special in-service training and $240,000 will be made available to select a team of the six to eight best elementary math teachers to assust elementary math teachers countywide.

"I believe all three programs are absolutely necessary for this school system if we are to assure our public that we are doing all that we can to improve the learning of math in this county," Feeney told a meeting of school principals and other administrators yesterday.

Feeney also told the principals that 80 new "teacher coordinator" positions will be created this fall, replacing the positions of department chairmen in English, math, social studies and science at each of the 20 county high schools. Teacher coordinators will be freed from half the normal teaching load, and unlike the present department chairmen will have no "paper pushing" functions, according to a school official.

The new teachers, who will get extra pay, will work closely with teachers in the building, assisting them in planning, grouping children and monitoring the progress of instruction.

"They will be a bright spot in the future of the school system," said Feeney, who likened the move to "exactly the kind of change being called for by President Reagan and others who are seizing the issue of quality teaching and master teachers."