Stuart Dimmock, a father from Kent and a member of the New Party, is at London's High Court.
In late July, a judge there ruled that the decision to send the climate change film "An Inconvenient Truth" to England's secondary schools was lawful.
Mr Dimmock had argued that circulating the film amounted to indoctrination.
But the judge, Mr Justice Beatson, ruled: "The fact that the presenter is a public figure and active in US politics does not arguably make the film as a whole one of political indoctrination.
"Nor does the showing [of] it in an educational context as a supplement to other teaching methods, and accompanied by suitable reservations and indications as to what is political and controversial, arguably the 'promotion' of partisan political views."
