Section 52. The school committee shall serve without compensation, except that a member of a school committee of a city, town, regional school district or superintendency union may be compensated for his services by a majority vote of the city council in a city having a Plan D or Plan E charter; in a city not having a Plan D or Plan E charter by vote of the city council, subject to the provisions of the charter of such a city; in a town by a majority vote at a town meeting; and in a regional school district or school superintendency by a majority vote of the voting member towns authorized at their respective town meetings, the amount of such compensation, in each case, to be set by the respective cities, towns or groups of towns. No member of a school committee in any town shall be eligible to the position of teacher, or superintendent of public schools therein, or in any union school or superintendency union or district in which his town participates.