Parents, students, politicians and the city teachers' union have called for the mayor to lift the ban.
By the fourth year, 44 percent of city teachers still quit, a figure that has changed little over time.
Many officers feel they should get at least the same 5.5 percent raise city teachers won last year.
The mentors will consist of current and retired city teachers.
"As a city teacher, we haven't had a contract in two years."
Paid sabbaticals for city teachers have come under scrutiny as well.
Many city teachers returned from summer break yesterday angry over the lack of a new contract.
In the last decade, the number of city teachers has grown to 80,000, from 65,000.
Meanwhile, about 50 city teachers are applying for national certification in the coming school year, up from 20 this spring.
About 6,200 city teachers have taken preliminary steps toward retiring at the end of the school year.