Rivals for the Democratic nomination for D.C. mayor used a candidates' forum at Wilson High School last night to outline their views on ways to improve the city's troubled public school system.

Mayor Marion Barry told the gathering of about 250 that the school system should begin a twice-yearly review of its curriculum to ensure that jobs exist for the skills that city schools are teaching young people.

"But the most important thing," Barry said, "is creating an atmosphere at home so that children want to learn. That's what Effi Mrs. Barry and I are doing with our 23-month-old son, Christopher. He's picking up books now and reading because we told him reading is important."

Barry also declared that the numerous, highly publicized disputes his administration has had with the D.C. Board of Education ended in January when a new "sane and sensible school board" took office.

Each of the six other candidates challenged Barry on this, however, and blamed the mayor for continued friction with the school board over budgets. Cuts in school system spending have led to layoffs of 173 teachers and other school employes since Barry has been in office.

"The yearly battle of the budget drains energy and creates an atmosphere of anger between the school board and the mayor," said council member Betty Ann Kane (At-large), who, like Barry, is a former school board member. "I would suggest that anyone who believes in public education in this city should not support the incumbent. . . . . Our children can learn, our children can succeed if given the proper support from public officials."

Patricia Roberts Harris, former head of the Department of Health, Education and Welfare, proposed that the mayor's office and the school board reach agreement on spending before publicly presenting their budgets to allow the mayor to be "an advocate of the schools instead of an adversary."

Harris said parents in Ward 3, the solidly middle-class area west of Rock Creek Park in which last night's forum was held, have had to pay out of their own pockets for some art teachers and supplies in their public schools to enhance the quality of education.

"You are paying for services that the school system--with cooperation of the mayor--ought to be able to provide to all the children of this city," Harris said. "Until we have what is necessary for our schools we do not need to begin educational innovations . . . "

At-large council member John Ray offered the most specific proposals for improving public education, including a requirement that teachers be tested annually, increased enforcement of truancy laws, public election of the school board president and an annual formula-based school budget linked to the number of pupils in the system.

Council member Charlene Drew Jarvis (D-Ward 4) said she supports a "predictable funding source of revenue" for the schools as well as continued training of teachers after they are hired and higher academic standards throughout the school system.

Most of the candidates also criticized the Barry administration's deep spending cuts in the recreation department where 137 employes have been laid off in the past two years--20 percent of all city layoffs in that period. Barry pointed out, however, that the three City Council members who now oppose him in the mayor's race all voted for the budget that included the recreation cuts.

Also appearing at the forum sponsored by the Ward 3 Democratic Committee were candidates Morris Harper, a physician, and publisher Dennis Sobin, each of whom is making his first try for public office.