When it came time for the Madison School District to hire a physical education teacher, the Eastern Idaho district received just one application. The applicant, now on staff, is off to a good start, Superintendent Geoffrey Thomas said this week. But he’s also well aware of the odds. The shallower the applicant pool, the greater the chance of making a bad hire. Madison’s search is just one passage in an ongoing story. Idaho’s teacher shortage is widespread. And it’s unlikely to go away any time soon.