Eleven parents in the US have gone to court to protect the teaching of evolution at their local schools.
The Dover School board backs the teaching of intelligent design
The Dover Area School Board in the state of Pennsylvania requires science teachers to tell pupils that evolution is merely one unproven theory.
Teachers have to say that "intelligent design" - whose adherents believe life on earth was created by an intelligent being - is a possible alternative.
The parents say it is a religious belief that should not be taught.
They argue that its inclusion violates the constitutional separation of church and state.
The first witness for the parents, biology professor Kenneth Miller from Brown University, said there was "no controversy within science over the core proposition of evolutionary theory".
He also said intelligent design was not a "testable theory" and as such was rejected by scientists.
He then questioned why an intelligent creator should have created all the species known to us which are now extinct.
Biology has accepted Darwin's idea of evolution for well over 100 years
Defending the school district, Patrick Gillen said the case was about "free inquiry in education, not about a religious agenda".
"Dover's modest curriculum change embodies the essence of liberal education," he said.
The Dover school board instructs its teachers to read a statement to ninth-grade students before classes on evolution, saying that Darwin's theory is "not a fact", and that there are "gaps in the theory".
Students are then referred to an intelligent design textbook.
However, the head of the American Association for the Advancement of Science says that intelligent design "is not even a theory".
The case of the Dover school board is seen as vital by scientific organisations in restricting its spread, says the BBC's science correspondent, Roland Pease.
Intelligent design is being promoted in schools across more than 20 states in the US.
According to a CBS poll one year ago, 65% of Americans want creationism to be taught along with evolution; 37% would want it to be taught instead of evolution.
Fifty-five per cent believe God created humans as we know them today.