The Louisiana House has agreed to the main planks of a Common Core compromise, appearing to quiet the controversy over the education standards for the legislative session.

Near-unanimous votes Wednesday for the two bills came as Gov. Bobby Jindal announced his support for the deal.

One bill would set in motion a review of the multistate English and math standards with public meetings, legislative oversight and an up-or-down vote from Louisiana’s next governor. The companion bill would place limits on the state’s use of standardized testing material from a consortium aligned with Common Core.

The proposals move next to the Senate for consideration, where they weren’t expected to hit roadblocks. The divisive feud over the standards had been much louder in the House.