OVER THE YEARS, the reputation of public elementary schools in the District has been generally good. It was at the junior high school level and, even more, at the high school level that the confidence of parents dropped considerably. It became common for middle-class parents determined to provide their children with a good education to go to the considerable expense of sending them to a private or parochial school with a better program.

Many families, facing the further prospect of stiff college expenses, longed for more of the kind of public secondary schools, like Wilson High School, that would challenge their children. In the Banneker academic high school, many parents seem to feel that they have found such a school. Over 60 percent of the ninth-grade class that entes Banneker next fall will be made up of children coming from private and parochial schools. They appear for the most part to be students who began their education in the District's public schools but were pulled out after the early years.

Banneker has tougher grading standards and more homework than the city's other public schools. It requires students to perform several hours of community service. One of the school's goals that has surely impressed many parents is to see every senior enrolled in college. Of this year's 71 Banneker seniors, only four are still waiting for an acceptance. The institutions where those already accepted will go include Vassar, MIT, Princeton and the University of Virginia. Other students are headed for respected black colleges -- Spellman, Lincoln University and Morehouse. About a dozen students will be going to Howard University and the University of the District of Columbia.

In the midst of this good news, there is one point of concern. Only about 38 percent of the next incoming class at Banneker will be arriving from public schools in the District. That means that the area's private and parochial schools are providing stiff competition for Banneker slots for students in the city's public schools. It means that more public school students than might otherwise be the case will have to remain in the city's regular high schools.

It comes down to a challenge to the city's school system to make those regular high schools better. It's not simply a case of helping public school students compete with private and parochial students for places at Banneker. The city's students who do not attend private and parochial schools should be able to count on the city's regular high schools in order to learn.