The terms of appointed members of the Board of Education shall be four years, commencing on May 1 of the year a Mayor's term of office begins. If the General Assembly enacts legislation permitting the election of members of the Board on a non-partisan basis, then (1) the terms of elected members of the Board of Education shall begin on the first Monday in December and shall be six years except that of the first members elected, three shall be elected for terms of two years, three for terms of four years, and three for terms of six years, and (2) the terms of all members shall expire on the first Monday of December immediately following the municipal election at which the first elective Board is elected.