On Monday, Schmitt told the task force he was "well aware of the criticism" that parents, teachers and other members of the public have directed at the board. He said he hoped the board would address during his presidency transparency, accessibility and accountability.
The board is scheduled to hold a retreat Aug. 13, and Schmitt said the matter is on the agenda.
Members of the public and representatives of organizations offered opinions of the board selection; many backed election of at least some members.
"The League of Women Voters of Baltimore County is in favor of a hybrid board," said Judy Miller, chairwoman of the league's education policy committee. She added that whoever appointed the non-elected members should be responsible for maintaining diversity on the board if voters do not.
Dennis King, parent of a rising seventh-grader at Dumbarton Middle School, said, "There has to be a hybrid board," then added, "put a parent, put a teacher on the board."
He said non-partisan elections would be best, with three members and a president appointed locally and seven members elected.
Some of the 50 or more people who attended hooted and cheered at the suggestion.
The task force's recommendation is due Oct. 1 and will be delivered to Gov. Martin O'Malley, the state superintendent of .schools, County Executive Kevin Kamenetz, the county's delegates and state senators, the County Council, county school superintendent Joe Hairston and the county school board.
The result could become legislation for the 2012 General Assembly session, which begins in January.