Signaling the direction he would like to take the country’s schools if elected president, Mayor Giuliani is packing his education advisory team with voucher advocates, private-sector school consultants, and opponents of teachers unions.

A Stanford professor who spearheaded a national movement for private-school vouchers, Terry Moe, is chairing Mr. Giuliani’s 16-member advisory board. A former education secretary under President Bush who has said teachers unions hold a “death grip” on American schools, Rod Paige, and a former official at the for-profit school management company Edison Schools, Benno Schmidt, also will sit on the board.

The appointments announced by Mr. Giuliani’s campaign today come a day after Senator McCain made an indirect dig at the former mayor’s education record by praising Mayor Bloomberg for turning around a system Mr. McCain said had been “clearly broken.”

As mayor, Mr. Giuliani pushed an ambitious schools agenda: he pushed to establish mayoral control of the schools; staged a campaign to bring school to the city; and tried to hire Edison to take over failing city schools.

None of the efforts overcame substantial opposition from the teachers union and other groups. The backgrounds of Mr. Giuliani’s education advisers suggest he would push a similar agenda as president.