(a) There shall be a board of trustees for each city, town, county or district established, which shall be known as the public school teachers' retirement fund board, and shall be composed of nine (9) members who shall serve without compensation.
(b) The board shall consist of five (5) teachers, who shall be elected by the teachers of the city, town, county or district, as the case may be, the director of schools of the city, town, county or district and three (3) members of the school board of the city, town, county or district, elected by such board. The manner of election of the elective members shall be determined by the rules prescribed for the government of such bodies as heretofore provided.