The mayor of any city described in Section 32-3, at the first regular meeting of the city council, after each annual municipal election and after his installation into office, shall nominate and place before the council for confirmation as school directors or members of the board of education, as the case may be, 1 person from each ward of the city to serve for 2 years and 1 person from the city at large to serve for 1 year. If the persons so appointed are confirmed by a majority vote of the city council, to be entered of record, such persons shall constitute the board of education or school directors for the district. The person appointed from the city at large for 1 year shall be president of the board of education or school directors but shall have no vote except in case of a tie.