He angles to become the Republican nominee who replaces the outgoing Tom Luna, who announced he would not seek re-election.
He joins a race crowded by Republicans: Mountain Home's Sherri Ybarra, Grangeville teacher John Eynon and American Falls principal Randy Jensen.
The Democratic candidate Jana Jones was defeated in 2006 by Luna.
Grover announced his candidacy Friday at the Idaho Statehouse, after filing paperwork necessary to start raising money last week.
He says he wants to implement the recommendations of Gov. C.L. "Butch" Otter's task force.
Grover has worked in the Melba School District for seven years, including four years as district superintendent.
He and wife Candice have three daughters.