Section 16. There shall be a teachers' retirement board for the purpose of administering the teachers' retirement system established under the provisions of chapter 32. Such board shall consist of seven members as follows: the commissioner of education, or his designee, who shall be a member ex officio and who shall serve as chairman, the state treasurer, or his designee, the state auditor, or his designee, a fourth member who shall be appointed by the governor for a term of four years and who shall be a retired former public school teacher within the commonwealth, two members who shall be elected by the members in or retired from service of such system from among their number in such manner and for such term, not exceeding four years, as the commission shall determine, and a seventh member who shall be chosen by the other six for a term of four years. Future elections of the fifth and sixth members shall be held under the supervision of such retirement board and the terms of the fifth and sixth members shall be arranged so as not to expire in the year of expiration of the term of the seventh member. If a seventh member is not chosen by the other six members within 30 days after the expiration of the term of the seventh member, the governor shall appoint a seventh member for a term of four years. Each member of such retirement board shall continue to hold office until the expiration of his term and until the qualification of his successor. Upon the expiration of the term of office of any elected, chosen or appointed member or in case of a vacancy in either of said offices, a successor shall be elected, chosen or appointed as aforesaid for a four-year term or for the unexpired portion thereof, as the case may be, except that in no event shall the term of the seventh member expire in the same year as the term of either the fifth or sixth member.