There are three types of Boards or Councils that are most common to Catholic or independent schools, each of which varies in structure and authority:
A “Board of Trustees” (BOT) model is typical of most independent schools. It is comprised of either elected members (voted by the parents of the school) or appointed members (by the recommendation and approval of existing Trustees). As its name implies, an “independent” school BOT operates distinct from any higher “authority,” like a bishop, pastor or superintendent, and thus serves as the highest "authority" in the school. It hires the head of school and decides if the head's contract will be extended. It establishes tuition rates and salary increases, approves budgets, creates policies, and in rare circumstances, handles appeals of the headmaster’s decisions.
A “Board of Limited (or Specialized) Jurisdiction” (BLJ) is a model that might be seen in schools once founded by a religious order, now sharing their authority with lay Boards. or in some diocesan high schools.. Typically, the religious order (or bishop, if a diocesan school) retains specific areas of authority for the school, while delegating authority in all other areas. A religious order, for example, might retain authority to hire the school president or to oversee matters relating to the Catholic identity of the school, but then leave all other tasks to the board and leadership of the school. Typically for a diocesan high school, the bishop (usually through his surrogate, the superintendent, or perhaps through a diocesan finance council) would retain the authority to appoint the top leader of the school, approve annual budgets and authorize capital campaigns--all three, typically, as recommended by the Board-- but then delegate authority for the Board to set policies in all other areas. The bylaws or the constitution of the BLJ, signed by the religious order or bishop and the Board, would make these distinctions explicit.
An “Advisory Council” (AC) is the model for Prince of Peace, the elementary schools within the Diocese of Dallas, and most other elementary schools around the country. The Council's authority is advisory only. It recommends actions to the pastor, who has the authority to veto the recommendation. But if the Council is doing its work well, the vast majority of the time, the pastor accepts the recommendations of the Council, so the net impact of the Advisory Council’s work ends up similar to the other models.
With AC’s, the evaluation, hiring and firing of a president are the responsibility of the pastor (in the case of a parish school) or the bishop/superintendent (in the case of a diocesan high school). Pastors (and superintendents) would typically ask for candid feedback from the Council as part of their evaluation. In the case of a president-principal model, the president evaluates, hires and removes the principal, and would consult the Council in similar fashion.
-----
In all three models, the purpose of the Board/Council is primarily to extend and promote the mission of the school in terms of strategic planning, policy making, and securing and protecting the financial resources of the school. Wheres a Board or Council recommends policies that are broad in nature, indicating a direction--the "what?" and the "why?"--the school administration's 's job is to operationalize these policies in the day to day life of the school-- the "who?" and the "how?" and usually, the "when?"
The school president (or in the absence of a president, the principal) serves as the "executive secretary" for the Council.