She's the second board member involved in contentious student assignment debates over the past two years is running for statewide office.
GOP board member John Tedesco announced last week he's running for state schools superintendent.
Goldman said in a prepared statement Wood and Gov. Beverly Perdue have been sorely lacking in leadership.
"The taxpayers of North Carolina have grown fearful of the end result of the increasing number of public financial scandals, reports of fiscal mismanagement, and the dire emergency resulting from shoddy and fraudulent Medicaid casework," said Goldman.
Wood is running for re-election.
Goldman was elected to the board in 2009 when the GOP took the majority and served as vice chairman. The board shifted to a Democratic majority in the 2011 elections.