An Oklahoma senator complained that federal rules on teacher credentials had driven thousands of experienced educators out of rural schools. A North Carolina lawmaker complained that formulas for distributing federal education money favored big-city districts at the expense of poor students in small towns.

Education Secretary Arne Duncan, center in white shirt, and Housing and Urban Development Secretary Shaun Donovan, holding a binder, in August visited a school in Bethel, Alaska.

And a senator from Alaska wanted to know how school-turnaround strategies based on firing ineffective instructors would work in a remote village on the Bering Sea that she said already had tremendous teacher turnover.

Lawmakers who represent...