N.Y. Educ. Law § 4803
The board of managers of such school shall consist of not less than five members to be appointed by the mayor of such city and of which board the superintendent of schools in any such city shall be one member ex-officio. Members of the board other than the said superintendent shall be appointed from resident taxpayers of the city who shall serve for terms of four years commencing upon the first day of January succeeding the appointment. Such terms shall be so arranged that the terms of no two of the members so appointed shall expire in the same year, and for this purpose the terms of members first appointed hereunder shall be as follows: In case one member shall be appointed the term shall be four years; in case two members are appointed the term shall be four and two years respectively; in case three members are appointed the term shall be four, three and two years; in case four members shall be appointed the terms shall be four, three, two and one year respectively. Such terms shall commence on the first day of January succeeding the appointment and their successors shall be appointed for a full term of four years as above provided. Appointments to fill vacancies shall be for the unexpired portion of the terms. The members of the board shall serve without compensation. They shall receive their necessary expenses incurred in the performance of their duties. The amount of such expenses shall be charged against the city and paid in the same manner as other city charges. The board shall organize by the election of one of its members as chairman and another as secretary.
N.Y. Educ. Law § 4803