YOU COULD ALMOST HEAR the citywide sighs of parental relief (and some predictable grumbling from the youngsters' quarters) when the District public schools opened for business as usual Wednesday - after a sensible settlement that averted a teachers strike for now. The teachers contract - which first expired last January, then was extended for six months at the school board's request and after that was set aside by the board in June - has been reinstated for 90 days. And there is agreement on procedures for the amount of paid leave for teacher-negotiators.

The peace is only temporary, however, and the real issues in the negotiations are far more complex than the ground rules agreed to on Tuesday night. The job for the school board and the union now is to work out mutually acceptable contract changes designed to improve what's happened in the classrooms. That means developing fair methods of evaluating teachers that go beyond the institution of new curriculum standards - including agreement on procedures for the testing of teachers that at the same time maintain proper job protections. It also may involve modifications in teacher grievance procedures to clarify methods of disciplining, firing and defending teachers in the fairest way.

These happen also to be important matters to a third party not formally represented at the teacher-board bargaining table: the parents, who are just as interested in a settlement that serves to improve the goings-on in their childrens' classrooms. They, as well as the community at large, will need help understanding the concerns and objectives of the board and the union in order to make informed judgments as the negotiations proceed. The danger remains that negotiators will threaten war over each individual point in dispute rather than work for a package of agreements. The community stands ready to support policies aimed at improving the schools. But that public support can fall away entirely if negotiations degenerate into a hard-line confrontation in which the two sides heap blame upon each other and ignore the public's interest in the schools.