Last September, school speech therapist Kathy Hoffman was settling into the new academic year, working with youngsters in her small classroom behind a playground at Sahuaro Ranch Elementary School in a blue-collar neighborhood outside Phoenix.

This year, the political novice is gone from her classroom and on the campaign trail across Arizona full-time as the Democrats' choice in the race to become superintendent of public education, overseeing the state's schools. The job is typically held by career politicians or political insiders.

"My tipping point was realizing we need more teachers runnin...