The death by suicide of Cleveland Public Schools Superintendent Frederick Douglass Holliday will shake a school system that has suffered through more than its share of afflictions. The 77,000-student school system was paralyzed by a 77-day teachers strike in 1979. Financially, it was in receivership from April 1981 until July 1984 and under a court-ordered desegregation process that was met with bitter resistance in some neighborhoods. Cleveland was also a city in which political power was reluctantly changing hands from whites to blacks on the school board. Superintendent Holliday stepped into this cauldron 21/2 years ago. Now, reading scores are on the rise. Decline in enrollment, partially attributed to lack of confidence in the schools, has stabilized. Cleveland voters also approved a levy increase in 1983 that gave $32 million to the school system, enough to fund a long-awaited increase in teacher salaries.

Despite these gains, tensions in the city and on the school board remained high. Some on the seven-member Cleveland school board strongly supported Mr. Holliday. He was also adept in gaining the confidence of whites. But detractors on the board called him a showman and questioned his every move. Some members of the black community felt Mr. Holliday was too slow to act on desegregation. Church leaders and some of the city's highest officials were working to get Mr. Holliday a new term. The detractors worked with equal vigor.

Is there any wisdom in making the post of school superintendent the focal point for a city's quarrels, frustrations, distrust and divisions? The D.C. school system has had some experience with this. There was a divisiveness and turmoil on the board and a lack of progress in the schools. One superintendent was fired. Another, citing the rancor on the school board, quit. Now, with a reasonably harmonious board backing a competent school superintendent, students have made impressive gains.

In Cleveland, much soul-searching is taking place, and there are important things to discuss. The pressure of being a successful big-city school superintendent is immense. Nationwide, the dramatic turnover in superintendents and the exorbitant salary offers necessary to attract resilient candidates are disturbing. This unfortunate incident is also a reminder of the necessity of some minimal degree of harmony and consensus at the top. Before Cleveland officials select another superintendent, perhaps they will decide to agree on the educational goals they seek. In Cleveland, as in other large cities, the political leadership ought to ask whether it is setting impossible or inconsistent standards. When that is done, perhaps it will rally around its superintendent, realizing that, even then, his or her task will be enormous.