Donald Trump's administration could herald the teaching of creationism in schools and the controversial public funding of private schools, experts have warned.

Despite relatively few concrete policy decisions emerging from the president-elect's camp, his appointments have raised fears about the future of science, technology and maths teaching.

"Donald Trump has shown a contempt for science, a willingness to play fast and loose with the very idea of truth and an absence of intellectual curiosity," said Laurence Tribe, professor of constitutional law at Harvard Law School. "This leaves me with the sinking feeling that he will have a terribly destructive impact on the entire project of making excellent education broadly available," he added according to the Scientific American.

Trump's administration will have no direct control of what is taught in classrooms as it is devolved to state leaders. But science education advocates have warned the rhetoric of his campaign could allow teachers to treat subjects such as evolution and climate change as controversial topics.

Vice-President elect Mike Pence is an outspoken proponent of creationism. Myron Ebell, head of transitioning the US Environmental Protection Agency and director of the Center of Energy and Environment at the Competitive Enterprise Institute, is known to be a climate change sceptic.

And Trump himself tweeted "the concept of climate change was created by and for the Chinese".

Education boards in several pro-Trump states such as Louisiana and Texas are considering bills that would relegate these issues to disputed subjects, according to the Scientific American.

"We see 10 to 12 of the bills every year, and their intent is clearly to give teachers cover to teach nonscience in science classrooms," says Ann Reid, executive director of the National Center for Science Education (NCSE). "None have passed recently, but there's a danger that the people introducing these bills and school boards trying to change standards will be emboldened."

Reid added that NCSE surveys suggest some teachers avoid teaching evolution and climate change out of fear of parental complaints. She warned Trump's rhetoric will increase such pressure.

Where Trump's campaign is more concrete is the support for the controversial schools choice. This would give parents the power over where their child goes to school and access to government funding for both public and private education – including education in religious schools. 

Trump's education secretary Betsy DeVos is chairwoman of the American Federation for Children which lobbies for public funding for parents to send children to a school of their choice.

Pence has also backed schools choice as governor of Indiana and Trump has promised $20bn in federal funds to support the initiative.

Critics have said this could blur the religion–state distinction by channelling government money into private religious schools.