For the first time, 19 of Maryland's 24 school systems are offering free remedial courses this summer to students who failed the mathematics and citizenship tests required for graduation.

School officials said that the summer courses will save money and make it easier for teachers to reach students who need help.

In Charles County, where 604 of 1,707 ninth-grade students failed the math test when it was given last fall, officials say the cost of the five-week course will be about $5,000, compared with $20,000 for an additional staff member to run the program during the school year.

No high school credit will be earned by taking the free classes.

"When a student is pulled out of regular classes to get special remedial help, he often falls behind in other areas. This approach will avoid that problem," said Paul Williams, state director of school testing.

Once the state department of education has a chance to analyze summer test results, the summer school course may become a regular offering, Williams said.

In Charles, the passing rate for ninth-grade students taking the state's citizenship course increased from 37 percent last fall to 58 percent this spring. About 700 students failed, however.

In Montgomery County, where 75 percent of 7,631 ninth-graders passed the citizenship test last fall, three weeks of classes still will be offered to the 1,908 who failed, said Cornell T. Lewis director of adult and summer school education.

"That's still a sizeable number in a school district this large," he said.

Officials said that of 7,676 Montgomery freshman who took the Paul Williams mathematics test, 6,066 passed.

"We're not teaching to the test, because we don't know what's on it. Instead we have a series of course objectives that are also on the tests," Lewis said.

Williams said that, while school systems might teach government or civics differently, most basic mathematics courses will cover largely the same topics: area and measurement, operations, decimal systems, and problem-solving.

The Charles County classes started Monday and run through July 31. Information is available at 932-6610 or 870-3814.

In Montgomery County, call 942-8304 for high schools offering the classes from 9 a.m. to 12:30 p.m. next Monday through July 23.