Two months into a federal investigation of the $64 billion Pennsylvania public school pension fund, leaders of the state’s big-city teachers’ union are losing patience.

“Resign immediately,” Arthur Steinberg, president of the American Federation of Teachers of Pennsylvania, urged most PSERS board members last week. His union includes 36,000 teachers and other public school staff in Philadelphia, Pittsburgh, and several smaller communities.

Given the problems already acknowledged by the fund and with “scant information presently available to the public, it is difficult, if not impossible, to have any semblance of confidence in the PSERS board or staff to correct the course,” Steinberg said.

His letter noted how the system’s withdrawal of an exaggerated profit report has triggered mandatory higher paycheck deductions for working teachers to make up for weak investment results. The fund’s actions have prompted a federal criminal investigation and an internal investigation.

The union sent its call for resignations to Gov. Tom Wolf and state legislators, who together appoint nearly half of the board’s 15 members.

Steinberg limited the call to the dozen members on the board as of January, soon after the faulty investment numbers were approved. Three trustees who joined the board this year — State Sen. Katie Muth (D., Montgomery), newly elected state Treasurer Stacy Garrity, and Joe Torsella, the former treasurer — were excluded.

The request also amounted to a rebuke to the state’s largest teachers union, the far-larger Pennsylvania State Education Association. Five board members that the AFT would expel belong to the 168,000-member PSEA. The board’s chairman is a PSEA member, Christopher Santa Maria, a former president of the Lower Merion teachers’ bargaining unit who teaches social studies at Harriton High School there.

Under the complex selection process for the PSERS board, the five members who belong to the PSEA were elected to three-year terms in voting open only to current or former public school employees. Three of the seats are voted in by active teachers, one by nonteaching school staff, and one by retirees.

Asked about the rival union’s demand that its trustees step aside, the state education association said it was too early to replace anyone.

“PSEA is disappointed in the process at PSERS that led to the calculation error,” union spokesman Chris Lilienthal said. Still, he added, ”We think it is wise to wait for PSERS and the FBI to complete their work before making any judgments about what to do next.”

Besides the big-city schools, AFT also represents some public school worker groups in several suburban districts, including Coatesville, Neshaminy-Langhorne, Pottstown, and Southeast Delco.

Under state law, public school educators hired after 2011 have to pay more into the pension system if the fund falls short of periodic benchmark exams that measure financial performance. The PSERS board announced in December that it passed the most recent test, sparing teachers and others any increase in their payments. But it reversed course in April, sayings its previous math was flawed and that the true results required higher payments.

As The Inquirer has previously reported, federal subpoenas delivered to the agency and senior staffers in March called for documents related to the investment calculations, as well as material about the agency’s land purchases in Harrisburg.