MAYOR BARRY'S decision to give the city's public schools $4.5 million more for their budget accomplishes several important aims. First, it gives the school system the money it needs if it is to continue improving. The school board had asked for $265 million and, with this latest infusion of dollars, the school budget is now at $256 million. That is less than the school board asked for. And, frankly, it is less than we think the schools deserve for the coming year, considering that they will lose $13 million in aid as a result of federal budget cuts that were not considered when calculations were first made of the system's financial needs for next year. Stil, the mayor is clearly trying to help the schools.

The mayor's help also comes at just the right time to extend a hand to the new superintendent of schools, Floretta McKenzie, an impressive educator who is popular throughout the city. But is handicapped by budget woes, her success will be jeopardized.

The added dollars from the mayor help, too, with a ticklish problem: the absence of parents' confidence in public schools. The added $4.5 million may help to diminish parental concern about teachers being laid off next September or shifted from school to school. Last September there were crowded classrooms, classrooms that had constantly changing teachers and some that did not have any instructors at all on occasion.

The mayor needs to keep looking for at least $9 million more for the schools. Schools, like police and fire protection, should be a primary city government function. Especially now that the schools are beginning to improve, they require full funding at $265 million.