Each board of education shall, not later than one month after the date on which the newly elected members take office, elect from its number a chairperson and elect a secretary of such board and may prescribe their duties. The votes of each member of such board cast in such election shall be reduced to writing and made available for public inspection within forty-eight hours, excluding Saturday, Sunday or legal holidays, and shall also be recorded in the minutes of the meeting at which taken, which minutes shall be available for public inspection at all reasonable times. If such officers are not chosen after one month because of a tie vote of the members, the town council or, if there is no town council, the selectmen of the town shall choose such officers from the membership of the board. The chairperson of the board of education or, in case of such chairperson’s absence or inability to act, the secretary shall call a meeting of the board at least once in six months and whenever such chairperson deems it necessary or is requested in writing so to do by three of its members. If no meeting is called within fourteen days after such a request has been made, one may be called by any three members by giving the usual written notice to the other members.