(TNS) -- Education took center stage for six Republican presidential hopefuls Wednesday in New Hampshire, with each warning about a meddlesome federal government when it comes to academic standards.

Former Florida Gov. Jeb Bush and Ohio Gov. John Kasich stood by their past support for Common Core, but they emphasized the importance of local control and parental involvement.

N.J. Gov. Chris Christie, former Hewlett-Packard CEO Carly Fiorina, Louisiana Gov. Bobby Jindal, and Wisconsin Gov. Scott Walker took turns taking swings at the state curriculum standards during an education summit at Londonderry High School.

The candidates offered their support for school choice, accountability, merit pay for teachers, and reform. Advocate and moderator Campbell Brown asked each for their ideas on how to improve education and their position on hot topics.

"Let’s talk about Common Core," Brown asked Bush.

"What’s that?" he joked.

Bush, who supports the standards, responded that America cannot "keep dumbing down standards." He said states should continue to have ample room to design and set standards.

The summit was hosted by The Seventy Four, an education news website, and American Federation for Children, an organization that supports school choice.

Christie, Jindal, and Kasich have in the past supported Common Core standards, which outline what a student show know by the end of each grade.

Christie has since said the standards, which were first implemented by a predecessor, are not working in his state. Jindal, once a supporter, is now a vocal critic of Common Core. He says federal government intrusion made him sour on it.

Kasich stands by the standards. He said during the forum that local school board and parental involvement is a key part of it.

"There is no substitute for higher standards," Kasich said.

When the moderator asked Kasich about some Republicans turning their backs on Common Core, Kasich said he had looked into the curriculum standards over and over again.

"None of this is finger in the air stuff for me," he said.

Local control

Christie and Jindal emphasized their support for local control — as did Fiorina and Walker.

Fiorina said Common Core had mutated into a standardized bureaucratic swamp that is actually driving achievement down. It becomes punitive over time, she said.

Walker panned Common Core, calling it an example of the failure of federal government. He said the state budget in Wisconsin now includes language underscoring local school authority. The same budget removed funding for the Smarter Balanced assessment test, he said.

Fiorina said American students are falling behind peers from other countries. She called for a smaller U.S. Department of Education that has less responsibility, with more control directed at the state and local level.

She also spoke of a need for greater accountability and use of technology.

"Technology is not a silver bullet," she said. " It is a tool — no more, no less."

Walker recounted his fight with unions in Wisconsin. Too often teachers unions are focused on protecting teachers and not improving schools, according to Walker, referring to the battle with unions that resulted in a massive protest in Wisconsin.

When you think about the Occupy movement, he said, "It didn’t start on Wall Street, it started on my street."

©2015 The New Hampshire Union Leader (Manchester, N.H.) Distributed by Tribune Content Agency, LLC.