The measure has already passed through the state’s legislature, dominated by the conservative Tea Party wing of the Republican Party, and Governor Bill Haslam has until today to veto it.
If passed, Tennessee would become the second state after Louisiana to allow teachers to challenge the accepted science on evolution and climate change.
Critics say the law encourages the teaching of the theory of “intelligent design,” which holds that a higher being must have been responsible for the development of all life forms.
Mr Haslam, who is also a Republican, has said that he will “probably” approve the bill, which will automatically become law if he does nothing.
It is nicknamed after the 1925 “Scopes Monkey Trial,” which saw John Scopes, a Tennessee high school science teacher, charged with violating state law against teaching “that man has descended from a lower order of animals”.
Under the terms of the proposed new law: “Teachers shall be permitted to help students understand, analyse, critique and review in an objective manner the scientific strengths and scientific weaknesses of existing scientific theories covered in the course being taught.”
Bo Watson, a Republican senator who sponsored the Bill, said: “The idea behind this bill is that students should be encouraged to challenge current scientific thought and theory.”
The Tennessee Science Teachers Association and the American Civil Liberties Union have both urged the governor to veto the bill, and thousands of people have signed a petition against it.
“Our fear is that there are communities across this state where schools are very small and one teacher is the science department, and they also happen to teach a Sunday school class, and this gives them permission to bring that into the classroom. It’s a floodgate,” said Becky Ashe, president of the Association.
In a letter to Tennessee legislators, the National Academy of Sciences said the bill would “miseducate students, harm the state’s national reputation and weaken its efforts to compete in a science-driven global economy”.
The Discovery Institute, which helped draw up the proposed legislation, said however that it “promotes good science education by protecting the academic freedom of science teachers to fully and objectively discuss controversial scientific topics, like evolution”.
The US Supreme Court banned teachers from telling pupils that the theory of evolution is wrong in 1968, saying that to do so breached the principle of the separation of church and state.
In 1987, the Supreme Court ruled that the mandatory teaching of creationism was unconstitutional because it was illegal to advance a particular religion in schools.
Rosa Prince, New York